Resolving model parameter values from carbon and nitrogen stock measurements in a wide range of tropical mature forests using nonlinear inversion and regression trees

Treesearch

Shuguang Liua; Pamela Anderson; Guoyi Zhoud; Boone Kauffman; Flint Hughes; David Schimel; Vicente Watson; Joseph Tosi

2008-01-01

Objectively assessing the performance of a model and deriving model parameter values from observations are critical and challenging in landscape to regional modeling. In this paper, we applied a nonlinear inversion technique to calibrate the ecosystem model CENTURY against carbon (C) and nitrogen (N) stock measurements collected from 39 mature tropical forest sites in...

Learning Inverse Rig Mappings by Nonlinear Regression.

PubMed

Holden, Daniel; Saito, Jun; Komura, Taku

2017-03-01

We present a framework to design inverse rig-functions-functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.

An Application to the Prediction of LOD Change Based on General Regression Neural Network

NASA Astrophysics Data System (ADS)

Zhang, X. H.; Wang, Q. J.; Zhu, J. J.; Zhang, H.

2011-07-01

Traditional prediction of the LOD (length of day) change was based on linear models, such as the least square model and the autoregressive technique, etc. Due to the complex non-linear features of the LOD variation, the performances of the linear model predictors are not fully satisfactory. This paper applies a non-linear neural network - general regression neural network (GRNN) model to forecast the LOD change, and the results are analyzed and compared with those obtained with the back propagation neural network and other models. The comparison shows that the performance of the GRNN model in the prediction of the LOD change is efficient and feasible.

A general procedure to generate models for urban environmental-noise pollution using feature selection and machine learning methods.

PubMed

Torija, Antonio J; Ruiz, Diego P

2015-02-01

The prediction of environmental noise in urban environments requires the solution of a complex and non-linear problem, since there are complex relationships among the multitude of variables involved in the characterization and modelling of environmental noise and environmental-noise magnitudes. Moreover, the inclusion of the great spatial heterogeneity characteristic of urban environments seems to be essential in order to achieve an accurate environmental-noise prediction in cities. This problem is addressed in this paper, where a procedure based on feature-selection techniques and machine-learning regression methods is proposed and applied to this environmental problem. Three machine-learning regression methods, which are considered very robust in solving non-linear problems, are used to estimate the energy-equivalent sound-pressure level descriptor (LAeq). These three methods are: (i) multilayer perceptron (MLP), (ii) sequential minimal optimisation (SMO), and (iii) Gaussian processes for regression (GPR). In addition, because of the high number of input variables involved in environmental-noise modelling and estimation in urban environments, which make LAeq prediction models quite complex and costly in terms of time and resources for application to real situations, three different techniques are used to approach feature selection or data reduction. The feature-selection techniques used are: (i) correlation-based feature-subset selection (CFS), (ii) wrapper for feature-subset selection (WFS), and the data reduction technique is principal-component analysis (PCA). The subsequent analysis leads to a proposal of different schemes, depending on the needs regarding data collection and accuracy. The use of WFS as the feature-selection technique with the implementation of SMO or GPR as regression algorithm provides the best LAeq estimation (R(2)=0.94 and mean absolute error (MAE)=1.14-1.16 dB(A)). Copyright © 2014 Elsevier B.V. All rights reserved.

Does money matter in inflation forecasting?

NASA Astrophysics Data System (ADS)

Binner, J. M.; Tino, P.; Tepper, J.; Anderson, R.; Jones, B.; Kendall, G.

2010-11-01

This paper provides the most fully comprehensive evidence to date on whether or not monetary aggregates are valuable for forecasting US inflation in the early to mid 2000s. We explore a wide range of different definitions of money, including different methods of aggregation and different collections of included monetary assets. In our forecasting experiment we use two nonlinear techniques, namely, recurrent neural networks and kernel recursive least squares regression-techniques that are new to macroeconomics. Recurrent neural networks operate with potentially unbounded input memory, while the kernel regression technique is a finite memory predictor. The two methodologies compete to find the best fitting US inflation forecasting models and are then compared to forecasts from a naïve random walk model. The best models were nonlinear autoregressive models based on kernel methods. Our findings do not provide much support for the usefulness of monetary aggregates in forecasting inflation. Beyond its economic findings, our study is in the tradition of physicists’ long-standing interest in the interconnections among statistical mechanics, neural networks, and related nonparametric statistical methods, and suggests potential avenues of extension for such studies.

Catchments as non-linear filters: evaluating data-driven approaches for spatio-temporal predictions in ungauged basins

NASA Astrophysics Data System (ADS)

Bellugi, D. G.; Tennant, C.; Larsen, L.

2016-12-01

Catchment and climate heterogeneity complicate prediction of runoff across time and space, and resulting parameter uncertainty can lead to large accumulated errors in hydrologic models, particularly in ungauged basins. Recently, data-driven modeling approaches have been shown to avoid the accumulated uncertainty associated with many physically-based models, providing an appealing alternative for hydrologic prediction. However, the effectiveness of different methods in hydrologically and geomorphically distinct catchments, and the robustness of these methods to changing climate and changing hydrologic processes remain to be tested. Here, we evaluate the use of machine learning techniques to predict daily runoff across time and space using only essential climatic forcing (e.g. precipitation, temperature, and potential evapotranspiration) time series as model input. Model training and testing was done using a high quality dataset of daily runoff and climate forcing data for 25+ years for 600+ minimally-disturbed catchments (drainage area range 5-25,000 km2, median size 336 km2) that cover a wide range of climatic and physical characteristics. Preliminary results using Support Vector Regression (SVR) suggest that in some catchments this nonlinear-based regression technique can accurately predict daily runoff, while the same approach fails in other catchments, indicating that the representation of climate inputs and/or catchment filter characteristics in the model structure need further refinement to increase performance. We bolster this analysis by using Sparse Identification of Nonlinear Dynamics (a sparse symbolic regression technique) to uncover the governing equations that describe runoff processes in catchments where SVR performed well and for ones where it performed poorly, thereby enabling inference about governing processes. This provides a robust means of examining how catchment complexity influences runoff prediction skill, and represents a contribution towards the integration of data-driven inference and physically-based models.

Macrocell path loss prediction using artificial intelligence techniques

NASA Astrophysics Data System (ADS)

Usman, Abraham U.; Okereke, Okpo U.; Omizegba, Elijah E.

2014-04-01

The prediction of propagation loss is a practical non-linear function approximation problem which linear regression or auto-regression models are limited in their ability to handle. However, some computational Intelligence techniques such as artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs) have been shown to have great ability to handle non-linear function approximation and prediction problems. In this study, the multiple layer perceptron neural network (MLP-NN), radial basis function neural network (RBF-NN) and an ANFIS network were trained using actual signal strength measurement taken at certain suburban areas of Bauchi metropolis, Nigeria. The trained networks were then used to predict propagation losses at the stated areas under differing conditions. The predictions were compared with the prediction accuracy of the popular Hata model. It was observed that ANFIS model gave a better fit in all cases having higher R2 values in each case and on average is more robust than MLP and RBF models as it generalises better to a different data.

Critical Analysis of Dual-Probe Heat-Pulse Technique Applied to Measuring Thermal Diffusivity

NASA Astrophysics Data System (ADS)

Bovesecchi, G.; Coppa, P.; Corasaniti, S.; Potenza, M.

2018-07-01

The paper presents an analysis of the experimental parameters involved in application of the dual-probe heat pulse technique, followed by a critical review of methods for processing thermal response data (e.g., maximum detection and nonlinear least square regression) and the consequent obtainable uncertainty. Glycerol was selected as testing liquid, and its thermal diffusivity was evaluated over the temperature range from - 20 °C to 60 °C. In addition, Monte Carlo simulation was used to assess the uncertainty propagation for maximum detection. It was concluded that maximum detection approach to process thermal response data gives the closest results to the reference data inasmuch nonlinear regression results are affected by major uncertainties due to partial correlation between the evaluated parameters. Besides, the interpolation of temperature data with a polynomial to find the maximum leads to a systematic difference between measured and reference data, as put into evidence by the Monte Carlo simulations; through its correction, this systematic error can be reduced to a negligible value, about 0.8 %.

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool.

PubMed

Aqil, Muhammad; Kita, Ichiro; Yano, Akira; Nishiyama, Soichi

2007-10-01

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.

Classifying depression patients and normal subjects using machine learning techniques and nonlinear features from EEG signal.

PubMed

Hosseinifard, Behshad; Moradi, Mohammad Hassan; Rostami, Reza

2013-03-01

Diagnosing depression in the early curable stages is very important and may even save the life of a patient. In this paper, we study nonlinear analysis of EEG signal for discriminating depression patients and normal controls. Forty-five unmedicated depressed patients and 45 normal subjects were participated in this study. Power of four EEG bands and four nonlinear features including detrended fluctuation analysis (DFA), higuchi fractal, correlation dimension and lyapunov exponent were extracted from EEG signal. For discriminating the two groups, k-nearest neighbor, linear discriminant analysis and logistic regression as the classifiers are then used. Highest classification accuracy of 83.3% is obtained by correlation dimension and LR classifier among other nonlinear features. For further improvement, all nonlinear features are combined and applied to classifiers. A classification accuracy of 90% is achieved by all nonlinear features and LR classifier. In all experiments, genetic algorithm is employed to select the most important features. The proposed technique is compared and contrasted with the other reported methods and it is demonstrated that by combining nonlinear features, the performance is enhanced. This study shows that nonlinear analysis of EEG can be a useful method for discriminating depressed patients and normal subjects. It is suggested that this analysis may be a complementary tool to help psychiatrists for diagnosing depressed patients. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Improved spatial regression analysis of diffusion tensor imaging for lesion detection during longitudinal progression of multiple sclerosis in individual subjects

NASA Astrophysics Data System (ADS)

Liu, Bilan; Qiu, Xing; Zhu, Tong; Tian, Wei; Hu, Rui; Ekholm, Sven; Schifitto, Giovanni; Zhong, Jianhui

2016-03-01

Subject-specific longitudinal DTI study is vital for investigation of pathological changes of lesions and disease evolution. Spatial Regression Analysis of Diffusion tensor imaging (SPREAD) is a non-parametric permutation-based statistical framework that combines spatial regression and resampling techniques to achieve effective detection of localized longitudinal diffusion changes within the whole brain at individual level without a priori hypotheses. However, boundary blurring and dislocation limit its sensitivity, especially towards detecting lesions of irregular shapes. In the present study, we propose an improved SPREAD (dubbed improved SPREAD, or iSPREAD) method by incorporating a three-dimensional (3D) nonlinear anisotropic diffusion filtering method, which provides edge-preserving image smoothing through a nonlinear scale space approach. The statistical inference based on iSPREAD was evaluated and compared with the original SPREAD method using both simulated and in vivo human brain data. Results demonstrated that the sensitivity and accuracy of the SPREAD method has been improved substantially by adapting nonlinear anisotropic filtering. iSPREAD identifies subject-specific longitudinal changes in the brain with improved sensitivity, accuracy, and enhanced statistical power, especially when the spatial correlation is heterogeneous among neighboring image pixels in DTI.

A Nonlinear Regression Model Estimating Single Source Concentrations of Primary and Secondarily Formed 2.5

EPA Science Inventory

Various approaches and tools exist to estimate local and regional PM_2.5 impacts from a single emissions source, ranging from simple screening techniques to Gaussian based dispersion models and complex grid-based Eulerian photochemical transport models. These approache...

Correlation and simple linear regression.

PubMed

Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G

2003-06-01

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

Detecting outliers when fitting data with nonlinear regression – a new method based on robust nonlinear regression and the false discovery rate

PubMed Central

Motulsky, Harvey J; Brown, Ronald E

2006-01-01

Background Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives. PMID:16526949

Multiple regression technique for Pth degree polynominals with and without linear cross products

NASA Technical Reports Server (NTRS)

Davis, J. W.

1973-01-01

A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.

An Experimental Study in Determining Energy Expenditure from Treadmill Walking using Hip-Worn Inertial Sensors

PubMed Central

Vathsangam, Harshvardhan; Emken, Adar; Schroeder, E. Todd; Spruijt-Metz, Donna; Sukhatme, Gaurav S.

2011-01-01

This paper describes an experimental study in estimating energy expenditure from treadmill walking using a single hip-mounted triaxial inertial sensor comprised of a triaxial accelerometer and a triaxial gyroscope. Typical physical activity characterization using accelerometer generated counts suffers from two drawbacks - imprecison (due to proprietary counts) and incompleteness (due to incomplete movement description). We address these problems in the context of steady state walking by directly estimating energy expenditure with data from a hip-mounted inertial sensor. We represent the cyclic nature of walking with a Fourier transform of sensor streams and show how one can map this representation to energy expenditure (as measured by V O2 consumption, mL/min) using three regression techniques - Least Squares Regression (LSR), Bayesian Linear Regression (BLR) and Gaussian Process Regression (GPR). We perform a comparative analysis of the accuracy of sensor streams in predicting energy expenditure (measured by RMS prediction accuracy). Triaxial information is more accurate than uniaxial information. LSR based approaches are prone to outlier sensitivity and overfitting. Gyroscopic information showed equivalent if not better prediction accuracy as compared to accelerometers. Combining accelerometer and gyroscopic information provided better accuracy than using either sensor alone. We also analyze the best algorithmic approach among linear and nonlinear methods as measured by RMS prediction accuracy and run time. Nonlinear regression methods showed better prediction accuracy but required an order of magnitude of run time. This paper emphasizes the role of probabilistic techniques in conjunction with joint modeling of triaxial accelerations and rotational rates to improve energy expenditure prediction for steady-state treadmill walking. PMID:21690001

Fundamental Analysis of the Linear Multiple Regression Technique for Quantification of Water Quality Parameters from Remote Sensing Data. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Whitlock, C. H., III

1977-01-01

Constituents with linear radiance gradients with concentration may be quantified from signals which contain nonlinear atmospheric and surface reflection effects for both homogeneous and non-homogeneous water bodies provided accurate data can be obtained and nonlinearities are constant with wavelength. Statistical parameters must be used which give an indication of bias as well as total squared error to insure that an equation with an optimum combination of bands is selected. It is concluded that the effect of error in upwelled radiance measurements is to reduce the accuracy of the least square fitting process and to increase the number of points required to obtain a satisfactory fit. The problem of obtaining a multiple regression equation that is extremely sensitive to error is discussed.

Combined chamber-tower approach: Using eddy covariance measurements to cross-validate carbon fluxes modeled from manual chamber campaigns

NASA Astrophysics Data System (ADS)

Brümmer, C.; Moffat, A. M.; Huth, V.; Augustin, J.; Herbst, M.; Kutsch, W. L.

2016-12-01

Manual carbon dioxide flux measurements with closed chambers at scheduled campaigns are a versatile method to study management effects at small scales in multiple-plot experiments. The eddy covariance technique has the advantage of quasi-continuous measurements but requires large homogeneous areas of a few hectares. To evaluate the uncertainties associated with interpolating from individual campaigns to the whole vegetation period, we installed both techniques at an agricultural site in Northern Germany. The presented comparison covers two cropping seasons, winter oilseed rape in 2012/13 and winter wheat in 2013/14. Modeling half-hourly carbon fluxes from campaigns is commonly performed based on non-linear regressions for the light response and respiration. The daily averages of net CO2 modeled from chamber data deviated from eddy covariance measurements in the range of ± 5 g C m-2 day-1. To understand the observed differences and to disentangle the effects, we performed four additional setups (expert versus default settings of the non-linear regressions based algorithm, purely empirical modeling with artificial neural networks versus non-linear regressions, cross-validating using eddy covariance measurements as campaign fluxes, weekly versus monthly scheduling of campaigns) to model the half-hourly carbon fluxes for the whole vegetation period. The good agreement of the seasonal course of net CO2 at plot and field scale for our agricultural site demonstrates that both techniques are robust and yield consistent results at seasonal time scale even for a managed ecosystem with high temporal dynamics in the fluxes. This allows combining the respective advantages of factorial experiments at plot scale with dense time series data at field scale. Furthermore, the information from the quasi-continuous eddy covariance measurements can be used to derive vegetation proxies to support the interpolation of carbon fluxes in-between the manual chamber campaigns.

Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

NASA Astrophysics Data System (ADS)

Wu, Cheng; Zhen Yu, Jian

2018-03-01

Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Additivity of nonlinear biomass equations

Treesearch

Bernard R. Parresol

2001-01-01

Two procedures that guarantee the property of additivity among the components of tree biomass and total tree biomass utilizing nonlinear functions are developed. Procedure 1 is a simple combination approach, and procedure 2 is based on nonlinear joint-generalized regression (nonlinear seemingly unrelated regressions) with parameter restrictions. Statistical theory is...

The 11-year solar cycle in current reanalyses: a (non)linear attribution study of the middle atmosphere

NASA Astrophysics Data System (ADS)

Kuchar, A.; Sacha, P.; Miksovsky, J.; Pisoft, P.

2015-06-01

This study focusses on the variability of temperature, ozone and circulation characteristics in the stratosphere and lower mesosphere with regard to the influence of the 11-year solar cycle. It is based on attribution analysis using multiple nonlinear techniques (support vector regression, neural networks) besides the multiple linear regression approach. The analysis was applied to several current reanalysis data sets for the 1979-2013 period, including MERRA, ERA-Interim and JRA-55, with the aim to compare how these types of data resolve especially the double-peaked solar response in temperature and ozone variables and the consequent changes induced by these anomalies. Equatorial temperature signals in the tropical stratosphere were found to be in qualitative agreement with previous attribution studies, although the agreement with observational results was incomplete, especially for JRA-55. The analysis also pointed to the solar signal in the ozone data sets (i.e. MERRA and ERA-Interim) not being consistent with the observed double-peaked ozone anomaly extracted from satellite measurements. The results obtained by linear regression were confirmed by the nonlinear approach through all data sets, suggesting that linear regression is a relevant tool to sufficiently resolve the solar signal in the middle atmosphere. The seasonal evolution of the solar response was also discussed in terms of dynamical causalities in the winter hemispheres. The hypothetical mechanism of a weaker Brewer-Dobson circulation at solar maxima was reviewed together with a discussion of polar vortex behaviour.

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

The Influential Effect of Blending, Bump, Changing Period, and Eclipsing Cepheids on the Leavitt Law

NASA Astrophysics Data System (ADS)

García-Varela, A.; Muñoz, J. R.; Sabogal, B. E.; Vargas Domínguez, S.; Martínez, J.

2016-06-01

The investigation of the nonlinearity of the Leavitt law (LL) is a topic that began more than seven decades ago, when some of the studies in this field found that the LL has a break at about 10 days. The goal of this work is to investigate a possible statistical cause of this nonlinearity. By applying linear regressions to OGLE-II and OGLE-IV data, we find that to obtain the LL by using linear regression, robust techniques to deal with influential points and/or outliers are needed instead of the ordinary least-squares regression traditionally used. In particular, by using M- and MM-regressions we establish firmly and without doubt the linearity of the LL in the Large Magellanic Cloud, without rejecting or excluding Cepheid data from the analysis. This implies that light curves of Cepheids suggesting blending, bumps, eclipses, or period changes do not affect the LL for this galaxy. For the Small Magellanic Cloud, when including Cepheids of this kind, it is not possible to find an adequate model, probably because of the geometry of the galaxy. In that case, a possible influence of these stars could exist.

Support vector machine regression (SVR/LS-SVM)--an alternative to neural networks (ANN) for analytical chemistry? Comparison of nonlinear methods on near infrared (NIR) spectroscopy data.

PubMed

Balabin, Roman M; Lomakina, Ekaterina I

2011-04-21

In this study, we make a general comparison of the accuracy and robustness of five multivariate calibration models: partial least squares (PLS) regression or projection to latent structures, polynomial partial least squares (Poly-PLS) regression, artificial neural networks (ANNs), and two novel techniques based on support vector machines (SVMs) for multivariate data analysis: support vector regression (SVR) and least-squares support vector machines (LS-SVMs). The comparison is based on fourteen (14) different datasets: seven sets of gasoline data (density, benzene content, and fractional composition/boiling points), two sets of ethanol gasoline fuel data (density and ethanol content), one set of diesel fuel data (total sulfur content), three sets of petroleum (crude oil) macromolecules data (weight percentages of asphaltenes, resins, and paraffins), and one set of petroleum resins data (resins content). Vibrational (near-infrared, NIR) spectroscopic data are used to predict the properties and quality coefficients of gasoline, biofuel/biodiesel, diesel fuel, and other samples of interest. The four systems presented here range greatly in composition, properties, strength of intermolecular interactions (e.g., van der Waals forces, H-bonds), colloid structure, and phase behavior. Due to the high diversity of chemical systems studied, general conclusions about SVM regression methods can be made. We try to answer the following question: to what extent can SVM-based techniques replace ANN-based approaches in real-world (industrial/scientific) applications? The results show that both SVR and LS-SVM methods are comparable to ANNs in accuracy. Due to the much higher robustness of the former, the SVM-based approaches are recommended for practical (industrial) application. This has been shown to be especially true for complicated, highly nonlinear objects.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

A Comparative Investigation of the Combined Effects of Pre-Processing, Wavelength Selection, and Regression Methods on Near-Infrared Calibration Model Performance.

PubMed

Wan, Jian; Chen, Yi-Chieh; Morris, A Julian; Thennadil, Suresh N

2017-07-01

Near-infrared (NIR) spectroscopy is being widely used in various fields ranging from pharmaceutics to the food industry for analyzing chemical and physical properties of the substances concerned. Its advantages over other analytical techniques include available physical interpretation of spectral data, nondestructive nature and high speed of measurements, and little or no need for sample preparation. The successful application of NIR spectroscopy relies on three main aspects: pre-processing of spectral data to eliminate nonlinear variations due to temperature, light scattering effects and many others, selection of those wavelengths that contribute useful information, and identification of suitable calibration models using linear/nonlinear regression . Several methods have been developed for each of these three aspects and many comparative studies of different methods exist for an individual aspect or some combinations. However, there is still a lack of comparative studies for the interactions among these three aspects, which can shed light on what role each aspect plays in the calibration and how to combine various methods of each aspect together to obtain the best calibration model. This paper aims to provide such a comparative study based on four benchmark data sets using three typical pre-processing methods, namely, orthogonal signal correction (OSC), extended multiplicative signal correction (EMSC) and optical path-length estimation and correction (OPLEC); two existing wavelength selection methods, namely, stepwise forward selection (SFS) and genetic algorithm optimization combined with partial least squares regression for spectral data (GAPLSSP); four popular regression methods, namely, partial least squares (PLS), least absolute shrinkage and selection operator (LASSO), least squares support vector machine (LS-SVM), and Gaussian process regression (GPR). The comparative study indicates that, in general, pre-processing of spectral data can play a significant role in the calibration while wavelength selection plays a marginal role and the combination of certain pre-processing, wavelength selection, and nonlinear regression methods can achieve superior performance over traditional linear regression-based calibration.

Delineating chalk sand distribution of Ekofisk formation using probabilistic neural network (PNN) and stepwise regression (SWR): Case study Danish North Sea field

NASA Astrophysics Data System (ADS)

Haris, A.; Nafian, M.; Riyanto, A.

2017-07-01

Danish North Sea Fields consist of several formations (Ekofisk, Tor, and Cromer Knoll) that was started from the age of Paleocene to Miocene. In this study, the integration of seismic and well log data set is carried out to determine the chalk sand distribution in the Danish North Sea field. The integration of seismic and well log data set is performed by using the seismic inversion analysis and seismic multi-attribute. The seismic inversion algorithm, which is used to derive acoustic impedance (AI), is model-based technique. The derived AI is then used as external attributes for the input of multi-attribute analysis. Moreover, the multi-attribute analysis is used to generate the linear and non-linear transformation of among well log properties. In the case of the linear model, selected transformation is conducted by weighting step-wise linear regression (SWR), while for the non-linear model is performed by using probabilistic neural networks (PNN). The estimated porosity, which is resulted by PNN shows better suited to the well log data compared with the results of SWR. This result can be understood since PNN perform non-linear regression so that the relationship between the attribute data and predicted log data can be optimized. The distribution of chalk sand has been successfully identified and characterized by porosity value ranging from 23% up to 30%.

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.

1979-01-01

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Travel Demand Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Southworth, Frank; Garrow, Dr. Laurie

This chapter describes the principal types of both passenger and freight demand models in use today, providing a brief history of model development supported by references to a number of popular texts on the subject, and directing the reader to papers covering some of the more recent technical developments in the area. Over the past half century a variety of methods have been used to estimate and forecast travel demands, drawing concepts from economic/utility maximization theory, transportation system optimization and spatial interaction theory, using and often combining solution techniques as varied as Box-Jenkins methods, non-linear multivariate regression, non-linear mathematical programming,more » and agent-based microsimulation.« less

Experiments to Determine Whether Recursive Partitioning (CART) or an Artificial Neural Network Overcomes Theoretical Limitations of Cox Proportional Hazards Regression

NASA Technical Reports Server (NTRS)

Kattan, Michael W.; Hess, Kenneth R.; Kattan, Michael W.

1998-01-01

New computationally intensive tools for medical survival analyses include recursive partitioning (also called CART) and artificial neural networks. A challenge that remains is to better understand the behavior of these techniques in effort to know when they will be effective tools. Theoretically they may overcome limitations of the traditional multivariable survival technique, the Cox proportional hazards regression model. Experiments were designed to test whether the new tools would, in practice, overcome these limitations. Two datasets in which theory suggests CART and the neural network should outperform the Cox model were selected. The first was a published leukemia dataset manipulated to have a strong interaction that CART should detect. The second was a published cirrhosis dataset with pronounced nonlinear effects that a neural network should fit. Repeated sampling of 50 training and testing subsets was applied to each technique. The concordance index C was calculated as a measure of predictive accuracy by each technique on the testing dataset. In the interaction dataset, CART outperformed Cox (P less than 0.05) with a C improvement of 0.1 (95% Cl, 0.08 to 0.12). In the nonlinear dataset, the neural network outperformed the Cox model (P less than 0.05), but by a very slight amount (0.015). As predicted by theory, CART and the neural network were able to overcome limitations of the Cox model. Experiments like these are important to increase our understanding of when one of these new techniques will outperform the standard Cox model. Further research is necessary to predict which technique will do best a priori and to assess the magnitude of superiority.

Using Classification and Regression Trees (CART) and random forests to analyze attrition: Results from two simulations.

PubMed

Hayes, Timothy; Usami, Satoshi; Jacobucci, Ross; McArdle, John J

2015-12-01

In this article, we describe a recent development in the analysis of attrition: using classification and regression trees (CART) and random forest methods to generate inverse sampling weights. These flexible machine learning techniques have the potential to capture complex nonlinear, interactive selection models, yet to our knowledge, their performance in the missing data analysis context has never been evaluated. To assess the potential benefits of these methods, we compare their performance with commonly employed multiple imputation and complete case techniques in 2 simulations. These initial results suggest that weights computed from pruned CART analyses performed well in terms of both bias and efficiency when compared with other methods. We discuss the implications of these findings for applied researchers. (c) 2015 APA, all rights reserved).

Using Classification and Regression Trees (CART) and Random Forests to Analyze Attrition: Results From Two Simulations

PubMed Central

Hayes, Timothy; Usami, Satoshi; Jacobucci, Ross; McArdle, John J.

2016-01-01

In this article, we describe a recent development in the analysis of attrition: using classification and regression trees (CART) and random forest methods to generate inverse sampling weights. These flexible machine learning techniques have the potential to capture complex nonlinear, interactive selection models, yet to our knowledge, their performance in the missing data analysis context has never been evaluated. To assess the potential benefits of these methods, we compare their performance with commonly employed multiple imputation and complete case techniques in 2 simulations. These initial results suggest that weights computed from pruned CART analyses performed well in terms of both bias and efficiency when compared with other methods. We discuss the implications of these findings for applied researchers. PMID:26389526

Applying additive modeling and gradient boosting to assess the effects of watershed and reach characteristics on riverine assemblages

USGS Publications Warehouse

Maloney, Kelly O.; Schmid, Matthias; Weller, Donald E.

2012-01-01

Issues with ecological data (e.g. non-normality of errors, nonlinear relationships and autocorrelation of variables) and modelling (e.g. overfitting, variable selection and prediction) complicate regression analyses in ecology. Flexible models, such as generalized additive models (GAMs), can address data issues, and machine learning techniques (e.g. gradient boosting) can help resolve modelling issues. Gradient boosted GAMs do both. Here, we illustrate the advantages of this technique using data on benthic macroinvertebrates and fish from 1573 small streams in Maryland, USA.

Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

Application of Neural Networks to Wind tunnel Data Response Surface Methods

NASA Technical Reports Server (NTRS)

Lo, Ching F.; Zhao, J. L.; DeLoach, Richard

2000-01-01

The integration of nonlinear neural network methods with conventional linear regression techniques is demonstrated for representative wind tunnel force balance data modeling. This work was motivated by a desire to formulate precision intervals for response surfaces produced by neural networks. Applications are demonstrated for representative wind tunnel data acquired at NASA Langley Research Center and the Arnold Engineering Development Center in Tullahoma, TN.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Linear regression models for solvent accessibility prediction in proteins.

PubMed

Wagner, Michael; Adamczak, Rafał; Porollo, Aleksey; Meller, Jarosław

2005-04-01

The relative solvent accessibility (RSA) of an amino acid residue in a protein structure is a real number that represents the solvent exposed surface area of this residue in relative terms. The problem of predicting the RSA from the primary amino acid sequence can therefore be cast as a regression problem. Nevertheless, RSA prediction has so far typically been cast as a classification problem. Consequently, various machine learning techniques have been used within the classification framework to predict whether a given amino acid exceeds some (arbitrary) RSA threshold and would thus be predicted to be "exposed," as opposed to "buried." We have recently developed novel methods for RSA prediction using nonlinear regression techniques which provide accurate estimates of the real-valued RSA and outperform classification-based approaches with respect to commonly used two-class projections. However, while their performance seems to provide a significant improvement over previously published approaches, these Neural Network (NN) based methods are computationally expensive to train and involve several thousand parameters. In this work, we develop alternative regression models for RSA prediction which are computationally much less expensive, involve orders-of-magnitude fewer parameters, and are still competitive in terms of prediction quality. In particular, we investigate several regression models for RSA prediction using linear L1-support vector regression (SVR) approaches as well as standard linear least squares (LS) regression. Using rigorously derived validation sets of protein structures and extensive cross-validation analysis, we compare the performance of the SVR with that of LS regression and NN-based methods. In particular, we show that the flexibility of the SVR (as encoded by metaparameters such as the error insensitivity and the error penalization terms) can be very beneficial to optimize the prediction accuracy for buried residues. We conclude that the simple and computationally much more efficient linear SVR performs comparably to nonlinear models and thus can be used in order to facilitate further attempts to design more accurate RSA prediction methods, with applications to fold recognition and de novo protein structure prediction methods.

A statistical methodology for estimating transport parameters: Theory and applications to one-dimensional advectivec-dispersive systems

USGS Publications Warehouse

Wagner, Brian J.; Gorelick, Steven M.

1986-01-01

A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2–3 times more reliable than estimates based on temporal data for all parameters except velocity. Comparison of estimated linear and nonlinear confidence intervals based upon Monte Carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero-order production coefficient when data are collected over time. In addition, examples demonstrate transport parameter estimation for two real one-dimensional systems. First, the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data. We compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments. Second, the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport. The model is applied to analyze the trends, variability, and interrelationship of parameters in a mourtain stream in northern California.

Using GA-Ridge regression to select hydro-geological parameters influencing groundwater pollution vulnerability.

PubMed

Ahn, Jae Joon; Kim, Young Min; Yoo, Keunje; Park, Joonhong; Oh, Kyong Joo

2012-11-01

For groundwater conservation and management, it is important to accurately assess groundwater pollution vulnerability. This study proposed an integrated model using ridge regression and a genetic algorithm (GA) to effectively select the major hydro-geological parameters influencing groundwater pollution vulnerability in an aquifer. The GA-Ridge regression method determined that depth to water, net recharge, topography, and the impact of vadose zone media were the hydro-geological parameters that influenced trichloroethene pollution vulnerability in a Korean aquifer. When using these selected hydro-geological parameters, the accuracy was improved for various statistical nonlinear and artificial intelligence (AI) techniques, such as multinomial logistic regression, decision trees, artificial neural networks, and case-based reasoning. These results provide a proof of concept that the GA-Ridge regression is effective at determining influential hydro-geological parameters for the pollution vulnerability of an aquifer, and in turn, improves the AI performance in assessing groundwater pollution vulnerability.

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

HOS network-based classification of power quality events via regression algorithms

NASA Astrophysics Data System (ADS)

Palomares Salas, José Carlos; González de la Rosa, Juan José; Sierra Fernández, José María; Pérez, Agustín Agüera

2015-12-01

This work compares seven regression algorithms implemented in artificial neural networks (ANNs) supported by 14 power-quality features, which are based in higher-order statistics. Combining time and frequency domain estimators to deal with non-stationary measurement sequences, the final goal of the system is the implementation in the future smart grid to guarantee compatibility between all equipment connected. The principal results are based in spectral kurtosis measurements, which easily adapt to the impulsive nature of the power quality events. These results verify that the proposed technique is capable of offering interesting results for power quality (PQ) disturbance classification. The best results are obtained using radial basis networks, generalized regression, and multilayer perceptron, mainly due to the non-linear nature of data.

Solar cycle in current reanalyses: (non)linear attribution study

NASA Astrophysics Data System (ADS)

Kuchar, A.; Sacha, P.; Miksovsky, J.; Pisoft, P.

2014-12-01

This study focusses on the variability of temperature, ozone and circulation characteristics in the stratosphere and lower mesosphere with regard to the influence of the 11 year solar cycle. It is based on attribution analysis using multiple nonlinear techniques (Support Vector Regression, Neural Networks) besides the traditional linear approach. The analysis was applied to several current reanalysis datasets for the 1979-2013 period, including MERRA, ERA-Interim and JRA-55, with the aim to compare how this type of data resolves especially the double-peaked solar response in temperature and ozone variables and the consequent changes induced by these anomalies. Equatorial temperature signals in the lower and upper stratosphere were found to be sufficiently robust and in qualitative agreement with previous observational studies. The analysis also pointed to the solar signal in the ozone datasets (i.e. MERRA and ERA-Interim) not being consistent with the observed double-peaked ozone anomaly extracted from satellite measurements. Consequently the results obtained by linear regression were confirmed by the nonlinear approach through all datasets, suggesting that linear regression is a relevant tool to sufficiently resolve the solar signal in the middle atmosphere. Furthermore, the seasonal dependence of the solar response was also discussed, mainly as a source of dynamical causalities in the wave propagation characteristics in the zonal wind and the induced meridional circulation in the winter hemispheres. The hypothetical mechanism of a weaker Brewer Dobson circulation was reviewed together with discussion of polar vortex stability.

Evaluation of laser cutting process with auxiliary gas pressure by soft computing approach

NASA Astrophysics Data System (ADS)

Lazov, Lyubomir; Nikolić, Vlastimir; Jovic, Srdjan; Milovančević, Miloš; Deneva, Heristina; Teirumenieka, Erika; Arsic, Nebojsa

2018-06-01

Evaluation of the optimal laser cutting parameters is very important for the high cut quality. This is highly nonlinear process with different parameters which is the main challenge in the optimization process. Data mining methodology is one of most versatile method which can be used laser cutting process optimization. Support vector regression (SVR) procedure is implemented since it is a versatile and robust technique for very nonlinear data regression. The goal in this study was to determine the optimal laser cutting parameters to ensure robust condition for minimization of average surface roughness. Three cutting parameters, the cutting speed, the laser power, and the assist gas pressure, were used in the investigation. As a laser type TruLaser 1030 technological system was used. Nitrogen as an assisted gas was used in the laser cutting process. As the data mining method, support vector regression procedure was used. Data mining prediction accuracy was very high according the coefficient (R2) of determination and root mean square error (RMSE): R2 = 0.9975 and RMSE = 0.0337. Therefore the data mining approach could be used effectively for determination of the optimal conditions of the laser cutting process.

Nonlinear models for estimating GSFC travel requirements

NASA Technical Reports Server (NTRS)

Buffalano, C.; Hagan, F. J.

1974-01-01

A methodology is presented for estimating travel requirements for a particular period of time. Travel models were generated using nonlinear regression analysis techniques on a data base of FY-72 and FY-73 information from 79 GSFC projects. Although the subject matter relates to GSFX activities, the type of analysis used and the manner of selecting the relevant variables would be of interest to other NASA centers, government agencies, private corporations and, in general, any organization with a significant travel budget. Models were developed for each of six types of activity: flight projects (in-house and out-of-house), experiments on non-GSFC projects, international projects, ART/SRT, data analysis, advanced studies, tracking and data, and indirects.

Characterization of acid functional groups of carbon dots by nonlinear regression data fitting of potentiometric titration curves

NASA Astrophysics Data System (ADS)

Alves, Larissa A.; de Castro, Arthur H.; de Mendonça, Fernanda G.; de Mesquita, João P.

2016-05-01

The oxygenated functional groups present on the surface of carbon dots with an average size of 2.7 ± 0.5 nm were characterized by a variety of techniques. In particular, we discussed the fit data of potentiometric titration curves using a nonlinear regression method based on the Levenberg-Marquardt algorithm. The results obtained by statistical treatment of the titration curve data showed that the best fit was obtained considering the presence of five Brønsted-Lowry acids on the surface of the carbon dots with constant ionization characteristics of carboxylic acids, cyclic ester, phenolic and pyrone-like groups. The total number of oxygenated acid groups obtained was 5 mmol g-1, with approximately 65% (∼2.9 mmol g-1) originating from groups with pKa < 6. The methodology showed good reproducibility and stability with standard deviations below 5%. The nature of the groups was independent of small variations in experimental conditions, i.e. the mass of carbon dots titrated and initial concentration of HCl solution. Finally, we believe that the methodology used here, together with other characterization techniques, is a simple, fast and powerful tool to characterize the complex acid-base properties of these so interesting and intriguing nanoparticles.

Criterion for evaluating the predictive ability of nonlinear regression models without cross-validation.

PubMed

Kaneko, Hiromasa; Funatsu, Kimito

2013-09-23

We propose predictive performance criteria for nonlinear regression models without cross-validation. The proposed criteria are the determination coefficient and the root-mean-square error for the midpoints between k-nearest-neighbor data points. These criteria can be used to evaluate predictive ability after the regression models are updated, whereas cross-validation cannot be performed in such a situation. The proposed method is effective and helpful in handling big data when cross-validation cannot be applied. By analyzing data from numerical simulations and quantitative structural relationships, we confirm that the proposed criteria enable the predictive ability of the nonlinear regression models to be appropriately quantified.

Identification of cow milk in goat milk by nonlinear chemical fingerprint technique.

PubMed

Ma, Yong-Jie; Dong, Wen-Bin; Fan, Cheng; Wang, Er-Dan

2017-10-01

The objective of this paper was to develop a nonlinear chemical fingerprint technique for identifying and detecting adulteration of goat milk with cow milk. In this study, by taking the Belousov-Zhabotinsky oscillatory chemical reaction using acetone and substrates in goat milk or cow milk as main dissipative substances, when the same dosage of goat milk and cow milk was introduced to the "H +  + Mn 2+  + BrO 3 -  + acetone" oscillating system respectively, nonlinear chemical fingerprints were obtained for goat milk and cow milk from the same origin. The results showed that inductive time value and the content of cow milk in goat milk had a linear relationship in the range of 0-100% and the corresponding regression coefficient was 0.9991. A detection limit of 0.0107 g/g was obtained, and the content of cow milk in mixed milk was calculated. The proposed method in this study was simple, economical and effective. In addition, the method did not need the pretreatment and separation of samples for identifying and evaluating cow milk adulteration in goat milk. Copyright © 2017. Published by Elsevier B.V.

Fatigue design of a cellular phone folder using regression model-based multi-objective optimization

NASA Astrophysics Data System (ADS)

Kim, Young Gyun; Lee, Jongsoo

2016-08-01

In a folding cellular phone, the folding device is repeatedly opened and closed by the user, which eventually results in fatigue damage, particularly to the front of the folder. Hence, it is important to improve the safety and endurance of the folder while also reducing its weight. This article presents an optimal design for the folder front that maximizes its fatigue endurance while minimizing its thickness. Design data for analysis and optimization were obtained experimentally using a test jig. Multi-objective optimization was carried out using a nonlinear regression model. Three regression methods were employed: back-propagation neural networks, logistic regression and support vector machines. The AdaBoost ensemble technique was also used to improve the approximation. Two-objective Pareto-optimal solutions were identified using the non-dominated sorting genetic algorithm (NSGA-II). Finally, a numerically optimized solution was validated against experimental product data, in terms of both fatigue endurance and thickness index.

Two-dimensional advective transport in ground-water flow parameter estimation

USGS Publications Warehouse

Anderman, E.R.; Hill, M.C.; Poeter, E.P.

1996-01-01

Nonlinear regression is useful in ground-water flow parameter estimation, but problems of parameter insensitivity and correlation often exist given commonly available hydraulic-head and head-dependent flow (for example, stream and lake gain or loss) observations. To address this problem, advective-transport observations are added to the ground-water flow, parameter-estimation model MODFLOWP using particle-tracking methods. The resulting model is used to investigate the importance of advective-transport observations relative to head-dependent flow observations when either or both are used in conjunction with hydraulic-head observations in a simulation of the sewage-discharge plume at Otis Air Force Base, Cape Cod, Massachusetts, USA. The analysis procedure for evaluating the probable effect of new observations on the regression results consists of two steps: (1) parameter sensitivities and correlations calculated at initial parameter values are used to assess the model parameterization and expected relative contributions of different types of observations to the regression; and (2) optimal parameter values are estimated by nonlinear regression and evaluated. In the Cape Cod parameter-estimation model, advective-transport observations did not significantly increase the overall parameter sensitivity; however: (1) inclusion of advective-transport observations decreased parameter correlation enough for more unique parameter values to be estimated by the regression; (2) realistic uncertainties in advective-transport observations had a small effect on parameter estimates relative to the precision with which the parameters were estimated; and (3) the regression results and sensitivity analysis provided insight into the dynamics of the ground-water flow system, especially the importance of accurate boundary conditions. In this work, advective-transport observations improved the calibration of the model and the estimation of ground-water flow parameters, and use of regression and related techniques produced significant insight into the physical system.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Examining the influence of link function misspecification in conventional regression models for developing crash modification factors.

PubMed

Wu, Lingtao; Lord, Dominique

2017-05-01

This study further examined the use of regression models for developing crash modification factors (CMFs), specifically focusing on the misspecification in the link function. The primary objectives were to validate the accuracy of CMFs derived from the commonly used regression models (i.e., generalized linear models or GLMs with additive linear link functions) when some of the variables have nonlinear relationships and quantify the amount of bias as a function of the nonlinearity. Using the concept of artificial realistic data, various linear and nonlinear crash modification functions (CM-Functions) were assumed for three variables. Crash counts were randomly generated based on these CM-Functions. CMFs were then derived from regression models for three different scenarios. The results were compared with the assumed true values. The main findings are summarized as follows: (1) when some variables have nonlinear relationships with crash risk, the CMFs for these variables derived from the commonly used GLMs are all biased, especially around areas away from the baseline conditions (e.g., boundary areas); (2) with the increase in nonlinearity (i.e., nonlinear relationship becomes stronger), the bias becomes more significant; (3) the quality of CMFs for other variables having linear relationships can be influenced when mixed with those having nonlinear relationships, but the accuracy may still be acceptable; and (4) the misuse of the link function for one or more variables can also lead to biased estimates for other parameters. This study raised the importance of the link function when using regression models for developing CMFs. Copyright © 2017 Elsevier Ltd. All rights reserved.

A data-driven approach for modeling post-fire debris-flow volumes and their uncertainty

USGS Publications Warehouse

Friedel, Michael J.

2011-01-01

This study demonstrates the novel application of genetic programming to evolve nonlinear post-fire debris-flow volume equations from variables associated with a data-driven conceptual model of the western United States. The search space is constrained using a multi-component objective function that simultaneously minimizes root-mean squared and unit errors for the evolution of fittest equations. An optimization technique is then used to estimate the limits of nonlinear prediction uncertainty associated with the debris-flow equations. In contrast to a published multiple linear regression three-variable equation, linking basin area with slopes greater or equal to 30 percent, burn severity characterized as area burned moderate plus high, and total storm rainfall, the data-driven approach discovers many nonlinear and several dimensionally consistent equations that are unbiased and have less prediction uncertainty. Of the nonlinear equations, the best performance (lowest prediction uncertainty) is achieved when using three variables: average basin slope, total burned area, and total storm rainfall. Further reduction in uncertainty is possible for the nonlinear equations when dimensional consistency is not a priority and by subsequently applying a gradient solver to the fittest solutions. The data-driven modeling approach can be applied to nonlinear multivariate problems in all fields of study.

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

ERIC Educational Resources Information Center

Drabinová, Adéla; Martinková, Patrícia

2017-01-01

In this article we present a general approach not relying on item response theory models (non-IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non-IRT approach, NLR can…

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Lofberg, Johan; Brenner, Martin J.

2006-01-01

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Use of non-linear mixed-effects modelling and regression analysis to predict the number of somatic coliphages by plaque enumeration after 3 hours of incubation.

PubMed

Mendez, Javier; Monleon-Getino, Antonio; Jofre, Juan; Lucena, Francisco

2017-10-01

The present study aimed to establish the kinetics of the appearance of coliphage plaques using the double agar layer titration technique to evaluate the feasibility of using traditional coliphage plaque forming unit (PFU) enumeration as a rapid quantification method. Repeated measurements of the appearance of plaques of coliphages titrated according to ISO 10705-2 at different times were analysed using non-linear mixed-effects regression to determine the most suitable model of their appearance kinetics. Although this model is adequate, to simplify its applicability two linear models were developed to predict the numbers of coliphages reliably, using the PFU counts as determined by the ISO after only 3 hours of incubation. One linear model, when the number of plaques detected was between 4 and 26 PFU after 3 hours, had a linear fit of: (1.48 × Counts 3 h + 1.97); and the other, values >26 PFU, had a fit of (1.18 × Counts 3 h + 2.95). If the number of plaques detected was <4 PFU after 3 hours, we recommend incubation for (18 ± 3) hours. The study indicates that the traditional coliphage plating technique has a reasonable potential to provide results in a single working day without the need to invest in additional laboratory equipment.

A novel approach for prediction of tacrolimus blood concentration in liver transplantation patients in the intensive care unit through support vector regression.

PubMed

Van Looy, Stijn; Verplancke, Thierry; Benoit, Dominique; Hoste, Eric; Van Maele, Georges; De Turck, Filip; Decruyenaere, Johan

2007-01-01

Tacrolimus is an important immunosuppressive drug for organ transplantation patients. It has a narrow therapeutic range, toxic side effects, and a blood concentration with wide intra- and interindividual variability. Hence, it is of the utmost importance to monitor tacrolimus blood concentration, thereby ensuring clinical effect and avoiding toxic side effects. Prediction models for tacrolimus blood concentration can improve clinical care by optimizing monitoring of these concentrations, especially in the initial phase after transplantation during intensive care unit (ICU) stay. This is the first study in the ICU in which support vector machines, as a new data modeling technique, are investigated and tested in their prediction capabilities of tacrolimus blood concentration. Linear support vector regression (SVR) and nonlinear radial basis function (RBF) SVR are compared with multiple linear regression (MLR). Tacrolimus blood concentrations, together with 35 other relevant variables from 50 liver transplantation patients, were extracted from our ICU database. This resulted in a dataset of 457 blood samples, on average between 9 and 10 samples per patient, finally resulting in a database of more than 16,000 data values. Nonlinear RBF SVR, linear SVR, and MLR were performed after selection of clinically relevant input variables and model parameters. Differences between observed and predicted tacrolimus blood concentrations were calculated. Prediction accuracy of the three methods was compared after fivefold cross-validation (Friedman test and Wilcoxon signed rank analysis). Linear SVR and nonlinear RBF SVR had mean absolute differences between observed and predicted tacrolimus blood concentrations of 2.31 ng/ml (standard deviation [SD] 2.47) and 2.38 ng/ml (SD 2.49), respectively. MLR had a mean absolute difference of 2.73 ng/ml (SD 3.79). The difference between linear SVR and MLR was statistically significant (p < 0.001). RBF SVR had the advantage of requiring only 2 input variables to perform this prediction in comparison to 15 and 16 variables needed by linear SVR and MLR, respectively. This is an indication of the superior prediction capability of nonlinear SVR. Prediction of tacrolimus blood concentration with linear and nonlinear SVR was excellent, and accuracy was superior in comparison with an MLR model.

Assessing the Impact of Drug Use on Hospital Costs

PubMed Central

Stuart, Bruce C; Doshi, Jalpa A; Terza, Joseph V

2009-01-01

Objective To assess whether outpatient prescription drug utilization produces offsets in the cost of hospitalization for Medicare beneficiaries. Data Sources/Study Setting The study analyzed a sample (N=3,101) of community-dwelling fee-for-service U.S. Medicare beneficiaries drawn from the 1999 and 2000 Medicare Current Beneficiary Surveys. Study Design Using a two-part model specification, we regressed any hospital admission (part 1: probit) and hospital spending by those with one or more admissions (part 2: nonlinear least squares regression) on drug use in a standard model with strong covariate controls and a residual inclusion instrumental variable (IV) model using an exogenous measure of drug coverage as the instrument. Principal Findings The covariate control model predicted that each additional prescription drug used (mean=30) raised hospital spending by $16 (p<.001). The residual inclusion IV model prediction was that each additional prescription fill reduced hospital spending by $104 (p<.001). Conclusions The findings indicate that drug use is associated with cost offsets in hospitalization among Medicare beneficiaries, once omitted variable bias is corrected using an IV technique appropriate for nonlinear applications. PMID:18783453

Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media

USGS Publications Warehouse

Cooley, R.L.; Christensen, S.

2006-01-01

Groundwater models need to account for detailed but generally unknown spatial variability (heterogeneity) of the hydrogeologic model inputs. To address this problem we replace the large, m-dimensional stochastic vector ?? that reflects both small and large scales of heterogeneity in the inputs by a lumped or smoothed m-dimensional approximation ????*, where ?? is an interpolation matrix and ??* is a stochastic vector of parameters. Vector ??* has small enough dimension to allow its estimation with the available data. The consequence of the replacement is that model function f(????*) written in terms of the approximate inputs is in error with respect to the same model function written in terms of ??, ??,f(??), which is assumed to be nearly exact. The difference f(??) - f(????*), termed model error, is spatially correlated, generates prediction biases, and causes standard confidence and prediction intervals to be too small. Model error is accounted for in the weighted nonlinear regression methodology developed to estimate ??* and assess model uncertainties by incorporating the second-moment matrix of the model errors into the weight matrix. Techniques developed by statisticians to analyze classical nonlinear regression methods are extended to analyze the revised method. The analysis develops analytical expressions for bias terms reflecting the interaction of model nonlinearity and model error, for correction factors needed to adjust the sizes of confidence and prediction intervals for this interaction, and for correction factors needed to adjust the sizes of confidence and prediction intervals for possible use of a diagonal weight matrix in place of the correct one. If terms expressing the degree of intrinsic nonlinearity for f(??) and f(????*) are small, then most of the biases are small and the correction factors are reduced in magnitude. Biases, correction factors, and confidence and prediction intervals were obtained for a test problem for which model error is large to test robustness of the methodology. Numerical results conform with the theoretical analysis. ?? 2005 Elsevier Ltd. All rights reserved.

Least-squares sequential parameter and state estimation for large space structures

NASA Technical Reports Server (NTRS)

Thau, F. E.; Eliazov, T.; Montgomery, R. C.

1982-01-01

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Finite-sample and asymptotic sign-based tests for parameters of non-linear quantile regression with Markov noise

NASA Astrophysics Data System (ADS)

Sirenko, M. A.; Tarasenko, P. F.; Pushkarev, M. I.

2017-01-01

One of the most noticeable features of sign-based statistical procedures is an opportunity to build an exact test for simple hypothesis testing of parameters in a regression model. In this article, we expanded a sing-based approach to the nonlinear case with dependent noise. The examined model is a multi-quantile regression, which makes it possible to test hypothesis not only of regression parameters, but of noise parameters as well.

A study of machine learning regression methods for major elemental analysis of rocks using laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Boucher, Thomas F.; Ozanne, Marie V.; Carmosino, Marco L.; Dyar, M. Darby; Mahadevan, Sridhar; Breves, Elly A.; Lepore, Kate H.; Clegg, Samuel M.

2015-05-01

The ChemCam instrument on the Mars Curiosity rover is generating thousands of LIBS spectra and bringing interest in this technique to public attention. The key to interpreting Mars or any other types of LIBS data are calibrations that relate laboratory standards to unknowns examined in other settings and enable predictions of chemical composition. Here, LIBS spectral data are analyzed using linear regression methods including partial least squares (PLS-1 and PLS-2), principal component regression (PCR), least absolute shrinkage and selection operator (lasso), elastic net, and linear support vector regression (SVR-Lin). These were compared against results from nonlinear regression methods including kernel principal component regression (K-PCR), polynomial kernel support vector regression (SVR-Py) and k-nearest neighbor (kNN) regression to discern the most effective models for interpreting chemical abundances from LIBS spectra of geological samples. The results were evaluated for 100 samples analyzed with 50 laser pulses at each of five locations averaged together. Wilcoxon signed-rank tests were employed to evaluate the statistical significance of differences among the nine models using their predicted residual sum of squares (PRESS) to make comparisons. For MgO, SiO2, Fe2O3, CaO, and MnO, the sparse models outperform all the others except for linear SVR, while for Na2O, K2O, TiO2, and P2O5, the sparse methods produce inferior results, likely because their emission lines in this energy range have lower transition probabilities. The strong performance of the sparse methods in this study suggests that use of dimensionality-reduction techniques as a preprocessing step may improve the performance of the linear models. Nonlinear methods tend to overfit the data and predict less accurately, while the linear methods proved to be more generalizable with better predictive performance. These results are attributed to the high dimensionality of the data (6144 channels) relative to the small number of samples studied. The best-performing models were SVR-Lin for SiO2, MgO, Fe2O3, and Na2O, lasso for Al2O3, elastic net for MnO, and PLS-1 for CaO, TiO2, and K2O. Although these differences in model performance between methods were identified, most of the models produce comparable results when p ≤ 0.05 and all techniques except kNN produced statistically-indistinguishable results. It is likely that a combination of models could be used together to yield a lower total error of prediction, depending on the requirements of the user.

An Excel Solver Exercise to Introduce Nonlinear Regression

ERIC Educational Resources Information Center

Pinder, Jonathan P.

2013-01-01

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a "black box" to the students. Thus, although correct models are…

A linear spectral matching technique for retrieving equivalent water thickness and biochemical constituents of green vegetation

NASA Technical Reports Server (NTRS)

Gao, Bo-Cai; Goetz, Alexander F. H.

1992-01-01

Over the last decade, technological advances in airborne imaging spectrometers, having spectral resolution comparable with laboratory spectrometers, have made it possible to estimate biochemical constituents of vegetation canopies. Wessman estimated lignin concentration from data acquired with NASA's Airborne Imaging Spectrometer (AIS) over Blackhawk Island in Wisconsin. A stepwise linear regression technique was used to determine the single spectral channel or channels in the AIS data that best correlated with measured lignin contents using chemical methods. The regression technique does not take advantage of the spectral shape of the lignin reflectance feature as a diagnostic tool nor the increased discrimination among other leaf components with overlapping spectral features. A nonlinear least squares spectral matching technique was recently reported for deriving both the equivalent water thicknesses of surface vegetation and the amounts of water vapor in the atmosphere from contiguous spectra measured with the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The same technique was applied to a laboratory reflectance spectrum of fresh, green leaves. The result demonstrates that the fresh leaf spectrum in the 1.0-2.5 microns region consists of spectral components of dry leaves and the spectral component of liquid water. A linear least squares spectral matching technique for retrieving equivalent water thickness and biochemical components of green vegetation is described.

Experimental and computational prediction of glass transition temperature of drugs.

PubMed

Alzghoul, Ahmad; Alhalaweh, Amjad; Mahlin, Denny; Bergström, Christel A S

2014-12-22

Glass transition temperature (Tg) is an important inherent property of an amorphous solid material which is usually determined experimentally. In this study, the relation between Tg and melting temperature (Tm) was evaluated using a data set of 71 structurally diverse druglike compounds. Further, in silico models for prediction of Tg were developed based on calculated molecular descriptors and linear (multilinear regression, partial least-squares, principal component regression) and nonlinear (neural network, support vector regression) modeling techniques. The models based on Tm predicted Tg with an RMSE of 19.5 K for the test set. Among the five computational models developed herein the support vector regression gave the best result with RMSE of 18.7 K for the test set using only four chemical descriptors. Hence, two different models that predict Tg of drug-like molecules with high accuracy were developed. If Tm is available, a simple linear regression can be used to predict Tg. However, the results also suggest that support vector regression and calculated molecular descriptors can predict Tg with equal accuracy, already before compound synthesis.

A gap-filling model for eddy covariance latent heat flux: Estimating evapotranspiration of a subtropical seasonal evergreen broad-leaved forest as an example

NASA Astrophysics Data System (ADS)

Chen, Yi-Ying; Chu, Chia-Ren; Li, Ming-Hsu

2012-10-01

SummaryIn this paper we present a semi-parametric multivariate gap-filling model for tower-based measurement of latent heat flux (LE). Two statistical techniques, the principal component analysis (PCA) and a nonlinear interpolation approach were integrated into this LE gap-filling model. The PCA was first used to resolve the multicollinearity relationships among various environmental variables, including radiation, soil moisture deficit, leaf area index, wind speed, etc. Two nonlinear interpolation methods, multiple regressions (MRS) and the K-nearest neighbors (KNNs) were examined with random selected flux gaps for both clear sky and nighttime/cloudy data to incorporate into this LE gap-filling model. Experimental results indicated that the KNN interpolation approach is able to provide consistent LE estimations while MRS presents over estimations during nighttime/cloudy. Rather than using empirical regression parameters, the KNN approach resolves the nonlinear relationship between the gap-filled LE flux and principal components with adaptive K values under different atmospheric states. The developed LE gap-filling model (PCA with KNN) works with a RMSE of 2.4 W m-2 (˜0.09 mm day-1) at a weekly time scale by adding 40% artificial flux gaps into original dataset. Annual evapotranspiration at this study site were estimated at 736 mm (1803 MJ) and 728 mm (1785 MJ) for year 2008 and 2009, respectively.

Rapid prediction of total petroleum hydrocarbons concentration in contaminated soil using vis-NIR spectroscopy and regression techniques.

PubMed

Douglas, R K; Nawar, S; Alamar, M C; Mouazen, A M; Coulon, F

2018-03-01

Visible and near infrared spectrometry (vis-NIRS) coupled with data mining techniques can offer fast and cost-effective quantitative measurement of total petroleum hydrocarbons (TPH) in contaminated soils. Literature showed however significant differences in the performance on the vis-NIRS between linear and non-linear calibration methods. This study compared the performance of linear partial least squares regression (PLSR) with a nonlinear random forest (RF) regression for the calibration of vis-NIRS when analysing TPH in soils. 88 soil samples (3 uncontaminated and 85 contaminated) collected from three sites located in the Niger Delta were scanned using an analytical spectral device (ASD) spectrophotometer (350-2500nm) in diffuse reflectance mode. Sequential ultrasonic solvent extraction-gas chromatography (SUSE-GC) was used as reference quantification method for TPH which equal to the sum of aliphatic and aromatic fractions ranging between C 10 and C 35 . Prior to model development, spectra were subjected to pre-processing including noise cut, maximum normalization, first derivative and smoothing. Then 65 samples were selected as calibration set and the remaining 20 samples as validation set. Both vis-NIR spectrometry and gas chromatography profiles of the 85 soil samples were subjected to RF and PLSR with leave-one-out cross-validation (LOOCV) for the calibration models. Results showed that RF calibration model with a coefficient of determination (R 2 ) of 0.85, a root means square error of prediction (RMSEP) 68.43mgkg -1 , and a residual prediction deviation (RPD) of 2.61 outperformed PLSR (R 2 =0.63, RMSEP=107.54mgkg -1 and RDP=2.55) in cross-validation. These results indicate that RF modelling approach is accounting for the nonlinearity of the soil spectral responses hence, providing significantly higher prediction accuracy compared to the linear PLSR. It is recommended to adopt the vis-NIRS coupled with RF modelling approach as a portable and cost effective method for the rapid quantification of TPH in soils. Copyright © 2017 Elsevier B.V. All rights reserved.

A stepwise regression tree for nonlinear approximation: applications to estimating subpixel land cover

USGS Publications Warehouse

Huang, C.; Townshend, J.R.G.

2003-01-01

A stepwise regression tree (SRT) algorithm was developed for approximating complex nonlinear relationships. Based on the regression tree of Breiman et al . (BRT) and a stepwise linear regression (SLR) method, this algorithm represents an improvement over SLR in that it can approximate nonlinear relationships and over BRT in that it gives more realistic predictions. The applicability of this method to estimating subpixel forest was demonstrated using three test data sets, on all of which it gave more accurate predictions than SLR and BRT. SRT also generated more compact trees and performed better than or at least as well as BRT at all 10 equal forest proportion interval ranging from 0 to 100%. This method is appealing to estimating subpixel land cover over large areas.

Application of nonlinear regression in the development of a wide range formulation for HCFC-22

NASA Astrophysics Data System (ADS)

Kamei, A.; Beyerlein, S. W.; Jacobsen, R. T.

1995-09-01

An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based on P-ρ-T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.

Temperature profile retrievals with extended Kalman-Bucy filters

NASA Technical Reports Server (NTRS)

Ledsham, W. H.; Staelin, D. H.

1979-01-01

The Extended Kalman-Bucy Filter is a powerful technique for estimating non-stationary random parameters in situations where the received signal is a noisy non-linear function of those parameters. A practical causal filter for retrieving atmospheric temperature profiles from radiances observed at a single scan angle by the Scanning Microwave Spectrometer (SCAMS) carried on the Nimbus 6 satellite typically shows approximately a 10-30% reduction in rms error about the mean at almost all levels below 70 mb when compared with a regression inversion.

Incremental online learning in high dimensions.

PubMed

Vijayakumar, Sethu; D'Souza, Aaron; Schaal, Stefan

2005-12-01

Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high-dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally efficient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression. We discuss when and how local learning techniques can successfully work in high-dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the LWPR algorithm. The properties of LWPR are that it (1) learns rapidly with second-order learning methods based on incremental training, (2) uses statistically sound stochastic leave-one-out cross validation for learning without the need to memorize training data, (3) adjusts its weighting kernels based on only local information in order to minimize the danger of negative interference of incremental learning, (4) has a computational complexity that is linear in the number of inputs, and (5) can deal with a large number of-possibly redundant-inputs, as shown in various empirical evaluations with up to 90 dimensional data sets. For a probabilistic interpretation, predictive variance and confidence intervals are derived. To our knowledge, LWPR is the first truly incremental spatially localized learning method that can successfully and efficiently operate in very high-dimensional spaces.

Expanding the occupational health methodology: A concatenated artificial neural network approach to model the burnout process in Chinese nurses.

PubMed

Ladstätter, Felix; Garrosa, Eva; Moreno-Jiménez, Bernardo; Ponsoda, Vicente; Reales Aviles, José Manuel; Dai, Junming

2016-01-01

Artificial neural networks are sophisticated modelling and prediction tools capable of extracting complex, non-linear relationships between predictor (input) and predicted (output) variables. This study explores this capacity by modelling non-linearities in the hardiness-modulated burnout process with a neural network. Specifically, two multi-layer feed-forward artificial neural networks are concatenated in an attempt to model the composite non-linear burnout process. Sensitivity analysis, a Monte Carlo-based global simulation technique, is then utilised to examine the first-order effects of the predictor variables on the burnout sub-dimensions and consequences. Results show that (1) this concatenated artificial neural network approach is feasible to model the burnout process, (2) sensitivity analysis is a prolific method to study the relative importance of predictor variables and (3) the relationships among variables involved in the development of burnout and its consequences are to different degrees non-linear. Many relationships among variables (e.g., stressors and strains) are not linear, yet researchers use linear methods such as Pearson correlation or linear regression to analyse these relationships. Artificial neural network analysis is an innovative method to analyse non-linear relationships and in combination with sensitivity analysis superior to linear methods.

Kernel Partial Least Squares for Nonlinear Regression and Discrimination

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.

Symplectic geometry spectrum regression for prediction of noisy time series

NASA Astrophysics Data System (ADS)

Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie

2016-05-01

We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).

Linearity versus Nonlinearity of Offspring-Parent Regression: An Experimental Study of Drosophila Melanogaster

PubMed Central

Gimelfarb, A.; Willis, J. H.

1994-01-01

An experiment was conducted to investigate the offspring-parent regression for three quantitative traits (weight, abdominal bristles and wing length) in Drosophila melanogaster. Linear and polynomial models were fitted for the regressions of a character in offspring on both parents. It is demonstrated that responses by the characters to selection predicted by the nonlinear regressions may differ substantially from those predicted by the linear regressions. This is true even, and especially, if selection is weak. The realized heritability for a character under selection is shown to be determined not only by the offspring-parent regression but also by the distribution of the character and by the form and strength of selection. PMID:7828818

Measuring multi-joint stiffness during single movements: numerical validation of a novel time-frequency approach.

PubMed

Piovesan, Davide; Pierobon, Alberto; DiZio, Paul; Lackner, James R

2012-01-01

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

Supervised Learning for Dynamical System Learning.

PubMed

Hefny, Ahmed; Downey, Carlton; Gordon, Geoffrey J

2015-01-01

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L 1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Prediction of ozone concentration in tropospheric levels using artificial neural networks and support vector machine at Rio de Janeiro, Brazil

NASA Astrophysics Data System (ADS)

Luna, A. S.; Paredes, M. L. L.; de Oliveira, G. C. G.; Corrêa, S. M.

2014-12-01

It is well known that air quality is a complex function of emissions, meteorology and topography, and statistical tools provide a sound framework for relating these variables. The observed data were contents of nitrogen dioxide (NO2), nitrogen monoxide (NO), nitrogen oxides (NOx), carbon monoxide (CO), ozone (O3), scalar wind speed (SWS), global solar radiation (GSR), temperature (TEM), moisture content in the air (HUM), collected by a mobile automatic monitoring station at Rio de Janeiro City in two places of the metropolitan area during 2011 and 2012. The aims of this study were: (1) to analyze the behavior of the variables, using the method of PCA for exploratory data analysis; (2) to propose forecasts of O3 levels from primary pollutants and meteorological factors, using nonlinear regression methods like ANN and SVM, from primary pollutants and meteorological factors. The PCA technique showed that for first dataset, variables NO, NOx and SWS have a greater impact on the concentration of O3 and the other data set had the TEM and GSR as the most influential variables. The obtained results from the nonlinear regression techniques ANN and SVM were remarkably closely and acceptable to one dataset presenting coefficient of determination for validation respectively 0.9122 and 0.9152, and root mean square error of 7.66 and 7.85, respectively. For these datasets, the PCA, SVM and ANN had demonstrated their robustness as useful tools for evaluation, and forecast scenarios for air quality.

Multilayer Perceptron for Robust Nonlinear Interval Regression Analysis Using Genetic Algorithms

PubMed Central

2014-01-01

On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets. PMID:25110755

Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.

PubMed

Hu, Yi-Chung

2014-01-01

On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets.

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Learning curve of single port laparoscopic cholecystectomy determined using the non-linear ordinary least squares method based on a non-linear regression model: An analysis of 150 consecutive patients.

PubMed

Han, Hyung Joon; Choi, Sae Byeol; Park, Man Sik; Lee, Jin Suk; Kim, Wan Bae; Song, Tae Jin; Choi, Sang Yong

2011-07-01

Single port laparoscopic surgery has come to the forefront of minimally invasive surgery. For those familiar with conventional techniques, however, this type of operation demands a different type of eye/hand coordination and involves unfamiliar working instruments. Herein, the authors describe the learning curve and the clinical outcomes of single port laparoscopic cholecystectomy for 150 consecutive patients with benign gallbladder disease. All patients underwent single port laparoscopic cholecystectomy using a homemade glove port by one of five operators with different levels of experiences of laparoscopic surgery. The learning curve for each operator was fitted using the non-linear ordinary least squares method based on a non-linear regression model. Mean operating time was 77.6 ± 28.5 min. Fourteen patients (6.0%) were converted to conventional laparoscopic cholecystectomy. Complications occurred in 15 patients (10.0%), as follows: bile duct injury (n = 2), surgical site infection (n = 8), seroma (n = 2), and wound pain (n = 3). One operator achieved a learning curve plateau at 61.4 min per procedure after 8.5 cases and his time improved by 95.3 min as compared with initial operation time. Younger surgeons showed significant decreases in mean operation time and achieved stable mean operation times. In particular, younger surgeons showed significant decreases in operation times after 20 cases. Experienced laparoscopic surgeons can safely perform single port laparoscopic cholecystectomy using conventional or angled laparoscopic instruments. The present study shows that an operator can overcome the single port laparoscopic cholecystectomy learning curve in about eight cases.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

NASA Technical Reports Server (NTRS)

Costiner, Sorin; Taasan, Shlomo

1994-01-01

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

Identification of an internal combustion engine model by nonlinear multi-input multi-output system identification. Ph.D. Thesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luh, G.C.

1994-01-01

This thesis presents the application of advanced modeling techniques to construct nonlinear forward and inverse models of internal combustion engines for the detection and isolation of incipient faults. The NARMAX (Nonlinear Auto-Regressive Moving Average modeling with eXogenous inputs) technique of system identification proposed by Leontaritis and Billings was used to derive the nonlinear model of a internal combustion engine, over operating conditions corresponding to the I/M240 cycle. The I/M240 cycle is a standard proposed by the United States Environmental Protection Agency to measure tailpipe emissions in inspection and maintenance programs and consists of a driving schedule developed for the purposemore » of testing compliance with federal vehicle emission standards for carbon monoxide, unburned hydrocarbons, and nitrogen oxides. The experimental work for model identification and validation was performed on a 3.0 liter V6 engine installed in an engine test cell at the Center for Automotive Research at The Ohio State University. In this thesis, different types of model structures were proposed to obtain multi-input multi-output (MIMO) nonlinear NARX models. A modification of the algorithm proposed by He and Asada was used to estimate the robust orders of the derived MIMO nonlinear models. A methodology for the analysis of inverse NARX model was developed. Two methods were proposed to derive the inverse NARX model: (1) inversion from the forward NARX model; and (2) direct identification of inverse model from the output-input data set. In this thesis, invertibility, minimum-phase characteristic of zero dynamics, and stability analysis of NARX forward model are also discussed. Stability in the sense of Lyapunov is also investigated to check the stability of the identified forward and inverse models. This application of inverse problem leads to the estimation of unknown inputs and to actuator fault diagnosis.« less

Does the high–tech industry consistently reduce CO{sub 2} emissions? Results from nonparametric additive regression model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Bin; Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013; Lin, Boqiang, E-mail: bqlin@xmu.edu.cn

China is currently the world's largest carbon dioxide (CO{sub 2}) emitter. Moreover, total energy consumption and CO{sub 2} emissions in China will continue to increase due to the rapid growth of industrialization and urbanization. Therefore, vigorously developing the high–tech industry becomes an inevitable choice to reduce CO{sub 2} emissions at the moment or in the future. However, ignoring the existing nonlinear links between economic variables, most scholars use traditional linear models to explore the impact of the high–tech industry on CO{sub 2} emissions from an aggregate perspective. Few studies have focused on nonlinear relationships and regional differences in China. Basedmore » on panel data of 1998–2014, this study uses the nonparametric additive regression model to explore the nonlinear effect of the high–tech industry from a regional perspective. The estimated results show that the residual sum of squares (SSR) of the nonparametric additive regression model in the eastern, central and western regions are 0.693, 0.054 and 0.085 respectively, which are much less those that of the traditional linear regression model (3.158, 4.227 and 7.196). This verifies that the nonparametric additive regression model has a better fitting effect. Specifically, the high–tech industry produces an inverted “U–shaped” nonlinear impact on CO{sub 2} emissions in the eastern region, but a positive “U–shaped” nonlinear effect in the central and western regions. Therefore, the nonlinear impact of the high–tech industry on CO{sub 2} emissions in the three regions should be given adequate attention in developing effective abatement policies. - Highlights: • The nonlinear effect of the high–tech industry on CO{sub 2} emissions was investigated. • The high–tech industry yields an inverted “U–shaped” effect in the eastern region. • The high–tech industry has a positive “U–shaped” nonlinear effect in other regions. • The linear impact of the high–tech industry in the eastern region is the strongest.« less

Z-scan: A simple technique for determination of third-order optical nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Vijender, E-mail: chahal-gju@rediffmail.com; Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in

Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to bemore » 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.« less

Extending the Distributed Lag Model framework to handle chemical mixtures.

PubMed

Bello, Ghalib A; Arora, Manish; Austin, Christine; Horton, Megan K; Wright, Robert O; Gennings, Chris

2017-07-01

Distributed Lag Models (DLMs) are used in environmental health studies to analyze the time-delayed effect of an exposure on an outcome of interest. Given the increasing need for analytical tools for evaluation of the effects of exposure to multi-pollutant mixtures, this study attempts to extend the classical DLM framework to accommodate and evaluate multiple longitudinally observed exposures. We introduce 2 techniques for quantifying the time-varying mixture effect of multiple exposures on an outcome of interest. Lagged WQS, the first technique, is based on Weighted Quantile Sum (WQS) regression, a penalized regression method that estimates mixture effects using a weighted index. We also introduce Tree-based DLMs, a nonparametric alternative for assessment of lagged mixture effects. This technique is based on the Random Forest (RF) algorithm, a nonparametric, tree-based estimation technique that has shown excellent performance in a wide variety of domains. In a simulation study, we tested the feasibility of these techniques and evaluated their performance in comparison to standard methodology. Both methods exhibited relatively robust performance, accurately capturing pre-defined non-linear functional relationships in different simulation settings. Further, we applied these techniques to data on perinatal exposure to environmental metal toxicants, with the goal of evaluating the effects of exposure on neurodevelopment. Our methods identified critical neurodevelopmental windows showing significant sensitivity to metal mixtures. Copyright © 2017 Elsevier Inc. All rights reserved.

A stepwise model to predict monthly streamflow

NASA Astrophysics Data System (ADS)

Mahmood Al-Juboori, Anas; Guven, Aytac

2016-12-01

In this study, a stepwise model empowered with genetic programming is developed to predict the monthly flows of Hurman River in Turkey and Diyalah and Lesser Zab Rivers in Iraq. The model divides the monthly flow data to twelve intervals representing the number of months in a year. The flow of a month, t is considered as a function of the antecedent month's flow (t - 1) and it is predicted by multiplying the antecedent monthly flow by a constant value called K. The optimum value of K is obtained by a stepwise procedure which employs Gene Expression Programming (GEP) and Nonlinear Generalized Reduced Gradient Optimization (NGRGO) as alternative to traditional nonlinear regression technique. The degree of determination and root mean squared error are used to evaluate the performance of the proposed models. The results of the proposed model are compared with the conventional Markovian and Auto Regressive Integrated Moving Average (ARIMA) models based on observed monthly flow data. The comparison results based on five different statistic measures show that the proposed stepwise model performed better than Markovian model and ARIMA model. The R2 values of the proposed model range between 0.81 and 0.92 for the three rivers in this study.

A non-linear data mining parameter selection algorithm for continuous variables

PubMed Central

Razavi, Marianne; Brady, Sean

2017-01-01

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables. PMID:29131829

Techniques for forced response involving discrete nonlinearities. I - Theory. II - Applications

NASA Astrophysics Data System (ADS)

Avitabile, Peter; Callahan, John O.

Several new techniques developed for the forced response analysis of systems containing discrete nonlinear connection elements are presented and compared to the traditional methods. In particular, the techniques examined are the Equivalent Reduced Model Technique (ERMT), Modal Modification Response Technique (MMRT), and Component Element Method (CEM). The general theory of the techniques is presented, and applications are discussed with particular reference to the beam nonlinear system model using ERMT, MMRT, and CEM; frame nonlinear response using the three techniques; and comparison of the results obtained by using the ERMT, MMRT, and CEM models.

Application of Statistical Downscaling Techniques to Predict Rainfall and Its Spatial Analysis Over Subansiri River Basin of Assam, India

NASA Astrophysics Data System (ADS)

Barman, S.; Bhattacharjya, R. K.

2017-12-01

The River Subansiri is the major north bank tributary of river Brahmaputra. It originates from the range of Himalayas beyond the Great Himalayan range at an altitude of approximately 5340m. Subansiri basin extends from tropical to temperate zones and hence exhibits a great diversity in rainfall characteristics. In the Northern and Central Himalayan tracts, precipitation is scarce on account of high altitudes. On the other hand, Southeast part of the Subansiri basin comprising the sub-Himalayan and the plain tract in Arunachal Pradesh and Assam, lies in the tropics. Due to Northeast as well as Southwest monsoon, precipitation occurs in this region in abundant quantities. Particularly, Southwest monsoon causes very heavy precipitation in the entire Subansiri basin during May to October. In this study, the rainfall over Subansiri basin has been studied at 24 different locations by multiple linear and non-linear regression based statistical downscaling techniques and by Artificial Neural Network based model. APHRODITE's gridded rainfall data of 0.25˚ x 0.25˚ resolutions and climatic parameters of HadCM3 GCM of resolution 2.5˚ x 3.75˚ (latitude by longitude) have been used in this study. It has been found that multiple non-linear regression based statistical downscaling technique outperformed the other techniques. Using this method, the future rainfall pattern over the Subansiri basin has been analyzed up to the year 2099 for four different time periods, viz., 2020-39, 2040-59, 2060-79, and 2080-99 at all the 24 locations. On the basis of historical rainfall, the months have been categorized as wet months, months with moderate rainfall and dry months. The spatial changes in rainfall patterns for all these three types of months have also been analyzed over the basin. Potential decrease of rainfall in the wet months and months with moderate rainfall and increase of rainfall in the dry months are observed for the future rainfall pattern of the Subansiri basin.

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan

2016-11-01

In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.

Myoglobin structure and function: A multiweek biochemistry laboratory project.

PubMed

Silverstein, Todd P; Kirk, Sarah R; Meyer, Scott C; Holman, Karen L McFarlane

2015-01-01

We have developed a multiweek laboratory project in which students isolate myoglobin and characterize its structure, function, and redox state. The important laboratory techniques covered in this project include size-exclusion chromatography, electrophoresis, spectrophotometric titration, and FTIR spectroscopy. Regarding protein structure, students work with computer modeling and visualization of myoglobin and its homologues, after which they spectroscopically characterize its thermal denaturation. Students also study protein function (ligand binding equilibrium) and are instructed on topics in data analysis (calibration curves, nonlinear vs. linear regression). This upper division biochemistry laboratory project is a challenging and rewarding one that not only exposes students to a wide variety of important biochemical laboratory techniques but also ties those techniques together to work with a single readily available and easily characterized protein, myoglobin. © 2015 International Union of Biochemistry and Molecular Biology.

Partitioning sources of variation in vertebrate species richness

USGS Publications Warehouse

Boone, R.B.; Krohn, W.B.

2000-01-01

Aim: To explore biogeographic patterns of terrestrial vertebrates in Maine, USA using techniques that would describe local and spatial correlations with the environment. Location: Maine, USA. Methods: We delineated the ranges within Maine (86,156 km2) of 275 species using literature and expert review. Ranges were combined into species richness maps, and compared to geomorphology, climate, and woody plant distributions. Methods were adapted that compared richness of all vertebrate classes to each environmental correlate, rather than assessing a single explanatory theory. We partitioned variation in species richness into components using tree and multiple linear regression. Methods were used that allowed for useful comparisons between tree and linear regression results. For both methods we partitioned variation into broad-scale (spatially autocorrelated) and fine-scale (spatially uncorrelated) explained and unexplained components. By partitioning variance, and using both tree and linear regression in analyses, we explored the degree of variation in species richness for each vertebrate group that Could be explained by the relative contribution of each environmental variable. Results: In tree regression, climate variation explained richness better (92% of mean deviance explained for all species) than woody plant variation (87%) and geomorphology (86%). Reptiles were highly correlated with environmental variation (93%), followed by mammals, amphibians, and birds (each with 84-82% deviance explained). In multiple linear regression, climate was most closely associated with total vertebrate richness (78%), followed by woody plants (67%) and geomorphology (56%). Again, reptiles were closely correlated with the environment (95%), followed by mammals (73%), amphibians (63%) and birds (57%). Main conclusions: Comparing variation explained using tree and multiple linear regression quantified the importance of nonlinear relationships and local interactions between species richness and environmental variation, identifying the importance of linear relationships between reptiles and the environment, and nonlinear relationships between birds and woody plants, for example. Conservation planners should capture climatic variation in broad-scale designs; temperatures may shift during climate change, but the underlying correlations between the environment and species richness will presumably remain.

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

PubMed Central

Piovesan, Davide; Pierobon, Alberto; DiZio, Paul; Lackner, James R.

2012-01-01

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases. PMID:22448233

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

NASA Technical Reports Server (NTRS)

Starlinger, Alois; Duffy, Stephen F.; Palko, Joseph L.

1993-01-01

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Nonparametric Stochastic Model for Uncertainty Quantifi cation of Short-term Wind Speed Forecasts

NASA Astrophysics Data System (ADS)

AL-Shehhi, A. M.; Chaouch, M.; Ouarda, T.

2014-12-01

Wind energy is increasing in importance as a renewable energy source due to its potential role in reducing carbon emissions. It is a safe, clean, and inexhaustible source of energy. The amount of wind energy generated by wind turbines is closely related to the wind speed. Wind speed forecasting plays a vital role in the wind energy sector in terms of wind turbine optimal operation, wind energy dispatch and scheduling, efficient energy harvesting etc. It is also considered during planning, design, and assessment of any proposed wind project. Therefore, accurate prediction of wind speed carries a particular importance and plays significant roles in the wind industry. Many methods have been proposed in the literature for short-term wind speed forecasting. These methods are usually based on modeling historical fixed time intervals of the wind speed data and using it for future prediction. The methods mainly include statistical models such as ARMA, ARIMA model, physical models for instance numerical weather prediction and artificial Intelligence techniques for example support vector machine and neural networks. In this paper, we are interested in estimating hourly wind speed measures in United Arab Emirates (UAE). More precisely, we predict hourly wind speed using a nonparametric kernel estimation of the regression and volatility functions pertaining to nonlinear autoregressive model with ARCH model, which includes unknown nonlinear regression function and volatility function already discussed in the literature. The unknown nonlinear regression function describe the dependence between the value of the wind speed at time t and its historical data at time t -1, t - 2, … , t - d. This function plays a key role to predict hourly wind speed process. The volatility function, i.e., the conditional variance given the past, measures the risk associated to this prediction. Since the regression and the volatility functions are supposed to be unknown, they are estimated using nonparametric kernel methods. In addition, to the pointwise hourly wind speed forecasts, a confidence interval is also provided which allows to quantify the uncertainty around the forecasts.

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

A comparison of non-parametric techniques to estimate incident photosynthetically active radiation from MODIS for monitoring primary production

NASA Astrophysics Data System (ADS)

Brown, M. G. L.; He, T.; Liang, S.

2016-12-01

Satellite-derived estimates of incident photosynthetically active radiation (PAR) can be used to monitor global change, are required by most terrestrial ecosystem models, and can be used to estimate primary production according to the theory of light use efficiency. Compared with parametric approaches, non-parametric techniques that include an artificial neural network (ANN), support vector machine regression (SVM), an artificial bee colony (ABC), and a look-up table (LUT) do not require many ancillary data as inputs for the estimation of PAR from satellite data. In this study, a selection of machine learning methods to estimate PAR from MODIS top of atmosphere (TOA) radiances are compared to a LUT approach to determine which techniques might best handle the nonlinear relationship between TOA radiance and incident PAR. Evaluation of these methods (ANN, SVM, and LUT) is performed with ground measurements at seven SURFRAD sites. Due to the design of the ANN, it can handle the nonlinear relationship between TOA radiance and PAR better than linearly interpolating between the values in the LUT; however, training the ANN has to be carried out on an angular-bin basis, which results in a LUT of ANNs. The SVM model may be better for incorporating multiple viewing angles than the ANN; however, both techniques require a large amount of training data, which may introduce a regional bias based on where the most training and validation data are available. Based on the literature, the ABC is a promising alternative to an ANN, SVM regression and a LUT, but further development for this application is required before concrete conclusions can be drawn. For now, the LUT method outperforms the machine-learning techniques, but future work should be directed at developing and testing the ABC method. A simple, robust method to estimate direct and diffuse incident PAR, with minimal inputs and a priori knowledge, would be very useful for monitoring global change of primary production, particularly of pastures and rangeland, which have implications for livestock and food security. Future work will delve deeper into the utility of satellite-derived PAR estimation for monitoring primary production in pasture and rangelands.

Application of nonlinear-regression methods to a ground-water flow model of the Albuquerque Basin, New Mexico

USGS Publications Warehouse

Tiedeman, C.R.; Kernodle, J.M.; McAda, D.P.

1998-01-01

This report documents the application of nonlinear-regression methods to a numerical model of ground-water flow in the Albuquerque Basin, New Mexico. In the Albuquerque Basin, ground water is the primary source for most water uses. Ground-water withdrawal has steadily increased since the 1940's, resulting in large declines in water levels in the Albuquerque area. A ground-water flow model was developed in 1994 and revised and updated in 1995 for the purpose of managing basin ground- water resources. In the work presented here, nonlinear-regression methods were applied to a modified version of the previous flow model. Goals of this work were to use regression methods to calibrate the model with each of six different configurations of the basin subsurface and to assess and compare optimal parameter estimates, model fit, and model error among the resulting calibrations. The Albuquerque Basin is one in a series of north trending structural basins within the Rio Grande Rift, a region of Cenozoic crustal extension. Mountains, uplifts, and fault zones bound the basin, and rock units within the basin include pre-Santa Fe Group deposits, Tertiary Santa Fe Group basin fill, and post-Santa Fe Group volcanics and sediments. The Santa Fe Group is greater than 14,000 feet (ft) thick in the central part of the basin. During deposition of the Santa Fe Group, crustal extension resulted in development of north trending normal faults with vertical displacements of as much as 30,000 ft. Ground-water flow in the Albuquerque Basin occurs primarily in the Santa Fe Group and post-Santa Fe Group deposits. Water flows between the ground-water system and surface-water bodies in the inner valley of the basin, where the Rio Grande, a network of interconnected canals and drains, and Cochiti Reservoir are located. Recharge to the ground-water flow system occurs as infiltration of precipitation along mountain fronts and infiltration of stream water along tributaries to the Rio Grande; subsurface flow from adjacent regions; irrigation and septic field seepage; and leakage through the Rio Grande, canal, and Cochiti Reservoir beds. Ground water is discharged from the basin by withdrawal; evapotranspiration; subsurface flow; and flow to the Rio Grande, canals, and drains. The transient, three-dimensional numerical model of ground-water flow to which nonlinear-regression methods were applied simulates flow in the Albuquerque Basin from 1900 to March 1995. Six different basin subsurface configurations are considered in the model. These configurations are designed to test the effects of (1) varying the simulated basin thickness, (2) including a hypothesized hydrogeologic unit with large hydraulic conductivity in the western part of the basin (the west basin high-K zone), and (3) substantially lowering the simulated hydraulic conductivity of a fault in the western part of the basin (the low-K fault zone). The model with each of the subsurface configurations was calibrated using a nonlinear least- squares regression technique. The calibration data set includes 802 hydraulic-head measurements that provide broad spatial and temporal coverage of basin conditions, and one measurement of net flow from the Rio Grande and drains to the ground-water system in the Albuquerque area. Data are weighted on the basis of estimates of the standard deviations of measurement errors. The 10 to 12 parameters to which the calibration data as a whole are generally most sensitive were estimated by nonlinear regression, whereas the remaining model parameter values were specified. Results of model calibration indicate that the optimal parameter estimates as a whole are most reasonable in calibrations of the model with with configurations 3 (which contains 1,600-ft-thick basin deposits and the west basin high-K zone), 4 (which contains 5,000-ft-thick basin de

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

A robust background regression based score estimation algorithm for hyperspectral anomaly detection

NASA Astrophysics Data System (ADS)

Zhao, Rui; Du, Bo; Zhang, Liangpei; Zhang, Lefei

2016-12-01

Anomaly detection has become a hot topic in the hyperspectral image analysis and processing fields in recent years. The most important issue for hyperspectral anomaly detection is the background estimation and suppression. Unreasonable or non-robust background estimation usually leads to unsatisfactory anomaly detection results. Furthermore, the inherent nonlinearity of hyperspectral images may cover up the intrinsic data structure in the anomaly detection. In order to implement robust background estimation, as well as to explore the intrinsic data structure of the hyperspectral image, we propose a robust background regression based score estimation algorithm (RBRSE) for hyperspectral anomaly detection. The Robust Background Regression (RBR) is actually a label assignment procedure which segments the hyperspectral data into a robust background dataset and a potential anomaly dataset with an intersection boundary. In the RBR, a kernel expansion technique, which explores the nonlinear structure of the hyperspectral data in a reproducing kernel Hilbert space, is utilized to formulate the data as a density feature representation. A minimum squared loss relationship is constructed between the data density feature and the corresponding assigned labels of the hyperspectral data, to formulate the foundation of the regression. Furthermore, a manifold regularization term which explores the manifold smoothness of the hyperspectral data, and a maximization term of the robust background average density, which suppresses the bias caused by the potential anomalies, are jointly appended in the RBR procedure. After this, a paired-dataset based k-nn score estimation method is undertaken on the robust background and potential anomaly datasets, to implement the detection output. The experimental results show that RBRSE achieves superior ROC curves, AUC values, and background-anomaly separation than some of the other state-of-the-art anomaly detection methods, and is easy to implement in practice.

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

A simplified competition data analysis for radioligand specific activity determination.

PubMed

Venturino, A; Rivera, E S; Bergoc, R M; Caro, R A

1990-01-01

Non-linear regression and two-step linear fit methods were developed to determine the actual specific activity of 125I-ovine prolactin by radioreceptor self-displacement analysis. The experimental results obtained by the different methods are superposable. The non-linear regression method is considered to be the most adequate procedure to calculate the specific activity, but if its software is not available, the other described methods are also suitable.

Machine Learning to Improve Energy Expenditure Estimation in Children With Disabilities: A Pilot Study in Duchenne Muscular Dystrophy.

PubMed

Pande, Amit; Mohapatra, Prasant; Nicorici, Alina; Han, Jay J

2016-07-19

Children with physical impairments are at a greater risk for obesity and decreased physical activity. A better understanding of physical activity pattern and energy expenditure (EE) would lead to a more targeted approach to intervention. This study focuses on studying the use of machine-learning algorithms for EE estimation in children with disabilities. A pilot study was conducted on children with Duchenne muscular dystrophy (DMD) to identify important factors for determining EE and develop a novel algorithm to accurately estimate EE from wearable sensor-collected data. There were 7 boys with DMD, 6 healthy control boys, and 22 control adults recruited. Data were collected using smartphone accelerometer and chest-worn heart rate sensors. The gold standard EE values were obtained from the COSMED K4b2 portable cardiopulmonary metabolic unit worn by boys (aged 6-10 years) with DMD and controls. Data from this sensor setup were collected simultaneously during a series of concurrent activities. Linear regression and nonlinear machine-learning-based approaches were used to analyze the relationship between accelerometer and heart rate readings and COSMED values. Existing calorimetry equations using linear regression and nonlinear machine-learning-based models, developed for healthy adults and young children, give low correlation to actual EE values in children with disabilities (14%-40%). The proposed model for boys with DMD uses ensemble machine learning techniques and gives a 91% correlation with actual measured EE values (root mean square error of 0.017). Our results confirm that the methods developed to determine EE using accelerometer and heart rate sensor values in normal adults are not appropriate for children with disabilities and should not be used. A much more accurate model is obtained using machine-learning-based nonlinear regression specifically developed for this target population. ©Amit Pande, Prasant Mohapatra, Alina Nicorici, Jay J Han. Originally published in JMIR Rehabilitation and Assistive Technology (http://rehab.jmir.org), 19.07.2016.

Toward energy harvesting using active materials and conversion improvement by nonlinear processing.

PubMed

Guyomar, Daniel; Badel, Adrien; Lefeuvre, Elie; Richard, Claude

2005-04-01

This paper presents a new technique of electrical energy generation using mechanically excited piezoelectric materials and a nonlinear process. This technique, called synchronized switch harvesting (SSH), is derived from the synchronized switch damping (SSD), which is a nonlinear technique previously developed to address the problem of vibration damping on mechanical structures. This technique results in a significant increase of the electromechanical conversion capability of piezoelectric materials. Comparatively with standard technique, the electrical harvested power may be increased above 900%. The performance of the nonlinear processing is demonstrated on structures excited at their resonance frequency as well as out of resonance.

Predicting radiotherapy outcomes using statistical learning techniques

NASA Astrophysics Data System (ADS)

El Naqa, Issam; Bradley, Jeffrey D.; Lindsay, Patricia E.; Hope, Andrew J.; Deasy, Joseph O.

2009-09-01

Radiotherapy outcomes are determined by complex interactions between treatment, anatomical and patient-related variables. A common obstacle to building maximally predictive outcome models for clinical practice is the failure to capture potential complexity of heterogeneous variable interactions and applicability beyond institutional data. We describe a statistical learning methodology that can automatically screen for nonlinear relations among prognostic variables and generalize to unseen data before. In this work, several types of linear and nonlinear kernels to generate interaction terms and approximate the treatment-response function are evaluated. Examples of institutional datasets of esophagitis, pneumonitis and xerostomia endpoints were used. Furthermore, an independent RTOG dataset was used for 'generalizabilty' validation. We formulated the discrimination between risk groups as a supervised learning problem. The distribution of patient groups was initially analyzed using principle components analysis (PCA) to uncover potential nonlinear behavior. The performance of the different methods was evaluated using bivariate correlations and actuarial analysis. Over-fitting was controlled via cross-validation resampling. Our results suggest that a modified support vector machine (SVM) kernel method provided superior performance on leave-one-out testing compared to logistic regression and neural networks in cases where the data exhibited nonlinear behavior on PCA. For instance, in prediction of esophagitis and pneumonitis endpoints, which exhibited nonlinear behavior on PCA, the method provided 21% and 60% improvements, respectively. Furthermore, evaluation on the independent pneumonitis RTOG dataset demonstrated good generalizabilty beyond institutional data in contrast with other models. This indicates that the prediction of treatment response can be improved by utilizing nonlinear kernel methods for discovering important nonlinear interactions among model variables. These models have the capacity to predict on unseen data. Part of this work was first presented at the Seventh International Conference on Machine Learning and Applications, San Diego, CA, USA, 11-13 December 2008.

Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

PubMed

Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

2017-09-01

Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

Regression of non-linear coupling of noise in LIGO detectors

NASA Astrophysics Data System (ADS)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.

A controlled experiment in ground water flow model calibration

USGS Publications Warehouse

Hill, M.C.; Cooley, R.L.; Pollock, D.W.

1998-01-01

Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.

Estimating Biochemical Parameters of Tea (camellia Sinensis (L.)) Using Hyperspectral Techniques

NASA Astrophysics Data System (ADS)

Bian, M.; Skidmore, A. K.; Schlerf, M.; Liu, Y.; Wang, T.

2012-07-01

Tea (Camellia Sinensis (L.)) is an important economic crop and the market price of tea depends largely on its quality. This research aims to explore the potential of hyperspectral remote sensing on predicting the concentration of biochemical components, namely total tea polyphenols, as indicators of tea quality at canopy scale. Experiments were carried out for tea plants growing in the field and greenhouse. Partial least squares regression (PLSR), which has proven to be the one of the most successful empirical approach, was performed to establish the relationship between reflectance and biochemical concentration across six tea varieties in the field. Moreover, a novel integrated approach involving successive projections algorithms as band selection method and neural networks was developed and applied to detect the concentration of total tea polyphenols for one tea variety, in order to explore and model complex nonlinearity relationships between independent (wavebands) and dependent (biochemicals) variables. The good prediction accuracies (r2 > 0.8 and relative RMSEP < 10 %) achieved for tea plants using both linear (partial lease squares regress) and nonlinear (artificial neural networks) modelling approaches in this study demonstrates the feasibility of using airborne and spaceborne sensors to cover wide areas of tea plantation for in situ monitoring of tea quality cheaply and rapidly.

Multi-gene genetic programming based predictive models for municipal solid waste gasification in a fluidized bed gasifier.

PubMed

Pandey, Daya Shankar; Pan, Indranil; Das, Saptarshi; Leahy, James J; Kwapinski, Witold

2015-03-01

A multi-gene genetic programming technique is proposed as a new method to predict syngas yield production and the lower heating value for municipal solid waste gasification in a fluidized bed gasifier. The study shows that the predicted outputs of the municipal solid waste gasification process are in good agreement with the experimental dataset and also generalise well to validation (untrained) data. Published experimental datasets are used for model training and validation purposes. The results show the effectiveness of the genetic programming technique for solving complex nonlinear regression problems. The multi-gene genetic programming are also compared with a single-gene genetic programming model to show the relative merits and demerits of the technique. This study demonstrates that the genetic programming based data-driven modelling strategy can be a good candidate for developing models for other types of fuels as well. Copyright © 2014 Elsevier Ltd. All rights reserved.

Improving near-infrared prediction model robustness with support vector machine regression: a pharmaceutical tablet assay example.

PubMed

Igne, Benoît; Drennen, James K; Anderson, Carl A

2014-01-01

Changes in raw materials and process wear and tear can have significant effects on the prediction error of near-infrared calibration models. When the variability that is present during routine manufacturing is not included in the calibration, test, and validation sets, the long-term performance and robustness of the model will be limited. Nonlinearity is a major source of interference. In near-infrared spectroscopy, nonlinearity can arise from light path-length differences that can come from differences in particle size or density. The usefulness of support vector machine (SVM) regression to handle nonlinearity and improve the robustness of calibration models in scenarios where the calibration set did not include all the variability present in test was evaluated. Compared to partial least squares (PLS) regression, SVM regression was less affected by physical (particle size) and chemical (moisture) differences. The linearity of the SVM predicted values was also improved. Nevertheless, although visualization and interpretation tools have been developed to enhance the usability of SVM-based methods, work is yet to be done to provide chemometricians in the pharmaceutical industry with a regression method that can supplement PLS-based methods.

The Use of Linear Instrumental Variables Methods in Health Services Research and Health Economics: A Cautionary Note

PubMed Central

Terza, Joseph V; Bradford, W David; Dismuke, Clara E

2008-01-01

Objective To investigate potential bias in the use of the conventional linear instrumental variables (IV) method for the estimation of causal effects in inherently nonlinear regression settings. Data Sources Smoking Supplement to the 1979 National Health Interview Survey, National Longitudinal Alcohol Epidemiologic Survey, and simulated data. Study Design Potential bias from the use of the linear IV method in nonlinear models is assessed via simulation studies and real world data analyses in two commonly encountered regression setting: (1) models with a nonnegative outcome (e.g., a count) and a continuous endogenous regressor; and (2) models with a binary outcome and a binary endogenous regressor. Principle Findings The simulation analyses show that substantial bias in the estimation of causal effects can result from applying the conventional IV method in inherently nonlinear regression settings. Moreover, the bias is not attenuated as the sample size increases. This point is further illustrated in the survey data analyses in which IV-based estimates of the relevant causal effects diverge substantially from those obtained with appropriate nonlinear estimation methods. Conclusions We offer this research as a cautionary note to those who would opt for the use of linear specifications in inherently nonlinear settings involving endogeneity. PMID:18546544

Development of a pneumatic high-angle-of-attack Flush Airdata Sensing (HI-FADS) system

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.; Moes, Timothy R.; Leondes, Cornelius T.

1992-01-01

The HI-FADS system design is an evolution of the FADS systems (e.g., Larson et al., 1980, 1987), which emphasizes the entire airdata system development. This paper describes the HI-FADS measurement system, with particular consideration given to the basic measurement hardware and the development of the HI-FADS aerodynamic model and the basic nonlinear regression algorithm. Algorithm initialization techniques are developed, and potential algorithm divergence problems are discussed. Data derived from HI-FADS flight tests are used to demonstrate the system accuracies and to illustrate the developed concepts and methods.

A comparison of linear and nonlinear statistical techniques in performance attribution.

PubMed

Chan, N H; Genovese, C R

2001-01-01

Performance attribution is usually conducted under the linear framework of multifactor models. Although commonly used by practitioners in finance, linear multifactor models are known to be less than satisfactory in many situations. After a brief survey of nonlinear methods, nonlinear statistical techniques are applied to performance attribution of a portfolio constructed from a fixed universe of stocks using factors derived from some commonly used cross sectional linear multifactor models. By rebalancing this portfolio monthly, the cumulative returns for procedures based on standard linear multifactor model and three nonlinear techniques-model selection, additive models, and neural networks-are calculated and compared. It is found that the first two nonlinear techniques, especially in combination, outperform the standard linear model. The results in the neural-network case are inconclusive because of the great variety of possible models. Although these methods are more complicated and may require some tuning, toolboxes are developed and suggestions on calibration are proposed. This paper demonstrates the usefulness of modern nonlinear statistical techniques in performance attribution.

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data.

PubMed

Lim, Changwon

2015-03-30

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose-response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program. Copyright © 2014 John Wiley & Sons, Ltd.

Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data

NASA Technical Reports Server (NTRS)

Brandon, Jay M.; Morelli, Eugene A.

2014-01-01

Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

A Learning Progression Should Address Regression: Insights from Developing Non-Linear Reasoning in Ecology

ERIC Educational Resources Information Center

Hovardas, Tasos

2016-01-01

Although ecological systems at varying scales involve non-linear interactions, learners insist thinking in a linear fashion when they deal with ecological phenomena. The overall objective of the present contribution was to propose a hypothetical learning progression for developing non-linear reasoning in prey-predator systems and to provide…

Global image registration using a symmetric block-matching approach

PubMed Central

Modat, Marc; Cash, David M.; Daga, Pankaj; Winston, Gavin P.; Duncan, John S.; Ourselin, Sébastien

2014-01-01

Abstract. Most medical image registration algorithms suffer from a directionality bias that has been shown to largely impact subsequent analyses. Several approaches have been proposed in the literature to address this bias in the context of nonlinear registration, but little work has been done for global registration. We propose a symmetric approach based on a block-matching technique and least-trimmed square regression. The proposed method is suitable for multimodal registration and is robust to outliers in the input images. The symmetric framework is compared with the original asymmetric block-matching technique and is shown to outperform it in terms of accuracy and robustness. The methodology presented in this article has been made available to the community as part of the NiftyReg open-source package. PMID:26158035

Three-dimensional characterization of the effective second-order nonlinearity in periodically poled crystals

NASA Astrophysics Data System (ADS)

Holmgren, Stefan J.; Pasiskevicius, Valdas; Wang, Shunhua; Laurell, Fredrik

2003-09-01

A novel technique for characterization of the second-order nonlinearity in nonlinear crystals is presented. It utilizes group-velocity walk-off between femtosecond pulses in type II SHG to achieve three-dimensional resolution of the nonlinearity. The longitudinal and transversal spatial resolution can be set independently. The technique is especially useful for characterizing quasi-phase-matched nonlinear crystals, and it is demonstrated in potassium titanyl phosphate.

Nonlinear acoustic spectroscopy of cracked flaws and disbonds: Fundamentals, techniques, and applications

NASA Astrophysics Data System (ADS)

Maev, R. Gr.; Solodov, I. Yu.

2000-05-01

Classical nonlinear acoustics of solids operates with distributed material nonlinearity related to unharmonicity of molecular interaction forces. Weakening of molecular bonds in a defect area or intermittent lack of elastic coupling between the faces of a vibrating crack or unbond ("clapping") results in anomalously high local contact acoustic nonlinearity (CAN). CAN properties and spectral features are different from those of the classical analog and important to develop new acoustic NDE techniques. Three approaches to nonlinear NDE methodology have been experimentally verified: low-frequency (hundreds of Hz) vibration technique, intermediate-frequency (hundreds of kHz) standing wave and high-frequency (tens of MHz) propagation modes. Low-frequency nonlinear contact vibrations revealed multiple sub- and super-harmonics generation featuring non-monotonous (sinx/x type) spectra. Parametric instability observed in resonator with a nonlinear contact leads to the output spectrum splitting up into successive sub-harmonics as the wave amplitude increases. High-frequency experiments demonstrated abnormal increases in the third harmonic amplitude: 3 or 4 order enhancement of the 3-ω nonlinear parameter was measured for the nonlinear contact. The CAN spectral features in both acoustic and vibration modes were used for nonlinear NDE of simulated and realistic flaws in glass, metal welds, etc. The sensitivities of the techniques are compared and their practical applicability assessed.

PM10 modeling in the Oviedo urban area (Northern Spain) by using multivariate adaptive regression splines

NASA Astrophysics Data System (ADS)

Nieto, Paulino José García; Antón, Juan Carlos Álvarez; Vilán, José Antonio Vilán; García-Gonzalo, Esperanza

2014-10-01

The aim of this research work is to build a regression model of the particulate matter up to 10 micrometers in size (PM10) by using the multivariate adaptive regression splines (MARS) technique in the Oviedo urban area (Northern Spain) at local scale. This research work explores the use of a nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) which has the ability to approximate the relationship between the inputs and outputs, and express the relationship mathematically. In this sense, hazardous air pollutants or toxic air contaminants refer to any substance that may cause or contribute to an increase in mortality or serious illness, or that may pose a present or potential hazard to human health. To accomplish the objective of this study, the experimental dataset of nitrogen oxides (NOx), carbon monoxide (CO), sulfur dioxide (SO2), ozone (O3) and dust (PM10) were collected over 3 years (2006-2008) and they are used to create a highly nonlinear model of the PM10 in the Oviedo urban nucleus (Northern Spain) based on the MARS technique. One main objective of this model is to obtain a preliminary estimate of the dependence between PM10 pollutant in the Oviedo urban area at local scale. A second aim is to determine the factors with the greatest bearing on air quality with a view to proposing health and lifestyle improvements. The United States National Ambient Air Quality Standards (NAAQS) establishes the limit values of the main pollutants in the atmosphere in order to ensure the health of healthy people. Firstly, this MARS regression model captures the main perception of statistical learning theory in order to obtain a good prediction of the dependence among the main pollutants in the Oviedo urban area. Secondly, the main advantages of MARS are its capacity to produce simple, easy-to-interpret models, its ability to estimate the contributions of the input variables, and its computational efficiency. Finally, on the basis of these numerical calculations, using the multivariate adaptive regression splines (MARS) technique, conclusions of this research work are exposed.

Development of non-linear models predicting daily fine particle concentrations using aerosol optical depth retrievals and ground-based measurements at a municipality in the Brazilian Amazon region

NASA Astrophysics Data System (ADS)

Gonçalves, Karen dos Santos; Winkler, Mirko S.; Benchimol-Barbosa, Paulo Roberto; de Hoogh, Kees; Artaxo, Paulo Eduardo; de Souza Hacon, Sandra; Schindler, Christian; Künzli, Nino

2018-07-01

Epidemiological studies generally use particulate matter measurements with diameter less 2.5 μm (PM2.5) from monitoring networks. Satellite aerosol optical depth (AOD) data has considerable potential in predicting PM2.5 concentrations, and thus provides an alternative method for producing knowledge regarding the level of pollution and its health impact in areas where no ground PM2.5 measurements are available. This is the case in the Brazilian Amazon rainforest region where forest fires are frequent sources of high pollution. In this study, we applied a non-linear model for predicting PM2.5 concentration from AOD retrievals using interaction terms between average temperature, relative humidity, sine, cosine of date in a period of 365,25 days and the square of the lagged relative residual. Regression performance statistics were tested comparing the goodness of fit and R2 based on results from linear regression and non-linear regression for six different models. The regression results for non-linear prediction showed the best performance, explaining on average 82% of the daily PM2.5 concentrations when considering the whole period studied. In the context of Amazonia, it was the first study predicting PM2.5 concentrations using the latest high-resolution AOD products also in combination with the testing of a non-linear model performance. Our results permitted a reliable prediction considering the AOD-PM2.5 relationship and set the basis for further investigations on air pollution impacts in the complex context of Brazilian Amazon Region.

Contribution a la caracterisation des betons endommages par des methodes de l'acoustique non lineaire. Application a la reaction alcalis-silice

NASA Astrophysics Data System (ADS)

Kodjo, Apedovi

The aim of this thesis is to contribute to the non-destructive characterization of concrete materials damaged by alkali-silica reaction (ASR). For this purpose, some nonlinear characterization techniques have been developed, as well as a nonlinear resonance test device. In order to optimize the sensitivity of the test device, the excitation module and signal processing have been improved. The nonlinear tests were conducted on seven samples of concrete damaged by ASR, three samples of concrete damaged by heat, three concrete samples damaged mechanically and three sound concrete samples. Since, nonlinear behaviour of the material is often attribute to its micro-defects hysteretic behaviour, it was shown at first that concrete damaged by ASR exhibits an hysteresis behaviour. To conduct this study, an acoustoelastic test was set, and then nonlinear resonance test device was used for characterizing sound concrete and concrete damaged by ASR. It was shown that the nonlinear technique can be used for characterizing the material without knowing its initial state, and also for detecting early damage in the reactive material. Studies were also carried out on the effect of moisture regarding the nonlinear parameters; they allowed understanding the low values of nonlinear parameters measured on concrete samples that were kept in high moisture conditions. In order to find a specific characteristic of damage caused by ASR, the viscosity of ASR gel was used. An approach, based on static creep analysis, performed on the material, while applying the nonlinear resonance technique. The spring-damping model of Maxwell was used for the interpretation of the results. Then, the creep time was analysed on samples damaged by ASR. It appears that the ASR gel increases the creep time. Finally, the limitations of the nonlinear resonance technique for in situ application have been explained and a new applicable nonlinear technique was initiated. This technique use an external source such as a mass for making non-linearity behaviour in the material, while an ultrasound wave is investigating the medium. Keywords. Concrete, Alkali-silica reaction, Nonlinear acoustics, Nonlinearity, Hysteresis, Damage diagnostics.

Revisiting tests for neglected nonlinearity using artificial neural networks.

PubMed

Cho, Jin Seo; Ishida, Isao; White, Halbert

2011-05-01

Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity, paying careful attention to both components of the null. We derive the asymptotic null distribution under each component separately and analyze their interaction. Somewhat remarkably, it turns out that the previously known asymptotic null distribution for the type 1 case still applies, but under somewhat stronger conditions than previously recognized. We present Monte Carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new, stronger regularity conditions are violated.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 1. Theory

USGS Publications Warehouse

Cooley, Richard L.

1982-01-01

Prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem. Two scales of prior information can be available: (1) prior information having known reliability (that is, bias and random error structure) and (2) prior information consisting of best available estimates of unknown reliability. A regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved, although biased, parameter estimates. Approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias, which is almost always much smaller than that resulting from standard ridge regression. It is shown that if both scales of prior information are available, then a combined regression analysis may be made.

Techniques for generation of control and guidance signals derived from optical fields, part 2

NASA Technical Reports Server (NTRS)

Hemami, H.; Mcghee, R. B.; Gardner, S. R.

1971-01-01

The development is reported of a high resolution technique for the detection and identification of landmarks from spacecraft optical fields. By making use of nonlinear regression analysis, a method is presented whereby a sequence of synthetic images produced by a digital computer can be automatically adjusted to provide a least squares approximation to a real image. The convergence of the method is demonstrated by means of a computer simulation for both elliptical and rectangular patterns. Statistical simulation studies with elliptical and rectangular patterns show that the computational techniques developed are able to at least match human pattern recognition capabilities, even in the presence of large amounts of noise. Unlike most pattern recognition techniques, this ability is unaffected by arbitrary pattern rotation, translation, and scale change. Further development of the basic approach may eventually allow a spacecraft or robot vehicle to be provided with an ability to very accurately determine its spatial relationship to arbitrary known objects within its optical field of view.

Nonlinear ultrasonic fatigue crack detection using a single piezoelectric transducer

NASA Astrophysics Data System (ADS)

An, Yun-Kyu; Lee, Dong Jun

2016-04-01

This paper proposes a new nonlinear ultrasonic technique for fatigue crack detection using a single piezoelectric transducer (PZT). The proposed technique identifies a fatigue crack using linear (α) and nonlinear (β) parameters obtained from only a single PZT mounted on a target structure. Based on the different physical characteristics of α and β, a fatigue crack-induced feature is able to be effectively isolated from the inherent nonlinearity of a target structure and data acquisition system. The proposed technique requires much simpler test setup and less processing costs than the existing nonlinear ultrasonic techniques, but fast and powerful. To validate the proposed technique, a real fatigue crack is created in an aluminum plate, and then false positive and negative tests are carried out under varying temperature conditions. The experimental results reveal that the fatigue crack is successfully detected, and no positive false alarm is indicated.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

[Prediction of Encapsulation Temperatures of Copolymer Films in Photovoltaic Cells Using Hyperspectral Imaging Techniques and Chemometrics].

PubMed

Lin, Ping; Chen, Yong-ming; Yao, Zhi-lei

2015-11-01

A novel method of combination of the chemometrics and the hyperspectral imaging techniques was presented to detect the temperatures of Ethylene-Vinyl Acetate copolymer (EVA) films in photovoltaic cells during the thermal encapsulation process. Four varieties of the EVA films which had been heated at the temperatures of 128, 132, 142 and 148 °C during the photovoltaic cells production process were used for investigation in this paper. These copolymer encapsulation films were firstly scanned by the hyperspectral imaging equipment (Spectral Imaging Ltd. Oulu, Finland). The scanning band range of hyperspectral equipemnt was set between 904.58 and 1700.01 nm. The hyperspectral dataset of copolymer films was randomly divided into two parts for the training and test purpose. Each type of the training set and test set contained 90 and 10 instances, respectively. The obtained hyperspectral images of EVA films were dealt with by using the ENVI (Exelis Visual Information Solutions, USA) software. The size of region of interest (ROI) of each obtained hyperspectral image of EVA film was set as 150 x 150 pixels. The average of reflectance hyper spectra of all the pixels in the ROI was used as the characteristic curve to represent the instance. There kinds of chemometrics methods including partial least squares regression (PLSR), multi-class support vector machine (SVM) and large margin nearest neighbor (LMNN) were used to correlate the characteristic hyper spectra with the encapsulation temperatures of of copolymer films. The plot of weighted regression coefficients illustrated that both bands of short- and long-wave near infrared hyperspectral data contributed to enhancing the prediction accuracy of the forecast model. Because the attained reflectance hyperspectral data of EVA materials displayed the strong nonlinearity, the prediction performance of linear modeling method of PLSR declined and the prediction precision only reached to 95%. The kernel-based forecast models were introduced to eliminate the impact of nonlinear hyperspectral data to some extent through mapping the original nonlinear hyperspectral data to the high dimensional linear feature space, so the relationship between the nonlinear hyperspectral data and the encapsulation temperatures of EVA films was fully disclosed finally. Compared with the prediction results of three proposed models, the prediction performance of LMNN was superior to the other two, whose final recognition accuracy achieved 100%. The results indicated that the methods of combination of LMNN model with the hyperspectral imaging techniques was the best one for accurately and rapidly determining the encapsulation temperatures of EVA films of photovoltaic cells. In addition, this paper had created the ideal conditions for automatically monitoring and effectively controlling the encapsulation temperatures of EVA films in the photovoltaic cells production process.

Measurement of ultrafast optical Kerr effect of Ge-Sb-Se chalcogenide slab waveguides by the beam self-trapping technique

NASA Astrophysics Data System (ADS)

Kuriakose, Tintu; Baudet, Emeline; Halenkovič, Tomáš; Elsawy, Mahmoud M. R.; Němec, Petr; Nazabal, Virginie; Renversez, Gilles; Chauvet, Mathieu

2017-11-01

We present a reliable and original experimental technique based on the analysis of beam self-trapping to measure ultrafast optical nonlinearities in planar waveguides. The technique is applied to the characterization of Ge-Sb-Se chalcogenide films that allow Kerr induced self-focusing and soliton formation. Linear and nonlinear optical constants of three different chalcogenide waveguides are studied at 1200 and 1550 nm in femtosecond regime. Waveguide propagation loss and two photon absorption coefficients are determined by transmission analysis. Beam broadening and narrowing results are compared with simulations of the nonlinear Schrödinger equation solved by BPM method to deduce the Kerr n2 coefficients. Kerr optical nonlinearities obtained by our original technique compare favorably with the values obtained by Z-scan technique. Nonlinear refractive index as high as (69 ± 11) × 10-18m2 / W is measured in Ge12.5Sb25Se62.5 at 1200 nm with low nonlinear absorption and low propagation losses which reveals the great characteristics of our waveguides for ultrafast all optical switching and integrated photonic devices.

Single-chip source-free terahertz spectroscope across 0.04-0.99 THz: combining sub-wavelength near-field sensing and regression analysis.

PubMed

Wu, Xue; Sengupta, Kaushik

2018-03-19

This paper demonstrates a methodology to miniaturize THz spectroscopes into a single silicon chip by eliminating traditional solid-state architectural components such as complex tunable THz and optical sources, nonlinear mixing and amplifiers. The proposed method achieves this by extracting incident THz spectral signatures from the surface of an on-chip antenna itself. The information is sensed through the spectrally-sensitive 2D distribution of the impressed current surface under the THz incident field. By converting the antenna from a single-port to a massively multi-port architecture with integrated electronics and deep subwavelength sensing, THz spectral estimation is converted into a linear estimation problem. We employ rigorous regression techniques and analysis to demonstrate a single silicon chip system operating at room temperature across 0.04-0.99 THz with 10 MHz accuracy in spectrum estimation of THz tones across the entire spectrum.

An evaluation of bias in propensity score-adjusted non-linear regression models.

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

Multi-Target Regression via Robust Low-Rank Learning.

PubMed

Zhen, Xiantong; Yu, Mengyang; He, Xiaofei; Li, Shuo

2018-02-01

Multi-target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining, computer vision and medical image analysis, while great challenges arise from jointly handling inter-target correlations and input-output relationships. In this paper, we propose Multi-layer Multi-target Regression (MMR) which enables simultaneously modeling intrinsic inter-target correlations and nonlinear input-output relationships in a general framework via robust low-rank learning. Specifically, the MMR can explicitly encode inter-target correlations in a structure matrix by matrix elastic nets (MEN); the MMR can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input-output relationships; the MMR can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence. The MMR leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi-layer learning architectures for inter-target correlation modeling. More importantly, it offers a new multi-layer learning paradigm for multi-target regression which is endowed with high generality, flexibility and expressive ability. Extensive experimental evaluation on 18 diverse real-world datasets demonstrates that our MMR can achieve consistently high performance and outperforms representative state-of-the-art algorithms, which shows its great effectiveness and generality for multivariate prediction.

RBF kernel based support vector regression to estimate the blood volume and heart rate responses during hemodialysis.

PubMed

Javed, Faizan; Chan, Gregory S H; Savkin, Andrey V; Middleton, Paul M; Malouf, Philip; Steel, Elizabeth; Mackie, James; Lovell, Nigel H

2009-01-01

This paper uses non-linear support vector regression (SVR) to model the blood volume and heart rate (HR) responses in 9 hemodynamically stable kidney failure patients during hemodialysis. Using radial bias function (RBF) kernels the non-parametric models of relative blood volume (RBV) change with time as well as percentage change in HR with respect to RBV were obtained. The e-insensitivity based loss function was used for SVR modeling. Selection of the design parameters which includes capacity (C), insensitivity region (e) and the RBF kernel parameter (sigma) was made based on a grid search approach and the selected models were cross-validated using the average mean square error (AMSE) calculated from testing data based on a k-fold cross-validation technique. Linear regression was also applied to fit the curves and the AMSE was calculated for comparison with SVR. For the model based on RBV with time, SVR gave a lower AMSE for both training (AMSE=1.5) as well as testing data (AMSE=1.4) compared to linear regression (AMSE=1.8 and 1.5). SVR also provided a better fit for HR with RBV for both training as well as testing data (AMSE=15.8 and 16.4) compared to linear regression (AMSE=25.2 and 20.1).

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Geographical variation of cerebrovascular disease in New York State: the correlation with income

PubMed Central

Han, Daikwon; Carrow, Shannon S; Rogerson, Peter A; Munschauer, Frederick E

2005-01-01

Background Income is known to be associated with cerebrovascular disease; however, little is known about the more detailed relationship between cerebrovascular disease and income. We examined the hypothesis that the geographical distribution of cerebrovascular disease in New York State may be predicted by a nonlinear model using income as a surrogate socioeconomic risk factor. Results We used spatial clustering methods to identify areas with high and low prevalence of cerebrovascular disease at the ZIP code level after smoothing rates and correcting for edge effects; geographic locations of high and low clusters of cerebrovascular disease in New York State were identified with and without income adjustment. To examine effects of income, we calculated the excess number of cases using a non-linear regression with cerebrovascular disease rates taken as the dependent variable and income and income squared taken as independent variables. The resulting regression equation was: excess rate = 32.075 - 1.22*10-4(income) + 8.068*10-10(income2), and both income and income squared variables were significant at the 0.01 level. When income was included as a covariate in the non-linear regression, the number and size of clusters of high cerebrovascular disease prevalence decreased. Some 87 ZIP codes exceeded the critical value of the local statistic yielding a relative risk of 1.2. The majority of low cerebrovascular disease prevalence geographic clusters disappeared when the non-linear income effect was included. For linear regression, the excess rate of cerebrovascular disease falls with income; each $10,000 increase in median income of each ZIP code resulted in an average reduction of 3.83 observed cases. The significant nonlinear effect indicates a lessening of this income effect with increasing income. Conclusion Income is a non-linear predictor of excess cerebrovascular disease rates, with both low and high observed cerebrovascular disease rate areas associated with higher income. Income alone explains a significant amount of the geographical variance in cerebrovascular disease across New York State since both high and low clusters of cerebrovascular disease dissipate or disappear with income adjustment. Geographical modeling, including non-linear effects of income, may allow for better identification of other non-traditional risk factors. PMID:16242043

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PubMed

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET d based models should be further evaluated in clinically realistic scenarios. © 2017 American Association of Physicists in Medicine.

Statistical inference methods for sparse biological time series data.

PubMed

Ndukum, Juliet; Fonseca, Luís L; Santos, Helena; Voit, Eberhard O; Datta, Susmita

2011-04-25

Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values <0.0001). We have developed a nonlinear mixed effects model that is appropriate for the analysis of sparse metabolic and physiological time profiles. The model permits sound statistical inference procedures, based on ANOVA likelihood ratio tests, for testing the significance of differences between short time course data under different biological perturbations.

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1999-01-01

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Spacecraft nonlinear control

NASA Technical Reports Server (NTRS)

Sheen, Jyh-Jong; Bishop, Robert H.

1992-01-01

The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

Forecasting space weather: Can new econometric methods improve accuracy?

NASA Astrophysics Data System (ADS)

Reikard, Gordon

2011-06-01

Space weather forecasts are currently used in areas ranging from navigation and communication to electric power system operations. The relevant forecast horizons can range from as little as 24 h to several days. This paper analyzes the predictability of two major space weather measures using new time series methods, many of them derived from econometrics. The data sets are the A p geomagnetic index and the solar radio flux at 10.7 cm. The methods tested include nonlinear regressions, neural networks, frequency domain algorithms, GARCH models (which utilize the residual variance), state transition models, and models that combine elements of several techniques. While combined models are complex, they can be programmed using modern statistical software. The data frequency is daily, and forecasting experiments are run over horizons ranging from 1 to 7 days. Two major conclusions stand out. First, the frequency domain method forecasts the A p index more accurately than any time domain model, including both regressions and neural networks. This finding is very robust, and holds for all forecast horizons. Combining the frequency domain method with other techniques yields a further small improvement in accuracy. Second, the neural network forecasts the solar flux more accurately than any other method, although at short horizons (2 days or less) the regression and net yield similar results. The neural net does best when it includes measures of the long-term component in the data.

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

Improved quantification of important beer quality parameters based on nonlinear calibration methods applied to FT-MIR spectra.

PubMed

Cernuda, Carlos; Lughofer, Edwin; Klein, Helmut; Forster, Clemens; Pawliczek, Marcin; Brandstetter, Markus

2017-01-01

During the production process of beer, it is of utmost importance to guarantee a high consistency of the beer quality. For instance, the bitterness is an essential quality parameter which has to be controlled within the specifications at the beginning of the production process in the unfermented beer (wort) as well as in final products such as beer and beer mix beverages. Nowadays, analytical techniques for quality control in beer production are mainly based on manual supervision, i.e., samples are taken from the process and analyzed in the laboratory. This typically requires significant lab technicians efforts for only a small fraction of samples to be analyzed, which leads to significant costs for beer breweries and companies. Fourier transform mid-infrared (FT-MIR) spectroscopy was used in combination with nonlinear multivariate calibration techniques to overcome (i) the time consuming off-line analyses in beer production and (ii) already known limitations of standard linear chemometric methods, like partial least squares (PLS), for important quality parameters Speers et al. (J I Brewing. 2003;109(3):229-235), Zhang et al. (J I Brewing. 2012;118(4):361-367) such as bitterness, citric acid, total acids, free amino nitrogen, final attenuation, or foam stability. The calibration models are established with enhanced nonlinear techniques based (i) on a new piece-wise linear version of PLS by employing fuzzy rules for local partitioning the latent variable space and (ii) on extensions of support vector regression variants (-PLSSVR and ν-PLSSVR), for overcoming high computation times in high-dimensional problems and time-intensive and inappropriate settings of the kernel parameters. Furthermore, we introduce a new model selection scheme based on bagged ensembles in order to improve robustness and thus predictive quality of the final models. The approaches are tested on real-world calibration data sets for wort and beer mix beverages, and successfully compared to linear methods, showing a clear out-performance in most cases and being able to meet the model quality requirements defined by the experts at the beer company. Figure Workflow for calibration of non-Linear model ensembles from FT-MIR spectra in beer production .

Signal and noise extraction from analog memory elements for neuromorphic computing.

PubMed

Gong, N; Idé, T; Kim, S; Boybat, I; Sebastian, A; Narayanan, V; Ando, T

2018-05-29

Dense crossbar arrays of non-volatile memory (NVM) can potentially enable massively parallel and highly energy-efficient neuromorphic computing systems. The key requirements for the NVM elements are continuous (analog-like) conductance tuning capability and switching symmetry with acceptable noise levels. However, most NVM devices show non-linear and asymmetric switching behaviors. Such non-linear behaviors render separation of signal and noise extremely difficult with conventional characterization techniques. In this study, we establish a practical methodology based on Gaussian process regression to address this issue. The methodology is agnostic to switching mechanisms and applicable to various NVM devices. We show tradeoff between switching symmetry and signal-to-noise ratio for HfO 2 -based resistive random access memory. Then, we characterize 1000 phase-change memory devices based on Ge 2 Sb 2 Te 5 and separate total variability into device-to-device variability and inherent randomness from individual devices. These results highlight the usefulness of our methodology to realize ideal NVM devices for neuromorphic computing.

Study of nonlinear refraction of organic dye by Z-scan technique using He-Ne laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Medhekar, S.; Kumar, R.; Mukherjee, S.

2013-02-05

Laser induced third-order nonlinear optical responses of Brilliant Green solution has been investigated by utilizing single beam Z-scan technique with a continuous-wave He-Ne laser radiation at 632.8 nm. It was observed that the material exhibits self-defocusing type optical nonlinearity. The measurements of nonlinear refraction were carried out at different dye concentrations and found that the increase in solution concentration leads to the linear increase of the nonlinear refractive index. The experimental results confirm great potential of the Brilliant Green for the application in nonlinear optical devices.

Measuring of nonlinear properties of spatial light modulator with different wavelengths

NASA Astrophysics Data System (ADS)

Khalid, Farah G.; Younis Al-Dabagh, Samar; Ahmed, Sudad S.; Mahmood, Aseel I.; Al-Naimee, Kais

2018-05-01

The non-linear optical properties of Spatial Light Modulator(SLM) represented by Nonlinear Refractive Index (NLR) and nonlinear Absorption coefficient has been measured in this work using highly sensitive method known as Z-scan technique for different wavelengths (red and green). The capability to do instant measurements of different nonlinear optical parameters lead to consider these techniques as a one of the most desired and effective methods that could apply for different materials. The results showed that the NLR were in the same power for the different wavelengths while the nonlinear absorption is higher in case of green laser.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

TG study of the Li0.4Fe2.4Zn0.2O4 ferrite synthesis

NASA Astrophysics Data System (ADS)

Lysenko, E. N.; Nikolaev, E. V.; Surzhikov, A. P.

2016-02-01

In this paper, the kinetic analysis of Li-Zn ferrite synthesis was studied using thermogravimetry (TG) method through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression). Using TG-curves obtained for the four heating rates and Netzsch Thermokinetics software package, the kinetic models with minimal adjustable parameters were selected to quantitatively describe the reaction of Li-Zn ferrite synthesis. It was shown that the experimental TG-curves clearly suggest a two-step process for the ferrite synthesis and therefore a model-fitting kinetic analysis based on multivariate non-linear regressions was conducted. The complex reaction was described by a two-step reaction scheme consisting of sequential reaction steps. It is established that the best results were obtained using the Yander three-dimensional diffusion model at the first stage and Ginstling-Bronstein model at the second step. The kinetic parameters for lithium-zinc ferrite synthesis reaction were found and discussed.

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Monthly monsoon rainfall forecasting using artificial neural networks

NASA Astrophysics Data System (ADS)

Ganti, Ravikumar

2014-10-01

Indian agriculture sector heavily depends on monsoon rainfall for successful harvesting. In the past, prediction of rainfall was mainly performed using regression models, which provide reasonable accuracy in the modelling and forecasting of complex physical systems. Recently, Artificial Neural Networks (ANNs) have been proposed as efficient tools for modelling and forecasting. A feed-forward multi-layer perceptron type of ANN architecture trained using the popular back-propagation algorithm was employed in this study. Other techniques investigated for modeling monthly monsoon rainfall include linear and non-linear regression models for comparison purposes. The data employed in this study include monthly rainfall and monthly average of the daily maximum temperature in the North Central region in India. Specifically, four regression models and two ANN model's were developed. The performance of various models was evaluated using a wide variety of standard statistical parameters and scatter plots. The results obtained in this study for forecasting monsoon rainfalls using ANNs have been encouraging. India's economy and agricultural activities can be effectively managed with the help of the availability of the accurate monsoon rainfall forecasts.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

Estimating procedure times for surgeries by determining location parameters for the lognormal model.

PubMed

Spangler, William E; Strum, David P; Vargas, Luis G; May, Jerrold H

2004-05-01

We present an empirical study of methods for estimating the location parameter of the lognormal distribution. Our results identify the best order statistic to use, and indicate that using the best order statistic instead of the median may lead to less frequent incorrect rejection of the lognormal model, more accurate critical value estimates, and higher goodness-of-fit. Using simulation data, we constructed and compared two models for identifying the best order statistic, one based on conventional nonlinear regression and the other using a data mining/machine learning technique. Better surgical procedure time estimates may lead to improved surgical operations.

The application of neural network model to the simulation nitrous oxide emission in the hydro-fluctuation belt of Three Gorges Reservoir

NASA Astrophysics Data System (ADS)

Song, Lanlan

2017-04-01

Nitrous oxide is much more potent greenhouse gas than carbon dioxide. However, the estimation of N2O flux is usually clouded with uncertainty, mainly due to high spatial and temporal variations. This hampers the development of general mechanistic models for N2O emission as well, as most previously developed models were empirical or exhibited low predictability with numerous assumptions. In this study, we tested General Regression Neural Networks (GRNN) as an alternative to classic empirical models for simulating N2O emission in riparian zones of Reservoirs. GRNN and nonlinear regression (NLR) were applied to estimate the N2O flux of 1-year observations in riparian zones of Three Gorge Reservoir. NLR resulted in lower prediction power and higher residuals compared to GRNN. Although nonlinear regression model estimated similar average values of N2O, it could not capture the fluctuation patterns accurately. In contrast, GRNN model achieved a fairly high predictability, with an R2 of 0.59 for model validation, 0.77 for model calibration (training), and a low root mean square error (RMSE), indicating a high capacity to simulate the dynamics of N2O flux. According to a sensitivity analysis of the GRNN, nonlinear relationships between input variables and N2O flux were well explained. Our results suggest that the GRNN developed in this study has a greater performance in simulating variations in N2O flux than nonlinear regressions.

Online Bimanual Manipulation Using Surface Electromyography and Incremental Learning.

PubMed

Strazzulla, Ilaria; Nowak, Markus; Controzzi, Marco; Cipriani, Christian; Castellini, Claudio

2017-03-01

The paradigm of simultaneous and proportional myocontrol of hand prostheses is gaining momentum in the rehabilitation robotics community. As opposed to the traditional surface electromyography classification schema, in simultaneous and proportional control the desired force/torque at each degree of freedom of the hand/wrist is predicted in real-time, giving to the individual a more natural experience, reducing the cognitive effort and improving his dexterity in daily-life activities. In this study we apply such an approach in a realistic manipulation scenario, using 10 non-linear incremental regression machines to predict the desired torques for each motor of two robotic hands. The prediction is enforced using two sets of surface electromyography electrodes and an incremental, non-linear machine learning technique called Incremental Ridge Regression with Random Fourier Features. Nine able-bodied subjects were engaged in a functional test with the aim to evaluate the performance of the system. The robotic hands were mounted on two hand/wrist orthopedic splints worn by healthy subjects and controlled online. An average completion rate of more than 95% was achieved in single-handed tasks and 84% in bimanual tasks. On average, 5 min of retraining were necessary on a total session duration of about 1 h and 40 min. This work sets a beginning in the study of bimanual manipulation with prostheses and will be carried on through experiments in unilateral and bilateral upper limb amputees thus increasing its scientific value.

Prediction of HDR quality by combining perceptually transformed display measurements with machine learning

NASA Astrophysics Data System (ADS)

Choudhury, Anustup; Farrell, Suzanne; Atkins, Robin; Daly, Scott

2017-09-01

We present an approach to predict overall HDR display quality as a function of key HDR display parameters. We first performed subjective experiments on a high quality HDR display that explored five key HDR display parameters: maximum luminance, minimum luminance, color gamut, bit-depth and local contrast. Subjects rated overall quality for different combinations of these display parameters. We explored two models | a physical model solely based on physically measured display characteristics and a perceptual model that transforms physical parameters using human vision system models. For the perceptual model, we use a family of metrics based on a recently published color volume model (ICT-CP), which consists of the PQ luminance non-linearity (ST2084) and LMS-based opponent color, as well as an estimate of the display point spread function. To predict overall visual quality, we apply linear regression and machine learning techniques such as Multilayer Perceptron, RBF and SVM networks. We use RMSE and Pearson/Spearman correlation coefficients to quantify performance. We found that the perceptual model is better at predicting subjective quality than the physical model and that SVM is better at prediction than linear regression. The significance and contribution of each display parameter was investigated. In addition, we found that combined parameters such as contrast do not improve prediction. Traditional perceptual models were also evaluated and we found that models based on the PQ non-linearity performed better.

Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics.

PubMed

Stratoudaki, Theodosia; Ellwood, Robert; Sharples, Steve; Clark, Matthew; Somekh, Michael G; Collison, Ian J

2011-04-01

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Treatment of systematic errors in land data assimilation systems

NASA Astrophysics Data System (ADS)

Crow, W. T.; Yilmaz, M.

2012-12-01

Data assimilation systems are generally designed to minimize the influence of random error on the estimation of system states. Yet, experience with land data assimilation systems has also revealed the presence of large systematic differences between model-derived and remotely-sensed estimates of land surface states. Such differences are commonly resolved prior to data assimilation through implementation of a pre-processing rescaling step whereby observations are scaled (or non-linearly transformed) to somehow "match" comparable predictions made by an assimilation model. While the rationale for removing systematic differences in means (i.e., bias) between models and observations is well-established, relatively little theoretical guidance is currently available to determine the appropriate treatment of higher-order moments during rescaling. This talk presents a simple analytical argument to define an optimal linear-rescaling strategy for observations prior to their assimilation into a land surface model. While a technique based on triple collocation theory is shown to replicate this optimal strategy, commonly-applied rescaling techniques (e.g., so called "least-squares regression" and "variance matching" approaches) are shown to represent only sub-optimal approximations to it. Since the triple collocation approach is likely infeasible in many real-world circumstances, general advice for deciding between various feasible (yet sub-optimal) rescaling approaches will be presented with an emphasis of the implications of this work for the case of directly assimilating satellite radiances. While the bulk of the analysis will deal with linear rescaling techniques, its extension to nonlinear cases will also be discussed.

Correlation techniques to determine model form in robust nonlinear system realization/identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1991-01-01

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Third order nonlinearity in pulsed laser deposited LiNbO{sub 3} thin films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tumuluri, Anil; Rapolu, Mounika; Rao, S. Venugopal, E-mail: kcjrsp@uohyd.ernet.in, E-mail: svrsp@uohyd.ernet.in

2016-05-06

Lithium niobate (LiNbO{sub 3}) thin films were prepared using pulsed laser deposition technique. Structural properties of the same were examined from XRD and optical band gap of the thin films were measured from transmittance spectra recorded using UV-Visible spectrophotometer. Nonlinear optical properties of the thin films were recorded using Z-Scan technique. The films were exhibiting third order nonlinearity and their corresponding two photon absorption, nonlinear refractive index, real and imaginary part of nonlinear susceptibility were calculated from open aperture and closed aperture transmission curves. From these studies, it suggests that these films have potential applications in nonlinear optical devices.

Development of solution techniques for nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Vos, R. G.; Andrews, J. S.

1974-01-01

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

New Approach To Hour-By-Hour Weather Forecast

NASA Astrophysics Data System (ADS)

Liao, Q. Q.; Wang, B.

2017-12-01

Fine hourly forecast in single station weather forecast is required in many human production and life application situations. Most previous MOS (Model Output Statistics) which used a linear regression model are hard to solve nonlinear natures of the weather prediction and forecast accuracy has not been sufficient at high temporal resolution. This study is to predict the future meteorological elements including temperature, precipitation, relative humidity and wind speed in a local region over a relatively short period of time at hourly level. By means of hour-to-hour NWP (Numeral Weather Prediction)meteorological field from Forcastio (https://darksky.net/dev/docs/forecast) and real-time instrumental observation including 29 stations in Yunnan and 3 stations in Tianjin of China from June to October 2016, predictions are made of the 24-hour hour-by-hour ahead. This study presents an ensemble approach to combine the information of instrumental observation itself and NWP. Use autoregressive-moving-average (ARMA) model to predict future values of the observation time series. Put newest NWP products into the equations derived from the multiple linear regression MOS technique. Handle residual series of MOS outputs with autoregressive (AR) model for the linear property presented in time series. Due to the complexity of non-linear property of atmospheric flow, support vector machine (SVM) is also introduced . Therefore basic data quality control and cross validation makes it able to optimize the model function parameters , and do 24 hours ahead residual reduction with AR/SVM model. Results show that AR model technique is better than corresponding multi-variant MOS regression method especially at the early 4 hours when the predictor is temperature. MOS-AR combined model which is comparable to MOS-SVM model outperform than MOS. Both of their root mean square error and correlation coefficients for 2 m temperature are reduced to 1.6 degree Celsius and 0.91 respectively. The forecast accuracy of 24- hour forecast deviation no more than 2 degree Celsius is 78.75 % for MOS-AR model and 81.23 % for AR model.

A regularization corrected score method for nonlinear regression models with covariate error.

PubMed

Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

2013-03-01

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer. Copyright © 2013, The International Biometric Society.

Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

NASA Astrophysics Data System (ADS)

Costiner, Sorin; Ta'asan, Shlomo

1995-07-01

Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

Kalman filter approach for uncertainty quantification in time-resolved laser-induced incandescence.

PubMed

Hadwin, Paul J; Sipkens, Timothy A; Thomson, Kevin A; Liu, Fengshan; Daun, Kyle J

2018-03-01

Time-resolved laser-induced incandescence (TiRe-LII) data can be used to infer spatially and temporally resolved volume fractions and primary particle size distributions of soot-laden aerosols, but these estimates are corrupted by measurement noise as well as uncertainties in the spectroscopic and heat transfer submodels used to interpret the data. Estimates of the temperature, concentration, and size distribution of soot primary particles within a sample aerosol are typically made by nonlinear regression of modeled spectral incandescence decay, or effective temperature decay, to experimental data. In this work, we employ nonstationary Bayesian estimation techniques to infer aerosol properties from simulated and experimental LII signals, specifically the extended Kalman filter and Schmidt-Kalman filter. These techniques exploit the time-varying nature of both the measurements and the models, and they reveal how uncertainty in the estimates computed from TiRe-LII data evolves over time. Both techniques perform better when compared with standard deterministic estimates; however, we demonstrate that the Schmidt-Kalman filter produces more realistic uncertainty estimates.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu

2014-01-15

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less

Damage assessment in reinforced concrete using nonlinear vibration techniques

NASA Astrophysics Data System (ADS)

Van Den Abeele, K.; De Visscher, J.

2000-07-01

Reinforced concrete (RC) structures are subject to microcrack initiation and propagation at load levels far below the actual failure load. In this paper, nonlinear vibration techniques are applied to investigate stages of progressive damage in RC beams induced by static loading tests. At different levels of damage, a modal analysis is carried out, assuming the structure to behave linearly. At the same time, measurement of resonant frequencies and damping ratios as function of vibration amplitude are performed using a frequency domain technique as well as a time domain technique. We compare the results of the linear and nonlinear techniques, and value them against the visual damage evaluation.

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Field Measurement of the Acoustic Nonlinearity Parameter in Turbine Blades

NASA Technical Reports Server (NTRS)

Hinton, Yolanda L.; Na, Jeong K.; Yost, William T.; Kessel, Gregory L.

2000-01-01

Nonlinear acoustics techniques were used to measure fatigue in turbine blades in a power generation plant. The measurements were made in the field using a reference based measurement technique, and a reference sample previously measured in the laboratory. The acoustic nonlinearity parameter showed significant increase with fatigue in the blades, as indicated by service age and areas of increased stress. The technique shows promise for effectively measuring fatigue in field applications and predicting subsequent failures.

Correction of Phase Distortion by Nonlinear Optical Techniques

DTIC Science & Technology

1981-05-01

I I I I ifi 00 o o \\] CORRECTION OF PHASE DISTORTION BY NONLINEAR OPTICAL TECHNIQUES op Hughes Research Laboratories 3011 Malibu Canyon...CORRECTION OF PHASE DISTORTION BY NONLINEAR OPTICAL TECHNIQUES • , — •■ FBiMowmln»"Own. we^owr^wwcw n R.C./Lind| W.B./Browne C.R. Giuliano, R.K... phase conjugation. Adaptive optics , Laser compensation, SBS, Four-wave mixing. 20. ABSTRACT (ConllmM on i tmrr and Identity bv block number

Quantitative structure-activity relationship study of P2X7 receptor inhibitors using combination of principal component analysis and artificial intelligence methods.

PubMed

Ahmadi, Mehdi; Shahlaei, Mohsen

2015-01-01

P2X7 antagonist activity for a set of 49 molecules of the P2X7 receptor antagonists, derivatives of purine, was modeled with the aid of chemometric and artificial intelligence techniques. The activity of these compounds was estimated by means of combination of principal component analysis (PCA), as a well-known data reduction method, genetic algorithm (GA), as a variable selection technique, and artificial neural network (ANN), as a non-linear modeling method. First, a linear regression, combined with PCA, (principal component regression) was operated to model the structure-activity relationships, and afterwards a combination of PCA and ANN algorithm was employed to accurately predict the biological activity of the P2X7 antagonist. PCA preserves as much of the information as possible contained in the original data set. Seven most important PC's to the studied activity were selected as the inputs of ANN box by an efficient variable selection method, GA. The best computational neural network model was a fully-connected, feed-forward model with 7-7-1 architecture. The developed ANN model was fully evaluated by different validation techniques, including internal and external validation, and chemical applicability domain. All validations showed that the constructed quantitative structure-activity relationship model suggested is robust and satisfactory.

Quantitative structure–activity relationship study of P2X7 receptor inhibitors using combination of principal component analysis and artificial intelligence methods

PubMed Central

Ahmadi, Mehdi; Shahlaei, Mohsen

2015-01-01

P2X7 antagonist activity for a set of 49 molecules of the P2X7 receptor antagonists, derivatives of purine, was modeled with the aid of chemometric and artificial intelligence techniques. The activity of these compounds was estimated by means of combination of principal component analysis (PCA), as a well-known data reduction method, genetic algorithm (GA), as a variable selection technique, and artificial neural network (ANN), as a non-linear modeling method. First, a linear regression, combined with PCA, (principal component regression) was operated to model the structure–activity relationships, and afterwards a combination of PCA and ANN algorithm was employed to accurately predict the biological activity of the P2X7 antagonist. PCA preserves as much of the information as possible contained in the original data set. Seven most important PC's to the studied activity were selected as the inputs of ANN box by an efficient variable selection method, GA. The best computational neural network model was a fully-connected, feed-forward model with 7−7−1 architecture. The developed ANN model was fully evaluated by different validation techniques, including internal and external validation, and chemical applicability domain. All validations showed that the constructed quantitative structure–activity relationship model suggested is robust and satisfactory. PMID:26600858

Postprocessing techniques for 3D non-linear structures

NASA Technical Reports Server (NTRS)

Gallagher, Richard S.

1987-01-01

How graphics postprocessing techniques are currently used to examine the results of 3-D nonlinear analyses, some new techniques which take advantage of recent technology, and how these results relate to both the finite element model and its geometric parent are reviewed.

Melamine detection by mid- and near-infrared (MIR/NIR) spectroscopy: a quick and sensitive method for dairy products analysis including liquid milk, infant formula, and milk powder.

PubMed

Balabin, Roman M; Smirnov, Sergey V

2011-07-15

Melamine (2,4,6-triamino-1,3,5-triazine) is a nitrogen-rich chemical implicated in the pet and human food recalls and in the global food safety scares involving milk products. Due to the serious health concerns associated with melamine consumption and the extensive scope of affected products, rapid and sensitive methods to detect melamine's presence are essential. We propose the use of spectroscopy data-produced by near-infrared (near-IR/NIR) and mid-infrared (mid-IR/MIR) spectroscopies, in particular-for melamine detection in complex dairy matrixes. None of the up-to-date reported IR-based methods for melamine detection has unambiguously shown its wide applicability to different dairy products as well as limit of detection (LOD) below 1 ppm on independent sample set. It was found that infrared spectroscopy is an effective tool to detect melamine in dairy products, such as infant formula, milk powder, or liquid milk. ALOD below 1 ppm (0.76±0.11 ppm) can be reached if a correct spectrum preprocessing (pretreatment) technique and a correct multivariate (MDA) algorithm-partial least squares regression (PLS), polynomial PLS (Poly-PLS), artificial neural network (ANN), support vector regression (SVR), or least squares support vector machine (LS-SVM)-are used for spectrum analysis. The relationship between MIR/NIR spectrum of milk products and melamine content is nonlinear. Thus, nonlinear regression methods are needed to correctly predict the triazine-derivative content of milk products. It can be concluded that mid- and near-infrared spectroscopy can be regarded as a quick, sensitive, robust, and low-cost method for liquid milk, infant formula, and milk powder analysis. Copyright © 2011 Elsevier B.V. All rights reserved.

Gaussian process regression for tool wear prediction

NASA Astrophysics Data System (ADS)

Kong, Dongdong; Chen, Yongjie; Li, Ning

2018-05-01

To realize and accelerate the pace of intelligent manufacturing, this paper presents a novel tool wear assessment technique based on the integrated radial basis function based kernel principal component analysis (KPCA_IRBF) and Gaussian process regression (GPR) for real-timely and accurately monitoring the in-process tool wear parameters (flank wear width). The KPCA_IRBF is a kind of new nonlinear dimension-increment technique and firstly proposed for feature fusion. The tool wear predictive value and the corresponding confidence interval are both provided by utilizing the GPR model. Besides, GPR performs better than artificial neural networks (ANN) and support vector machines (SVM) in prediction accuracy since the Gaussian noises can be modeled quantitatively in the GPR model. However, the existence of noises will affect the stability of the confidence interval seriously. In this work, the proposed KPCA_IRBF technique helps to remove the noises and weaken its negative effects so as to make the confidence interval compressed greatly and more smoothed, which is conducive for monitoring the tool wear accurately. Moreover, the selection of kernel parameter in KPCA_IRBF can be easily carried out in a much larger selectable region in comparison with the conventional KPCA_RBF technique, which helps to improve the efficiency of model construction. Ten sets of cutting tests are conducted to validate the effectiveness of the presented tool wear assessment technique. The experimental results show that the in-process flank wear width of tool inserts can be monitored accurately by utilizing the presented tool wear assessment technique which is robust under a variety of cutting conditions. This study lays the foundation for tool wear monitoring in real industrial settings.

Comparison of in situ and in vitro techniques for measuring ruminal degradation of animal by-product proteins.

PubMed

England, M L; Broderick, G A; Shaver, R D; Combs, D K

1997-11-01

Ruminally undegraded protein (RUP) values of blood meal (n = 2), hydrolyzed feather meal (n = 2), fish meal (n = 2), meat and bone meal, and soybean meal were estimated using an in situ method, an inhibitor in vitro method, and an inhibitor in vitro technique applying Michaelis-Menten saturation kinetics. Degradation rates for in situ and inhibitor in vitro methods were calculated by regression of the natural log of the proportion of crude protein (CP) remaining undegraded versus time. Nonlinear regression analysis of the integrated Michaelis-Menten equation was used to determine maximum velocity, the Michaelis constant, and degradation rate (the ratio of maximum velocity to the Michaelis constant). A ruminal passage rate of 0.06/h was assumed in the calculation of RUP. The in situ and inhibitor in vitro techniques yielded similar estimates of ruminal degradation. Mean RUP estimated for soybean meal, blood meal, hydrolyzed feather meal, fish meal, and meat and bone meal were, respectively, 28.6, 86.0, 77.4, 52.9, and 52.6% of CP by the in situ method and 26.4, 86.1, 76.0, 59.6, and 49.5% of CP by the inhibitor in vitro technique. The Michaelis-Menten inhibitor in vitro technique yielded more rapid CP degradation rates and decreased estimates of RUP. The inhibitor in vitro method required less time and labor than did the other two techniques to estimate the RUP values of animal by-product proteins. Results from in vitro incubations with pepsin.HCl suggested that low postruminal digestibility of hydrolyzed feather meal may impair its value as a source of RUP.

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

The mechanical properties of high speed GTAW weld and factors of nonlinear multiple regression model under external transverse magnetic field

NASA Astrophysics Data System (ADS)

Lu, Lin; Chang, Yunlong; Li, Yingmin; He, Youyou

2013-05-01

A transverse magnetic field was introduced to the arc plasma in the process of welding stainless steel tubes by high-speed Tungsten Inert Gas Arc Welding (TIG for short) without filler wire. The influence of external magnetic field on welding quality was investigated. 9 sets of parameters were designed by the means of orthogonal experiment. The welding joint tensile strength and form factor of weld were regarded as the main standards of welding quality. A binary quadratic nonlinear regression equation was established with the conditions of magnetic induction and flow rate of Ar gas. The residual standard deviation was calculated to adjust the accuracy of regression model. The results showed that, the regression model was correct and effective in calculating the tensile strength and aspect ratio of weld. Two 3D regression models were designed respectively, and then the impact law of magnetic induction on welding quality was researched.

Nonlinear regression method for estimating neutral wind and temperature from Fabry-Perot interferometer data.

PubMed

Harding, Brian J; Gehrels, Thomas W; Makela, Jonathan J

2014-02-01

The Earth's thermosphere plays a critical role in driving electrodynamic processes in the ionosphere and in transferring solar energy to the atmosphere, yet measurements of thermospheric state parameters, such as wind and temperature, are sparse. One of the most popular techniques for measuring these parameters is to use a Fabry-Perot interferometer to monitor the Doppler width and breadth of naturally occurring airglow emissions in the thermosphere. In this work, we present a technique for estimating upper-atmospheric winds and temperatures from images of Fabry-Perot fringes captured by a CCD detector. We estimate instrument parameters from fringe patterns of a frequency-stabilized laser, and we use these parameters to estimate winds and temperatures from airglow fringe patterns. A unique feature of this technique is the model used for the laser and airglow fringe patterns, which fits all fringes simultaneously and attempts to model the effects of optical defects. This technique yields accurate estimates for winds, temperatures, and the associated uncertainties in these parameters, as we show with a Monte Carlo simulation.

Comparison of data mining techniques applied to fetal heart rate parameters for the early identification of IUGR fetuses.

PubMed

Magenes, G; Bellazzi, R; Malovini, A; Signorini, M G

2016-08-01

The onset of fetal pathologies can be screened during pregnancy by means of Fetal Heart Rate (FHR) monitoring and analysis. Noticeable advances in understanding FHR variations were obtained in the last twenty years, thanks to the introduction of quantitative indices extracted from the FHR signal. This study searches for discriminating Normal and Intra Uterine Growth Restricted (IUGR) fetuses by applying data mining techniques to FHR parameters, obtained from recordings in a population of 122 fetuses (61 healthy and 61 IUGRs), through standard CTG non-stress test. We computed N=12 indices (N=4 related to time domain FHR analysis, N=4 to frequency domain and N=4 to non-linear analysis) and normalized them with respect to the gestational week. We compared, through a 10-fold crossvalidation procedure, 15 data mining techniques in order to select the more reliable approach for identifying IUGR fetuses. The results of this comparison highlight that two techniques (Random Forest and Logistic Regression) show the best classification accuracy and that both outperform the best single parameter in terms of mean AUROC on the test sets.

Estimation of Unsteady Aerodynamic Models from Dynamic Wind Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick; Klein, Vladislav

2011-01-01

Demanding aerodynamic modelling requirements for military and civilian aircraft have motivated researchers to improve computational and experimental techniques and to pursue closer collaboration in these areas. Model identification and validation techniques are key components for this research. This paper presents mathematical model structures and identification techniques that have been used successfully to model more general aerodynamic behaviours in single-degree-of-freedom dynamic testing. Model parameters, characterizing aerodynamic properties, are estimated using linear and nonlinear regression methods in both time and frequency domains. Steps in identification including model structure determination, parameter estimation, and model validation, are addressed in this paper with examples using data from one-degree-of-freedom dynamic wind tunnel and water tunnel experiments. These techniques offer a methodology for expanding the utility of computational methods in application to flight dynamics, stability, and control problems. Since flight test is not always an option for early model validation, time history comparisons are commonly made between computational and experimental results and model adequacy is inferred by corroborating results. An extension is offered to this conventional approach where more general model parameter estimates and their standard errors are compared.

Tests of Sunspot Number Sequences: 3. Effects of Regression Procedures on the Calibration of Historic Sunspot Data

NASA Astrophysics Data System (ADS)

Lockwood, M.; Owens, M. J.; Barnard, L.; Usoskin, I. G.

2016-11-01

We use sunspot-group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups [RB] above a variable cut-off threshold of observed total whole spot area (uncorrected for foreshortening) to simulate what a lower-acuity observer would have seen. The synthesised annual means of RB are then re-scaled to the full observed RGO group number [RA] using a variety of regression techniques. It is found that a very high correlation between RA and RB (r_{AB} > 0.98) does not prevent large errors in the intercalibration (for example sunspot-maximum values can be over 30 % too large even for such levels of r_{AB}). In generating the backbone sunspot number [R_{BB}], Svalgaard and Schatten ( Solar Phys., 2016) force regression fits to pass through the scatter-plot origin, which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot-cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile ("Q-Q") plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least-squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot-group numbers). However, other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar-cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data.

Reduced-Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

Reduced Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.

2004-01-01

A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Interactions between large-scale modes of climate and their relationship with Australian climate and hydrology

NASA Astrophysics Data System (ADS)

Whan, K. R.; Lindesay, J. A.; Timbal, B.; Raupach, M. R.; Williams, E.

2010-12-01

Australia’s natural environment is adapted to low rainfall availability and high variability but human systems are less able to adapt to variability in the hydrological cycle. Understanding the mechanisms underlying drought persistence and severity is vital to contextualising future climate change. Multiple external forcings mean the mechanisms of drought occurrence in south-eastern Australian are complex. The key influences on SEA climate are El Niño-Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), the Southern Annular Mode (SAM) and the sub-tropical ridge (STR); each of these large-scale climate modes (LSCM) has been studied widely. The need for research into the interactions among the modes has been noted [1], although to date this has received limited attention. Relationships between LSCM and hydrometeorological variability are nonlinear, making linearity assumptions underlying usual statistical techniques (e.g. correlation, principle components analysis) questionable. In the current research a statistical technique that can deal with nonlinear interactions is applied to a new dataset enabling a full examination of the Australian water balance. The Australian Water Availability Project (AWAP) dataset models the Australian water balance on a fine grid [2]. Hydrological parameters (e.g. soil moisture, evaporation, runoff) are modelled from meteorological data, allowing the complete Australian water balance (climate and hydrology) to be examined and the mechanisms of drought to be studied holistically. Classification and regression trees (CART) are a powerful regression-based technique that is capable of accounting for nonlinear effects. Although it has limited previous application in climate research [3] this methodology is particularly informative in cases with multiple predictors and nonlinear relationships such as climate variability. Statistical relationships between variables are the basis for the decision rules in CART that are used to split the data into increasingly homogeneous groups. CART is applied to the AWAP dataset to identify the hydroclimatic regimes associated with various combinations of LSCM and the importance of each mode in producing the regime. Analysis of the LSCM is conducted on a range of hydroclimatic variables to assess the relative and combined influences of these LSCM on the Australian water balance. This gives information about interactions between LSCM that are vital for specific hydroclimatic states (e.g. drought) and about which combinations of LSCM result in specific regimes. The dominant LSCM in different seasons and the relationships among the climate drivers have been identified. 1. Ummenhofer, C., et al., What causes southeast Australia's worst droughts? Geophysical Research Letters, 2009. 36: p. L04706. 2. Raupach, M., et al., Australian Water Availability Project (AWAP). CSIRO Marine and Atmospheric Research Component: Final Report for Phase 3. 2008. 3. Burrows, W., et al., CART Decision-Tree Statistical Analysis and Prediction of Summer Season Maximum Surface Ozone for the Vancouver, Montreal and Atlantic Regions of Canada. Journal of Applied Meteorology, 1995. 34: p. 1848-1862.

Quantifying Vegetation Biophysical Variables from Imaging Spectroscopy Data: A Review on Retrieval Methods

NASA Astrophysics Data System (ADS)

Verrelst, Jochem; Malenovský, Zbyněk; Van der Tol, Christiaan; Camps-Valls, Gustau; Gastellu-Etchegorry, Jean-Philippe; Lewis, Philip; North, Peter; Moreno, Jose

2018-06-01

An unprecedented spectroscopic data stream will soon become available with forthcoming Earth-observing satellite missions equipped with imaging spectroradiometers. This data stream will open up a vast array of opportunities to quantify a diversity of biochemical and structural vegetation properties. The processing requirements for such large data streams require reliable retrieval techniques enabling the spatiotemporally explicit quantification of biophysical variables. With the aim of preparing for this new era of Earth observation, this review summarizes the state-of-the-art retrieval methods that have been applied in experimental imaging spectroscopy studies inferring all kinds of vegetation biophysical variables. Identified retrieval methods are categorized into: (1) parametric regression, including vegetation indices, shape indices and spectral transformations; (2) nonparametric regression, including linear and nonlinear machine learning regression algorithms; (3) physically based, including inversion of radiative transfer models (RTMs) using numerical optimization and look-up table approaches; and (4) hybrid regression methods, which combine RTM simulations with machine learning regression methods. For each of these categories, an overview of widely applied methods with application to mapping vegetation properties is given. In view of processing imaging spectroscopy data, a critical aspect involves the challenge of dealing with spectral multicollinearity. The ability to provide robust estimates, retrieval uncertainties and acceptable retrieval processing speed are other important aspects in view of operational processing. Recommendations towards new-generation spectroscopy-based processing chains for operational production of biophysical variables are given.

Modern modeling techniques had limited external validity in predicting mortality from traumatic brain injury.

PubMed

van der Ploeg, Tjeerd; Nieboer, Daan; Steyerberg, Ewout W

2016-10-01

Prediction of medical outcomes may potentially benefit from using modern statistical modeling techniques. We aimed to externally validate modeling strategies for prediction of 6-month mortality of patients suffering from traumatic brain injury (TBI) with predictor sets of increasing complexity. We analyzed individual patient data from 15 different studies including 11,026 TBI patients. We consecutively considered a core set of predictors (age, motor score, and pupillary reactivity), an extended set with computed tomography scan characteristics, and a further extension with two laboratory measurements (glucose and hemoglobin). With each of these sets, we predicted 6-month mortality using default settings with five statistical modeling techniques: logistic regression (LR), classification and regression trees, random forests (RFs), support vector machines (SVM) and neural nets. For external validation, a model developed on one of the 15 data sets was applied to each of the 14 remaining sets. This process was repeated 15 times for a total of 630 validations. The area under the receiver operating characteristic curve (AUC) was used to assess the discriminative ability of the models. For the most complex predictor set, the LR models performed best (median validated AUC value, 0.757), followed by RF and support vector machine models (median validated AUC value, 0.735 and 0.732, respectively). With each predictor set, the classification and regression trees models showed poor performance (median validated AUC value, <0.7). The variability in performance across the studies was smallest for the RF- and LR-based models (inter quartile range for validated AUC values from 0.07 to 0.10). In the area of predicting mortality from TBI, nonlinear and nonadditive effects are not pronounced enough to make modern prediction methods beneficial. Copyright © 2016 Elsevier Inc. All rights reserved.

The Fringe-Imaging Skin Friction Technique PC Application User's Manual

NASA Technical Reports Server (NTRS)

Zilliac, Gregory G.

1999-01-01

A personal computer application (CXWIN4G) has been written which greatly simplifies the task of extracting skin friction measurements from interferograms of oil flows on the surface of wind tunnel models. Images are first calibrated, using a novel approach to one-camera photogrammetry, to obtain accurate spatial information on surfaces with curvature. As part of the image calibration process, an auxiliary file containing the wind tunnel model geometry is used in conjunction with a two-dimensional direct linear transformation to relate the image plane to the physical (model) coordinates. The application then applies a nonlinear regression model to accurately determine the fringe spacing from interferometric intensity records as required by the Fringe Imaging Skin Friction (FISF) technique. The skin friction is found through application of a simple expression that makes use of lubrication theory to relate fringe spacing to skin friction.

Assess and Predict Automatic Generation Control Performances for Thermal Power Generation Units Based on Modeling Techniques

NASA Astrophysics Data System (ADS)

Zhao, Yan; Yang, Zijiang; Gao, Song; Liu, Jinbiao

2018-02-01

Automatic generation control(AGC) is a key technology to maintain real time power generation and load balance, and to ensure the quality of power supply. Power grids require each power generation unit to have a satisfactory AGC performance, being specified in two detailed rules. The two rules provide a set of indices to measure the AGC performance of power generation unit. However, the commonly-used method to calculate these indices is based on particular data samples from AGC responses and will lead to incorrect results in practice. This paper proposes a new method to estimate the AGC performance indices via system identification techniques. In addition, a nonlinear regression model between performance indices and load command is built in order to predict the AGC performance indices. The effectiveness of the proposed method is validated through industrial case studies.

Binding affinity toward human prion protein of some anti-prion compounds - Assessment based on QSAR modeling, molecular docking and non-parametric ranking.

PubMed

Kovačević, Strahinja; Karadžić, Milica; Podunavac-Kuzmanović, Sanja; Jevrić, Lidija

2018-01-01

The present study is based on the quantitative structure-activity relationship (QSAR) analysis of binding affinity toward human prion protein (huPrP C ) of quinacrine, pyridine dicarbonitrile, diphenylthiazole and diphenyloxazole analogs applying different linear and non-linear chemometric regression techniques, including univariate linear regression, multiple linear regression, partial least squares regression and artificial neural networks. The QSAR analysis distinguished molecular lipophilicity as an important factor that contributes to the binding affinity. Principal component analysis was used in order to reveal similarities or dissimilarities among the studied compounds. The analysis of in silico absorption, distribution, metabolism, excretion and toxicity (ADMET) parameters was conducted. The ranking of the studied analogs on the basis of their ADMET parameters was done applying the sum of ranking differences, as a relatively new chemometric method. The main aim of the study was to reveal the most important molecular features whose changes lead to the changes in the binding affinities of the studied compounds. Another point of view on the binding affinity of the most promising analogs was established by application of molecular docking analysis. The results of the molecular docking were proven to be in agreement with the experimental outcome. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonlinear plasmonic imaging techniques and their biological applications

NASA Astrophysics Data System (ADS)

Deka, Gitanjal; Sun, Chi-Kuang; Fujita, Katsumasa; Chu, Shi-Wei

2017-01-01

Nonlinear optics, when combined with microscopy, is known to provide advantages including novel contrast, deep tissue observation, and minimal invasiveness. In addition, special nonlinearities, such as switch on/off and saturation, can enhance the spatial resolution below the diffraction limit, revolutionizing the field of optical microscopy. These nonlinear imaging techniques are extremely useful for biological studies on various scales from molecules to cells to tissues. Nevertheless, in most cases, nonlinear optical interaction requires strong illumination, typically at least gigawatts per square centimeter intensity. Such strong illumination can cause significant phototoxicity or even photodamage to fragile biological samples. Therefore, it is highly desirable to find mechanisms that allow the reduction of illumination intensity. Surface plasmon, which is the collective oscillation of electrons in metal under light excitation, is capable of significantly enhancing the local field around the metal nanostructures and thus boosting up the efficiency of nonlinear optical interactions of the surrounding materials or of the metal itself. In this mini-review, we discuss the recent progress of plasmonics in nonlinear optical microscopy with a special focus on biological applications. The advancement of nonlinear imaging modalities (including incoherent/coherent Raman scattering, two/three-photon luminescence, and second/third harmonic generations that have been amalgamated with plasmonics), as well as the novel subdiffraction limit imaging techniques based on nonlinear behaviors of plasmonic scattering, is addressed.

Health state utility instruments compared: inquiring into nonlinearity across EQ-5D-5L, SF-6D, HUI-3 and 15D.

PubMed

Gamst-Klaussen, Thor; Chen, Gang; Lamu, Admassu N; Olsen, Jan Abel

2016-07-01

Different health state utility (HSU) instruments produce different utilities for the same individuals, thereby compromising the intended comparability of economic evaluations of health care interventions. When developing crosswalks, previous studies have indicated nonlinear relationships. This paper inquires into the degree of nonlinearity across the four most widely used HSU-instruments and proposes exchange rates that differ depending on the severity levels of the health state utility scale. Overall, 7933 respondents from six countries, 1760 in a non-diagnosed healthy group and 6173 in seven disease groups, reported their health states using four different instruments: EQ-5D-5L, SF-6D, HUI-3 and 15D. Quantile regressions investigate the degree of nonlinear relationships between these instruments. To compare the instruments across different disease severities, we split the health state utility scale into utility intervals with 0.2 successive decrements in utility starting from perfect health at 1.00. Exchange rates (ERs) are calculated as the mean utility difference between two utility intervals on one HSU-instrument divided by the difference in mean utility on another HSU-instrument. Quantile regressions reveal significant nonlinear relationships across all four HSU-instruments. The degrees of nonlinearities differ, with a maximum degree of difference in the coefficients along the health state utility scale of 3.34 when SF-6D is regressed on EQ-5D. At the lower end of the health state utility scale, the exchange rate from SF-6D to EQ-5D is 2.11, whilst at the upper end it is 0.38. Comparisons at different utility levels illustrate the fallacy of using linear functions as crosswalks between HSU-instruments. The existence of nonlinear relationships between different HSU-instruments suggests that level-specific exchange rates should be used when converting a change in utility on the instrument used, onto a corresponding utility change had another instrument been used. Accounting for nonlinearities will increase the validity of the comparison for decision makers when faced with a choice between interventions whose calculations of QALY gains have been based on different HSU-instruments.

Nonlinear Real-Time Optical Signal Processing

DTIC Science & Technology

1990-09-01

pattern recognition. Additional work concerns the relationship of parallel computation paradigms to optical computing and halftone screen techniques...paradigms to optical computing and halftone screen techniques for implementing general nonlinear functions. 3\\ 2 Research Progress This section...Vol. 23, No. 8, pp. 34-57, 1986. 2.4 Nonlinear Optical Processing with Halftones : Degradation and Compen- sation Models This paper is concerned with

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum

2006-01-01

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

LDV measurement of small nonlinearities in flat and curved membranes. A model for eardrum nonlinear acoustic behaviour

NASA Astrophysics Data System (ADS)

Kilian, Gladiné; Pieter, Muyshondt; Joris, Dirckx

2016-06-01

Laser Doppler Vibrometry is an intrinsic highly linear measurement technique which makes it a great tool to measure extremely small nonlinearities in the vibration response of a system. Although the measurement technique is highly linear, other components in the experimental setup may introduce nonlinearities. An important source of artificially introduced nonlinearities is the speaker, which generates the stimulus. In this work, two correction methods to remove the effects of stimulus nonlinearity are investigated. Both correction methods were found to give similar results but have different pros and cons. The aim of this work is to investigate the importance of the conical shape of the eardrum as a source of nonlinearity in hearing. We present measurements on flat and indented membranes. The data shows that the curved membrane exhibit slightly higher levels of nonlinearity compared to the flat membrane.

Nonlinear ultrasonics for material state awareness

NASA Astrophysics Data System (ADS)

Jacobs, L. J.

2014-02-01

Predictive health monitoring of structural components will require the development of advanced sensing techniques capable of providing quantitative information on the damage state of structural materials. By focusing on nonlinear acoustic techniques, it is possible to measure absolute, strength based material parameters that can then be coupled with uncertainty models to enable accurate and quantitative life prediction. Starting at the material level, this review will present current research that involves a combination of sensing techniques and physics-based models to characterize damage in metallic materials. In metals, these nonlinear ultrasonic measurements can sense material state, before the formation of micro- and macro-cracks. Typically, cracks of a measurable size appear quite late in a component's total life, while the material's integrity in terms of toughness and strength gradually decreases due to the microplasticity (dislocations) and associated change in the material's microstructure. This review focuses on second harmonic generation techniques. Since these nonlinear acoustic techniques are acoustic wave based, component interrogation can be performed with bulk, surface and guided waves using the same underlying material physics; these nonlinear ultrasonic techniques provide results which are independent of the wave type used. Recent physics-based models consider the evolution of damage due to dislocations, slip bands, interstitials, and precipitates in the lattice structure, which can lead to localized damage.

Deriving the Regression Equation without Using Calculus

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy

NASA Astrophysics Data System (ADS)

Casdagli, M. C.; Iasemidis, L. D.; Sackellares, J. C.; Roper, S. N.; Gilmore, R. L.; Savit, R. S.

Invasive electroencephalographic (EEG) recordings from depth and subdural electrodes, performed in eight patients with temporal lobe epilepsy, are analyzed using a variety of nonlinear techniques. A surrogate data technique is used to find strong evidence for nonlinearities in epileptogenic regions of the brain. Most of these nonlinearities are characterized as “spiking” by a wavelet analysis. A small fraction of the nonlinearities are characterized as “recurrent” by a nonlinear prediction algorithm. Recurrent activity is found to occur in spatio-temporal patterns related to the location of the epileptogenic focus. Residual delay maps, used to characterize “lag-one nonlinearity”, are remarkably stationary for a given electrode, and exhibit striking variations among electrodes. The clinical and theoretical implications of these results are discussed.

Boosted Regression Tree Models to Explain Watershed Nutrient Concentrations and Biological Condition

EPA Science Inventory

Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on ...

Noninvasive and fast measurement of blood glucose in vivo by near infrared (NIR) spectroscopy

NASA Astrophysics Data System (ADS)

Jintao, Xue; Liming, Ye; Yufei, Liu; Chunyan, Li; Han, Chen

2017-05-01

This research was to develop a method for noninvasive and fast blood glucose assay in vivo. Near-infrared (NIR) spectroscopy, a more promising technique compared to other methods, was investigated in rats with diabetes and normal rats. Calibration models are generated by two different multivariate strategies: partial least squares (PLS) as linear regression method and artificial neural networks (ANN) as non-linear regression method. The PLS model was optimized individually by considering spectral range, spectral pretreatment methods and number of model factors, while the ANN model was studied individually by selecting spectral pretreatment methods, parameters of network topology, number of hidden neurons, and times of epoch. The results of the validation showed the two models were robust, accurate and repeatable. Compared to the ANN model, the performance of the PLS model was much better, with lower root mean square error of validation (RMSEP) of 0.419 and higher correlation coefficients (R) of 96.22%.

Optical nonlinearity in gelatin layer film containing Au nanoparticles

NASA Astrophysics Data System (ADS)

Hirose, Tomohiro; Arisawa, Michiko; Omatsu, Takashige; Kuge, Ken'ichi; Hasegawa, Akira; Tateda, Mitsuhiro

2002-09-01

We demonstrate a novel technique to fabricate a gelatin film containing Au-nano-particles. The technique is based on silver halide photographic development. We investigated third-order non-linearity of the film by forward-four-wave-mixing technique. Peak absorption appeared at the wavelength of 560nm. Self-diffraction by the use of third order nonlinear grating formed by intense pico-second pulses was observed. Experimental diffraction efficiency was proportional to the square of the pump intensity. Third-order susceptibility c(3) of the film was estimated to be 1.8?~10^-7esu.

Improved Indentation Test for Measuring Nonlinear Elasticity

NASA Technical Reports Server (NTRS)

Eldridge, Jeffrey I.

2004-01-01

A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.

Plasmon assisted enhanced nonlinear refraction of monodispersed silver nanoparticles and their tunability.

PubMed

Lama, Pemba; Suslov, Anatoliy; Walser, Ardie D; Dorsinville, Roger

2014-06-02

Nonlinear optical characterizations were performed on monodispersed silver (Ag) nanoparticles (NPs) of various sizes using a picosecond Z-scan technique with excitation wavelengths of 532 nm and 1064 nm. The Ag NPs were fabricated using a heterogeneous condensation technique in a gas medium. The nonlinear refraction values were higher for the monodispersed Ag NPs whose surface plasmon resonance (SPR) peak is closer to the excitation wavelength. The higher nonlinear optical response is explained in terms of an electric field enhancement near the SPR. Moreover, the fabrication method allows the tailoring of the nonlinear refraction index of the Ag NPs by tuning the SPR peak of the sample. A comparison of the nonlinear refraction index of the monodispersed and polydispersed Ag NPs showed that the nonlinear refractive index of the monodispersed Ag NPs is higher.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-07-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach was justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatland sites in Finland and a tundra site in Siberia. The flux measurements were performed using transparent chambers on vegetated surfaces and opaque chambers on bare peat surfaces. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes and even lower for longer closure times. The degree of underestimation increased with increasing CO2 flux strength and is dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Strengthen forensic entomology in court--the need for data exploration and the validation of a generalised additive mixed model.

PubMed

Baqué, Michèle; Amendt, Jens

2013-01-01

Developmental data of juvenile blow flies (Diptera: Calliphoridae) are typically used to calculate the age of immature stages found on or around a corpse and thus to estimate a minimum post-mortem interval (PMI(min)). However, many of those data sets don't take into account that immature blow flies grow in a non-linear fashion. Linear models do not supply a sufficient reliability on age estimates and may even lead to an erroneous determination of the PMI(min). According to the Daubert standard and the need for improvements in forensic science, new statistic tools like smoothing methods and mixed models allow the modelling of non-linear relationships and expand the field of statistical analyses. The present study introduces into the background and application of these statistical techniques by analysing a model which describes the development of the forensically important blow fly Calliphora vicina at different temperatures. The comparison of three statistical methods (linear regression, generalised additive modelling and generalised additive mixed modelling) clearly demonstrates that only the latter provided regression parameters that reflect the data adequately. We focus explicitly on both the exploration of the data--to assure their quality and to show the importance of checking it carefully prior to conducting the statistical tests--and the validation of the resulting models. Hence, we present a common method for evaluating and testing forensic entomological data sets by using for the first time generalised additive mixed models.

Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.

PubMed

Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second degree where the parabola is its graphical representation.

Two-step superresolution approach for surveillance face image through radial basis function-partial least squares regression and locality-induced sparse representation

NASA Astrophysics Data System (ADS)

Jiang, Junjun; Hu, Ruimin; Han, Zhen; Wang, Zhongyuan; Chen, Jun

2013-10-01

Face superresolution (SR), or face hallucination, refers to the technique of generating a high-resolution (HR) face image from a low-resolution (LR) one with the help of a set of training examples. It aims at transcending the limitations of electronic imaging systems. Applications of face SR include video surveillance, in which the individual of interest is often far from cameras. A two-step method is proposed to infer a high-quality and HR face image from a low-quality and LR observation. First, we establish the nonlinear relationship between LR face images and HR ones, according to radial basis function and partial least squares (RBF-PLS) regression, to transform the LR face into the global face space. Then, a locality-induced sparse representation (LiSR) approach is presented to enhance the local facial details once all the global faces for each LR training face are constructed. A comparison of some state-of-the-art SR methods shows the superiority of the proposed two-step approach, RBF-PLS global face regression followed by LiSR-based local patch reconstruction. Experiments also demonstrate the effectiveness under both simulation conditions and some real conditions.

A data-driven dynamics simulation framework for railway vehicles

NASA Astrophysics Data System (ADS)

Nie, Yinyu; Tang, Zhao; Liu, Fengjia; Chang, Jian; Zhang, Jianjun

2018-03-01

The finite element (FE) method is essential for simulating vehicle dynamics with fine details, especially for train crash simulations. However, factors such as the complexity of meshes and the distortion involved in a large deformation would undermine its calculation efficiency. An alternative method, the multi-body (MB) dynamics simulation provides satisfying time efficiency but limited accuracy when highly nonlinear dynamic process is involved. To maintain the advantages of both methods, this paper proposes a data-driven simulation framework for dynamics simulation of railway vehicles. This framework uses machine learning techniques to extract nonlinear features from training data generated by FE simulations so that specific mesh structures can be formulated by a surrogate element (or surrogate elements) to replace the original mechanical elements, and the dynamics simulation can be implemented by co-simulation with the surrogate element(s) embedded into a MB model. This framework consists of a series of techniques including data collection, feature extraction, training data sampling, surrogate element building, and model evaluation and selection. To verify the feasibility of this framework, we present two case studies, a vertical dynamics simulation and a longitudinal dynamics simulation, based on co-simulation with MATLAB/Simulink and Simpack, and a further comparison with a popular data-driven model (the Kriging model) is provided. The simulation result shows that using the legendre polynomial regression model in building surrogate elements can largely cut down the simulation time without sacrifice in accuracy.

Nonlinear Constitutive Modeling of Piezoelectric Ceramics

NASA Astrophysics Data System (ADS)

Xu, Jia; Li, Chao; Wang, Haibo; Zhu, Zhiwen

2017-12-01

Nonlinear constitutive modeling of piezoelectric ceramics is discussed in this paper. Van der Pol item is introduced to explain the simple hysteretic curve. Improved nonlinear difference items are used to interpret the hysteresis phenomena of piezoelectric ceramics. The fitting effect of the model on experimental data is proved by the partial least-square regression method. The results show that this method can describe the real curve well. The results of this paper are helpful to piezoelectric ceramics constitutive modeling.

Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials

NASA Astrophysics Data System (ADS)

Ju, Taeho

To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear mixing technique is adapted to develop an NDE technique for characterizing thermal aging of adhesive joints. To this end, a nonlinear spring model is used to simulate the effect of the adhesive layer. Based on this nonlinear spring model, analytical expressions of the resonant wave generated by the adhesive layers is obtained through an asymptotic analysis when the adhesive layer thickness is much smaller than the pertinent wavelength. The solutions are expressed in terms of the properties of the adhesive layer. The nonlinear spring model shows a good agreement with the finite layer model solutions in the limit of a small thickness to wavelength ratio. Third, to demonstrate the effectiveness of this newly developed technique, measurements are conducted on adhesive joint samples made of two aluminum adherends bonded together by a polymer adhesive tape. The samples are aged in a thermal chamber to induce thermal ageing degradation in the adhesive layer. Using the developed wave-mixing technique in conjunction with the nonlinear spring model, we show that the thermal aging damage of the adhesive layer can be quantified from only one side of the sample. Finally, by mixing two L-waves, we develop a mixing technique to nondestructively evaluate the damage induced by alkali-silica reaction (ASR) in concrete. Experimental measurements are conducted on concrete prism samples that contain reactive aggregates and have been subjected to different ASR conditioning. This new technique takes into consideration of the significant attenuation caused by ASR-induced microcracks and scattering by the aggregates. The measurement results show that the ANLP has a much greater sensitivity to ASR damage than other parameters such as attenuation and wave speed. More remarkably, it is also found that the measured acoustic nonlinearity parameter is well-correlated with the reduction of the compressive strength induced by ASR damage. Thus, ANLP can be used to nondestructively track ASR damage in concrete.

Validity of the reduced-sample insulin modified frequently-sampled intravenous glucose tolerance test using the nonlinear regression approach.

PubMed

Sumner, Anne E; Luercio, Marcella F; Frempong, Barbara A; Ricks, Madia; Sen, Sabyasachi; Kushner, Harvey; Tulloch-Reid, Marshall K

2009-02-01

The disposition index, the product of the insulin sensitivity index (S(I)) and the acute insulin response to glucose, is linked in African Americans to chromosome 11q. This link was determined with S(I) calculated with the nonlinear regression approach to the minimal model and data from the reduced-sample insulin-modified frequently-sampled intravenous glucose tolerance test (Reduced-Sample-IM-FSIGT). However, the application of the nonlinear regression approach to calculate S(I) using data from the Reduced-Sample-IM-FSIGT has been challenged as being not only inaccurate but also having a high failure rate in insulin-resistant subjects. Our goal was to determine the accuracy and failure rate of the Reduced-Sample-IM-FSIGT using the nonlinear regression approach to the minimal model. With S(I) from the Full-Sample-IM-FSIGT considered the standard and using the nonlinear regression approach to the minimal model, we compared the agreement between S(I) from the Full- and Reduced-Sample-IM-FSIGT protocols. One hundred African Americans (body mass index, 31.3 +/- 7.6 kg/m(2) [mean +/- SD]; range, 19.0-56.9 kg/m(2)) had FSIGTs. Glucose (0.3 g/kg) was given at baseline. Insulin was infused from 20 to 25 minutes (total insulin dose, 0.02 U/kg). For the Full-Sample-IM-FSIGT, S(I) was calculated based on the glucose and insulin samples taken at -1, 1, 2, 3, 4, 5, 6, 7, 8,10, 12, 14, 16, 19, 22, 23, 24, 25, 27, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, and 180 minutes. For the Reduced-Sample-FSIGT, S(I) was calculated based on the time points that appear in bold. Agreement was determined by Spearman correlation, concordance, and the Bland-Altman method. In addition, for both protocols, the population was divided into tertiles of S(I). Insulin resistance was defined by the lowest tertile of S(I) from the Full-Sample-IM-FSIGT. The distribution of subjects across tertiles was compared by rank order and kappa statistic. We found that the rate of failure of resolution of S(I) by the Reduced-Sample-IM-FSIGT was 3% (3/100). For the remaining 97 subjects, S(I) for the Full- and Reduced-Sample-IM-FSIGTs were as follows: 3.76 +/- 2.41 L mU(-1) min(-1) (range, 0.58-14.50) and 4.29 +/- 2.89 L mU(-1) min(-1) (range, 0.52-14.42); relative error, 21% +/- 18%; Spearman r = 0.97; and concordance, 0.94 (both P < .001). After log transformation, the Bland-Altman limits of agreement were -0.29 and 0.53. The exact agreement for distribution of the population in the insulin-resistant tertile vs the insulin-sensitive tertiles was 92%, kappa of 0.82 +/- 0.06. Using the nonlinear regression approach and data from the Reduced-Sample-IM-FSIGT in subjects with a wide range of insulin sensitivity, failure to resolve S(I) occurred in only 3% of subjects. The agreement and maintenance of rank order of S(I) between protocols support the use of the nonlinear regression approach to the minimal model and the Reduced-Sample-IM-FSIGT in clinical studies.

Nonlinear Flying Qualities Criteria for Large-Amplitude Maneuvers

DTIC Science & Technology

1984-12-01

theory which are pertinent to the formation of a nonlinear flying qualities methodology. This report surveys nonlinear system theory and describes...the development of an applied flying qualities methodology based on a canonical system theory and using research in relative controllability...The Nonlinear Flying Qualities (NFQ) for Large-Amplitude Maneuvers Program examined promising techniques from nonlinear analysis and nonlinear system

Active Learning to Understand Infectious Disease Models and Improve Policy Making

PubMed Central

Vladislavleva, Ekaterina; Broeckhove, Jan; Beutels, Philippe; Hens, Niel

2014-01-01

Modeling plays a major role in policy making, especially for infectious disease interventions but such models can be complex and computationally intensive. A more systematic exploration is needed to gain a thorough systems understanding. We present an active learning approach based on machine learning techniques as iterative surrogate modeling and model-guided experimentation to systematically analyze both common and edge manifestations of complex model runs. Symbolic regression is used for nonlinear response surface modeling with automatic feature selection. First, we illustrate our approach using an individual-based model for influenza vaccination. After optimizing the parameter space, we observe an inverse relationship between vaccination coverage and cumulative attack rate reinforced by herd immunity. Second, we demonstrate the use of surrogate modeling techniques on input-response data from a deterministic dynamic model, which was designed to explore the cost-effectiveness of varicella-zoster virus vaccination. We use symbolic regression to handle high dimensionality and correlated inputs and to identify the most influential variables. Provided insight is used to focus research, reduce dimensionality and decrease decision uncertainty. We conclude that active learning is needed to fully understand complex systems behavior. Surrogate models can be readily explored at no computational expense, and can also be used as emulator to improve rapid policy making in various settings. PMID:24743387

Active learning to understand infectious disease models and improve policy making.

PubMed

Willem, Lander; Stijven, Sean; Vladislavleva, Ekaterina; Broeckhove, Jan; Beutels, Philippe; Hens, Niel

2014-04-01

Modeling plays a major role in policy making, especially for infectious disease interventions but such models can be complex and computationally intensive. A more systematic exploration is needed to gain a thorough systems understanding. We present an active learning approach based on machine learning techniques as iterative surrogate modeling and model-guided experimentation to systematically analyze both common and edge manifestations of complex model runs. Symbolic regression is used for nonlinear response surface modeling with automatic feature selection. First, we illustrate our approach using an individual-based model for influenza vaccination. After optimizing the parameter space, we observe an inverse relationship between vaccination coverage and cumulative attack rate reinforced by herd immunity. Second, we demonstrate the use of surrogate modeling techniques on input-response data from a deterministic dynamic model, which was designed to explore the cost-effectiveness of varicella-zoster virus vaccination. We use symbolic regression to handle high dimensionality and correlated inputs and to identify the most influential variables. Provided insight is used to focus research, reduce dimensionality and decrease decision uncertainty. We conclude that active learning is needed to fully understand complex systems behavior. Surrogate models can be readily explored at no computational expense, and can also be used as emulator to improve rapid policy making in various settings.

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-01-15

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage

PubMed Central

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-01-01

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts. PMID:28773017

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage.

PubMed

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-06-16

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts.

QSRR modeling for diverse drugs using different feature selection methods coupled with linear and nonlinear regressions.

PubMed

Goodarzi, Mohammad; Jensen, Richard; Vander Heyden, Yvan

2012-12-01

A Quantitative Structure-Retention Relationship (QSRR) is proposed to estimate the chromatographic retention of 83 diverse drugs on a Unisphere poly butadiene (PBD) column, using isocratic elutions at pH 11.7. Previous work has generated QSRR models for them using Classification And Regression Trees (CART). In this work, Ant Colony Optimization is used as a feature selection method to find the best molecular descriptors from a large pool. In addition, several other selection methods have been applied, such as Genetic Algorithms, Stepwise Regression and the Relief method, not only to evaluate Ant Colony Optimization as a feature selection method but also to investigate its ability to find the important descriptors in QSRR. Multiple Linear Regression (MLR) and Support Vector Machines (SVMs) were applied as linear and nonlinear regression methods, respectively, giving excellent correlation between the experimental, i.e. extrapolated to a mobile phase consisting of pure water, and predicted logarithms of the retention factors of the drugs (logk(w)). The overall best model was the SVM one built using descriptors selected by ACO. Copyright © 2012 Elsevier B.V. All rights reserved.

Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations among Latent Variables

ERIC Educational Resources Information Center

Pek, Jolynn; Chalmers, R. Philip; Kok, Bethany E.; Losardo, Diane

2015-01-01

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…

INNOVATIVE INSTRUMENTATION AND ANALYSIS OF THE TEMPERATURE MEASUREMENT FOR HIGH TEMPERATURE GASIFICATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seong W. Lee

2004-10-01

The systematic tests of the gasifier simulator on the clean thermocouple were completed in this reporting period. Within the systematic tests on the clean thermocouple, five (5) factors were considered as the experimental parameters including air flow rate, water flow rate, fine dust particle amount, ammonia addition and high/low frequency device (electric motor). The fractional factorial design method was used in the experiment design with sixteen (16) data sets of readings. Analysis of Variances (ANOVA) was applied to the results from systematic tests. The ANOVA results show that the un-balanced motor vibration frequency did not have the significant impact onmore » the temperature changes in the gasifier simulator. For the fine dust particles testing, the amount of fine dust particles has significant impact to the temperature measurements in the gasifier simulator. The effects of the air and water on the temperature measurements show the same results as reported in the previous report. The ammonia concentration was included as an experimental parameter for the reducing environment in this reporting period. The ammonia concentration does not seem to be a significant factor on the temperature changes. The linear regression analysis was applied to the temperature reading with five (5) factors. The accuracy of the linear regression is relatively low, which is less than 10% accuracy. Nonlinear regression was also conducted to the temperature reading with the same factors. Since the experiments were designed in two (2) levels, the nonlinear regression is not very effective with the dataset (16 readings). An extra central point test was conducted. With the data of the center point testing, the accuracy of the nonlinear regression is much better than the linear regression.« less

Non-Linear Relationship between Economic Growth and CO2 Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models

PubMed Central

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-01-01

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO2 emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO2 emissions is significantly higher than those of GDPpc and Es on per capita CO2 emissions. PMID:29236083

Analysis of nonlinear relationships in dual epidemics, and its application to the management of grapevine downy and powdery mildews.

PubMed

Savary, Serge; Delbac, Lionel; Rochas, Amélie; Taisant, Guillaume; Willocquet, Laetitia

2009-08-01

Dual epidemics are defined as epidemics developing on two or several plant organs in the course of a cropping season. Agricultural pathosystems where such epidemics develop are often very important, because the harvestable part is one of the organs affected. These epidemics also are often difficult to manage, because the linkage between epidemiological components occurring on different organs is poorly understood, and because prediction of the risk toward the harvestable organs is difficult. In the case of downy mildew (DM) and powdery mildew (PM) of grapevine, nonlinear modeling and logistic regression indicated nonlinearity in the foliage-cluster relationships. Nonlinear modeling enabled the parameterization of a transmission coefficient that numerically links the two components, leaves and clusters, in DM and PM epidemics. Logistic regression analysis yielded a series of probabilistic models that enabled predicting preset levels of cluster infection risks based on DM and PM severities on the foliage at successive crop stages. The usefulness of this framework for tactical decision-making for disease control is discussed.

Non-Linear Relationship between Economic Growth and CO₂ Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models.

PubMed

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-12-13

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO₂ emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO₂ emissions is significantly higher than those of GDPpc and Es on per capita CO₂ emissions.

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals.

PubMed

Miniaci, M; Gliozzi, A S; Morvan, B; Krushynska, A; Bosia, F; Scalerandi, M; Pugno, N M

2017-05-26

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

Comparison of Sub-Pixel Classification Approaches for Crop-Specific Mapping

EPA Science Inventory

This paper examined two non-linear models, Multilayer Perceptron (MLP) regression and Regression Tree (RT), for estimating sub-pixel crop proportions using time-series MODIS-NDVI data. The sub-pixel proportions were estimated for three major crop types including corn, soybean, a...

Variable selection in near-infrared spectroscopy: benchmarking of feature selection methods on biodiesel data.

PubMed

Balabin, Roman M; Smirnov, Sergey V

2011-04-29

During the past several years, near-infrared (near-IR/NIR) spectroscopy has increasingly been adopted as an analytical tool in various fields from petroleum to biomedical sectors. The NIR spectrum (above 4000 cm(-1)) of a sample is typically measured by modern instruments at a few hundred of wavelengths. Recently, considerable effort has been directed towards developing procedures to identify variables (wavelengths) that contribute useful information. Variable selection (VS) or feature selection, also called frequency selection or wavelength selection, is a critical step in data analysis for vibrational spectroscopy (infrared, Raman, or NIRS). In this paper, we compare the performance of 16 different feature selection methods for the prediction of properties of biodiesel fuel, including density, viscosity, methanol content, and water concentration. The feature selection algorithms tested include stepwise multiple linear regression (MLR-step), interval partial least squares regression (iPLS), backward iPLS (BiPLS), forward iPLS (FiPLS), moving window partial least squares regression (MWPLS), (modified) changeable size moving window partial least squares (CSMWPLS/MCSMWPLSR), searching combination moving window partial least squares (SCMWPLS), successive projections algorithm (SPA), uninformative variable elimination (UVE, including UVE-SPA), simulated annealing (SA), back-propagation artificial neural networks (BP-ANN), Kohonen artificial neural network (K-ANN), and genetic algorithms (GAs, including GA-iPLS). Two linear techniques for calibration model building, namely multiple linear regression (MLR) and partial least squares regression/projection to latent structures (PLS/PLSR), are used for the evaluation of biofuel properties. A comparison with a non-linear calibration model, artificial neural networks (ANN-MLP), is also provided. Discussion of gasoline, ethanol-gasoline (bioethanol), and diesel fuel data is presented. The results of other spectroscopic techniques application, such as Raman, ultraviolet-visible (UV-vis), or nuclear magnetic resonance (NMR) spectroscopies, can be greatly improved by an appropriate feature selection choice. Copyright © 2011 Elsevier B.V. All rights reserved.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-11-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Application of Quasi-Linearization Techniques to Rail Vehicle Dynamic Analyses

DOT National Transportation Integrated Search

1978-11-01

The objective of the work reported here was to define methods for applying the describing function technique to realistic models of nonlinear rail cars. The describing function method offers a compromise between the accuracy of nonlinear digital simu...

Z-scan measurements using femtosecond continuum generation

NASA Astrophysics Data System (ADS)

de Boni, Leonardo; Andrade, Acácio A.; Misoguti, Lino; Mendonça, Cléber R.; Zilio, Sérgio Carlos

2004-08-01

We present a single beam Z-scan technique using an intense, broadband, white-light continuum (WLC) beam for the direct measurement of nonlinear absorption spectra. In order to demonstrate the validity of our technique, we compared the results of tetraaniline and Sudan 3 solutions obtained with WLC and conventional single wavelength light sources. Both approaches lead to the same nonlinear spectrum, indicating that the association of the Z-scan technique and the WLC source results in an useful method for the measurement of nonlinear spectra of both absorbing (saturable absorption or reverse saturable absorption) and transparent (two-photon absorption) samples.

System performance enhancement with pre-distorted OOFDM signal waveforms in DM/DD systems.

PubMed

Sánchez, C; Ortega, B; Capmany, J

2014-03-24

In this work we propose a pre-distortion technique for the mitigation of the nonlinear distortion present in directly modulated/detected OOFDM systems and explore the system performance achieved under varying system parameters. Simulation results show that the proposed pre-distortion technique efficiently mitigates the nonlinear distortion, achieving transmission information rates around 40 Gbits/s and 18.5 Gbits/s over 40 km and 100 km of single mode fiber links, respectively, under optimum operating conditions. Moreover, the proposed pre-distortion technique can potentially provide higher system performance to that obtained with nonlinear equalization at the receiver.

Single crystals and nonlinear process for outstanding vibration-powered electrical generators.

PubMed

Badel, Adrien; Benayad, Abdelmjid; Lefeuvre, Elie; Lebrun, Laurent; Richard, Claude; Guyomar, Daniel

2006-04-01

This paper compares the performances of vibration-powered electrical generators using a piezoelectric ceramic and a piezoelectric single crystal associated to several power conditioning circuits. A new approach of the piezoelectric power conversion based on a nonlinear voltage processing is presented, leading to three novel high performance power conditioning interfaces. Theoretical predictions and experimental results show that the nonlinear processing technique may increase the power harvested by a factor of 8 compared to standard techniques. Moreover, it is shown that, for a given energy harvesting technique, generators using single crystals deliver 20 times more power than generators using piezoelectric ceramics.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

PubMed Central

Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946

Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

PubMed

Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2016-04-12

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

Comparison of Random Forest and Parametric Imputation Models for Imputing Missing Data Using MICE: A CALIBER Study

PubMed Central

Shah, Anoop D.; Bartlett, Jonathan W.; Carpenter, James; Nicholas, Owen; Hemingway, Harry

2014-01-01

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The “true” imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001–2010) with complete data on all covariates. Variables were artificially made “missing at random,” and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data. PMID:24589914

Comparison of random forest and parametric imputation models for imputing missing data using MICE: a CALIBER study.

PubMed

Shah, Anoop D; Bartlett, Jonathan W; Carpenter, James; Nicholas, Owen; Hemingway, Harry

2014-03-15

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The "true" imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001-2010) with complete data on all covariates. Variables were artificially made "missing at random," and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data.

Thermally stimulated nonlinear refraction in gelatin stabilized Cu-PVP nanocomposite thin films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tamgadge, Y. S., E-mail: ystamgadge@gmail.com; Atkare, D. V.; Pahurkar, V. G.

2016-05-06

This article illustrates investigations on thermally stimulated third order nonlinear refraction of Cu-PVP nanocomposite thin films. Cu nanoparticles have been synthesized using chemical reduction method and thin films in PVP matrix have been obtained using spin coating technique. Thin films have been characterized by X-ray diffraction (XRD) and Ultraviolet-visible (UV-vis) spectroscopyfor structural and linear optical studies. Third order nonlinear refraction studies have been performed using closed aperture z-scan technique under continuous wave (CW) He-Ne laser. Cu-PVP nanocomposites are found to exhibit strong nonlinear refractive index stimulated by thermal lensing effect.

Mode-selective mapping and control of vectorial nonlinear-optical processes in multimode photonic-crystal fibers.

PubMed

Hu, Ming-Lie; Wang, Ching-Yue; Song, You-Jian; Li, Yan-Feng; Chai, Lu; Serebryannikov, Evgenii; Zheltikov, Aleksei

2006-02-06

We demonstrate an experimental technique that allows a mapping of vectorial nonlinear-optical processes in multimode photonic-crystal fibers (PCFs). Spatial and polarization modes of PCFs are selectively excited in this technique by varying the tilt angle of the input beam and rotating the polarization of the input field. Intensity spectra of the PCF output plotted as a function of the input field power and polarization then yield mode-resolved maps of nonlinear-optical interactions in multimode PCFs, facilitating the analysis and control of nonlinear-optical transformations of ultrashort laser pulses in such fibers.

Path-Following Solutions Of Nonlinear Equations

NASA Technical Reports Server (NTRS)

Barger, Raymond L.; Walters, Robert W.

1989-01-01

Report describes some path-following techniques for solution of nonlinear equations and compares with other methods. Use of multipurpose techniques applicable at more than one stage of path-following computation results in system relatively simple to understand, program, and use. Comparison of techniques with method of parametric differentiation (MPD) reveals definite advantages for path-following methods. Emphasis in investigation on multiuse techniques being applied at more than one stage of path-following computation. Incorporation of multipurpose techniques results in concise computer code relatively simple to use.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Baseband pulse shaping for pi /4 FQPSK in nonlinearly amplified mobile channels

NASA Astrophysics Data System (ADS)

Subasinghe-Dias, Dileeka; Feher, Kamilo

1994-10-01

We apply baseband pulse shaping techniques for pi /4 QPSK in order to reduce the spectral regeneration of the bandlimited carrier after nonlinear amplification. These Feher's patented techniques, namely, pi /4 FQPSK (superposed QPSK) and pi /4 CTPSK (controlled transition PSK), may also be noncoherently demodulated. Application of these techniques is in fast fading, power efficient channels, typical of the mobile radio environment. Patents related to FQPSK are described. Computer simulation and experimental studies demonstrate that with these baseband waveshaping techniques, carrier envelope fluctuations are significantly reduced, and the out-of-band power after nonlinear amplification is suppressed by up to 20 dB compared to pi /4 QPSK. In frequency noninterleaved land or satellite mobile radio systems operating in a nonlinear, fading and ACI (adjacent channel interference) environment, these techniques may achieve 20%-50% higher spectral efficiency compared to pi /4 QPSK. In mobile cellular systems using pi /4 QPSK, such as the new North American and the Japanese digital cellular systems, the application of these baseband pulse shapes may allow more convenient and less costly amplifier linearization.

Estimation of liver T₂ in transfusion-related iron overload in patients with weighted least squares T₂ IDEAL.

PubMed

Vasanawala, Shreyas S; Yu, Huanzhou; Shimakawa, Ann; Jeng, Michael; Brittain, Jean H

2012-01-01

MRI imaging of hepatic iron overload can be achieved by estimating T(2) values using multiple-echo sequences. The purpose of this work is to develop and clinically evaluate a weighted least squares algorithm based on T(2) Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) technique for volumetric estimation of hepatic T(2) in the setting of iron overload. The weighted least squares T(2) IDEAL technique improves T(2) estimation by automatically decreasing the impact of later, noise-dominated echoes. The technique was evaluated in 37 patients with iron overload. Each patient underwent (i) a standard 2D multiple-echo gradient echo sequence for T(2) assessment with nonlinear exponential fitting, and (ii) a 3D T(2) IDEAL technique, with and without a weighted least squares fit. Regression and Bland-Altman analysis demonstrated strong correlation between conventional 2D and T(2) IDEAL estimation. In cases of severe iron overload, T(2) IDEAL without weighted least squares reconstruction resulted in a relative overestimation of T(2) compared with weighted least squares. Copyright © 2011 Wiley-Liss, Inc.

Nonlinear Modeling of Joint Dominated Structures

NASA Technical Reports Server (NTRS)

Chapman, J. M.

1990-01-01

The development and verification of an accurate structural model of the nonlinear joint-dominated NASA Langley Mini-Mast truss are described. The approach is to characterize the structural behavior of the Mini-Mast joints and struts using a test configuration that can directly measure the struts' overall stiffness and damping properties, incorporate this data into the structural model using the residual force technique, and then compare the predicted response with empirical data taken by NASA/LaRC during the modal survey tests of the Mini-Mast. A new testing technique, referred to as 'link' testing, was developed and used to test prototype struts of the Mini-Masts. Appreciable nonlinearities including the free-play and hysteresis were demonstrated. Since static and dynamic tests performed on the Mini-Mast also exhibited behavior consistent with joints having free-play and hysteresis, nonlinear models of the Mini-Mast were constructed and analyzed. The Residual Force Technique was used to analyze the nonlinear model of the Mini-Mast having joint free-play and hysteresis.

Multipulse technique exploiting the intermodulation of ultrasound waves in a nonlinear medium.

PubMed

Biagi, Elena; Breschi, Luca; Vannacci, Enrico; Masotti, Leonardo

2009-03-01

In recent years, the nonlinear properties of materials have attracted much interest in nondestructive testing and in ultrasound diagnostic applications. Acoustic nonlinear parameters represent an opportunity to improve the information that can be extracted from a medium such as structural organization and pathologic status of tissue. In this paper, a method called pulse subtraction intermodulation (PSI), based on a multipulse technique, is presented and investigated both theoretically and experimentally. This method allows separation of the intermodulation products, which arise when 2 separate frequencies are transmitted in a nonlinear medium, from fundamental and second harmonic components, making them available for improved imaging techniques or signal processing algorithms devoted to tissue characterization. The theory of intermodulation product generation was developed according the Khokhlov-Zabolotskaya-Kuznetsov (KZK) nonlinear propagation equation, which is consistent with experimental results. The description of the proposed method, characterization of the intermodulation spectral contents, and quantitative results coming from in vitro experimentation are reported and discussed in this paper.

Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique.

PubMed

Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan

2009-01-01

The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.

Coherent source interaction, third-order nonlinear response of synthesized PEG coated magnetite nanoparticles in polyethylene glycol and its application

NASA Astrophysics Data System (ADS)

Gopal, S. Veena; Chitrambalam, S.; Joe, I. Hubert

2018-01-01

Third-order nonlinear response of synthesized polyethylene glycol coated Fe3O4 nanoparticles dispersed in a suitable solvent, polyethylene glycol has been studied. The structural characterization of the synthesized magnetite nanoparticles were carried out. The linear optical property of the synthesized magnetite nanoparticles was investigated using UV-visible technique. Both closed and open aperture Z-scan techniques have been performed at 532 nm with pulse width 5 ns and repetition rate 10 Hz. It was found that polyethylene glycol coated magnetite exhibits reverse saturable absorption, with significant nonlinear absorption coefficient. Two-photon absorption intensity dependent positive nonlinear refraction coefficients indicate self focusing phenomena. Results show that higher concentration gives better nonlinear and optical limiting properties.

Implementation of Nonlinear Control Laws for an Optical Delay Line

NASA Technical Reports Server (NTRS)

Hench, John J.; Lurie, Boris; Grogan, Robert; Johnson, Richard

2000-01-01

This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.

Multireference adaptive noise canceling applied to the EEG.

PubMed

James, C J; Hagan, M T; Jones, R D; Bones, P J; Carroll, G J

1997-08-01

The technique of multireference adaptive noise canceling (MRANC) is applied to enhance transient nonstationarities in the electroeancephalogram (EEG), with the adaptation implemented by means of a multilayer-perception artificial neural network (ANN). The method was applied to recorded EEG segments and the performance on documented nonstationarities recorded. The results show that the neural network (nonlinear) gives an improvement in performance (i.e., signal-to-noise ratio (SNR) of the nonstationarities) compared to a linear implementation of MRANC. In both cases an improvement in the SNR was obtained. The advantage of the spatial filtering aspect of MRANC is highlighted when the performance of MRANC is compared to that of the inverse auto-regressive filtering of the EEG, a purely temporal filter.

Residential magnetic fields predicted from wiring configurations: I. Exposure model.

PubMed

Bowman, J D; Thomas, D C; Jiang, L; Jiang, F; Peters, J M

1999-10-01

A physically based model for residential magnetic fields from electric transmission and distribution wiring was developed to reanalyze the Los Angeles study of childhood leukemia by London et al. For this exposure model, magnetic field measurements were fitted to a function of wire configuration attributes that was derived from a multipole expansion of the Law of Biot and Savart. The model parameters were determined by nonlinear regression techniques, using wiring data, distances, and the geometric mean of the ELF magnetic field magnitude from 24-h bedroom measurements taken at 288 homes during the epidemiologic study. The best fit to the measurement data was obtained with separate models for the two major utilities serving Los Angeles County. This model's predictions produced a correlation of 0.40 with the measured fields, an improvement on the 0.27 correlation obtained with the Wertheimer-Leeper (WL) wire code. For the leukemia risk analysis in a companion paper, the regression model predicts exposures to the 24-h geometric mean of the ELF magnetic fields in Los Angeles homes where only wiring data and distances have been obtained. Since these input parameters for the exposure model usually do not change for many years, the predicted magnetic fields will be stable over long time periods, just like the WL code. If the geometric mean is not the exposure metric associated with cancer, this regression technique could be used to estimate long-term exposures to temporal variability metrics and other characteristics of the ELF magnetic field which may be cancer risk factors.

Application of machine learning for the evaluation of turfgrass plots using aerial images

NASA Astrophysics Data System (ADS)

Ding, Ke; Raheja, Amar; Bhandari, Subodh; Green, Robert L.

2016-05-01

Historically, investigation of turfgrass characteristics have been limited to visual ratings. Although relevant information may result from such evaluations, final inferences may be questionable because of the subjective nature in which the data is collected. Recent advances in computer vision techniques allow researchers to objectively measure turfgrass characteristics such as percent ground cover, turf color, and turf quality from the digital images. This paper focuses on developing a methodology for automated assessment of turfgrass quality from aerial images. Images of several turfgrass plots of varying quality were gathered using a camera mounted on an unmanned aerial vehicle. The quality of these plots were also evaluated based on visual ratings. The goal was to use the aerial images to generate quality evaluations on a regular basis for the optimization of water treatment. Aerial images are used to train a neural network so that appropriate features such as intensity, color, and texture of the turfgrass are extracted from these images. Neural network is a nonlinear classifier commonly used in machine learning. The output of the neural network trained model is the ratings of the grass, which is compared to the visual ratings. Currently, the quality and the color of turfgrass, measured as the greenness of the grass, are evaluated. The textures are calculated using the Gabor filter and co-occurrence matrix. Other classifiers such as support vector machines and simpler linear regression models such as Ridge regression and LARS regression are also used. The performance of each model is compared. The results show encouraging potential for using machine learning techniques for the evaluation of turfgrass quality and color.

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape

PubMed Central

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables. PMID:29713298

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape.

PubMed

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables.

Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

NASA Astrophysics Data System (ADS)

Vasant, P.; Ganesan, T.; Elamvazuthi, I.

2012-11-01

A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.

Nonlinear system identification technique validation

NASA Astrophysics Data System (ADS)

Rudko, M.; Bussgang, J. J.

1982-01-01

This final technical report describes the results obtained by SIGNATRON, Inc. of Lexington MA on Air Force Contract F30602-80-C-0104 for Rome Air Development Center. The objective of this effort is to develop a technique for identifying system response of nonlinear circuits by measurements of output response to known inputs. The report describes results of a study into the system identification technique based on the pencil-of-function method previously explored by Jain (1974) and Ewen (1979). The procedure identified roles of the linear response and is intended as a first step in nonlinear response and is intended as a first step in nonlinear circuit identification. There are serious implementation problems associated with the original approach such as loss of accuracy due to repeated integrations, lack of good measures of accuracy and computational iteration to identify the number of poles.

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

NASA Technical Reports Server (NTRS)

Hague, D. S.; Merz, A. W.

1975-01-01

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Decision-feedback detection strategy for nonlinear frequency-division multiplexing

NASA Astrophysics Data System (ADS)

Civelli, Stella; Forestieri, Enrico; Secondini, Marco

2018-04-01

By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previously adopted techniques in terms of Q-factor. The obtained improvement demonstrates that, by tailoring the detection strategy to the peculiar properties of the nonlinear Fourier transform, it is possible to boost the performance of NFDM systems and overcome current limitations imposed by the use of more conventional detection techniques suitable for the linear regime.

Third-Order Optical Nonlinearities of Squarylium Dyes with Benzothiazole Donor Groups Measured Using the Picosecond Z-Scan Technique

NASA Astrophysics Data System (ADS)

Li, Zhong-Yu; Xu, Song; Chen, Zi-Hui; Zhang, Fu-Shi; Kasatani, Kazuo

2011-08-01

Third-order optical nonlinearities of two squarylium dyes with benzothiazole donor groups (BSQ1 and BSQ2) in chloroform solution are measured by a picosecond Z-scan technique at 532 nm. It is found that the two compounds show the saturation absorption and nonlinear self-focus refraction effect. The molecular second hyperpolarizabilities are calculated to be 7.46 × 10-31 esu and 5.01 × 10-30 esu for BSQ1 and BSQ2, respectively. The large optical nonlinearities of squarylium dyes can be attributed to their rigid and intramolecular charge transfer structure. The difference in γ values is attributed to the chloro group of benzene rings of BSQ2 and the one-photon resonance effect. It is found that the third-order nonlinear susceptibilities of two squarylium dyes are mainly determined by the real parts of χ(3), and the large optical nonlinearities of studied squarylium dyes can be attributed to the nonlinear refraction.

Synthesis of nanocomposites based on carbon nanotube/smart copolymer with nonlinear optical properties

NASA Astrophysics Data System (ADS)

Sousani, Abbas; Motiei, Hamideh; Najafimoghadam, Peyman; Hasanzade, Reza

2017-05-01

In this study new nanocompoites based on polyglycidylmethacrylate grafted 4-[(4-methoxyphenyl) diazenyl] phenol (Azo-PGMA) and Carboxylicacid functionalized multi-walled carbon nanotubes (MWCNT-COOH) were prepared. The nanocomposites structure was characterized by FT-IR, TGA and SEM. The Z-scan technique was applied for measuring the nonlinear parameters of nanocomposites. The samples after solving in AWM solution (equal ratio of acetone, deionized water and methanol) were investigated by using closed aperture Z-scan technique and a diode-pumped laser at the line 532 nm. All the nonlinear refractive index of the samples at three concentrations of carbon nanotubes in three different intensities of the laser beam were investigated and the nonlinear optical response of them are compared under the same condition. Because of high order of nonlinear refractive coefficient and good nonlinearity, these compounds are suitable candidate for optical switching, optical limiting and electro-optical devices.

Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays.

PubMed

Sánchez-Esquivel, Héctor; Raygoza-Sanchez, Karen Y; Rangel-Rojo, Raúl; Kalinic, Boris; Michieli, Niccolò; Cesca, Tiziana; Mattei, Giovanni

2018-03-15

In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.

Optical scatterometry of quarter-micron patterns using neural regression

NASA Astrophysics Data System (ADS)

Bischoff, Joerg; Bauer, Joachim J.; Haak, Ulrich; Hutschenreuther, Lutz; Truckenbrodt, Horst

1998-06-01

With shrinking dimensions and increasing chip areas, a rapid and non-destructive full wafer characterization after every patterning cycle is an inevitable necessity. In former publications it was shown that Optical Scatterometry (OS) has the potential to push the attainable feature limits of optical techniques from 0.8 . . . 0.5 microns for imaging methods down to 0.1 micron and below. Thus the demands of future metrology can be met. Basically being a nonimaging method, OS combines light scatter (or diffraction) measurements with modern data analysis schemes to solve the inverse scatter issue. For very fine patterns with lambda-to-pitch ratios grater than one, the specular reflected light versus the incidence angle is recorded. Usually, the data analysis comprises two steps -- a training cycle connected the a rigorous forward modeling and the prediction itself. Until now, two data analysis schemes are usually applied -- the multivariate regression based Partial Least Squares method (PLS) and a look-up-table technique which is also referred to as Minimum Mean Square Error approach (MMSE). Both methods are afflicted with serious drawbacks. On the one hand, the prediction accuracy of multivariate regression schemes degrades with larger parameter ranges due to the linearization properties of the method. On the other hand, look-up-table methods are rather time consuming during prediction thus prolonging the processing time and reducing the throughput. An alternate method is an Artificial Neural Network (ANN) based regression which combines the advantages of multivariate regression and MMSE. Due to the versatility of a neural network, not only can its structure be adapted more properly to the scatter problem, but also the nonlinearity of the neuronal transfer functions mimic the nonlinear behavior of optical diffraction processes more adequately. In spite of these pleasant properties, the prediction speed of ANN regression is comparable with that of the PLS-method. In this paper, the viability and performance of ANN-regression will be demonstrated with the example of sub-quarter-micron resist metrology. To this end, 0.25 micrometer line/space patterns have been printed in positive photoresist by means of DUV projection lithography. In order to evaluate the total metrology chain from light scatter measurement through data analysis, a thorough modeling has been performed. Assuming a trapezoidal shape of the developed resist profile, a training data set was generated by means of the Rigorous Coupled Wave Approach (RCWA). After training the model, a second data set was computed and deteriorated by Gaussian noise to imitate real measuring conditions. Then, these data have been fed into the models established before resulting in a Standard Error of Prediction (SEP) which corresponds to the measuring accuracy. Even with putting only little effort in the design of a back-propagation network, the ANN is clearly superior to the PLS-method. Depending on whether a network with one or two hidden layers was used, accuracy gains between 2 and 5 can be achieved compared with PLS regression. Furthermore, the ANN is less noise sensitive, for there is only a doubling of the SEP at 5% noise for ANN whereas for PLS the accuracy degrades rapidly with increasing noise. The accuracy gain also depends on the light polarization and on the measured parameters. Finally, these results have been proven experimentally, where the OS-results are in good accordance with the profiles obtained from cross- sectioning micrographs.

Parallel processors and nonlinear structural dynamics algorithms and software

NASA Technical Reports Server (NTRS)

Belytschko, Ted

1990-01-01

Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.

Order reduction, identification and localization studies of dynamical systems

NASA Astrophysics Data System (ADS)

Ma, Xianghong

In this thesis methods are developed for performing order reduction, system identification and induction of nonlinear localization in complex mechanical dynamic systems. General techniques are proposed for constructing low-order models of linear and nonlinear mechanical systems; in addition, novel mechanical designs are considered for inducing nonlinear localization phenomena for the purpose of enhancing their dynamical performance. The thesis is in three major parts. In the first part, the transient dynamics of an impulsively loaded multi-bay truss is numerically computed by employing the Direct Global Matrix (DGM) approach. The approach is applicable to large-scale flexible structures with periodicity. Karhunen-Loeve (K-L) decomposition is used to discretize the dynamics of the truss and to create the low-order models of the truss. The leading order K-L modes are recovered by an experiment, which shows the feasibility of K-L based order reduction technique. In the second part of the thesis, nonlinear localization in dynamical systems is studied through two applications. In the seismic base isolation study, it is shown that the dynamics are sensitive to the presence of nonlinear elements and that passive motion confinement can be induced under proper design. In the coupled rod system, numerical simulation of the transient dynamics shows that a nonlinear backlash spring can induce either nonlinear localization or delocalization in the form of beat phenomena. K-L decomposition and poincare maps are utilized to study the nonlinear effects. The study shows that nonlinear localization can be induced in complex structures through backlash. In the third and final part of the thesis, a new technique based on Green!s function method is proposed to identify the dynamics of practical bolted joints. By modeling the difference between the dynamics of the bolted structure and the corresponding unbolted one, one constructs a nonparametric model for the joint dynamics. Two applications are given with a bolted beam and a truss joint in order to show the applicability of the technique.

Separation of the low-frequency atmospheric variability into non-Gaussian multidimensional sources by Independent Subspace Analysis

NASA Astrophysics Data System (ADS)

Pires, Carlos; Ribeiro, Andreia

2016-04-01

An efficient nonlinear method of statistical source separation of space-distributed non-Gaussian distributed data is proposed. The method relies in the so called Independent Subspace Analysis (ISA), being tested on a long time-series of the stream-function field of an atmospheric quasi-geostrophic 3-level model (QG3) simulating the winter's monthly variability of the Northern Hemisphere. ISA generalizes the Independent Component Analysis (ICA) by looking for multidimensional and minimally dependent, uncorrelated and non-Gaussian distributed statistical sources among the rotated projections or subspaces of the multivariate probability distribution of the leading principal components of the working field whereas ICA restrict to scalar sources. The rationale of that technique relies upon the projection pursuit technique, looking for data projections of enhanced interest. In order to accomplish the decomposition, we maximize measures of the sources' non-Gaussianity by contrast functions which are given by squares of nonlinear, cross-cumulant-based correlations involving the variables spanning the sources. Therefore sources are sought matching certain nonlinear data structures. The maximized contrast function is built in such a way that it provides the minimization of the mean square of the residuals of certain nonlinear regressions. The issuing residuals, followed by spherization, provide a new set of nonlinear variable changes that are at once uncorrelated, quasi-independent and quasi-Gaussian, representing an advantage with respect to the Independent Components (scalar sources) obtained by ICA where the non-Gaussianity is concentrated into the non-Gaussian scalar sources. The new scalar sources obtained by the above process encompass the attractor's curvature thus providing improved nonlinear model indices of the low-frequency atmospheric variability which is useful since large circulation indices are nonlinearly correlated. The non-Gaussian tested sources (dyads and triads, respectively of two and three dimensions) lead to a dense data concentration along certain curves or surfaces, nearby which the clusters' centroids of the joint probability density function tend to be located. That favors a better splitting of the QG3 atmospheric model's weather regimes: the positive and negative phases of the Arctic Oscillation and positive and negative phases of the North Atlantic Oscillation. The leading model's non-Gaussian dyad is associated to a positive correlation between: 1) the squared anomaly of the extratropical jet-stream and 2) the meridional jet-stream meandering. Triadic sources coming from maximized third-order cross cumulants between pairwise uncorrelated components reveal situations of triadic wave resonance and nonlinear triadic teleconnections, only possible thanks to joint non-Gaussianity. That kind of triadic synergies are accounted for an Information-Theoretic measure: the Interaction Information. The dominant model's triad occurs between anomalies of: 1) the North Pole anomaly pressure 2) the jet-stream intensity at the Eastern North-American boundary and 3) the jet-stream intensity at the Eastern Asian boundary. Publication supported by project FCT UID/GEO/50019/2013 - Instituto Dom Luiz.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 2. Applications

USGS Publications Warehouse

Cooley, Richard L.

1983-01-01

This paper investigates factors influencing the degree of improvement in estimates of parameters of a nonlinear regression groundwater flow model by incorporating prior information of unknown reliability. Consideration of expected behavior of the regression solutions and results of a hypothetical modeling problem lead to several general conclusions. First, if the parameters are properly scaled, linearized expressions for the mean square error (MSE) in parameter estimates of a nonlinear model will often behave very nearly as if the model were linear. Second, by using prior information, the MSE in properly scaled parameters can be reduced greatly over the MSE of ordinary least squares estimates of parameters. Third, plots of estimated MSE and the estimated standard deviation of MSE versus an auxiliary parameter (the ridge parameter) specifying the degree of influence of the prior information on regression results can help determine the potential for improvement of parameter estimates. Fourth, proposed criteria can be used to make appropriate choices for the ridge parameter and another parameter expressing degree of overall bias in the prior information. Results of a case study of Truckee Meadows, Reno-Sparks area, Washoe County, Nevada, conform closely to the results of the hypothetical problem. In the Truckee Meadows case, incorporation of prior information did not greatly change the parameter estimates from those obtained by ordinary least squares. However, the analysis showed that both sets of estimates are more reliable than suggested by the standard errors from ordinary least squares.

Pointwise influence matrices for functional-response regression.

PubMed

Reiss, Philip T; Huang, Lei; Wu, Pei-Shien; Chen, Huaihou; Colcombe, Stan

2017-12-01

We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise influence matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor. This procedure adapts to varying complexity of the nonlinear model at different locations along the function, and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain. © 2017, The International Biometric Society.

Nonlinear association between betel quid chewing and oral cancer: Implications for prevention.

PubMed

Madathil, Sreenath Arekunnath; Rousseau, Marie-Claude; Wynant, Willy; Schlecht, Nicolas F; Netuveli, Gopalakrishnan; Franco, Eduardo L; Nicolau, Belinda

2016-09-01

Betel quid chewing is a major oral cancer risk factor and the human papillomaviruses (HPV) may play an aetiological role in these cancers. However, little is known about the shape of the dose-response relationship between the betel quid chewing habit and oral cancer risk in populations without HPV. We estimate the shape of this dose-response relationship, and discuss implications for prevention. Cases with oral squamous cell carcinoma (350) and non-cancer controls (371) were recruited from two major teaching hospitals in South India. Information on socio-demographic and behavioral factors was collected using a questionnaire and the life grid technique. The effect of daily amount of use and duration of the habit were estimated jointly as risk associated with cumulative exposure (chew-years). The shape of the dose-response curve was estimated using restricted cubic spline transformation of chew-years in a conditional logistic regression model. Risk estimates for low dose combinations of daily amount and duration of the habit were computed from flexible regression. Most (72%) oral cancer cases were betel quid chewers in contrast to only 18% of controls. A nonlinear dose-response relationship was observed; the risk increased steeply at low doses and plateaued at high exposures to betel quid (>425 chew-years). A threefold increase in risk (OR=3.92, 95%CI: 1.87-8.21) was observed for the lowest dose; equivalent to the use of one quid per day for one year. Our findings may be used to counsel people to refrain from even low betel quid chewing. Copyright © 2016 Elsevier Ltd. All rights reserved.

Comparative data mining analysis for information retrieval of MODIS images: monitoring lake turbidity changes at Lake Okeechobee, Florida

NASA Astrophysics Data System (ADS)

Chang, Ni-Bin; Daranpob, Ammarin; Yang, Y. Jeffrey; Jin, Kang-Ren

2009-09-01

In the remote sensing field, a frequently recurring question is: Which computational intelligence or data mining algorithms are most suitable for the retrieval of essential information given that most natural systems exhibit very high non-linearity. Among potential candidates might be empirical regression, neural network model, support vector machine, genetic algorithm/genetic programming, analytical equation, etc. This paper compares three types of data mining techniques, including multiple non-linear regression, artificial neural networks, and genetic programming, for estimating multi-temporal turbidity changes following hurricane events at Lake Okeechobee, Florida. This retrospective analysis aims to identify how the major hurricanes impacted the water quality management in 2003-2004. The Moderate Resolution Imaging Spectroradiometer (MODIS) Terra 8-day composite imageries were used to retrieve the spatial patterns of turbidity distributions for comparison against the visual patterns discernible in the in-situ observations. By evaluating four statistical parameters, the genetic programming model was finally selected as the most suitable data mining tool for classification in which the MODIS band 1 image and wind speed were recognized as the major determinants by the model. The multi-temporal turbidity maps generated before and after the major hurricane events in 2003-2004 showed that turbidity levels were substantially higher after hurricane episodes. The spatial patterns of turbidity confirm that sediment-laden water travels to the shore where it reduces the intensity of the light necessary to submerged plants for photosynthesis. This reduction results in substantial loss of biomass during the post-hurricane period.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. III - Perturbation theory

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1986-01-01

A technique to construct a uniformly valid perturbation series solution to a particular class of nonlinear difference equations is shown. The method allows the determination of approximations to the periodic solutions to these equations. An example illustrating the technique is presented.

The influence of and the identification of nonlinearity in flexible structures

NASA Technical Reports Server (NTRS)

Zavodney, Lawrence D.

1988-01-01

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models.

PubMed

Niroomandi, S; Alfaro, I; Cueto, E; Chinesta, F

2012-01-01

Model reduction techniques have shown to constitute a valuable tool for real-time simulation in surgical environments and other fields. However, some limitations, imposed by real-time constraints, have not yet been overcome. One of such limitations is the severe limitation in time (established in 500Hz of frequency for the resolution) that precludes the employ of Newton-like schemes for solving non-linear models as the ones usually employed for modeling biological tissues. In this work we present a technique able to deal with geometrically non-linear models, based on the employ of model reduction techniques, together with an efficient non-linear solver. Examples of the performance of the technique over some examples will be given. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Explaining Match Outcome During The Men’s Basketball Tournament at The Olympic Games

PubMed Central

Leicht, Anthony S.; Gómez, Miguel A.; Woods, Carl T.

2017-01-01

In preparation for the Olympics, there is a limited opportunity for coaches and athletes to interact regularly with team performance indicators providing important guidance to coaches for enhanced match success at the elite level. This study examined the relationship between match outcome and team performance indicators during men’s basketball tournaments at the Olympic Games. Twelve team performance indicators were collated from all men’s teams and matches during the basketball tournament of the 2004-2016 Olympic Games (n = 156). Linear and non-linear analyses examined the relationship between match outcome and team performance indicator characteristics; namely, binary logistic regression and a conditional interference (CI) classification tree. The most parsimonious logistic regression model retained ‘assists’, ‘defensive rebounds’, ‘field-goal percentage’, ‘fouls’, ‘fouls against’, ‘steals’ and ‘turnovers’ (delta AIC <0.01; Akaike weight = 0.28) with a classification accuracy of 85.5%. Conversely, four performance indicators were retained with the CI classification tree with an average classification accuracy of 81.4%. However, it was the combination of ‘field-goal percentage’ and ‘defensive rebounds’ that provided the greatest probability of winning (93.2%). Match outcome during the men’s basketball tournaments at the Olympic Games was identified by a unique combination of performance indicators. Despite the average model accuracy being marginally higher for the logistic regression analysis, the CI classification tree offered a greater practical utility for coaches through its resolution of non-linear phenomena to guide team success. Key points A unique combination of team performance indicators explained 93.2% of winning observations in men’s basketball at the Olympics. Monitoring of these team performance indicators may provide coaches with the capability to devise multiple game plans or strategies to enhance their likelihood of winning. Incorporation of machine learning techniques with team performance indicators may provide a valuable and strategic approach to explain patterns within multivariate datasets in sport science. PMID:29238245

Understanding Child Stunting in India: A Comprehensive Analysis of Socio-Economic, Nutritional and Environmental Determinants Using Additive Quantile Regression

PubMed Central

Fenske, Nora; Burns, Jacob; Hothorn, Torsten; Rehfuess, Eva A.

2013-01-01

Background Most attempts to address undernutrition, responsible for one third of global child deaths, have fallen behind expectations. This suggests that the assumptions underlying current modelling and intervention practices should be revisited. Objective We undertook a comprehensive analysis of the determinants of child stunting in India, and explored whether the established focus on linear effects of single risks is appropriate. Design Using cross-sectional data for children aged 0–24 months from the Indian National Family Health Survey for 2005/2006, we populated an evidence-based diagram of immediate, intermediate and underlying determinants of stunting. We modelled linear, non-linear, spatial and age-varying effects of these determinants using additive quantile regression for four quantiles of the Z-score of standardized height-for-age and logistic regression for stunting and severe stunting. Results At least one variable within each of eleven groups of determinants was significantly associated with height-for-age in the 35% Z-score quantile regression. The non-modifiable risk factors child age and sex, and the protective factors household wealth, maternal education and BMI showed the largest effects. Being a twin or multiple birth was associated with dramatically decreased height-for-age. Maternal age, maternal BMI, birth order and number of antenatal visits influenced child stunting in non-linear ways. Findings across the four quantile and two logistic regression models were largely comparable. Conclusions Our analysis confirms the multifactorial nature of child stunting. It emphasizes the need to pursue a systems-based approach and to consider non-linear effects, and suggests that differential effects across the height-for-age distribution do not play a major role. PMID:24223839

Understanding child stunting in India: a comprehensive analysis of socio-economic, nutritional and environmental determinants using additive quantile regression.

PubMed

Fenske, Nora; Burns, Jacob; Hothorn, Torsten; Rehfuess, Eva A

2013-01-01

Most attempts to address undernutrition, responsible for one third of global child deaths, have fallen behind expectations. This suggests that the assumptions underlying current modelling and intervention practices should be revisited. We undertook a comprehensive analysis of the determinants of child stunting in India, and explored whether the established focus on linear effects of single risks is appropriate. Using cross-sectional data for children aged 0-24 months from the Indian National Family Health Survey for 2005/2006, we populated an evidence-based diagram of immediate, intermediate and underlying determinants of stunting. We modelled linear, non-linear, spatial and age-varying effects of these determinants using additive quantile regression for four quantiles of the Z-score of standardized height-for-age and logistic regression for stunting and severe stunting. At least one variable within each of eleven groups of determinants was significantly associated with height-for-age in the 35% Z-score quantile regression. The non-modifiable risk factors child age and sex, and the protective factors household wealth, maternal education and BMI showed the largest effects. Being a twin or multiple birth was associated with dramatically decreased height-for-age. Maternal age, maternal BMI, birth order and number of antenatal visits influenced child stunting in non-linear ways. Findings across the four quantile and two logistic regression models were largely comparable. Our analysis confirms the multifactorial nature of child stunting. It emphasizes the need to pursue a systems-based approach and to consider non-linear effects, and suggests that differential effects across the height-for-age distribution do not play a major role.

An iterative hyperelastic parameters reconstruction for breast cancer assessment

NASA Astrophysics Data System (ADS)

Mehrabian, Hatef; Samani, Abbas

2008-03-01

In breast elastography, breast tissues usually undergo large compressions resulting in significant geometric and structural changes, and consequently nonlinear mechanical behavior. In this study, an elastography technique is presented where parameters characterizing tissue nonlinear behavior is reconstructed. Such parameters can be used for tumor tissue classification. To model the nonlinear behavior, tissues are treated as hyperelastic materials. The proposed technique uses a constrained iterative inversion method to reconstruct the tissue hyperelastic parameters. The reconstruction technique uses a nonlinear finite element (FE) model for solving the forward problem. In this research, we applied Yeoh and Polynomial models to model the tissue hyperelasticity. To mimic the breast geometry, we used a computational phantom, which comprises of a hemisphere connected to a cylinder. This phantom consists of two types of soft tissue to mimic adipose and fibroglandular tissues and a tumor. Simulation results show the feasibility of the proposed method in reconstructing the hyperelastic parameters of the tumor tissue.

Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

PubMed

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system.

PubMed

Zhang, Junfeng; Chen, Wei; Gao, Mingyi; Shen, Gangxiang

2017-10-30

In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Physicochemical and Nonlinear Optical Properties of Novel Environmentally Benign Heterocyclic Azomethine Dyes: Experimental and Theoretical Studies

PubMed Central

Afzal, S. M.; Razvi, M. A. N.; Khan, Salman A.; Osman, Osman I.; Bakry, Ahmed H.; Asiri, Abdullah M.

2016-01-01

Novel heterocyclic azomethine dyes were prepared by the reaction of anthracene-9-carbaldehyde with different heterocyclic amines under microwave irradiation. Structures of the azomethine dyes were confirmed by the elemental analysis, mass spectrometry and several spectroscopic techniques. We studied absorbance and fluorescence spectra of the azomethine dyes in various solvents. They are found to be good absorbers and emitters. We also report photophysical properties like, extinction coefficient, oscillator strength, stokes shift and transition dipole moment. This reflects physicochemical behaviors of synthesized dyes. In addition, their intramolecular charge transfer and nonlinear optical properties, supported by natural bond orbital technique, were also studied computationally by density functional theory. The negative nonlinear refractive index and nonlinear absorption coefficient were measured for these dyes using the closed and open aperture Z-scan technique with a continuous wave helium-neon laser. These are found to vary linearly with solution concentration. PMID:27631371

Minimizing bias in biomass allometry: Model selection and log transformation of data

Treesearch

Joseph Mascaro; undefined undefined; Flint Hughes; Amanda Uowolo; Stefan A. Schnitzer

2011-01-01

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the raditional approach of log-transformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models....

A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

2012-01-01

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

Logarithmic Transformations in Regression: Do You Transform Back Correctly?

ERIC Educational Resources Information Center

Dambolena, Ismael G.; Eriksen, Steven E.; Kopcso, David P.

2009-01-01

The logarithmic transformation is often used in regression analysis for a variety of purposes such as the linearization of a nonlinear relationship between two or more variables. We have noticed that when this transformation is applied to the response variable, the computation of the point estimate of the conditional mean of the original response…

Photonic single nonlinear-delay dynamical node for information processing

NASA Astrophysics Data System (ADS)

Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

2012-06-01

An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

PubMed

Brown, A M

2001-06-01

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

Regression Models and Fuzzy Logic Prediction of TBM Penetration Rate

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu; Katushin, Dmitri; Antonov, Maksim; Veinthal, Renno

2017-03-01

This paper presents statistical analyses of rock engineering properties and the measured penetration rate of tunnel boring machine (TBM) based on the data of an actual project. The aim of this study is to analyze the influence of rock engineering properties including uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), rock brittleness index (BI), the distance between planes of weakness (DPW), and the alpha angle (Alpha) between the tunnel axis and the planes of weakness on the TBM rate of penetration (ROP). Four (4) statistical regression models (two linear and two nonlinear) are built to predict the ROP of TBM. Finally a fuzzy logic model is developed as an alternative method and compared to the four statistical regression models. Results show that the fuzzy logic model provides better estimations and can be applied to predict the TBM performance. The R-squared value (R2) of the fuzzy logic model scores the highest value of 0.714 over the second runner-up of 0.667 from the multiple variables nonlinear regression model.

Multivariate meta-analysis for non-linear and other multi-parameter associations

PubMed Central

Gasparrini, A; Armstrong, B; Kenward, M G

2012-01-01

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22807043

Cocaine Dependence Treatment Data: Methods for Measurement Error Problems With Predictors Derived From Stationary Stochastic Processes

PubMed Central

Guan, Yongtao; Li, Yehua; Sinha, Rajita

2011-01-01

In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike classical measurement error problems, the error we encounter here is heteroscedastic with an unknown distribution, and there are no replicates for the error-prone variables or instrumental variables. We propose two robust methods to correct for the bias: a computationally efficient method-of-moments-based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models. Simulations and an application to the cocaine dependence treatment data are used to illustrate the efficacy of the proposed methods. Asymptotic theory and variance estimation for the proposed subsampling extrapolation method and some additional simulation results are described in the online supplementary material. PMID:21984854

Creep analysis of silicone for podiatry applications.

PubMed

Janeiro-Arocas, Julia; Tarrío-Saavedra, Javier; López-Beceiro, Jorge; Naya, Salvador; López-Canosa, Adrián; Heredia-García, Nicolás; Artiaga, Ramón

2016-10-01

This work shows an effective methodology to characterize the creep-recovery behavior of silicones before their application in podiatry. The aim is to characterize, model and compare the creep-recovery properties of different types of silicone used in podiatry orthotics. Creep-recovery phenomena of silicones used in podiatry orthotics is characterized by dynamic mechanical analysis (DMA). Silicones provided by Herbitas are compared by observing their viscoelastic properties by Functional Data Analysis (FDA) and nonlinear regression. The relationship between strain and time is modeled by fixed and mixed effects nonlinear regression to compare easily and intuitively podiatry silicones. Functional ANOVA and Kohlrausch-Willians-Watts (KWW) model with fixed and mixed effects allows us to compare different silicones observing the values of fitting parameters and their physical meaning. The differences between silicones are related to the variations of breadth of creep-recovery time distribution and instantaneous deformation-permanent strain. Nevertheless, the mean creep-relaxation time is the same for all the studied silicones. Silicones used in palliative orthoses have higher instantaneous deformation-permanent strain and narrower creep-recovery distribution. The proposed methodology based on DMA, FDA and nonlinear regression is an useful tool to characterize and choose the proper silicone for each podiatry application according to their viscoelastic properties. Copyright © 2016 Elsevier Ltd. All rights reserved.

The Multiple Correspondence Analysis Method and Brain Functional Connectivity: Its Application to the Study of the Non-linear Relationships of Motor Cortex and Basal Ganglia.

PubMed

Rodriguez-Sabate, Clara; Morales, Ingrid; Sanchez, Alberto; Rodriguez, Manuel

2017-01-01

The complexity of basal ganglia (BG) interactions is often condensed into simple models mainly based on animal data and that present BG in closed-loop cortico-subcortical circuits of excitatory/inhibitory pathways which analyze the incoming cortical data and return the processed information to the cortex. This study was aimed at identifying functional relationships in the BG motor-loop of 24 healthy-subjects who provided written, informed consent and whose BOLD-activity was recorded by MRI methods. The analysis of the functional interaction between these centers by correlation techniques and multiple linear regression showed non-linear relationships which cannot be suitably addressed with these methods. The multiple correspondence analysis (MCA), an unsupervised multivariable procedure which can identify non-linear interactions, was used to study the functional connectivity of BG when subjects were at rest. Linear methods showed different functional interactions expected according to current BG models. MCA showed additional functional interactions which were not evident when using lineal methods. Seven functional configurations of BG were identified with MCA, two involving the primary motor and somatosensory cortex, one involving the deepest BG (external-internal globus pallidum, subthalamic nucleus and substantia nigral), one with the input-output BG centers (putamen and motor thalamus), two linking the input-output centers with other BG (external pallidum and subthalamic nucleus), and one linking the external pallidum and the substantia nigral. The results provide evidence that the non-linear MCA and linear methods are complementary and should be best used in conjunction to more fully understand the nature of functional connectivity of brain centers.

Nonlinear behavior of the tarka flute's distinctive sounds.

PubMed

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Nonlinear behavior of the tarka flute's distinctive sounds

NASA Astrophysics Data System (ADS)

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Overcoming learning barriers through knowledge management.

PubMed

Dror, Itiel E; Makany, Tamas; Kemp, Jonathan

2011-02-01

The ability to learn highly depends on how knowledge is managed. Specifically, different techniques for note-taking utilize different cognitive processes and strategies. In this paper, we compared dyslexic and control participants when using linear and non-linear note-taking. All our participants were professionals working in the banking and financial sector. We examined comprehension, accuracy, mental imagery & complexity, metacognition, and memory. We found that participants with dyslexia, when using a non-linear note-taking technique outperformed the control group using linear note-taking and matched the performance of the control group using non-linear note-taking. These findings emphasize how different knowledge management techniques can avoid some of the barriers to learners. Copyright © 2010 John Wiley & Sons, Ltd.

A technique using a nonlinear helicopter model for determining trims and derivatives

NASA Technical Reports Server (NTRS)

Ostroff, A. J.; Downing, D. R.; Rood, W. J.

1976-01-01

A technique is described for determining the trims and quasi-static derivatives of a flight vehicle for use in a linear perturbation model; both the coupled and uncoupled forms of the linear perturbation model are included. Since this technique requires a nonlinear vehicle model, detailed equations with constants and nonlinear functions for the CH-47B tandem rotor helicopter are presented. Tables of trims and derivatives are included for airspeeds between -40 and 160 knots and rates of descent between + or - 10.16 m/sec (+ or - 200 ft/min). As a verification, the calculated and referenced values of comparable trims, derivatives, and linear model poles are shown to have acceptable agreement.

Using CART to Identify Thresholds and Hierarchies in the Determinants of Funding Decisions.

PubMed

Schilling, Chris; Mortimer, Duncan; Dalziel, Kim

2017-02-01

There is much interest in understanding decision-making processes that determine funding outcomes for health interventions. We use classification and regression trees (CART) to identify cost-effectiveness thresholds and hierarchies in the determinants of funding decisions. The hierarchical structure of CART is suited to analyzing complex conditional and nonlinear relationships. Our analysis uncovered hierarchies where interventions were grouped according to their type and objective. Cost-effectiveness thresholds varied markedly depending on which group the intervention belonged to: lifestyle-type interventions with a prevention objective had an incremental cost-effectiveness threshold of $2356, suggesting that such interventions need to be close to cost saving or dominant to be funded. For lifestyle-type interventions with a treatment objective, the threshold was much higher at $37,024. Lower down the tree, intervention attributes such as the level of patient contribution and the eligibility for government reimbursement influenced the likelihood of funding within groups of similar interventions. Comparison between our CART models and previously published results demonstrated concurrence with standard regression techniques while providing additional insights regarding the role of the funding environment and the structure of decision-maker preferences.

Application of a parameter-estimation technique to modeling the regional aquifer underlying the eastern Snake River plain, Idaho

USGS Publications Warehouse

Garabedian, Stephen P.

1986-01-01

A nonlinear, least-squares regression technique for the estimation of ground-water flow model parameters was applied to the regional aquifer underlying the eastern Snake River Plain, Idaho. The technique uses a computer program to simulate two-dimensional, steady-state ground-water flow. Hydrologic data for the 1980 water year were used to calculate recharge rates, boundary fluxes, and spring discharges. Ground-water use was estimated from irrigated land maps and crop consumptive-use figures. These estimates of ground-water withdrawal, recharge rates, and boundary flux, along with leakance, were used as known values in the model calibration of transmissivity. Leakance values were adjusted between regression solutions by comparing model-calculated to measured spring discharges. In other simulations, recharge and leakance also were calibrated as prior-information regression parameters, which limits the variation of these parameters using a normalized standard error of estimate. Results from a best-fit model indicate a wide areal range in transmissivity from about 0.05 to 44 feet squared per second and in leakance from about 2.2x10 -9 to 6.0 x 10 -8 feet per second per foot. Along with parameter values, model statistics also were calculated, including the coefficient of correlation between calculated and observed head (0.996), the standard error of the estimates for head (40 feet), and the parameter coefficients of variation (about 10-40 percent). Additional boundary flux was added in some areas during calibration to achieve proper fit to ground-water flow directions. Model fit improved significantly when areas that violated model assumptions were removed. It also improved slightly when y-direction (northwest-southeast) transmissivity values were larger than x-direction (northeast-southwest) transmissivity values. The model was most sensitive to changes in recharge, and in some areas, to changes in transmissivity, particularly near the spring discharge area from Milner Dam to King Hill.

Combining macula clinical signs and patient characteristics for age-related macular degeneration diagnosis: a machine learning approach.

PubMed

Fraccaro, Paolo; Nicolo, Massimo; Bonetto, Monica; Giacomini, Mauro; Weller, Peter; Traverso, Carlo Enrico; Prosperi, Mattia; OSullivan, Dympna

2015-01-27

To investigate machine learning methods, ranging from simpler interpretable techniques to complex (non-linear) "black-box" approaches, for automated diagnosis of Age-related Macular Degeneration (AMD). Data from healthy subjects and patients diagnosed with AMD or other retinal diseases were collected during routine visits via an Electronic Health Record (EHR) system. Patients' attributes included demographics and, for each eye, presence/absence of major AMD-related clinical signs (soft drusen, retinal pigment epitelium, defects/pigment mottling, depigmentation area, subretinal haemorrhage, subretinal fluid, macula thickness, macular scar, subretinal fibrosis). Interpretable techniques known as white box methods including logistic regression and decision trees as well as less interpreitable techniques known as black box methods, such as support vector machines (SVM), random forests and AdaBoost, were used to develop models (trained and validated on unseen data) to diagnose AMD. The gold standard was confirmed diagnosis of AMD by physicians. Sensitivity, specificity and area under the receiver operating characteristic (AUC) were used to assess performance. Study population included 487 patients (912 eyes). In terms of AUC, random forests, logistic regression and adaboost showed a mean performance of (0.92), followed by SVM and decision trees (0.90). All machine learning models identified soft drusen and age as the most discriminating variables in clinicians' decision pathways to diagnose AMD. Both black-box and white box methods performed well in identifying diagnoses of AMD and their decision pathways. Machine learning models developed through the proposed approach, relying on clinical signs identified by retinal specialists, could be embedded into EHR to provide physicians with real time (interpretable) support.

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

ERIC Educational Resources Information Center

Mooijaart, Ab; Satorra, Albert

2009-01-01

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…

Nonlinear Simulation of the Tooth Enamel Spectrum for EPR Dosimetry

NASA Astrophysics Data System (ADS)

Kirillov, V. A.; Dubovsky, S. V.

2016-07-01

Software was developed where initial EPR spectra of tooth enamel were deconvoluted based on nonlinear simulation, line shapes and signal amplitudes in the model initial spectrum were calculated, the regression coefficient was evaluated, and individual spectra were summed. Software validation demonstrated that doses calculated using it agreed excellently with the applied radiation doses and the doses reconstructed by the method of additive doses.

Technique for Very High Order Nonlinear Simulation and Validation

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2001-01-01

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

Investigation of contact acoustic nonlinearities on metal and composite airframe structures via intensity based health monitoring.

PubMed

Romano, P Q; Conlon, S C; Smith, E C

2013-01-01

Nonlinear structural intensity (NSI) and nonlinear structural surface intensity (NSSI) based damage detection techniques were improved and extended to metal and composite airframe structures. In this study, the measurement of NSI maps at sub-harmonic frequencies was completed to provide enhanced understanding of the energy flow characteristics associated with the damage induced contact acoustic nonlinearity mechanism. Important results include NSI source localization visualization at ultra-subharmonic (nf/2) frequencies, and damage detection results utilizing structural surface intensity in the nonlinear domain. A detection metric relying on modulated wave spectroscopy was developed and implemented using the NSSI feature. The data fusion of the intensity formulation provided a distinct advantage, as both the single interrogation frequency NSSI and its modulated wave extension (NSSI-MW) exhibited considerably higher sensitivities to damage than using single-sensor (strain or acceleration) nonlinear detection metrics. The active intensity based techniques were also extended to composite materials, and results show both NSSI and NSSI-MW can be used to detect damage in the bond line of an integrally stiffened composite plate structure with high sensitivity. Initial damage detection measurements made on an OH-58 tailboom (Penn State Applied Research Laboratory, State College, PA) indicate the techniques can be transitioned to complex airframe structures achieving high detection sensitivities with minimal sensors and actuators.

Measurement of large nonlinear refractive index of natural pigment extracted from Hibiscus rosa-sinensis leaves with a low power CW laser and by spatial self-phase modulation technique

NASA Astrophysics Data System (ADS)

Biswas, S.; Kumbhakar, P.

2017-02-01

We have reported here, for the first time, to the best of our knowledge, a high nonlinear refractive index (n2e) of a natural pigment extracted from Hibiscus rosa-sinensis leaves by using spatial self-phase modulation technique (SSPM) with a low power CW He-Ne laser radiation at 632.8 nm. It is found by UV-Vis absorption spectroscopic analysis that chlrophyll-a, chlrophyll-b and carotenoid are present in the pigment extract with 56%, 25% and 19%, respectively. The photoluminescence (PL) emission characteristics of the extracted samples have also been measured at room temperature as well as in the temperature range of 283-333 K to investigate the effect of temperature on luminescent properties of the sample. By analyzing the SSPM experimental data, the nonlinear refractive index value of pigment extract has been determined to be 3.5 × 10- 5 cm2/W. The large nonlinear refractive index has been assigned due to asymmetrical structure, molecular reorientation and thermally induced nonlinearity in the sample. The presented results might open new avenues for the green and economical technique of syntheses of organic dyes with such a large nonlinear optical property.

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

Non-linearities in Theory-of-Mind Development.

PubMed

Blijd-Hoogewys, Els M A; van Geert, Paul L C

2016-01-01

Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.

Non-linearities in Theory-of-Mind Development

PubMed Central

Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.

2017-01-01

Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72–78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths. PMID:28101065

A system of nonlinear set valued variational inclusions.

PubMed

Tang, Yong-Kun; Chang, Shih-Sen; Salahuddin, Salahuddin

2014-01-01

In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved. 49J40; 47H06.

Synthesis of nonlinear control strategies from fuzzy logic control algorithms

NASA Technical Reports Server (NTRS)

Langari, Reza

1993-01-01

Fuzzy control has been recognized as an alternative to conventional control techniques in situations where the plant model is not sufficiently well known to warrant the application of conventional control techniques. Precisely what fuzzy control does and how it does what it does is not quite clear, however. This important issue is discussed and in particular it is shown how a given fuzzy control scheme can resolve into a nonlinear control law and that in those situations the success of fuzzy control hinges on its ability to compensate for nonlinearities in plant dynamics.

Crystal growth, piezoelectric, non-linear optical and mechanical properties of lithium hydrogen oxalate monohydrate single crystal

NASA Astrophysics Data System (ADS)

Chandran, Senthilkumar; Paulraj, Rajesh; Ramasamy, P.

2017-05-01

Semi-organic lithium hydrogen oxalate monohydrate non-linear optical single crystals have been grown by slow evaporation solution growth technique at 35 °C. Single crystal X-ray diffraction study showed that the grown crystal belongs to the triclinic system with space group P1. The mechanical strength decreases with increasing load. The piezoelectric coefficient is found to be 1.41 pC/N. The nonlinear optical property was measured using Kurtz Perry powder technique and SHG efficiency was almost equal to that of KDP.

Evaluation of confidence intervals for a steady-state leaky aquifer model

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

1999-01-01

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. and Cooley, R.L., Water Resources Research, 1987, 23(7), 1237-1250] was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.

Advanced Statistical Analyses to Reduce Inconsistency of Bond Strength Data.

PubMed

Minamino, T; Mine, A; Shintani, A; Higashi, M; Kawaguchi-Uemura, A; Kabetani, T; Hagino, R; Imai, D; Tajiri, Y; Matsumoto, M; Yatani, H

2017-11-01

This study was designed to clarify the interrelationship of factors that affect the value of microtensile bond strength (µTBS), focusing on nondestructive testing by which information of the specimens can be stored and quantified. µTBS test specimens were prepared from 10 noncarious human molars. Six factors of µTBS test specimens were evaluated: presence of voids at the interface, X-ray absorption coefficient of resin, X-ray absorption coefficient of dentin, length of dentin part, size of adhesion area, and individual differences of teeth. All specimens were observed nondestructively by optical coherence tomography and micro-computed tomography before µTBS testing. After µTBS testing, the effect of these factors on µTBS data was analyzed by the general linear model, linear mixed effects regression model, and nonlinear regression model with 95% confidence intervals. By the general linear model, a significant difference in individual differences of teeth was observed ( P < 0.001). A significantly positive correlation was shown between µTBS and length of dentin part ( P < 0.001); however, there was no significant nonlinearity ( P = 0.157). Moreover, a significantly negative correlation was observed between µTBS and size of adhesion area ( P = 0.001), with significant nonlinearity ( P = 0.014). No correlation was observed between µTBS and X-ray absorption coefficient of resin ( P = 0.147), and there was no significant nonlinearity ( P = 0.089). Additionally, a significantly positive correlation was observed between µTBS and X-ray absorption coefficient of dentin ( P = 0.022), with significant nonlinearity ( P = 0.036). A significant difference was also observed between the presence and absence of voids by linear mixed effects regression analysis. Our results showed correlations between various parameters of tooth specimens and µTBS data. To evaluate the performance of the adhesive more precisely, the effect of tooth variability and a method to reduce variation in bond strength values should also be considered.

Application of two neural network paradigms to the study of voluntary employee turnover.

PubMed

Somers, M J

1999-04-01

Two neural network paradigms--multilayer perceptron and learning vector quantization--were used to study voluntary employee turnover with a sample of 577 hospital employees. The objectives of the study were twofold. The 1st was to assess whether neural computing techniques offered greater predictive accuracy than did conventional turnover methodologies. The 2nd was to explore whether computer models of turnover based on neural network technologies offered new insights into turnover processes. When compared with logistic regression analysis, both neural network paradigms provided considerably more accurate predictions of turnover behavior, particularly with respect to the correct classification of leavers. In addition, these neural network paradigms captured nonlinear relationships that are relevant for theory development. Results are discussed in terms of their implications for future research.

From linear mechanics to nonlinear mechanics

NASA Technical Reports Server (NTRS)

Loeb, Julian

1955-01-01

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Frequency-domain nonlinear regression algorithm for spectral analysis of broadband SFG spectroscopy.

PubMed

He, Yuhan; Wang, Ying; Wang, Jingjing; Guo, Wei; Wang, Zhaohui

2016-03-01

The resonant spectral bands of the broadband sum frequency generation (BB-SFG) spectra are often distorted by the nonresonant portion and the lineshapes of the laser pulses. Frequency domain nonlinear regression (FDNLR) algorithm was proposed to retrieve the first-order polarization induced by the infrared pulse and to improve the analysis of SFG spectra through simultaneous fitting of a series of time-resolved BB-SFG spectra. The principle of FDNLR was presented, and the validity and reliability were tested by the analysis of the virtual and measured SFG spectra. The relative phase, dephasing time, and lineshapes of the resonant vibrational SFG bands can be retrieved without any preset assumptions about the SFG bands and the incident laser pulses.

Application of General Regression Neural Network to the Prediction of LOD Change

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Hong; Wang, Qi-Jie; Zhu, Jian-Jun; Zhang, Hao

2012-01-01

Traditional methods for predicting the change in length of day (LOD change) are mainly based on some linear models, such as the least square model and autoregression model, etc. However, the LOD change comprises complicated non-linear factors and the prediction effect of the linear models is always not so ideal. Thus, a kind of non-linear neural network — general regression neural network (GRNN) model is tried to make the prediction of the LOD change and the result is compared with the predicted results obtained by taking advantage of the BP (back propagation) neural network model and other models. The comparison result shows that the application of the GRNN to the prediction of the LOD change is highly effective and feasible.

A constructive nonlinear array (CNA) method for barely visible impact detection in composite materials

NASA Astrophysics Data System (ADS)

Malfense Fierro, Gian Piero; Meo, Michele

2017-04-01

Currently there are numerous phased array techniques such as Full Matrix Capture (FMC) and Total Focusing Method (TFM) that provide good damage assessment for composite materials. Although, linear methods struggle to evaluate and assess low levels of damage, while nonlinear methods have shown great promise in early damage detection. A sweep and subtraction evaluation method coupled with a constructive nonlinear array method (CNA) is proposed in order to assess damage specific nonlinearities, address issues with frequency selection when using nonlinear ultrasound imaging techniques and reduce equipment generated nonlinearities. These methods were evaluated using multiple excitation locations on an impacted composite panel with a complex damage (barely visible impact damage). According to various recent works, damage excitation can be accentuated by exciting at local defect resonance (LDR) frequencies; although these frequencies are not always easily determinable. The sweep methodology uses broadband excitation to determine both local defect and material resonances, by assessing local defect generated nonlinearities using a laser vibrometer it is possible to assess which frequencies excite the complex geometry of the crack. The dual effect of accurately determining local defect resonances, the use of an image subtraction method and the reduction of equipment based nonlinearities using CNA result in greater repeatability and clearer nonlinear imaging (NIM).

Anticipating Mathematics Performance: A Cross-Validation Comparison of AID3 and Regression. AIR 1988 Annual Forum Paper.

ERIC Educational Resources Information Center

Bloom, Allan M.; And Others

In response to the increasing importance of student performance in required classes, research was conducted to compare two prediction procedures, linear modeling using multiple regression and nonlinear modeling using AID3. Performance in the first college math course (College Mathematics, Calculus, or Business Calculus Matrices) was the dependent…

Modeling maximum daily temperature using a varying coefficient regression model

Treesearch

Han Li; Xinwei Deng; Dong-Yum Kim; Eric P. Smith

2014-01-01

Relationships between stream water and air temperatures are often modeled using linear or nonlinear regression methods. Despite a strong relationship between water and air temperatures and a variety of models that are effective for data summarized on a weekly basis, such models did not yield consistently good predictions for summaries such as daily maximum temperature...

Three-photon absorption and nonlinear refraction of BaMgF4 in the ultraviolet region.

PubMed

Ma, Yanzhi; Chen, Junjie; Zheng, Yuanlin; Chen, Xianfeng

2012-08-01

The nonlinear refraction and nonlinear absorption phenomena are investigated in BaMgF(4) single crystal using the Z-scan technique in the ultraviolet region with a pulsed laser at 400 nm with 1 ps pulse duration. The remarkable nonlinear absorption behavior is identified to be three-photon absorption under the experimental conditions. In addition, both nonlinear refraction and nonlinear absorption have relatively large values and possess small anisotropy along three different crystallographic axes. The large values of nonlinear refractive index are demonstrated through the self-phase modulation effect.

Naval Research Logistics Quarterly. Volume 28. Number 3,

DTIC Science & Technology

1981-09-01

denotes component-wise maximum. f has antone (isotone) differences on C x D if for cl < c2 and d, < d2, NAVAL RESEARCH LOGISTICS QUARTERLY VOL. 28...or negative correlations and linear or nonlinear regressions. Given are the mo- ments to order two and, for special cases, (he regression function and...data sets. We designate this bnb distribution as G - B - N(a, 0, v). The distribution admits only of positive correlation and linear regressions

A Bayesian methodological framework for accommodating interannual variability of nutrient loading with the SPARROW model

NASA Astrophysics Data System (ADS)

Wellen, Christopher; Arhonditsis, George B.; Labencki, Tanya; Boyd, Duncan

2012-10-01

Regression-type, hybrid empirical/process-based models (e.g., SPARROW, PolFlow) have assumed a prominent role in efforts to estimate the sources and transport of nutrient pollution at river basin scales. However, almost no attempts have been made to explicitly accommodate interannual nutrient loading variability in their structure, despite empirical and theoretical evidence indicating that the associated source/sink processes are quite variable at annual timescales. In this study, we present two methodological approaches to accommodate interannual variability with the Spatially Referenced Regressions on Watershed attributes (SPARROW) nonlinear regression model. The first strategy uses the SPARROW model to estimate a static baseline load and climatic variables (e.g., precipitation) to drive the interannual variability. The second approach allows the source/sink processes within the SPARROW model to vary at annual timescales using dynamic parameter estimation techniques akin to those used in dynamic linear models. Model parameterization is founded upon Bayesian inference techniques that explicitly consider calibration data and model uncertainty. Our case study is the Hamilton Harbor watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. Our analysis suggests that dynamic parameter estimation is the more parsimonious of the two strategies tested and can offer insights into the temporal structural changes associated with watershed functioning. Consistent with empirical and theoretical work, model estimated annual in-stream attenuation rates varied inversely with annual discharge. Estimated phosphorus source areas were concentrated near the receiving water body during years of high in-stream attenuation and dispersed along the main stems of the streams during years of low attenuation, suggesting that nutrient source areas are subject to interannual variability.

Nonlinear damage detection in composite structures using bispectral analysis

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele

2014-03-01

Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.

Numerical techniques for solving nonlinear instability problems in smokeless tactical solid rocket motors. [finite difference technique

NASA Technical Reports Server (NTRS)

Baum, J. D.; Levine, J. N.

1980-01-01

The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.

Advances in nonlinear optical materials and devices

NASA Technical Reports Server (NTRS)

Byer, Robert L.

1991-01-01

The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Boosting structured additive quantile regression for longitudinal childhood obesity data.

PubMed

Fenske, Nora; Fahrmeir, Ludwig; Hothorn, Torsten; Rzehak, Peter; Höhle, Michael

2013-07-25

Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.

A hybrid artificial neural network as a software sensor for optimal control of a wastewater treatment process.

PubMed

Choi, D J; Park, H

2001-11-01

For control and automation of biological treatment processes, lack of reliable on-line sensors to measure water quality parameters is one of the most important problems to overcome. Many parameters cannot be measured directly with on-line sensors. The accuracy of existing hardware sensors is also not sufficient and maintenance problems such as electrode fouling often cause trouble. This paper deals with the development of software sensor techniques that estimate the target water quality parameter from other parameters using the correlation between water quality parameters. We focus our attention on the preprocessing of noisy data and the selection of the best model feasible to the situation. Problems of existing approaches are also discussed. We propose a hybrid neural network as a software sensor inferring wastewater quality parameter. Multivariate regression, artificial neural networks (ANN), and a hybrid technique that combines principal component analysis as a preprocessing stage are applied to data from industrial wastewater processes. The hybrid ANN technique shows an enhancement of prediction capability and reduces the overfitting problem of neural networks. The result shows that the hybrid ANN technique can be used to extract information from noisy data and to describe the nonlinearity of complex wastewater treatment processes.

Tuning the nonlinear optical absorption in Au/BaTiO3 nanocomposites with gold nanoparticle concentration

NASA Astrophysics Data System (ADS)

Bijeesh, M. M.; Shakhi, P. K.; Varier, Geetha K.; Nandakumar, P.

2018-06-01

We report on the nonlinear optical absorption coefficient of Au/BaTiO3 nanocomposite films and its dependence on gold nanoparticle concentration. Au/BaTiO3 nanocomposite films with different molar ratio of Au/Ba are prepared by sol-gel technique and characterized by X-ray diffraction, UV Visible absorption spectroscopy and high resolution transmission electron microscopy. An open aperture Z-scan technique is employed to study the third order nonlinear optical properties of Au/BaTiO3 thin films. An Nd:YAG laser operating at 532 nm wavelength having a pulse width of 5 ns is used for the measurements. The two-photon absorption coefficient of the films increases linearly with gold nanoparticle concentration and significant enhancement of nonlinear optical absorption is observed. This ability to fine tune the nonlinear optical coefficients of Au/BaTiO3 films would be handy in optical device applications.

Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT

NASA Technical Reports Server (NTRS)

Trumper, David L.

1991-01-01

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.

Experimental evaluation of HJB optimal controllers for the attitude dynamics of a multirotor aerial vehicle.

PubMed

Prado, Igor Afonso Acampora; Pereira, Mateus de Freitas Virgílio; de Castro, Davi Ferreira; Dos Santos, Davi Antônio; Balthazar, Jose Manoel

2018-06-01

The present paper is concerned with the design and experimental evaluation of optimal control laws for the nonlinear attitude dynamics of a multirotor aerial vehicle. Three design methods based on Hamilton-Jacobi-Bellman equation are taken into account. The first one is a linear control with guarantee of stability for nonlinear systems. The second and third are a nonlinear suboptimal control techniques. These techniques are based on an optimal control design approach that takes into account the nonlinearities present in the vehicle dynamics. The stability Proof of the closed-loop system is presented. The performance of the control system designed is evaluated via simulations and also via an experimental scheme using the Quanser 3-DOF Hover. The experiments show the effectiveness of the linear control method over the nonlinear strategy. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

NASA Astrophysics Data System (ADS)

Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

2018-02-01

In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements

NASA Astrophysics Data System (ADS)

Kougioumtzoglou, Ioannis A.; dos Santos, Ketson R. M.; Comerford, Liam

2017-09-01

Various system identification techniques exist in the literature that can handle non-stationary measured time-histories, or cases of incomplete data, or address systems following a fractional calculus modeling. However, there are not many (if any) techniques that can address all three aforementioned challenges simultaneously in a consistent manner. In this paper, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. Several linear and nonlinear time-variant systems with fractional derivative elements are used as numerical examples to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

[Relationship between shift work and overweight/obesity in male steel workers].

PubMed

Xiao, M Y; Wang, Z Y; Fan, H M; Che, C L; Lu, Y; Cong, L X; Gao, X J; Liu, Y J; Yuan, J X; Li, X M; Hu, B; Chen, Y P

2016-11-10

Objective: To investigate the relationship between shift work and overweight/obesity in male steel workers. Methods: A questionnaire survey was conducted among the male steel workers selected during health examination in Tangshan Steel Company from March 2015 to March 2016. The relationship between shift work and overweight/obesity in the male steel workers were analyzed by using logistic regression model and restricted cubic splinemodel. Results: A total of 7 262 male steel workers were surveyed, the overall prevalence of overweight/obesitywas 64.5% (4 686/7 262), the overweight rate was 34.3% and the obesity rate was 30.2%, respectively. After adjusting for age, educational level and average family income level per month by multivariable logistic regression analysis, shift work was associated with overweight/obesity and obesity in the male steel workers. The OR was 1.19(95% CI : 1.05-1.35) and 1.15(95% CI : 1.00-1.32). Restricted cubic spline model analysis showed that the relationship between shift work years and overweight/obesity in the male steel workers was a nonlinear dose response one (nonlinear test χ 2 =7.43, P <0.05). Restricted cubic spline model analysis showed that the relationship between shift work years and obesity in the male steel workers was a nonlinear dose response one (nonlinear test χ 2 =10.48, P <0.05). Conclusion: Shift work was associated with overweight and obesity in the male steel workers, and shift work years and overweight/obesity had a nonlinear relationship.

Twist Model Development and Results from the Active Aeroelastic Wing F/A-18 Aircraft

NASA Technical Reports Server (NTRS)

Lizotte, Andrew M.; Allen, Michael J.

2007-01-01

Understanding the wing twist of the active aeroelastic wing (AAW) F/A-18 aircraft is a fundamental research objective for the program and offers numerous benefits. In order to clearly understand the wing flexibility characteristics, a model was created to predict real-time wing twist. A reliable twist model allows the prediction of twist for flight simulation, provides insight into aircraft performance uncertainties, and assists with computational fluid dynamic and aeroelastic issues. The left wing of the aircraft was heavily instrumented during the first phase of the active aeroelastic wing program allowing deflection data collection. Traditional data processing steps were taken to reduce flight data, and twist predictions were made using linear regression techniques. The model predictions determined a consistent linear relationship between the measured twist and aircraft parameters, such as surface positions and aircraft state variables. Error in the original model was reduced in some cases by using a dynamic pressure-based assumption. This technique produced excellent predictions for flight between the standard test points and accounted for nonlinearities in the data. This report discusses data processing techniques and twist prediction validation, and provides illustrative and quantitative results.

Twist Model Development and Results From the Active Aeroelastic Wing F/A-18 Aircraft

NASA Technical Reports Server (NTRS)

Lizotte, Andrew; Allen, Michael J.

2005-01-01

Understanding the wing twist of the active aeroelastic wing F/A-18 aircraft is a fundamental research objective for the program and offers numerous benefits. In order to clearly understand the wing flexibility characteristics, a model was created to predict real-time wing twist. A reliable twist model allows the prediction of twist for flight simulation, provides insight into aircraft performance uncertainties, and assists with computational fluid dynamic and aeroelastic issues. The left wing of the aircraft was heavily instrumented during the first phase of the active aeroelastic wing program allowing deflection data collection. Traditional data processing steps were taken to reduce flight data, and twist predictions were made using linear regression techniques. The model predictions determined a consistent linear relationship between the measured twist and aircraft parameters, such as surface positions and aircraft state variables. Error in the original model was reduced in some cases by using a dynamic pressure-based assumption and by using neural networks. These techniques produced excellent predictions for flight between the standard test points and accounted for nonlinearities in the data. This report discusses data processing techniques and twist prediction validation, and provides illustrative and quantitative results.

Artificial neural networks in gynaecological diseases: current and potential future applications.

PubMed

Siristatidis, Charalampos S; Chrelias, Charalampos; Pouliakis, Abraham; Katsimanis, Evangelos; Kassanos, Dimitrios

2010-10-01

Current (and probably future) practice of medicine is mostly associated with prediction and accurate diagnosis. Especially in clinical practice, there is an increasing interest in constructing and using valid models of diagnosis and prediction. Artificial neural networks (ANNs) are mathematical systems being used as a prospective tool for reliable, flexible and quick assessment. They demonstrate high power in evaluating multifactorial data, assimilating information from multiple sources and detecting subtle and complex patterns. Their capability and difference from other statistical techniques lies in performing nonlinear statistical modelling. They represent a new alternative to logistic regression, which is the most commonly used method for developing predictive models for outcomes resulting from partitioning in medicine. In combination with the other non-algorithmic artificial intelligence techniques, they provide useful software engineering tools for the development of systems in quantitative medicine. Our paper first presents a brief introduction to ANNs, then, using what we consider the best available evidence through paradigms, we evaluate the ability of these networks to serve as first-line detection and prediction techniques in some of the most crucial fields in gynaecology. Finally, through the analysis of their current application, we explore their dynamics for future use.

On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.

PubMed

Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L

2011-10-01

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.

A review on prognostic techniques for non-stationary and non-linear rotating systems

NASA Astrophysics Data System (ADS)

Kan, Man Shan; Tan, Andy C. C.; Mathew, Joseph

2015-10-01

The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.

Femtosecond imaging of nonlinear acoustics in gold.

PubMed

Pezeril, Thomas; Klieber, Christoph; Shalagatskyi, Viktor; Vaudel, Gwenaelle; Temnov, Vasily; Schmidt, Oliver G; Makarov, Denys

2014-02-24

We have developed a high-sensitivity, low-noise femtosecond imaging technique based on pump-probe time-resolved measurements with a standard CCD camera. The approach used in the experiment is based on lock-in acquisitions of images generated by a femtosecond laser probe synchronized to modulation of a femtosecond laser pump at the same rate. This technique allows time-resolved imaging of laser-excited phenomena with femtosecond time resolution. We illustrate the technique by time-resolved imaging of the nonlinear reshaping of a laser-excited picosecond acoustic pulse after propagation through a thin gold layer. Image analysis reveals the direct 2D visualization of the nonlinear acoustic propagation of the picosecond acoustic pulse. Many ultrafast pump-probe investigations can profit from this technique because of the wealth of information it provides over a typical single diode and lock-in amplifier setup, for example it can be used to image ultrasonic echoes in biological samples.

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1992-01-01

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element

PubMed Central

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667

In-situ monitoring of acoustic linear and nonlinear behavior of titanium alloys during cycling loading

NASA Astrophysics Data System (ADS)

Frouin, Jerome; Matikas, Theodore E.; Na, Jeong K.; Sathish, Shamachary

1999-02-01

An in-situ technique to measure sound velocity, ultrasonic attenuation and acoustic nonlinear property has been developed for characterization and early detection of fatigue damage in aerospace materials. A previous experiment using the f-2f technique on Ti-6Al-4V dog bone specimen fatigued at different stage of fatigue has shown that the material nonlinearity exhibit large change compared to the other ultrasonic parameter. Real-time monitoring of the nonlinearity may be a future tool to characterize early fatigue damage in the material. For this purpose we have developed a computer software and measurement technique including hardware for the automation of the measurement. New transducer holder and special grips are designed. The automation has allowed us to test the long-term stability of the electronics over a period of time and so proof of the linearity of the system. For the first time, a real-time experiment has been performed on a dog-bone specimen from zero fatigue al the way to the final fracture.

Nonlinear acoustics in cicada mating calls enhance sound propagation.

PubMed

Hughes, Derke R; Nuttall, Albert H; Katz, Richard A; Carter, G Clifford

2009-02-01

An analysis of cicada mating calls, measured in field experiments, indicates that the very high levels of acoustic energy radiated by this relatively small insect are mainly attributed to the nonlinear characteristics of the signal. The cicada emits one of the loudest sounds in all of the insect population with a sound production system occupying a physical space typically less than 3 cc. The sounds made by tymbals are amplified by the hollow abdomen, functioning as a tuned resonator, but models of the signal based solely on linear techniques do not fully account for a sound radiation capability that is so disproportionate to the insect's size. The nonlinear behavior of the cicada signal is demonstrated by combining the mutual information and surrogate data techniques; the results obtained indicate decorrelation when the phase-randomized and non-phase-randomized data separate. The Volterra expansion technique is used to fit the nonlinearity in the insect's call. The second-order Volterra estimate provides further evidence that the cicada mating calls are dominated by nonlinear characteristics and also suggests that the medium contributes to the cicada's efficient sound propagation. Application of the same principles has the potential to improve radiated sound levels for sonar applications.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1985-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1986-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

More green space is related to less antidepressant prescription rates in the Netherlands: A Bayesian geoadditive quantile regression approach.

PubMed

Helbich, Marco; Klein, Nadja; Roberts, Hannah; Hagedoorn, Paulien; Groenewegen, Peter P

2018-06-20

Exposure to green space seems to be beneficial for self-reported mental health. In this study we used an objective health indicator, namely antidepressant prescription rates. Current studies rely exclusively upon mean regression models assuming linear associations. It is, however, plausible that the presence of green space is non-linearly related with different quantiles of the outcome antidepressant prescription rates. These restrictions may contribute to inconsistent findings. Our aim was: a) to assess antidepressant prescription rates in relation to green space, and b) to analyze how the relationship varies non-linearly across different quantiles of antidepressant prescription rates. We used cross-sectional data for the year 2014 at a municipality level in the Netherlands. Ecological Bayesian geoadditive quantile regressions were fitted for the 15%, 50%, and 85% quantiles to estimate green space-prescription rate correlations, controlling for physical activity levels, socio-demographics, urbanicity, etc. RESULTS: The results suggested that green space was overall inversely and non-linearly associated with antidepressant prescription rates. More important, the associations differed across the quantiles, although the variation was modest. Significant non-linearities were apparent: The associations were slightly positive in the lower quantile and strongly negative in the upper one. Our findings imply that an increased availability of green space within a municipality may contribute to a reduction in the number of antidepressant prescriptions dispensed. Green space is thus a central health and community asset, whilst a minimum level of 28% needs to be established for health gains. The highest effectiveness occurred at a municipality surface percentage higher than 79%. This inverse dose-dependent relation has important implications for setting future community-level health and planning policies. Copyright © 2018 Elsevier Inc. All rights reserved.

A Unified Approach for Solving Nonlinear Regular Perturbation Problems

ERIC Educational Resources Information Center

Khuri, S. A.

2008-01-01

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

A note on the generation of phase plane plots on a digital computer. [for solution of nonlinear differential equations

NASA Technical Reports Server (NTRS)

Simon, M. K.

1980-01-01

A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated.

Recent Advances in Fiber Lasers for Nonlinear Microscopy

PubMed Central

Xu, C.; Wise, F. W.

2013-01-01

Nonlinear microscopy techniques developed over the past two decades have provided dramatic new capabilities for biological imaging. The initial demonstrations of nonlinear microscopies coincided with the development of solid-state femtosecond lasers, which continue to dominate applications of nonlinear microscopy. Fiber lasers offer attractive features for biological and biomedical imaging, and recent advances are leading to high-performance sources with the potential for robust, inexpensive, integrated instruments. This article discusses recent advances, and identifies challenges and opportunities for fiber lasers in nonlinear bioimaging. PMID:24416074

Advances in simultaneous atmospheric profile and cloud parameter regression based retrieval from high-spectral resolution radiance measurements

NASA Astrophysics Data System (ADS)

Weisz, Elisabeth; Smith, William L.; Smith, Nadia

2013-06-01

The dual-regression (DR) method retrieves information about the Earth surface and vertical atmospheric conditions from measurements made by any high-spectral resolution infrared sounder in space. The retrieved information includes temperature and atmospheric gases (such as water vapor, ozone, and carbon species) as well as surface and cloud top parameters. The algorithm was designed to produce a high-quality product with low latency and has been demonstrated to yield accurate results in real-time environments. The speed of the retrieval is achieved through linear regression, while accuracy is achieved through a series of classification schemes and decision-making steps. These steps are necessary to account for the nonlinearity of hyperspectral retrievals. In this work, we detail the key steps that have been developed in the DR method to advance accuracy in the retrieval of nonlinear parameters, specifically cloud top pressure. The steps and their impact on retrieval results are discussed in-depth and illustrated through relevant case studies. In addition to discussing and demonstrating advances made in addressing nonlinearity in a linear geophysical retrieval method, advances toward multi-instrument geophysical analysis by applying the DR to three different operational sounders in polar orbit are also noted. For any area on the globe, the DR method achieves consistent accuracy and precision, making it potentially very valuable to both the meteorological and environmental user communities.

Localization and identification of structural nonlinearities using cascaded optimization and neural networks

NASA Astrophysics Data System (ADS)

Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.

2017-10-01

In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

Development of a nonlinear switching function and its application to static lift characteristics of straight wings

NASA Technical Reports Server (NTRS)

Hewes, D. E.

1978-01-01

A mathematical modeling technique was developed for the lift characteristics of straight wings throughout a very wide angle of attack range. The technique employs a mathematical switching function that facilitates the representation of the nonlinear aerodynamic characteristics in the partially and fully stalled regions and permits matching empirical data within + or - 4 percent of maximum values. Although specifically developed for use in modeling the lift characteristics, the technique appears to have other applications in both aerodynamic and nonaerodynamic fields.

Femtosecond nonlinear optical properties of laser ablated gold nanoparticles in water

NASA Astrophysics Data System (ADS)

Krishnakanth, K. N.; Bharathi, M. S. S.; Hamad, S.; Rao, S. Venugopal

2018-04-01

Femtosecond third order nonlinear optical (NLO) properties of ultrafast laser ablated gold (Au) colloidsin distilled waterare investigatedusing degenerate four wave mixing technique with 50fs pulses at 800nm wavelength. The estimated value of χ(3) obtained for Au nanoparticles is 1.93×10-14 e.s.u. The characterization of the NPs was achieved done using TEM and HR-TEM techniques. We also present the time resolved studies of Au colloids by using DFWM technique in the forward BOXCAR phase matching geometry.

Nonlinear mirror modelocking of a bounce geometry laser.

PubMed

Thomas, G M; Bäuerle, A; Farrell, D J; Damzen, M J

2010-06-07

We present the investigation of nonlinear mirror modelocking (NLM) of a bounce amplifier laser. This technique, a potential rival to SESAM modelocking, uses a nonlinear crystal and a dichroic mirror to passively modelock a Nd:GdVO(4) slab bounce amplifier operating at 1063nm. At 11.3W, we present the highest power achieved using the NLM technique, using type-II phase-matched KTP, with a pulse duration of 57ps. Using type-I phase-matched BiBO, modelocking was achieved with a shorter pulse duration of 5.7ps at an average power of 7.1W.

Nonlinear optical characterization of ZnS thin film synthesized by chemical spray pyrolysis method

NASA Astrophysics Data System (ADS)

G, Sreeja V.; V, Sabitha P.; Anila, E. I.; R, Reshmi; John, Manu Punnan; Radhakrishnan, P.

2014-10-01

ZnS thin film was prepared by Chemical Spray Pyrolysis (CSP) method. The sample was characterized by X-ray diffraction method and Z scan technique. XRD pattern showed that ZnS thin film has hexagonal structure with an average size of about 5.6nm. The nonlinear optical properties of ZnS thin film was studied by open aperture Z-Scan technique using Q-switched Nd-Yag Laser at 532nm. The Z-scan plot showed that the investigated ZnS thin film has saturable absorption behavior. The nonlinear absorption coefficient and saturation intensity were also estimated.

Real-Time Global Nonlinear Aerodynamic Modeling for Learn-To-Fly

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2016-01-01

Flight testing and modeling techniques were developed to accurately identify global nonlinear aerodynamic models for aircraft in real time. The techniques were developed and demonstrated during flight testing of a remotely-piloted subscale propeller-driven fixed-wing aircraft using flight test maneuvers designed to simulate a Learn-To-Fly scenario. Prediction testing was used to evaluate the quality of the global models identified in real time. The real-time global nonlinear aerodynamic modeling algorithm will be integrated and further tested with learning adaptive control and guidance for NASA Learn-To-Fly concept flight demonstrations.

EFQPSK Versus CERN: A Comparative Study

NASA Technical Reports Server (NTRS)

Borah, Deva K.; Horan, Stephen

2001-01-01

This report presents a comparative study on Enhanced Feher's Quadrature Phase Shift Keying (EFQPSK) and Constrained Envelope Root Nyquist (CERN) techniques. These two techniques have been developed in recent times to provide high spectral and power efficiencies under nonlinear amplifier environment. The purpose of this study is to gain insights into these techniques and to help system planners and designers with an appropriate set of guidelines for using these techniques. The comparative study presented in this report relies on effective simulation models and procedures. Therefore, a significant part of this report is devoted to understanding the mathematical and simulation models of the techniques and their set-up procedures. In particular, mathematical models of EFQPSK and CERN, effects of the sampling rate in discrete time signal representation, and modeling of nonlinear amplifiers and predistorters have been considered in detail. The results of this study show that both EFQPSK and CERN signals provide spectrally efficient communications compared to filtered conventional linear modulation techniques when a nonlinear power amplifier is used. However, there are important differences. The spectral efficiency of CERN signals, with a small amount of input backoff, is significantly better than that of EFQPSK signals if the nonlinear amplifier is an ideal clipper. However, to achieve such spectral efficiencies with a practical nonlinear amplifier, CERN processing requires a predistorter which effectively translates the amplifier's characteristics close to those of an ideal clipper. Thus, the spectral performance of CERN signals strongly depends on the predistorter. EFQPSK signals, on the other hand, do not need such predistorters since their spectra are almost unaffected by the nonlinear amplifier, Ibis report discusses several receiver structures for EFQPSK signals. It is observed that optimal receiver structures can be realized for both coded and uncoded EFQPSK signals with not too much increase in computational complexity. When a nonlinear amplifier is used, the bit error rate (BER) performance of the CERN signals with a matched filter receiver is found to be more than one decibel (dB) worse compared to the bit error performance of EFQPSK signals. Although channel coding is found to provide BER performance improvement for both EFQPSK and CERN signals, the performance of EFQPSK signals remains better than that of CERN. Optimal receiver structures for CERN signals with nonlinear equalization is left as a possible future work. Based on the numerical results, it is concluded that, in nonlinear channels, CERN processing leads towards better bandwidth efficiency with a compromise in power efficiency. Hence for bandwidth efficient communications needs, CERN is a good solution provided effective adaptive predistorters can be realized. On the other hand, EFQPSK signals provide a good power efficient solution with a compromise in band width efficiency.

String Stability of a Linear Formation Flight Control System

NASA Technical Reports Server (NTRS)

Allen, Michael J.; Ryan, Jack; Hanson, Curtis E.; Parle, James F.

2002-01-01

String stability analysis of an autonomous formation flight system was performed using linear and nonlinear simulations. String stability is a measure of how position errors propagate from one vehicle to another in a cascaded system. In the formation flight system considered here, each i(sup th) aircraft uses information from itself and the preceding ((i-1)(sup th)) aircraft to track a commanded relative position. A possible solution for meeting performance requirements with such a system is to allow string instability. This paper explores two results of string instability and outlines analysis techniques for string unstable systems. The three analysis techniques presented here are: linear, nonlinear formation performance, and ride quality. The linear technique was developed from a worst-case scenario and could be applied to the design of a string unstable controller. The nonlinear formation performance and ride quality analysis techniques both use nonlinear formation simulation. Three of the four formation-controller gain-sets analyzed in this paper were limited more by ride quality than by performance. Formations of up to seven aircraft in a cascaded formation could be used in the presence of light gusts with this string unstable system.

Efficient Numerical Methods for Nonlinear-Facilitated Transport and Exchange in a Blood-Tissue Exchange Unit

PubMed Central

Poulain, Christophe A.; Finlayson, Bruce A.; Bassingthwaighte, James B.

2010-01-01

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data. PMID:9146808

The Changing Nonlinear Relationship between Income and Terrorism

PubMed Central

Enders, Walter; Hoover, Gary A.

2014-01-01

This article reinvestigates the relationship between real per capita gross domestic product (GDP) and terrorism. We devise a terrorism Lorenz curve to show that domestic and transnational terrorist attacks are each more concentrated in middle-income countries, thereby suggesting a nonlinear income–terrorism relationship. Moreover, this point of concentration shifted to lower income countries after the rising influence of the religious fundamentalist and nationalist/separatist terrorists in the early 1990s. For transnational terrorist attacks, this shift characterized not only the attack venue but also the perpetrators’ nationality. The article then uses nonlinear smooth transition regressions to establish the relationship between real per capita GDP and terrorism for eight alternative terrorism samples, accounting for venue, perpetrators’ nationality, terrorism type, and the period. Our nonlinear estimates are shown to be favored over estimates using linear or quadratic income determinants of terrorism. These nonlinear estimates are robust to additional controls. PMID:28579636

Model-free inference of direct network interactions from nonlinear collective dynamics.

PubMed

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Investigations on nucleation, HRXRD, optical, piezoelectric, polarizability and Z-scan analysis of L-arginine maleate dihydrate single crystals

NASA Astrophysics Data System (ADS)

Sakthy Priya, S.; Alexandar, A.; Surendran, P.; Lakshmanan, A.; Rameshkumar, P.; Sagayaraj, P.

2017-04-01

An efficient organic nonlinear optical single crystal of L-arginine maleate dihydrate (LAMD) has been grown by slow evaporation solution technique (SEST) and slow cooling technique (SCT). The crystalline perfection of the crystal was examined using high-resolution X-ray diffractometry (HRXRD) analysis. Photoluminescence study confirmed the optical properties and defects level in the crystal lattice. Electromechanical behaviour was observed using piezoelectric co-efficient (d33) analysis. The photoconductivity analysis confirmed the negative photoconducting nature of the material. The dielectric constant and loss were measured as a function of frequency with varying temperature and vice-versa. The laser damage threshold (LDT) measurement was carried out using Nd:YAG Laser with a wavelength of 1064 nm (Focal length is 35 cm) and the obtained results showed that LDT value of the crystal is high compared to KDP crystal. The high laser damage threshold of the grown crystal makes it a potential candidate for second and higher order nonlinear optical device application. The third order nonlinear optical parameters of LAMD crystal is determined by open-aperture and closed-aperture studies using Z-scan technique. The third order linear and nonlinear optical parameters such as the nonlinear refractive index (n2), two photon absorption coefficient (β), Real part (Reχ3) and imaginary part (Imχ3) of third-order nonlinear optical susceptibility are calculated.

A New SEYHAN's Approach in Case of Heterogeneity of Regression Slopes in ANCOVA.

PubMed

Ankarali, Handan; Cangur, Sengul; Ankarali, Seyit

2018-06-01

In this study, when the assumptions of linearity and homogeneity of regression slopes of conventional ANCOVA are not met, a new approach named as SEYHAN has been suggested to use conventional ANCOVA instead of robust or nonlinear ANCOVA. The proposed SEYHAN's approach involves transformation of continuous covariate into categorical structure when the relationship between covariate and dependent variable is nonlinear and the regression slopes are not homogenous. A simulated data set was used to explain SEYHAN's approach. In this approach, we performed conventional ANCOVA in each subgroup which is constituted according to knot values and analysis of variance with two-factor model after MARS method was used for categorization of covariate. The first model is a simpler model than the second model that includes interaction term. Since the model with interaction effect has more subjects, the power of test also increases and the existing significant difference is revealed better. We can say that linearity and homogeneity of regression slopes are not problem for data analysis by conventional linear ANCOVA model by helping this approach. It can be used fast and efficiently for the presence of one or more covariates.

Higher-order Multivariable Polynomial Regression to Estimate Human Affective States

NASA Astrophysics Data System (ADS)

Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

2016-03-01

From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.

Higher-order Multivariable Polynomial Regression to Estimate Human Affective States

PubMed Central

Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

2016-01-01

From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states. PMID:26996254

Nonlinear multilayers as optical limiters

NASA Astrophysics Data System (ADS)

Turner-Valle, Jennifer Anne

1998-10-01

In this work we present a non-iterative technique for computing the steady-state optical properties of nonlinear multilayers and we examine nonlinear multilayer designs for optical limiters. Optical limiters are filters with intensity-dependent transmission designed to curtail the transmission of incident light above a threshold irradiance value in order to protect optical sensors from damage due to intense light. Thin film multilayers composed of nonlinear materials exhibiting an intensity-dependent refractive index are used as the basis for optical limiter designs in order to enhance the nonlinear filter response by magnifying the electric field in the nonlinear materials through interference effects. The nonlinear multilayer designs considered in this work are based on linear optical interference filter designs which are selected for their spectral properties and electric field distributions. Quarter wave stacks and cavity filters are examined for their suitability as sensor protectors and their manufacturability. The underlying non-iterative technique used to calculate the optical response of these filters derives from recognizing that the multi-valued calculation of output irradiance as a function of incident irradiance may be turned into a single-valued calculation of incident irradiance as a function of output irradiance. Finally, the benefits and drawbacks of using nonlinear multilayer for optical limiting are examined and future research directions are proposed.

On the interannual oscillations in the northern temperate total ozone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krzyscin, J.W.

1994-07-01

The interannual variations in total ozone are studied using revised Dobson total ozone records (1961-1990) from 17 stations located within the latitude band 30 deg N - 60 deg N. To obtain the quasi-biennial oscillation (QBO), El Nino-Southern Oscillation (ENSO), and 11-year solar cycle manifestation in the `northern temperate` total ozone data, various multiple regression models are constructed by the least squares fitting to the observed ozone. The statistical relationships between the selected indices of the atmospheric variabilities and total ozone are described in the linear and nonlinear regression models. Nonlinear relationships to the predictor variables are found. That is,more » the total ozone variations are statistically modeled by nonlinear terms accounting for the coupling between QBO and ENSO, QBO and solar activity, and ENSO and solar activity. It is suggested that large reduction of total ozone values over the `northern temperate` region occurs in cold season when a strong ENSO warm event meets the west phase of the QBO during the period of high solar activity.« less

Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging

NASA Astrophysics Data System (ADS)

Kharin, Nikolay A.

2000-04-01

In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.

Nonlinear imaging (NIM) of barely visible impact damage (BVID) in composite panels using a semi and full air-coupled linear and nonlinear ultrasound technique

NASA Astrophysics Data System (ADS)

Malfense Fierro, Gian Piero; Meo, Michele

2018-03-01

Two non-contact methods were evaluated to address the reliability and reproducibility concerns affecting industry adoption of nonlinear ultrasound techniques for non-destructive testing and evaluation (NDT/E) purposes. A semi and a fully air-coupled linear and nonlinear ultrasound method was evaluated by testing for barely visible impact damage (BVID) in composite materials. Air coupled systems provide various advantages over contact driven systems; such as: ease of inspection, no contact and lubrication issues and a great potential for non-uniform geometry evaluation. The semi air-coupled setup used a suction attached piezoelectric transducer to excite the sample and an array of low-cost microphones to capture the signal over the inspection area, while the second method focused on a purely air-coupled setup, using an air-coupled transducer to excite the structure and capture the signal. One of the issues facing nonlinear and any air-coupled systems is transferring enough energy to stimulate wave propagation and in the case of nonlinear ultrasound; damage regions. Results for both methods provided nonlinear imaging (NIM) of damage regions using a sweep excitation methodology, with the semi aircoupled system providing clearer results.

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.

1972-01-01

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

MATERNAL CHRONOLOGICAL AGE, PRENATAL AND PERINATAL HISTORY, SOCIAL SUPPORT, AND PARENTING OF INFANTS

PubMed Central

Bornstein, Marc H.; Putnick, Diane L.; Suwalsky, Joan T. D.; Gini, Motti

2018-01-01

The role of maternal chronological age in prenatal and perinatal history, social support, and parenting practices of new mothers (N = 335) was examined. Primiparas of 5-month-old infants ranged in age from 13 to 42 years. Age effects were zero, linear, and nonlinear. Nonlinear age effects were significantly associated up to a certain age with little or no association afterward; by spline regression, estimated points at which the slope of the regression line changed were 25 years for prenatal and perinatal history, 31 years for social supports, and 27 years for parenting practices. Given the expanding age range of first-time parents, these findings underscore the importance of incorporating maternal age as a factor in studies of parenting and child development. PMID:16942495

Nonlinear Structural Analysis

NASA Technical Reports Server (NTRS)

1984-01-01

Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.

Third-order optical nonlinearities of sol-gel silica coating films containing metal porphyrin derivatives measured by resonant femtosecond degenerate four-wave mixing technique

NASA Astrophysics Data System (ADS)

Kasatani, Kazuo; Okamoto, Hiroaki; Takenaka, Shunsuke

2003-11-01

Third-order optical nonlinearities of sol-gel silica coating films containing metal porphyrin derivatives were measured under resonant conditions by the femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of two components, the coherent instantaneous nonlinear response and the delayed response with a decay time constant of several to several hundred ps. The latter can be attributed to population grating of an excited state, and contribution of slow component was very little for a zinc porphyrin derivative. The values of electronic component of the optical nonlinear susceptibility, χ(3) xxxx, for these films were ca. 2 x 10-10 esu.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Microwave phase conjugation using artificial nonlinear microwave surfaces

NASA Astrophysics Data System (ADS)

Chang, Yian

1997-09-01

A new technique is developed and demonstrated to simulate nonlinear materials in the microwave and millimeter wave regime. Such materials are required to extend nonlinear optical techniques into longer wavelength areas. Using an array of antenna coupled mixers as an artificial nonlinear surface, we have demonstrated two-dimensional free space microwave phase conjugation at 10 GHz. The basic concept is to replace the weak nonlinearity of electron distribution in a crystal with the strong nonlinear V-I response of a P-N junction. This demnstration uses a three-wave mixing method with the effective nonlinear susceptibility χ(2) provided by an artificial nonlinear surface. The pump signal at 2ω (20 GHz) can be injected to the mixing elements electrically or optically. Electrical injection was first used to prove the concept of artificial nonlinear surfaces. However, due to the loss and size of microwave components, electrical injection is not practical for an array of artificial nonlinear surfaces, as would be needed in a three-dimensional free space phase conjugation setup. Therefore optical injection was implemented to carry the 2ω microwave pump signal in phase to all mixing elements. In both cases, two-dimensional free space phase conjugation was observed by directly measuring the electric field amplitude and phase distribution. The electric field wavefronts exhibited retro-directivity and auto- correction characteristics of phase conjugation. This demonstration surface also shows a power gain of 10 dB, which is desired for potential communication applications.

Femtosecond Z-scan measurements of the nonlinear refractive index of fused silica

NASA Astrophysics Data System (ADS)

Zhang, Lin; Shi, Zhendong; Ma, Hua; Ren, Huan; Yuan, Quan; Ma, Yurong; Feng, Xiaoxuan; Chen, Bo; Yang, Yi

2018-01-01

Z-scan technology is a popular experimental technique for determining the nonlinear refractive index of the material. However, it encounters a great difficulty in measuring the weak nonlinear material like fused silica which is about two orders of magnitude below the nonlinear refractive index of most of the materials studied with the nanosecond and picosecond Z-scan methods. In this case, the change of refractive index introduced by accumulation of thermal effects cannot be neglected. In order to have a reliable measurement of the nonlinear refractive index, a metrology bench based on the femtosecond Z-scan technology is developed. The intensity modulation component and the differential measurement system are applied to guarantee the accuracy of the measuring system. Based on the femtosecond Z-scan theory, the femtosecond laser Z-scan technique is performed on fused silica, and the nonlinear refractive index of Fused silica is determined to be 9.2039×10-14esu for 800nm, 37fs pulse duration at I0=50GW/cm2 with a good repeatability of 6.7%.

Experimental study of nonlinear ultrasonic behavior of soil materials during the compaction.

PubMed

Chen, Jun; Wang, Hao; Yao, Yangping

2016-07-01

In this paper, the nonlinear ultrasonic behavior of unconsolidated granular medium - soil during the compaction is experimentally studied. The second harmonic generation technique is adopted to investigate the change of microstructural void in materials during the compaction process of loose soils. The nonlinear parameter is measured with the change of two important environmental factors i.e. moisture content and impact energy of compaction. It is found the nonlinear parameter of soil material presents a similar variation pattern with the void ratio of soil samples, corresponding to the increased moisture content and impact energy. A same optimum moisture content is found by observing the variation of nonlinear parameter and void ratio with respect to moisture content. The results indicate that the unconsolidated soil is manipulated by a strong material nonlinearity during the compaction procedure. The developed experimental technique based on the second harmonic generation could be a fast and convenient testing method for the determination of optimum moisture content of soil materials, which is very useful for the better compaction effect of filled embankment for civil infrastructures in-situ. Copyright © 2016 Elsevier B.V. All rights reserved.

Interferometric and nonlinear-optical spectral-imaging techniques for outer space and live cells

NASA Astrophysics Data System (ADS)

Itoh, Kazuyoshi

2015-12-01

Multidimensional signals such as the spectral images allow us to have deeper insights into the natures of objects. In this paper the spectral imaging techniques that are based on optical interferometry and nonlinear optics are presented. The interferometric imaging technique is based on the unified theory of Van Cittert-Zernike and Wiener-Khintchine theorems and allows us to retrieve a spectral image of an object in the far zone from the 3D spatial coherence function. The retrieval principle is explained using a very simple object. The promising applications to space interferometers for astronomy that are currently in progress will also be briefly touched on. An interesting extension of interferometric spectral imaging is a 3D and spectral imaging technique that records 4D information of objects where the 3D and spectral information is retrieved from the cross-spectral density function of optical field. The 3D imaging is realized via the numerical inverse propagation of the cross-spectral density. A few techniques suggested recently are introduced. The nonlinear optical technique that utilizes stimulated Raman scattering (SRS) for spectral imaging of biomedical targets is presented lastly. The strong signals of SRS permit us to get vibrational information of molecules in the live cell or tissue in real time. The vibrational information of unstained or unlabeled molecules is crucial especially for medical applications. The 3D information due to the optical nonlinearity is also the attractive feature of SRS spectral microscopy.

Integration of measurements with atmospheric dispersion models: Source term estimation for dispersal of (239)Pu due to non-nuclear detonation of high explosive

NASA Astrophysics Data System (ADS)

Edwards, L. L.; Harvey, T. F.; Freis, R. P.; Pitovranov, S. E.; Chernokozhin, E. V.

1992-10-01

The accuracy associated with assessing the environmental consequences of an accidental release of radioactivity is highly dependent on our knowledge of the source term characteristics and, in the case when the radioactivity is condensed on particles, the particle size distribution, all of which are generally poorly known. This paper reports on the development of a numerical technique that integrates the radiological measurements with atmospheric dispersion modeling. This results in a more accurate particle-size distribution and particle injection height estimation when compared with measurements of high explosive dispersal of (239)Pu. The estimation model is based on a non-linear least squares regression scheme coupled with the ARAC three-dimensional atmospheric dispersion models. The viability of the approach is evaluated by estimation of ADPIC model input parameters such as the ADPIC particle size mean aerodynamic diameter, the geometric standard deviation, and largest size. Additionally we estimate an optimal 'coupling coefficient' between the particles and an explosive cloud rise model. The experimental data are taken from the Clean Slate 1 field experiment conducted during 1963 at the Tonopah Test Range in Nevada. The regression technique optimizes the agreement between the measured and model predicted concentrations of (239)Pu by varying the model input parameters within their respective ranges of uncertainties. The technique generally estimated the measured concentrations within a factor of 1.5, with the worst estimate being within a factor of 5, very good in view of the complexity of the concentration measurements, the uncertainties associated with the meteorological data, and the limitations of the models. The best fit also suggest a smaller mean diameter and a smaller geometric standard deviation on the particle size as well as a slightly weaker particle to cloud coupling than previously reported.

Machine learning techniques for energy optimization in mobile embedded systems

NASA Astrophysics Data System (ADS)

Donohoo, Brad Kyoshi

Mobile smartphones and other portable battery operated embedded systems (PDAs, tablets) are pervasive computing devices that have emerged in recent years as essential instruments for communication, business, and social interactions. While performance, capabilities, and design are all important considerations when purchasing a mobile device, a long battery lifetime is one of the most desirable attributes. Battery technology and capacity has improved over the years, but it still cannot keep pace with the power consumption demands of today's mobile devices. This key limiter has led to a strong research emphasis on extending battery lifetime by minimizing energy consumption, primarily using software optimizations. This thesis presents two strategies that attempt to optimize mobile device energy consumption with negligible impact on user perception and quality of service (QoS). The first strategy proposes an application and user interaction aware middleware framework that takes advantage of user idle time between interaction events of the foreground application to optimize CPU and screen backlight energy consumption. The framework dynamically classifies mobile device applications based on their received interaction patterns, then invokes a number of different power management algorithms to adjust processor frequency and screen backlight levels accordingly. The second strategy proposes the usage of machine learning techniques to learn a user's mobile device usage pattern pertaining to spatiotemporal and device contexts, and then predict energy-optimal data and location interface configurations. By learning where and when a mobile device user uses certain power-hungry interfaces (3G, WiFi, and GPS), the techniques, which include variants of linear discriminant analysis, linear logistic regression, non-linear logistic regression, and k-nearest neighbor, are able to dynamically turn off unnecessary interfaces at runtime in order to save energy.

Quantitative methods for compensation of matrix effects and self-absorption in Laser Induced Breakdown Spectroscopy signals of solids

NASA Astrophysics Data System (ADS)

Takahashi, Tomoko; Thornton, Blair

2017-12-01

This paper reviews methods to compensate for matrix effects and self-absorption during quantitative analysis of compositions of solids measured using Laser Induced Breakdown Spectroscopy (LIBS) and their applications to in-situ analysis. Methods to reduce matrix and self-absorption effects on calibration curves are first introduced. The conditions where calibration curves are applicable to quantification of compositions of solid samples and their limitations are discussed. While calibration-free LIBS (CF-LIBS), which corrects matrix effects theoretically based on the Boltzmann distribution law and Saha equation, has been applied in a number of studies, requirements need to be satisfied for the calculation of chemical compositions to be valid. Also, peaks of all elements contained in the target need to be detected, which is a bottleneck for in-situ analysis of unknown materials. Multivariate analysis techniques are gaining momentum in LIBS analysis. Among the available techniques, principal component regression (PCR) analysis and partial least squares (PLS) regression analysis, which can extract related information to compositions from all spectral data, are widely established methods and have been applied to various fields including in-situ applications in air and for planetary explorations. Artificial neural networks (ANNs), where non-linear effects can be modelled, have also been investigated as a quantitative method and their applications are introduced. The ability to make quantitative estimates based on LIBS signals is seen as a key element for the technique to gain wider acceptance as an analytical method, especially in in-situ applications. In order to accelerate this process, it is recommended that the accuracy should be described using common figures of merit which express the overall normalised accuracy, such as the normalised root mean square errors (NRMSEs), when comparing the accuracy obtained from different setups and analytical methods.

Data mining in forecasting PVT correlations of crude oil systems based on Type1 fuzzy logic inference systems

NASA Astrophysics Data System (ADS)

El-Sebakhy, Emad A.

2009-09-01

Pressure-volume-temperature properties are very important in the reservoir engineering computations. There are many empirical approaches for predicting various PVT properties based on empirical correlations and statistical regression models. Last decade, researchers utilized neural networks to develop more accurate PVT correlations. These achievements of neural networks open the door to data mining techniques to play a major role in oil and gas industry. Unfortunately, the developed neural networks correlations are often limited, and global correlations are usually less accurate compared to local correlations. Recently, adaptive neuro-fuzzy inference systems have been proposed as a new intelligence framework for both prediction and classification based on fuzzy clustering optimization criterion and ranking. This paper proposes neuro-fuzzy inference systems for estimating PVT properties of crude oil systems. This new framework is an efficient hybrid intelligence machine learning scheme for modeling the kind of uncertainty associated with vagueness and imprecision. We briefly describe the learning steps and the use of the Takagi Sugeno and Kang model and Gustafson-Kessel clustering algorithm with K-detected clusters from the given database. It has featured in a wide range of medical, power control system, and business journals, often with promising results. A comparative study will be carried out to compare their performance of this new framework with the most popular modeling techniques, such as neural networks, nonlinear regression, and the empirical correlations algorithms. The results show that the performance of neuro-fuzzy systems is accurate, reliable, and outperform most of the existing forecasting techniques. Future work can be achieved by using neuro-fuzzy systems for clustering the 3D seismic data, identification of lithofacies types, and other reservoir characterization.

Nonlinear optical studies of curcumin metal derivatives with cw laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S.

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition modelmore » with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.« less

Separation of the long-term thermal effects from the strain measurements in the Geodynamics Laboratory of Lanzarote

NASA Astrophysics Data System (ADS)

Venedikov, A. P.; Arnoso, J.; Cai, W.; Vieira, R.; Tan, S.; Velez, E. J.

2006-01-01

A 12-year series (1992-2004) of strain measurements recorded in the Geodynamics Laboratory of Lanzarote is investigated. Through a tidal analysis the non-tidal component of the data is separated in order to use it for studying signals, useful for monitoring of the volcanic activity on the island. This component contains various perturbations of meteorological and oceanic origin, which should be eliminated in order to make the useful signals discernible. The paper is devoted to the estimation and elimination of the effect of the air temperature inside the station, which strongly dominates the strainmeter data. For solving this task, a regression model is applied, which includes a linear relation with the temperature and time-dependant polynomials. The regression includes nonlinearly a set of parameters, which are estimated by a properly applied Bayesian approach. The results obtained are: the regression coefficient of the strain data on temperature is equal to (-367.4 ± 0.8) × 10 -9 °C -1, the curve of the non-tidal component reduced by the effect of the temperature and a polynomial approximation of the reduced curve. The technique used here can be helpful to investigators in the domain of the earthquake and volcano monitoring. However, the fundamental and extremely difficult problem of what kind of signals in the reduced curves might be useful in this field is not considered here.

The Relationship between TOC and pH with Exchangeable Heavy Metal Levels in Lithuanian Podzols

NASA Astrophysics Data System (ADS)

Khaledian, Yones; Pereira, Paulo; Brevik, Eric C.; Pundyte, Neringa; Paliulis, Dainius

2017-04-01

Heavy metals can have a negative impact on public and environmental health. The objective of this study was to investigate the relationship between total organic carbon (TOC) and pH with exchangeable heavy metals (Pb, Cd, Cu and Zn) in order to predict exchangeable heavy metal content in soils sampled near Panevėžys and Kaunas, Lithuania. Principal component regression (PCR) and nonlinear regression methods were tested to find the statistical relationship between TOC and pH with heavy metals. The results of PCR [R2 = 0.68, RMSE = 0.07] and non-linear regression [R2 = 0.74, RMSE= 0.065] (pH with TOC and exchangeable parameters) were statistically significant. However, this was not observed in the relationships of pH and TOC separately with exchangeable heavy metals. The results indicated that pH had a higher correlation with exchangeable heavy metals (non-linear regression [R2 = 0.72, RMSE= 0.066]) than TOC with heavy metals [R2 = 0.30, RMSE= 0.004]. It can be concluded that even though there was a strong relationship between TOC and pH with exchangeable metals, the metal mobility (exchangeable metals) can be explained by pH better than TOC in this study. Finally, manipulating soil pH could likely be productive to assess and control heavy metals when financial and time limitations exist (Khaledian et al. 2016). Reference(s) Khaledian Y, Pereira P, Brevik E.C, Pundyte N, Paliulis D. 2016. The Influence of Organic Carbon and pH on Heavy Metals, Potassium, and Magnesium Levels in Lithuanian Podzols. Land Degradation and Development. DOI: 10.1002/ldr.2638

Online sparse Gaussian process based human motion intent learning for an electrically actuated lower extremity exoskeleton.

PubMed

Long, Yi; Du, Zhi-Jiang; Chen, Chao-Feng; Dong, Wei; Wang, Wei-Dong

2017-07-01

The most important step for lower extremity exoskeleton is to infer human motion intent (HMI), which contributes to achieve human exoskeleton collaboration. Since the user is in the control loop, the relationship between human robot interaction (HRI) information and HMI is nonlinear and complicated, which is difficult to be modeled by using mathematical approaches. The nonlinear approximation can be learned by using machine learning approaches. Gaussian Process (GP) regression is suitable for high-dimensional and small-sample nonlinear regression problems. GP regression is restrictive for large data sets due to its computation complexity. In this paper, an online sparse GP algorithm is constructed to learn the HMI. The original training dataset is collected when the user wears the exoskeleton system with friction compensation to perform unconstrained movement as far as possible. The dataset has two kinds of data, i.e., (1) physical HRI, which is collected by torque sensors placed at the interaction cuffs for the active joints, i.e., knee joints; (2) joint angular position, which is measured by optical position sensors. To reduce the computation complexity of GP, grey relational analysis (GRA) is utilized to specify the original dataset and provide the final training dataset. Those hyper-parameters are optimized offline by maximizing marginal likelihood and will be applied into online GP regression algorithm. The HMI, i.e., angular position of human joints, will be regarded as the reference trajectory for the mechanical legs. To verify the effectiveness of the proposed algorithm, experiments are performed on a subject at a natural speed. The experimental results show the HMI can be obtained in real time, which can be extended and employed in the similar exoskeleton systems.

Pan evaporation modeling using six different heuristic computing methods in different climates of China

NASA Astrophysics Data System (ADS)

Wang, Lunche; Kisi, Ozgur; Zounemat-Kermani, Mohammad; Li, Hui

2017-01-01

Pan evaporation (Ep) plays important roles in agricultural water resources management. One of the basic challenges is modeling Ep using limited climatic parameters because there are a number of factors affecting the evaporation rate. This study investigated the abilities of six different soft computing methods, multi-layer perceptron (MLP), generalized regression neural network (GRNN), fuzzy genetic (FG), least square support vector machine (LSSVM), multivariate adaptive regression spline (MARS), adaptive neuro-fuzzy inference systems with grid partition (ANFIS-GP), and two regression methods, multiple linear regression (MLR) and Stephens and Stewart model (SS) in predicting monthly Ep. Long-term climatic data at various sites crossing a wide range of climates during 1961-2000 are used for model development and validation. The results showed that the models have different accuracies in different climates and the MLP model performed superior to the other models in predicting monthly Ep at most stations using local input combinations (for example, the MAE (mean absolute errors), RMSE (root mean square errors), and determination coefficient (R2) are 0.314 mm/day, 0.405 mm/day and 0.988, respectively for HEB station), while GRNN model performed better in Tibetan Plateau (MAE, RMSE and R2 are 0.459 mm/day, 0.592 mm/day and 0.932, respectively). The accuracies of above models ranked as: MLP, GRNN, LSSVM, FG, ANFIS-GP, MARS and MLR. The overall results indicated that the soft computing techniques generally performed better than the regression methods, but MLR and SS models can be more preferred at some climatic zones instead of complex nonlinear models, for example, the BJ (Beijing), CQ (Chongqing) and HK (Haikou) stations. Therefore, it can be concluded that Ep could be successfully predicted using above models in hydrological modeling studies.

Development and field application of a nonlinear ultrasonic modulation technique for fatigue crack detection without reference data from an intact condition

NASA Astrophysics Data System (ADS)

Lim, Hyung Jin; Kim, Yongtak; Koo, Gunhee; Yang, Suyoung; Sohn, Hoon; Bae, In-hwan; Jang, Jeong-Hwan

2016-09-01

In this study, a fatigue crack detection technique, which detects a fatigue crack without relying on any reference data obtained from the intact condition of a target structure, is developed using nonlinear ultrasonic modulation and applied to a real bridge structure. Using two wafer-type lead zirconate titanate (PZT) transducers, ultrasonic excitations at two distinctive frequencies are applied to a target inspection spot and the corresponding ultrasonic response is measured by another PZT transducer. Then, the nonlinear modulation components produced by a breathing-crack are extracted from the measured ultrasonic response, and a statistical classifier, which can determine if the nonlinear modulation components are statistically significant in comparison with the background noise level, is proposed. The effectiveness of the proposed fatigue crack detection technique is experimentally validated using the data obtained from aluminum plates and aircraft fitting-lug specimens under varying temperature and loading conditions, and through a field testing of Yeongjong Grand Bridge in South Korea. The uniqueness of this study lies in that (1) detection of a micro fatigue crack with less than 1 μm width and fatigue cracks in the range of 10-20 μm in width using nonlinear ultrasonic modulation, (2) automated detection of fatigue crack formation without using reference data obtained from an intact condition, (3) reliable and robust diagnosis under varying temperature and loading conditions, (4) application of a local fatigue crack detection technique to online monitoring of a real bridge.

Nonlinear X-Ray and Auger Spectroscopy at X-Ray Free-Electron Laser Sources

NASA Astrophysics Data System (ADS)

Rohringer, Nina

2015-05-01

X-ray free-electron lasers (XFELs) open the pathway to transfer non-linear spectroscopic techniques to the x-ray domain. A promising all x-ray pump probe technique is based on coherent stimulated electronic x-ray Raman scattering, which was recently demonstrated in atomic neon. By tuning the XFEL pulse to core-excited resonances, a few seed photons in the spectral tail of the XFEL pulse drive an avalanche of resonant inelastic x-ray scattering events, resulting in exponential amplification of the scattering signal by of 6-7 orders of magnitude. Analysis of the line profile of the emitted radiation permits to demonstrate the cross over from amplified spontaneous emission to coherent stimulated resonance scattering. In combination with statistical covariance mapping, a high-resolution spectrum of the resonant inelastic scattering process can be obtained, opening the path to coherent stimulated x-ray Raman spectroscopy. An extension of these ideas to molecules and a realistic feasibility study of stimulated electronic x-ray Raman scattering in CO will be presented. Challenges to realizing stimulated electronic x-ray Raman scattering at present-day XFEL sources will be discussed, corroborated by results of a recent experiment at the LCLS XFEL. Due to the small gain cross section in molecular targets, other nonlinear spectroscopic techniques such as nonlinear Auger spectroscopy could become a powerful alternative. Theory predictions of a novel pump probe technique based on resonant nonlinear Auger spectroscopic will be discussed and the method will be compared to stimulated x-ray Raman spectroscopy.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

Flugge-Lotz, I; Taylor, C F; Lindberg, H E

1958-01-01

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Survey of optimization techniques for nonlinear spacecraft trajectory searches

NASA Technical Reports Server (NTRS)

Wang, Tseng-Chan; Stanford, Richard H.; Sunseri, Richard F.; Breckheimer, Peter J.

1988-01-01

Mathematical analysis of the optimal search of a nonlinear spacecraft trajectory to arrive at a set of desired targets is presented. A high precision integrated trajectory program and several optimization software libraries are used to search for a converged nonlinear spacecraft trajectory. Several examples for the Galileo Jupiter Orbiter and the Ocean Topography Experiment (TOPEX) are presented that illustrate a variety of the optimization methods used in nonlinear spacecraft trajectory searches.

Apparatus and method for epileptic seizure detection using non-linear techniques

DOEpatents

Hively, Lee M.; Clapp, Ned E.; Daw, C. Stuart; Lawkins, William F.

1998-01-01

Methods and apparatus for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence.

Cross-phase modulation spectral shifting: nonlinear phase contrast in a pump-probe microscope

PubMed Central

Wilson, Jesse W.; Samineni, Prathyush; Warren, Warren S.; Fischer, Martin C.

2012-01-01

Microscopy with nonlinear phase contrast is achieved by a simple modification to a nonlinear pump-probe microscope. The technique measures cross-phase modulation by detecting a pump-induced spectral shift in the probe pulse. Images with nonlinear phase contrast are acquired both in transparent and absorptive media. In paraffin-embedded biopsy sections, cross-phase modulation complements the chemically-specific pump-probe images with structural context. PMID:22567580

Inter-comparison of time series models of lake levels predicted by several modeling strategies

NASA Astrophysics Data System (ADS)

Khatibi, R.; Ghorbani, M. A.; Naghipour, L.; Jothiprakash, V.; Fathima, T. A.; Fazelifard, M. H.

2014-04-01

Five modeling strategies are employed to analyze water level time series of six lakes with different physical characteristics such as shape, size, altitude and range of variations. The models comprise chaos theory, Auto-Regressive Integrated Moving Average (ARIMA) - treated for seasonality and hence SARIMA, Artificial Neural Networks (ANN), Gene Expression Programming (GEP) and Multiple Linear Regression (MLR). Each is formulated on a different premise with different underlying assumptions. Chaos theory is elaborated in a greater detail as it is customary to identify the existence of chaotic signals by a number of techniques (e.g. average mutual information and false nearest neighbors) and future values are predicted using the Nonlinear Local Prediction (NLP) technique. This paper takes a critical view of past inter-comparison studies seeking a superior performance, against which it is reported that (i) the performances of all five modeling strategies vary from good to poor, hampering the recommendation of a clear-cut predictive model; (ii) the performances of the datasets of two cases are consistently better with all five modeling strategies; (iii) in other cases, their performances are poor but the results can still be fit-for-purpose; (iv) the simultaneous good performances of NLP and SARIMA pull their underlying assumptions to different ends, which cannot be reconciled. A number of arguments are presented including the culture of pluralism, according to which the various modeling strategies facilitate an insight into the data from different vantages.

Prediction on carbon dioxide emissions based on fuzzy rules

NASA Astrophysics Data System (ADS)

Pauzi, Herrini; Abdullah, Lazim

2014-06-01

There are several ways to predict air quality, varying from simple regression to models based on artificial intelligence. Most of the conventional methods are not sufficiently able to provide good forecasting performances due to the problems with non-linearity uncertainty and complexity of the data. Artificial intelligence techniques are successfully used in modeling air quality in order to cope with the problems. This paper describes fuzzy inference system (FIS) to predict CO2 emissions in Malaysia. Furthermore, adaptive neuro-fuzzy inference system (ANFIS) is used to compare the prediction performance. Data of five variables: energy use, gross domestic product per capita, population density, combustible renewable and waste and CO2 intensity are employed in this comparative study. The results from the two model proposed are compared and it is clearly shown that the ANFIS outperforms FIS in CO2 prediction.

Determining association constants from titration experiments in supramolecular chemistry.

PubMed

Thordarson, Pall

2011-03-01

The most common approach for quantifying interactions in supramolecular chemistry is a titration of the guest to solution of the host, noting the changes in some physical property through NMR, UV-Vis, fluorescence or other techniques. Despite the apparent simplicity of this approach, there are several issues that need to be carefully addressed to ensure that the final results are reliable. This includes the use of non-linear rather than linear regression methods, careful choice of stoichiometric binding model, the choice of method (e.g., NMR vs. UV-Vis) and concentration of host, the application of advanced data analysis methods such as global analysis and finally the estimation of uncertainties and confidence intervals for the results obtained. This tutorial review will give a systematic overview of all these issues-highlighting some of the key messages herein with simulated data analysis examples.

Bayesian Techniques for Plasma Theory to Bridge the Gap Between Space and Lab Plasmas

NASA Astrophysics Data System (ADS)

Crabtree, Chris; Ganguli, Gurudas; Tejero, Erik

2017-10-01

We will show how Bayesian techniques provide a general data analysis methodology that is better suited to investigate phenomena that require a nonlinear theory for an explanation. We will provide short examples of how Bayesian techniques have been successfully used in the radiation belts to provide precise nonlinear spectral estimates of whistler mode chorus and how these techniques have been verified in laboratory plasmas. We will demonstrate how Bayesian techniques allow for the direct competition of different physical theories with data acting as the necessary arbitrator. This work is supported by the Naval Research Laboratory base program and by the National Aeronautics and Space Administration under Grant No. NNH15AZ90I.

Gaussian processes: a method for automatic QSAR modeling of ADME properties.

PubMed

Obrezanova, Olga; Csanyi, Gabor; Gola, Joelle M R; Segall, Matthew D

2007-01-01

In this article, we discuss the application of the Gaussian Process method for the prediction of absorption, distribution, metabolism, and excretion (ADME) properties. On the basis of a Bayesian probabilistic approach, the method is widely used in the field of machine learning but has rarely been applied in quantitative structure-activity relationship and ADME modeling. The method is suitable for modeling nonlinear relationships, does not require subjective determination of the model parameters, works for a large number of descriptors, and is inherently resistant to overtraining. The performance of Gaussian Processes compares well with and often exceeds that of artificial neural networks. Due to these features, the Gaussian Processes technique is eminently suitable for automatic model generation-one of the demands of modern drug discovery. Here, we describe the basic concept of the method in the context of regression problems and illustrate its application to the modeling of several ADME properties: blood-brain barrier, hERG inhibition, and aqueous solubility at pH 7.4. We also compare Gaussian Processes with other modeling techniques.

Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

NASA Astrophysics Data System (ADS)

Pramodini, S.; Sudhakar, Y. N.; SelvaKumar, M.; Poornesh, P.

2014-04-01

We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He-Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of βeff, n2 and χ(3) were found to be of the order of 10-2 cm W-1, 10-5 esu and 10-7 esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications.

Signaling on the continuous spectrum of nonlinear optical fiber.

PubMed

Tavakkolnia, Iman; Safari, Majid

2017-08-07

This paper studies different signaling techniques on the continuous spectrum (CS) of nonlinear optical fiber defined by nonlinear Fourier transform. Three different signaling techniques are proposed and analyzed based on the statistics of the noise added to CS after propagation along the nonlinear optical fiber. The proposed methods are compared in terms of error performance, distance reach, and complexity. Furthermore, the effect of chromatic dispersion on the data rate and noise in nonlinear spectral domain is investigated. It is demonstrated that, for a given sequence of CS symbols, an optimal bandwidth (or symbol rate) can be determined so that the temporal duration of the propagated signal at the end of the fiber is minimized. In effect, the required guard interval between the subsequently transmitted data packets in time is minimized and the effective data rate is significantly enhanced. Moreover, by selecting the proper signaling method and design criteria a distance reach of 7100 km is reported by only singling on CS at a rate of 9.6 Gbps.

Nonlinear model-order reduction for compressible flow solvers using the Discrete Empirical Interpolation Method

NASA Astrophysics Data System (ADS)

Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis

2016-11-01

Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIM-approximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated to the flow around an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

PubMed

Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

2018-01-01

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Non-linear homogenized and heterogeneous FE models for FRCM reinforced masonry walls in diagonal compression

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Poggi, Carlo

2016-12-01

Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.

PubMed

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

PubMed Central

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

Local numerical modelling of ultrasonic guided waves in linear and nonlinear media

NASA Astrophysics Data System (ADS)

Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Invited Review Article: Imaging techniques for harmonic and multiphoton absorption fluorescence microscopy

PubMed Central

Carriles, Ramón; Schafer, Dawn N.; Sheetz, Kraig E.; Field, Jeffrey J.; Cisek, Richard; Barzda, Virginijus; Sylvester, Anne W.; Squier, Jeffrey A.

2009-01-01

We review the current state of multiphoton microscopy. In particular, the requirements and limitations associated with high-speed multiphoton imaging are considered. A description of the different scanning technologies such as line scan, multifoci approaches, multidepth microscopy, and novel detection techniques is given. The main nonlinear optical contrast mechanisms employed in microscopy are reviewed, namely, multiphoton excitation fluorescence, second harmonic generation, and third harmonic generation. Techniques for optimizing these nonlinear mechanisms through a careful measurement of the spatial and temporal characteristics of the focal volume are discussed, and a brief summary of photobleaching effects is provided. Finally, we consider three new applications of multiphoton microscopy: nonlinear imaging in microfluidics as applied to chemical analysis and the use of two-photon absorption and self-phase modulation as contrast mechanisms applied to imaging problems in the medical sciences. PMID:19725639

Isotherm investigation for the sorption of fluoride onto Bio-F: comparison of linear and non-linear regression method

NASA Astrophysics Data System (ADS)

Yadav, Manish; Singh, Nitin Kumar

2017-12-01

A comparison of the linear and non-linear regression method in selecting the optimum isotherm among three most commonly used adsorption isotherms (Langmuir, Freundlich, and Redlich-Peterson) was made to the experimental data of fluoride (F) sorption onto Bio-F at a solution temperature of 30 ± 1 °C. The coefficient of correlation (r2) was used to select the best theoretical isotherm among the investigated ones. A total of four Langmuir linear equations were discussed and out of which linear form of most popular Langmuir-1 and Langmuir-2 showed the higher coefficient of determination (0.976 and 0.989) as compared to other Langmuir linear equations. Freundlich and Redlich-Peterson isotherms showed a better fit to the experimental data in linear least-square method, while in non-linear method Redlich-Peterson isotherm equations showed the best fit to the tested data set. The present study showed that the non-linear method could be a better way to obtain the isotherm parameters and represent the most suitable isotherm. Redlich-Peterson isotherm was found to be the best representative (r2 = 0.999) for this sorption system. It is also observed that the values of β are not close to unity, which means the isotherms are approaching the Freundlich but not the Langmuir isotherm.

Influence of Ga doping ratio on the saturable absorption mechanism in Ga doped ZnO thin solid films processed by sol-gel spin coating technique

NASA Astrophysics Data System (ADS)

Sandeep, K. M.; Bhat, Shreesha; Dharmaprakash, S. M.; Byrappa, K.

2017-03-01

In the present study, the nonlinear optical properties of sol-gel spin coated gallium doped zinc oxide (GZO) thin solid films are explored with nanosecond laser pulses using the z-scan technique. The higher doping ratios of Ga result in a large redshift of the energy gap (0.38 eV) due to the existence of enhanced grain boundary defects in GZO films. A positive nonlinear absorption coefficient is observed in undoped 1 at.wt.% GZO and 2 at.wt.% GZO films, and a negative nonlinear absorption coefficient in 3 at.wt.% GZO film. Fewer defects in undoped 1% GZO and 2% GZO films resulted in reverse saturable absorption (RSA), whereas a saturable absorption (SA) mechanism is observed in 3% GZO films and is attributed to the enhanced defect concentration in the band structure of GZO. However, all the films showed a self-defocusing mechanism, derived by a closed aperture z-scan technique. The present work sheds light on the defect mechanism involved in the observed nonlinear properties of GZO films.

Nonlinear optical characterization of graphite oxide thin film by open aperture Z-scan technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sreeja, V. G.; Reshmi, R.; Devasia, Sebin

In this paper we explore the structural characterization of graphite oxide powder prepared from graphite powder by oxidation via modified Hummers method. The nonlinear optical properties of the spin coated graphite oxide thin film is also explored by open aperture Z-Scan technique. Structural and physiochemical properties of the samples were investigated with the help of Fourier Transform Infrared Spectroscopy (FTIR) and Raman Spectroscopy (Raman).The results of FT-IR and Raman spectroscopy showed that the graphite is oxidized by strong oxidants and the oxygen atoms are introduced into the graphite layers forming C=C, O-H and –C-H groups. The synthesized sample has goodmore » crystalline nature with lesser defects. The nonlinear optical property of GO thin film was studied by open aperture Z-Scan technique using Q-switched Nd-Yag Laser at 532 nm. The Z-scan plot showed that the investigated GO thin film has saturable absorption behavior. The nonlinear absorption coefficient and saturation intensity were also estimated to explore its applications in Q switched mode locking laser systems.« less

Neural robust stabilization via event-triggering mechanism and adaptive learning technique.

PubMed

Wang, Ding; Liu, Derong

2018-06-01

The robust control synthesis of continuous-time nonlinear systems with uncertain term is investigated via event-triggering mechanism and adaptive critic learning technique. We mainly focus on combining the event-triggering mechanism with adaptive critic designs, so as to solve the nonlinear robust control problem. This can not only make better use of computation and communication resources, but also conduct controller design from the view of intelligent optimization. Through theoretical analysis, the nonlinear robust stabilization can be achieved by obtaining an event-triggered optimal control law of the nominal system with a newly defined cost function and a certain triggering condition. The adaptive critic technique is employed to facilitate the event-triggered control design, where a neural network is introduced as an approximator of the learning phase. The performance of the event-triggered robust control scheme is validated via simulation studies and comparisons. The present method extends the application domain of both event-triggered control and adaptive critic control to nonlinear systems possessing dynamical uncertainties. Copyright © 2018 Elsevier Ltd. All rights reserved.

Optical nonlinearities of colloidal InP@ZnS core-shell quantum dots probed by Z-scan and two-photon excited emission

NASA Astrophysics Data System (ADS)

Wawrzynczyk, Dominika; Szeremeta, Janusz; Samoc, Marek; Nyk, Marcin

2015-11-01

Spectrally resolved nonlinear optical properties of colloidal InP@ZnS core-shell quantum dots of various sizes were investigated with the Z-scan technique and two-photon fluorescence excitation method using a femtosecond laser system tunable in the range from 750 nm to 1600 nm. In principle, both techniques should provide comparable results and can be interchangeably used for determination of the nonlinear optical absorption parameters, finding maximal values of the cross sections and optimizing them. We have observed slight differences between the two-photon absorption cross sections measured by the two techniques and attributed them to the presence of non-radiative paths of absorption or relaxation. The most significant value of two-photon absorption cross section σ2 for 4.3 nm size InP@ZnS quantum dot was equal to 2200 GM, while the two-photon excitation action cross section σ2Φ was found to be 682 GM at 880 nm. The properties of these cadmium-free colloidal quantum dots can be potentially useful for nonlinear bioimaging.

Study of nonlinear absorption properties of reduced graphene oxide by Z-scan technique

NASA Astrophysics Data System (ADS)

Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.

2017-05-01

Graphene has generated enormous research interest during the last decade due to its significant unique properties and wide applications in the field of optoelectronics and photonics. This research studied the structural and nonlinear absorption properties of reduced graphene oxide (rGO) synthesized by Modified Hummer's method. Structural and physiochemical properties of the rGO were explored with the help of Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy (Raman). Nonlinear absorption property in rGO, was investigated by open aperture Z-scan technique by using a continuous wave (CW) laser. The Z-scan results demonstrate saturable absorption property of rGO with a nonlinear absorption coefficient, β, of -2.62 × 10-4 cm/W, making it suitable for applications in Q switching, generation of ultra-fast high energy pulses in laser cavity and mode lockers.

Exact nonlinear model reduction for a von Kármán beam: Slow-fast decomposition and spectral submanifolds

NASA Astrophysics Data System (ADS)

Jain, Shobhit; Tiso, Paolo; Haller, George

2018-06-01

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Kármán beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a linear modal subspace, is then used to further reduce the beam equations within the slow manifold. This two-stage, mathematically exact procedure results in a drastic reduction of the finite-element beam model to a one-degree-of freedom nonlinear oscillator. We also introduce the technique of spectral quotient analysis, which gives the number of modes relevant for reduction as output rather than input to the reduction process.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Applications

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1998-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Sparse 4D TomoSAR imaging in the presence of non-linear deformation

NASA Astrophysics Data System (ADS)

Khwaja, Ahmed Shaharyar; ćetin, Müjdat

2018-04-01

In this paper, we present a sparse four-dimensional tomographic synthetic aperture radar (4D TomoSAR) imaging scheme that can estimate elevation and linear as well as non-linear seasonal deformation rates of scatterers using the interferometric phase. Unlike existing sparse processing techniques that use fixed dictionaries based on a linear deformation model, we use a variable dictionary for the non-linear deformation in the form of seasonal sinusoidal deformation, in addition to the fixed dictionary for the linear deformation. We estimate the amplitude of the sinusoidal deformation using an optimization method and create the variable dictionary using the estimated amplitude. We show preliminary results using simulated data that demonstrate the soundness of our proposed technique for sparse 4D TomoSAR imaging in the presence of non-linear deformation.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Application

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1997-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Spatial and temporal ultrafast imaging and control of terahertz wavepackets

NASA Astrophysics Data System (ADS)

Koehl, Richard Michael

Some polar optical phonons couple strongly to far- infrared electromagnetic radiation and move at light-like speeds through dielectric media. These phonon-polaritons retain both ionic and electromagnetic character. One of the fruitful implications of this mixing is that vibrational and electronic nonlinearities in ferroelectric and other highly anharmonic media interact with traveling electromagnetic waves spanning several frequency regimes, permitting nonlinear wave mixing at infrared and optical frequencies. Nonlinear optical mixing techniques are well-developed because optical light is easy to produce, but the lack of similar far- infrared sources has stymied similar efforts at terahertz frequencies. Nonlinear interactions in this frequency regime provide information about vibrational potential energy surfaces and are very strong when the lattice vibration is associated with a phase transition. In this thesis, I review methods based on a well known nonlinear optical technique, impulsive stimulated Raman scattering (ISRS), to monitor the progress of coherent phonon polaritons in a highly nonlinear ferroelectric, lithium tantalate. I also advance multiple-pulse ISRS optical techniques to attempt to elucidate information about the ferroelectric's vibrational potential energy surface, and I discuss significant recent progress that has been made in the development of ultrafast optical tools to generate far-infrared radiation through ISRS at specified times and spatial locations and control the interactions of coherent phonon-polariton wavepackets. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Strong Langmuir Turbulence and Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Glanz, James

1991-02-01

The staircase expansion is a new mathematical technique for deriving reduced, nonlinear-PDE descriptions from the plasma-moment equations. Such descriptions incorporate only the most significant linear and nonlinear terms of more complex systems. The technique is used to derive a set of Dawson-Zakharov or "master" equations, which unify and generalize previous work and show the limitations of models commonly used to describe nonlinear plasma waves. Fundamentally new wave-evolution equations are derived that admit of exact nonlinear solutions (solitary waves). Analytic calculations illustrate the competition between well-known effects of self-focusing, which require coupling to ion motion, and pure-electron nonlinearities, which are shown to be especially important in curved geometries. Also presented is an N -moment hydrodynamic model derived from the Vlasov equation. In this connection, the staircase expansion is shown to remain useful for all values of N >= 3. The relevance of the present work to nonlocally truncated hierarchies, which more accurately model dissipation, is briefly discussed. Finally, the general formalism is applied to the problem of electromagnetic emission from counterpropagating Langmuir pumps. It is found that previous treatments have neglected order-unity effects that increase the emission significantly. Detailed numerical results are presented to support these conclusions. The staircase expansion--so called because of its appearance when written out--should be effective whenever the largest contribution to the nonlinear wave remains "close" to some given frequency. Thus the technique should have application to studies of wake-field acceleration schemes and anomalous damping of plasma waves.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minissale, S.; Yerci, S.; Dal Negro, L.

We investigate the nonlinear optical properties of Si-rich silicon oxide (SRO) and Si-rich silicon nitride (SRN) samples as a function of silicon content, annealing temperature, and excitation wavelength. Using the Z-scan technique, we measure the non-linear refractive index n{sub 2} and the nonlinear absorption coefficient {beta} for a large number of samples fabricated by reactive co-sputtering. Moreover, we characterize the nonlinear optical parameters of SRN in the broad spectral region 1100-1500 nm and show the strongest nonlinearity at 1500 nm. These results demonstrate the potential of the SRN matrix for the engineering of compact devices with enhanced Kerr nonlinearities formore » silicon photonics applications.« less

The edge of chaos: A nonlinear view of psychoanalytic technique.

PubMed

Galatzer-Levy, Robert M

2016-04-01

The field of nonlinear dynamics (or chaos theory) provides ways to expand concepts of psychoanalytic process that have implications for the technique of psychoanalysis. This paper describes how concepts of "the edge of chaos," emergence, attractors, and coupled oscillators can help shape analytic technique resulting in an approach to doing analysis which is at the same time freer and more firmly based in an enlarged understanding of the ways in which psychoanalysis works than some current recommendation about technique. Illustrations from a lengthy analysis of an analysand with obsessive-compulsive disorder show this approach in action. Copyright © 2016 Institute of Psychoanalysis.

Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation

NASA Technical Reports Server (NTRS)

Rakoczy, John M.; Herren, Kenneth A.

2008-01-01

A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation

NASA Technical Reports Server (NTRS)

Rakoczy, John; Herren, Kenneth

2007-01-01

A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.

A VLF-based technique in applications to digital control of nonlinear hybrid multirate systems

NASA Astrophysics Data System (ADS)

Vassilyev, Stanislav; Ulyanov, Sergey; Maksimkin, Nikolay

2017-01-01

In this paper, a technique for rigorous analysis and design of nonlinear multirate digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is proposed. The control system model under consideration incorporates continuous-time dynamics of the plant and discrete-time dynamics of the controller and takes into account uncertainties of the plant, bounded disturbances, nonlinear characteristics of sensors and actuators. We consider a class of multirate systems where the control update rate is slower than the measurement sampling rates and periodic non-uniform sampling is admitted. The proposed technique does not use the preliminary discretization of the system, and, hence, allows one to eliminate the errors associated with the discretization and improve the accuracy of analysis. The technique is applied to synthesis of digital controller for a flexible spacecraft in the fine stabilization mode and decentralized controller for a formation of autonomous underwater vehicles. Simulation results are provided to validate the good performance of the designed controllers.

Using existing case-mix methods to fund trauma cases.

PubMed

Monakova, Julia; Blais, Irene; Botz, Charles; Chechulin, Yuriy; Picciano, Gino; Basinski, Antoni

2010-01-01

Policymakers frequently face the need to increase funding in isolated and frequently heterogeneous (clinically and in terms of resource consumption) patient subpopulations. This article presents a methodologic solution for testing the appropriateness of using existing grouping and weighting methodologies for funding subsets of patients in the scenario where a case-mix approach is preferable to a flat-rate based payment system. Using as an example the subpopulation of trauma cases of Ontario lead trauma hospitals, the statistical techniques of linear and nonlinear regression models, regression trees, and spline models were applied to examine the fit of the existing case-mix groups and reference weights for the trauma cases. The analyses demonstrated that for funding Ontario trauma cases, the existing case-mix systems can form the basis for rational and equitable hospital funding, decreasing the need to develop a different grouper for this subset of patients. This study confirmed that Injury Severity Score is a poor predictor of costs for trauma patients. Although our analysis used the Canadian case-mix classification system and cost weights, the demonstrated concept of using existing case-mix systems to develop funding rates for specific subsets of patient populations may be applicable internationally.

Linear and nonlinear spectroscopy from quantum master equations.

PubMed

Fetherolf, Jonathan H; Berkelbach, Timothy C

2017-12-28

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Linear and nonlinear spectroscopy from quantum master equations

NASA Astrophysics Data System (ADS)

Fetherolf, Jonathan H.; Berkelbach, Timothy C.

2017-12-01

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Near real-time analysis of extrinsic Fabry-Perot interferometric sensors under damped vibration using artificial neural networks

NASA Astrophysics Data System (ADS)

Dua, Rohit; Watkins, Steve E.

2009-03-01

Strain analysis due to vibration can provide insight into structural health. An Extrinsic Fabry-Perot Interferometric (EFPI) sensor under vibrational strain generates a non-linear modulated output. Advanced signal processing techniques, to extract important information such as absolute strain, are required to demodulate this non-linear output. Past research has employed Artificial Neural Networks (ANN) and Fast Fourier Transforms (FFT) to demodulate the EFPI sensor for limited conditions. These demodulation systems could only handle variations in absolute value of strain and frequency of actuation during a vibration event. This project uses an ANN approach to extend the demodulation system to include the variation in the damping coefficient of the actuating vibration, in a near real-time vibration scenario. A computer simulation provides training and testing data for the theoretical output of the EFPI sensor to demonstrate the approaches. FFT needed to be performed on a window of the EFPI output data. A small window of observation is obtained, while maintaining low absolute-strain prediction errors, heuristically. Results are obtained and compared from employing different ANN architectures including multi-layered feedforward ANN trained using Backpropagation Neural Network (BPNN), and Generalized Regression Neural Networks (GRNN). A two-layered algorithm fusion system is developed and tested that yields better results.

Single-shot measurement of nonlinear absorption and nonlinear refraction.

PubMed

Jayabalan, J; Singh, Asha; Oak, Shrikant M

2006-06-01

A single-shot method for measurement of nonlinear optical absorption and refraction is described and analyzed. A spatial intensity variation of an elliptical Gaussian beam in conjugation with an array detector is the key element of this method. The advantages of this single-shot technique were demonstrated by measuring the two-photon absorption and free-carrier absorption in GaAs as well as the nonlinear refractive index of CS2 using a modified optical Kerr setup.

Apparatus and method for epileptic seizure detection using non-linear techniques

DOEpatents

Hively, L.M.; Clapp, N.E.; Daw, C.S.; Lawkins, W.F.

1998-04-28

Methods and apparatus are disclosed for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence. 76 figs.

Third-order nonlinear optical properties of organic azo dyes by using strength of nonlinearity parameter and Z-scan technique

NASA Astrophysics Data System (ADS)

Motiei, H.; Jafari, A.; Naderali, R.

2017-02-01

In this paper, two chemically synthesized organic azo dyes, 2-(2,5-Dichloro-phenyazo)-5,5-dimethyl-cyclohexane-1,3-dione (azo dye (i)) and 5,5-Dimethyl-2-tolylazo-cyclohexane-1,3-dione (azo dye (ii)), have been studied from optical Kerr nonlinearity point of view. These materials were characterized by Ultraviolet-visible spectroscopy. Experiments were performed using a continous wave diode-pumped laser at 532 nm wavelength in three intensities of the laser beam. Nonlinear absorption (β), refractive index (n2) and third-order susceptibility (χ (3)) of dyes, were calculated. Nonlinear absorption coefficient of dyes have been calculated from two methods; 1) using theoretical fits and experimental data in the Z-scan technique, 2) using the strength of nonlinearity curves. The values of β obtained from both of the methods were approximately the same. The results demonstrated that azo dye (ii) displays better nonlinearity and has a lower two-photon absorption threshold than azo dye (i). Calculated parameter related to strength of nonlinearity for azo dye (ii) was higher than azo dye (i), It may be due to presence of methyl in azo dye (ii) instead of chlorine in azo dye (i). Furthermore, The measured values of third order susceptibility of azo dyes were from the order of 10-9 esu . These azo dyes can be suitable candidate for optical switching devices.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1978-01-01

4. TITLE (and Subtitle) 5. TYPE OF REPORT 6 PERIOD COVERED MATHEMATICAL TECHNIQUES FOR NONLINEAR SYSTEM THEORY Interim 6...ADDRESS 10. PROGRAM ELEMENT. PROJECT . TASK AREA & WORK UNIT NUMBERS Unlvers].ty of Flori.da Center for Mathematical System Theory ~~~~ Gainesville , FL...rings”, Mathematical System Theory , 9: 327—344. E. D. SONTAG (1976b1 “Linear systems over commutative rings: a survey”, Richerche di Automatica, 7: 1-34

Dynamics and control for Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Partll

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques were applied to derive the dynamics of a Differential Wheeled Mobile Robot (DWMR) in the companion paper. The present paper formulates a control system design for trajectory tracking of this class of robots. The method develops a feedback linearization technique for the nonlinear system using dynamic extension algorithm. The effectiveness of the nonlinear controller is illustrated with simulation example.

Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems.

PubMed

Dai, Shi-Lu; Wang, Cong; Wang, Min

2014-01-01

This paper studies the problem of learning from adaptive neural network (NN) control of a class of nonaffine nonlinear systems in uncertain dynamic environments. In the control design process, a stable adaptive NN tracking control design technique is proposed for the nonaffine nonlinear systems with a mild assumption by combining a filtered tracking error with the implicit function theorem, input-to-state stability, and the small-gain theorem. The proposed stable control design technique not only overcomes the difficulty in controlling nonaffine nonlinear systems but also relaxes constraint conditions of the considered systems. In the learning process, the partial persistent excitation (PE) condition of radial basis function NNs is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition and an appropriate state transformation, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the implicit desired control input dynamics in the stable control process and of storing the learned knowledge in memory. Subsequently, an NN learning control design technique that effectively exploits the learned knowledge without re-adapting to the controller parameters is proposed to achieve closed-loop stability and improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Estimating the concrete compressive strength using hard clustering and fuzzy clustering based regression techniques.

PubMed

Nagwani, Naresh Kumar; Deo, Shirish V

2014-01-01

Understanding of the compressive strength of concrete is important for activities like construction arrangement, prestressing operations, and proportioning new mixtures and for the quality assurance. Regression techniques are most widely used for prediction tasks where relationship between the independent variables and dependent (prediction) variable is identified. The accuracy of the regression techniques for prediction can be improved if clustering can be used along with regression. Clustering along with regression will ensure the more accurate curve fitting between the dependent and independent variables. In this work cluster regression technique is applied for estimating the compressive strength of the concrete and a novel state of the art is proposed for predicting the concrete compressive strength. The objective of this work is to demonstrate that clustering along with regression ensures less prediction errors for estimating the concrete compressive strength. The proposed technique consists of two major stages: in the first stage, clustering is used to group the similar characteristics concrete data and then in the second stage regression techniques are applied over these clusters (groups) to predict the compressive strength from individual clusters. It is found from experiments that clustering along with regression techniques gives minimum errors for predicting compressive strength of concrete; also fuzzy clustering algorithm C-means performs better than K-means algorithm.

Estimating the Concrete Compressive Strength Using Hard Clustering and Fuzzy Clustering Based Regression Techniques

PubMed Central

Nagwani, Naresh Kumar; Deo, Shirish V.

2014-01-01

Understanding of the compressive strength of concrete is important for activities like construction arrangement, prestressing operations, and proportioning new mixtures and for the quality assurance. Regression techniques are most widely used for prediction tasks where relationship between the independent variables and dependent (prediction) variable is identified. The accuracy of the regression techniques for prediction can be improved if clustering can be used along with regression. Clustering along with regression will ensure the more accurate curve fitting between the dependent and independent variables. In this work cluster regression technique is applied for estimating the compressive strength of the concrete and a novel state of the art is proposed for predicting the concrete compressive strength. The objective of this work is to demonstrate that clustering along with regression ensures less prediction errors for estimating the concrete compressive strength. The proposed technique consists of two major stages: in the first stage, clustering is used to group the similar characteristics concrete data and then in the second stage regression techniques are applied over these clusters (groups) to predict the compressive strength from individual clusters. It is found from experiments that clustering along with regression techniques gives minimum errors for predicting compressive strength of concrete; also fuzzy clustering algorithm C-means performs better than K-means algorithm. PMID:25374939

Applying a nonlinear, pitch-catch, ultrasonic technique for the detection of kissing bonds in friction stir welds.

PubMed

Delrue, Steven; Tabatabaeipour, Morteza; Hettler, Jan; Van Den Abeele, Koen

2016-05-01

Friction stir welding (FSW) is a promising technology for the joining of aluminum alloys and other metallic admixtures that are hard to weld by conventional fusion welding. Although FSW generally provides better fatigue properties than traditional fusion welding methods, fatigue properties are still significantly lower than for the base material. Apart from voids, kissing bonds for instance, in the form of closed cracks propagating along the interface of the stirred and heat affected zone, are inherent features of the weld and can be considered as one of the main causes of a reduced fatigue life of FSW in comparison to the base material. The main problem with kissing bond defects in FSW, is that they currently are very difficult to detect using existing NDT methods. Besides, in most cases, the defects are not directly accessible from the exposed surface. Therefore, new techniques capable of detecting small kissing bond flaws need to be introduced. In the present paper, a novel and practical approach is introduced based on a nonlinear, single-sided, ultrasonic technique. The proposed inspection technique uses two single element transducers, with the first transducer transmitting an ultrasonic signal that focuses the ultrasonic waves at the bottom side of the sample where cracks are most likely to occur. The large amount of energy at the focus activates the kissing bond, resulting in the generation of nonlinear features in the wave propagation. These nonlinear features are then captured by the second transducer operating in pitch-catch mode, and are analyzed, using pulse inversion, to reveal the presence of a defect. The performance of the proposed nonlinear, pitch-catch technique, is first illustrated using a numerical study of an aluminum sample containing simple, vertically oriented, incipient cracks. Later, the proposed technique is also applied experimentally on a real-life friction stir welded butt joint containing a kissing bond flaw. Copyright © 2016 Elsevier B.V. All rights reserved.

Correntropy-based partial directed coherence for testing multivariate Granger causality in nonlinear processes

NASA Astrophysics Data System (ADS)

Kannan, Rohit; Tangirala, Arun K.

2014-06-01

Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.

Effect of reduction time on third order optical nonlinearity of reduced graphene oxide

NASA Astrophysics Data System (ADS)

Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.

2017-04-01

We report the influence of reduction time on structural, linear and nonlinear optical properties of reduced graphene oxide (rGO) thin films synthesized by spin coating method. We observed that the structural, linear and nonlinear optical properties can be tuned with reduction time in GO is due to the increased structural ordering because of the restoration of sp2 carbon atoms with the time of reduction. The nonlinear absorption studies by open aperture Z-scan technique exhibited a saturable absorption. The nonlinear refraction studies showed the self de focusing nature of rGO by closed aperture Z scan technique. The nonlinear absorption coefficient and saturation intensity varies with the time for reduction of GO which is attributed to the depletion of valence band and the conduction band filling effect. Our results emphasize duration for reduction of GO dependent optical nonlinearity of rGO thin films to a great extent and explore its applications Q switched mode locking laser systems for generating ultra short laser pulses and in optical sensors. The rGO coated films were characterized by X-Ray diffraction method (XRD), Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, UV-Vis absorption spectroscopy (UV-Vis), Photoluminescence (PL) and Scanning electron microscope (SEM) measurements.

Traffic Predictive Control: Case Study and Evaluation

DOT National Transportation Integrated Search

2017-06-26

This project developed a quantile regression method for predicting future traffic flow at a signalized intersection by combining both historical and real-time data. The algorithm exploits nonlinear correlations in historical measurements and efficien...

Modelling daily water temperature from air temperature for the Missouri River.

PubMed

Zhu, Senlin; Nyarko, Emmanuel Karlo; Hadzima-Nyarko, Marijana

2018-01-01

The bio-chemical and physical characteristics of a river are directly affected by water temperature, which thereby affects the overall health of aquatic ecosystems. It is a complex problem to accurately estimate water temperature. Modelling of river water temperature is usually based on a suitable mathematical model and field measurements of various atmospheric factors. In this article, the air-water temperature relationship of the Missouri River is investigated by developing three different machine learning models (Artificial Neural Network (ANN), Gaussian Process Regression (GPR), and Bootstrap Aggregated Decision Trees (BA-DT)). Standard models (linear regression, non-linear regression, and stochastic models) are also developed and compared to machine learning models. Analyzing the three standard models, the stochastic model clearly outperforms the standard linear model and nonlinear model. All the three machine learning models have comparable results and outperform the stochastic model, with GPR having slightly better results for stations No. 2 and 3, while BA-DT has slightly better results for station No. 1. The machine learning models are very effective tools which can be used for the prediction of daily river temperature.

The nonlinear relations of the approximate number system and mathematical language to early mathematics development.

PubMed

Purpura, David J; Logan, Jessica A R

2015-12-01

Both mathematical language and the approximate number system (ANS) have been identified as strong predictors of early mathematics performance. Yet, these relations may be different depending on a child's developmental level. The purpose of this study was to evaluate the relations between these domains across different levels of ability. Participants included 114 children who were assessed in the fall and spring of preschool on a battery of academic and cognitive tasks. Children were 3.12 to 5.26 years old (M = 4.18, SD = .58) and 53.6% were girls. Both mixed-effect and quantile regressions were conducted. The mixed-effect regressions indicated that mathematical language, but not the ANS, nor other cognitive domains, predicted mathematics performance. However, the quantile regression analyses revealed a more nuanced relation among domains. Specifically, it was found that mathematical language and the ANS predicted mathematical performance at different points on the ability continuum. These dual nonlinear relations indicate that different mechanisms may enhance mathematical acquisition dependent on children's developmental abilities. (c) 2015 APA, all rights reserved).

On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

USGS Publications Warehouse

Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.

2011-01-01

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.

A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Karel, S.

1975-01-01

An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.

Nonlinear and Synchronous Dissolved Organic Matter Dynamics in Streams Across an Agriculture Land Use and Climate Setting

NASA Astrophysics Data System (ADS)

Xenopoulos, M. A.; Vogt, R. J.

2014-12-01

There is now increasing evidence that non-linearity is a common response in ecological systems to pressures caused by human activities. There is also increasing evidence that exogenous environmental drivers, such as climate, induce spatial and temporal synchrony in a wide range of ecological variables. Using Moran's I and Pearson's correlation, we quantified the synchrony of dissolved organic carbon concentration (DOC) and quality (DOM; e.g., specific UV absorbance, Fluorescence Index, PARAFAC), nutrients, discharge and temperature in 40 streams that span an agriculture gradient (0 to >70% cropland), over 10 years. We then used breakpoint regression, 2D-Kolmogorov-Smirnov test and significant zero crossings (SiZer) analyses to quantify the prevalence of nonlinearity and ecological thresholds (breakpoints) where applicable. There was a high degree of synchrony in DOM quality (r > 0.7) but not DOC (r < 0.4). The degree of synchrony was driven in part by the catchment's land use. With respect to the nonlinear analyses we found non-linearity in ~50% of bivariate datasets analyzed. Non-linearity was also driven in part by the catchment's land use. Breakpoints defined different DOM properties. Nonlinearity and synchronous behaviour in DOM are intimately linked to land use.

Genomic prediction based on data from three layer lines using non-linear regression models.

PubMed

Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L

2014-11-06

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional occurrence of large negative accuracies when the evaluated line was not included in the training dataset. Furthermore, when using a multi-line training dataset, non-linear models provided information on the genotype data that was complementary to the linear models, which indicates that the underlying data distributions of the three studied lines were indeed heterogeneous.

Design, synthesis and nonlinear optical properties of (E)-1-(4-substituted)-3-(4-hydroxy-3-nitrophenyl) prop-2-en-1-one compounds

NASA Astrophysics Data System (ADS)

Saha, Amrita; Shukla, Vijay; Choudhury, Sudip; Jayabalan, J.

2016-06-01

A new series of (E)-1-(4-substituted)-3-(4-hydroxy-3-nitrophenyl) prop-2-en-1-one compounds have been synthesized by Claisen-Schmidt condensation reaction. Nonlinear optical characterization were carried out using z-scan technique with nanosecond pulses. These samples are found to exhibit strong nonlinear absorption at 532 nm and the nonlinear absorption coefficient of these samples exponentially increases with the increase of phonon characteristic energy. This relation speaks the role of phonon in the origin of nonlinear absorption in these compounds. The reported dependence of optical nonlinearity of the chalcone derivatives on the phonon characteristic energy will help in designing similar class of new molecules with high nonlinear coefficients.

L1-Based Approximations of PDEs and Applications

DTIC Science & Technology

2012-09-05

the analysis of the Navier-Stokes equations. The early versions of artificial vis- cosities being overly dissipative, the interest for these technique ...Guermond, and B. Popov. Stability analysis of explicit en- tropy viscosity methods for non-linear scalar conservation equations. Math. Comp., 2012... methods for solv- ing mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems

Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

NASA Astrophysics Data System (ADS)

Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.

2017-12-01

We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

Real-Time Implementation of Nonlinear Processing Functions.

DTIC Science & Technology

1981-08-01

crystal devices and then to use them in a coherent optical data- processing apparatus using halftone masks custom designed at the University oi Southern...California. With the halftone mask technique, we have demonstrated logarithmic nonlinear transformation, allowing us to separate multiplicative images...improved.,_ This device allowed nonlinear functions to be implemented directly wit - out the need for specially made halftone masks. Besides

In situ nonlinear ultrasonic technique for monitoring microcracking in concrete subjected to creep and cyclic loading.

PubMed

Kim, Gun; Loreto, Giovanni; Kim, Jin-Yeon; Kurtis, Kimberly E; Wall, James J; Jacobs, Laurence J

2018-08-01

This research conducts in situ nonlinear ultrasonic (NLU) measurements for real time monitoring of load-induced damage in concrete. For the in situ measurements on a cylindrical specimen under sustained load, a previously developed second harmonic generation (SHG) technique with non-contact detection is adapted to a cylindrical specimen geometry. This new setup is validated by demonstrating that the measured nonlinear Rayleigh wave signals are equivalent to those in a flat half space, and thus the acoustic nonlinearity parameter, β can be defined and interpreted in the same way. Both the acoustic nonlinearity parameter and strain are measured to quantitatively assess the early-age damage in a set of concrete specimens subjected to either 25 days of creep, or 11 cycles of cyclic loading at room temperature. The experimental results show that the acoustic nonlinearity parameter is sensitive to early-stage microcrack formation under both loading conditions - the measured β can be directly linked to the accumulated microscale damage. This paper demonstrates the potential of NLU for the in situ monitoring of mechanical load-induced microscale damage in concrete components. Copyright © 2018 Elsevier B.V. All rights reserved.

Au NPs immersed in sol-gel matrix: nonlinear optical characterization

NASA Astrophysics Data System (ADS)

Aguilera-Zavala, Angélica; Trejo-Durán, Mónica; Ortiz-Jiménez, Orlando; Cornejo-Monroy, Delfino; Severiano-Carrillo, Israel; Alvarado-Méndez, Edgar

2016-09-01

Physical and optical characterization of thin films doped with Au Nanoparticles onto a silica substrate is presented. Films were prepared through sol-gel process, by using Au nanoparticles immersed in lipoic acid as dopant by means of hydrolysis and acid catalyzed reaction of tetraethyl-orthosilicate. The surface was characterized by SEM and AFM microscopies. Z-scan technique was used to measure nonlinear optical properties as nonlinear absorption and refraction indexes, using two different wavelengths. At 633 nm it was possible to observe nonlinear absorption only but at 514 nm both nonlinear properties were observed.

Nonlocal nonlinear refraction in Hibiscus sabdariffa with large phase shifts.

PubMed

Ramírez-Martínez, D; Alvarado-Méndez, E; Trejo-Durán, M; Vázquez-Guevara, M A

2014-10-20

In this work we present a study of nonlinear optical properties in organic materials (hibiscus sabdariffa). Our results demonstrate that the medium exhibits a highly nonlocal nonlinear response. We show preliminary numerical results of the transmittance as nonlocal response by considering, simultaneously, the nonlinear absorption and refraction in media. Numerical results are accord to measurement obtained by Z- scan technique where we observe large phase shifts. We also analyze the far field diffraction ring patterns of the sample.

Nonlinear compression of temporal solitons in an optical waveguide via inverse engineering

NASA Astrophysics Data System (ADS)

Paul, Koushik; Sarma, Amarendra K.

2018-03-01

We propose a novel method based on the so-called shortcut-to-adiabatic passage techniques to achieve fast compression of temporal solitons in a nonlinear waveguide. We demonstrate that soliton compression could be achieved, in principle, at an arbitrarily small distance by inverse-engineering the pulse width and the nonlinearity of the medium. The proposed scheme could possibly be exploited for various short-distance communication protocols and may be even in nonlinear guided wave-optics devices and generation of ultrashort soliton pulses.

Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2

NASA Technical Reports Server (NTRS)

Lyell, M. J.; Zhang, L.

1994-01-01

The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.