Translation-aware semantic segmentation via conditional least-square generative adversarial networks

NASA Astrophysics Data System (ADS)

Zhang, Mi; Hu, Xiangyun; Zhao, Like; Pang, Shiyan; Gong, Jinqi; Luo, Min

2017-10-01

Semantic segmentation has recently made rapid progress in the field of remote sensing and computer vision. However, many leading approaches cannot simultaneously translate label maps to possible source images with a limited number of training images. The core issue is insufficient adversarial information to interpret the inverse process and proper objective loss function to overcome the vanishing gradient problem. We propose the use of conditional least squares generative adversarial networks (CLS-GAN) to delineate visual objects and solve these problems. We trained the CLS-GAN network for semantic segmentation to discriminate dense prediction information either from training images or generative networks. We show that the optimal objective function of CLS-GAN is a special class of f-divergence and yields a generator that lies on the decision boundary of discriminator that reduces possible vanished gradient. We also demonstrate the effectiveness of the proposed architecture at translating images from label maps in the learning process. Experiments on a limited number of high resolution images, including close-range and remote sensing datasets, indicate that the proposed method leads to the improved semantic segmentation accuracy and can simultaneously generate high quality images from label maps.

Noise reduction for low-dose helical CT by 3D penalized weighted least-squares sinogram smoothing

NASA Astrophysics Data System (ADS)

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-03-01

Helical computed tomography (HCT) has several advantages over conventional step-and-shoot CT for imaging a relatively large object, especially for dynamic studies. However, HCT may increase X-ray exposure significantly to the patient. This work aims to reduce the radiation by lowering the X-ray tube current (mA) and filtering the low-mA (or dose) sinogram noise. Based on the noise properties of HCT sinogram, a three-dimensional (3D) penalized weighted least-squares (PWLS) objective function was constructed and an optimal sinogram was estimated by minimizing the objective function. To consider the difference of signal correlation among different direction of the HCT sinogram, an anisotropic Markov random filed (MRF) Gibbs function was designed as the penalty. The minimization of the objection function was performed by iterative Gauss-Seidel updating strategy. The effectiveness of the 3D-PWLS sinogram smoothing for low-dose HCT was demonstrated by a 3D Shepp-Logan head phantom study. Comparison studies with our previously developed KL domain PWLS sinogram smoothing algorithm indicate that the KL+2D-PWLS algorithm shows better performance on in-plane noise-resolution trade-off while the 3D-PLWS shows better performance on z-axis noise-resolution trade-off. Receiver operating characteristic (ROC) studies by using channelized Hotelling observer (CHO) shows that 3D-PWLS and KL+2DPWLS algorithms have similar performance on detectability in low-contrast environment.

Generalized adjustment by least squares ( GALS).

USGS Publications Warehouse

Elassal, A.A.

1983-01-01

The least-squares principle is universally accepted as the basis for adjustment procedures in the allied fields of geodesy, photogrammetry and surveying. A prototype software package for Generalized Adjustment by Least Squares (GALS) is described. The package is designed to perform all least-squares-related functions in a typical adjustment program. GALS is capable of supporting development of adjustment programs of any size or degree of complexity. -Author

Reconstruction of vibroacoustic responses of a highly nonspherical structure using Helmholtz equation least-squares method.

PubMed

Lu, Huancai; Wu, Sean F

2009-03-01

The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.

A Simple Introduction to Moving Least Squares and Local Regression Estimation

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

Garimella, Rao Veerabhadra

In this brief note, a highly simpli ed introduction to esimating functions over a set of particles is presented. The note starts from Global Least Squares tting, going on to Moving Least Squares estimation (MLS) and nally, Local Regression Estimation (LRE).

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Least-Squares Adaptive Control Using Chebyshev Orthogonal Polynomials

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Burken, John; Ishihara, Abraham

2011-01-01

This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.

On estimating gravity anomalies: A comparison of least squares collocation with least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1976-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described, and its numerical properties are compared with the numerical properties of the conventional least squares estimator.

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1977-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike's Information Criterion

ERIC Educational Resources Information Center

Ding, Cody S.; Davison, Mark L.

2010-01-01

Akaike's information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation…

Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

ERIC Educational Resources Information Center

Helmreich, James E.; Krog, K. Peter

2018-01-01

We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

Estimating Shape and Micro-Motion Parameter of Rotationally Symmetric Space Objects from the Infrared Signature

PubMed Central

Wu, Yabei; Lu, Huanzhang; Zhao, Fei; Zhang, Zhiyong

2016-01-01

Shape serves as an important additional feature for space target classification, which is complementary to those made available. Since different shapes lead to different projection functions, the projection property can be regarded as one kind of shape feature. In this work, the problem of estimating the projection function from the infrared signature of the object is addressed. We show that the projection function of any rotationally symmetric object can be approximately represented as a linear combination of some base functions. Based on this fact, the signal model of the emissivity-area product sequence is constructed, which is a particular mathematical function of the linear coefficients and micro-motion parameters. Then, the least square estimator is proposed to estimate the projection function and micro-motion parameters jointly. Experiments validate the effectiveness of the proposed method. PMID:27763500

Application of Least Mean Square Algorithms to Spacecraft Vibration Compensation

NASA Technical Reports Server (NTRS)

Woodard , Stanley E.; Nagchaudhuri, Abhijit

1998-01-01

This paper describes the application of the Least Mean Square (LMS) algorithm in tandem with the Filtered-X Least Mean Square algorithm for controlling a science instrument's line-of-sight pointing. Pointing error is caused by a periodic disturbance and spacecraft vibration. A least mean square algorithm is used on-orbit to produce the transfer function between the instrument's servo-mechanism and error sensor. The result is a set of adaptive transversal filter weights tuned to the transfer function. The Filtered-X LMS algorithm, which is an extension of the LMS, tunes a set of transversal filter weights to the transfer function between the disturbance source and the servo-mechanism's actuation signal. The servo-mechanism's resulting actuation counters the disturbance response and thus maintains accurate science instrumental pointing. A simulation model of the Upper Atmosphere Research Satellite is used to demonstrate the algorithms.

A Stochastic Total Least Squares Solution of Adaptive Filtering Problem

PubMed Central

Ahmad, Noor Atinah

2014-01-01

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs. PMID:24688412

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

Confidence Region of Least Squares Solution for Single-Arc Observations

NASA Astrophysics Data System (ADS)

Principe, G.; Armellin, R.; Lewis, H.

2016-09-01

The total number of active satellites, rocket bodies, and debris larger than 10 cm is currently about 20,000. Considering all resident space objects larger than 1 cm this rises to an estimated minimum of 500,000 objects. Latest generation sensor networks will be able to detect small-size objects, producing millions of observations per day. Due to observability constraints it is likely that long gaps between observations will occur for small objects. This requires to determine the space object (SO) orbit and to accurately describe the associated uncertainty when observations are acquired on a single arc. The aim of this work is to revisit the classical least squares method taking advantage of the high order Taylor expansions enabled by differential algebra. In particular, the high order expansion of the residuals with respect to the state is used to implement an arbitrary order least squares solver, avoiding the typical approximations of differential correction methods. In addition, the same expansions are used to accurately characterize the confidence region of the solution, going beyond the classical Gaussian distributions. The properties and performances of the proposed method are discussed using optical observations of objects in LEO, HEO, and GEO.

An adaptive learning control system for large flexible structures

NASA Technical Reports Server (NTRS)

Thau, F. E.

1985-01-01

The objective of the research has been to study the design of adaptive/learning control systems for the control of large flexible structures. In the first activity an adaptive/learning control methodology for flexible space structures was investigated. The approach was based on using a modal model of the flexible structure dynamics and an output-error identification scheme to identify modal parameters. In the second activity, a least-squares identification scheme was proposed for estimating both modal parameters and modal-to-actuator and modal-to-sensor shape functions. The technique was applied to experimental data obtained from the NASA Langley beam experiment. In the third activity, a separable nonlinear least-squares approach was developed for estimating the number of excited modes, shape functions, modal parameters, and modal amplitude and velocity time functions for a flexible structure. In the final research activity, a dual-adaptive control strategy was developed for regulating the modal dynamics and identifying modal parameters of a flexible structure. A min-max approach was used for finding an input to provide modal parameter identification while not exceeding reasonable bounds on modal displacement.

Least-Squares, Continuous Sensitivity Analysis for Nonlinear Fluid-Structure Interaction

DTIC Science & Technology

2009-08-20

Tangential stress optimization convergence to uniform value  1.797  as a function of eccentric anomaly   E and Objective function value as a...up to the domain dimension, domainn . Equation (3.7) expands as truncation error round-off error decreasing step size FD e rr or 54...force, and E is Young’s modulus. Equations (3.31) and (3.32) may be directly integrated to yield the stress and displacement solutions, which, for no

Representing uncertainty in objective functions: extension to include the influence of serial correlation

NASA Astrophysics Data System (ADS)

Croke, B. F.

2008-12-01

The role of performance indicators is to give an accurate indication of the fit between a model and the system being modelled. As all measurements have an associated uncertainty (determining the significance that should be given to the measurement), performance indicators should take into account uncertainties in the observed quantities being modelled as well as in the model predictions (due to uncertainties in inputs, model parameters and model structure). In the presence of significant uncertainty in observed and modelled output of a system, failure to adequately account for variations in the uncertainties means that the objective function only gives a measure of how well the model fits the observations, not how well the model fits the system being modelled. Since in most cases, the interest lies in fitting the system response, it is vital that the objective function(s) be designed to account for these uncertainties. Most objective functions (e.g. those based on the sum of squared residuals) assume homoscedastic uncertainties. If model contribution to the variations in residuals can be ignored, then transformations (e.g. Box-Cox) can be used to remove (or at least significantly reduce) heteroscedasticity. An alternative which is more generally applicable is to explicitly represent the uncertainties in the observed and modelled values in the objective function. Previous work on this topic addressed the modifications to standard objective functions (Nash-Sutcliffe efficiency, RMSE, chi- squared, coefficient of determination) using the optimal weighted averaging approach. This paper extends this previous work; addressing the issue of serial correlation. A form for an objective function that includes serial correlation will be presented, and the impact on model fit discussed.

Optimization on Paddy Crops in Central Java (with Solver, SVD on Least Square and ACO (Ant Colony Algorithm))

NASA Astrophysics Data System (ADS)

Parhusip, H. A.; Trihandaru, S.; Susanto, B.; Prasetyo, S. Y. J.; Agus, Y. H.; Simanjuntak, B. H.

2017-03-01

Several algorithms and objective functions on paddy crops have been studied to get optimal paddy crops in Central Java based on the data given from Surakarta and Boyolali. The algorithms are linear solver, least square and Ant Colony Algorithms (ACO) to develop optimization procedures on paddy crops modelled with Modified GSTAR (Generalized Space-Time Autoregressive) and nonlinear models where the nonlinear models are quadratic and power functions. The studied data contain paddy crops from Surakarta and Boyolali determining the best period of planting in the year 1992-2012 for Surakarta where 3 periods for planting are known and the optimal amount of paddy crops in Boyolali in the year 2008-2013. Having these analyses may guide the local agriculture government to give a decision on rice sustainability in its region. The best period for planting in Surakarta is observed, i.e. the best period is in September-December based on the data 1992-2012 by considering the planting area, the cropping area, and the paddy crops are the most important factors to be taken into account. As a result, we can refer the paddy crops in this best period (about 60.4 thousand tons per year) as the optimal results in 1992-2012 where the used objective function is quadratic. According to the research, the optimal paddy crops in Boyolali about 280 thousand tons per year where the studied factors are the amount of rainfalls, the harvested area and the paddy crops in 2008-2013. In this case, linear and power functions are studied to be the objective functions. Compared to all studied algorithms, the linear solver is still recommended to be an optimization tool for a local agriculture government to predict paddy crops in future.

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.

1996-01-01

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Least Squares Metric, Unidimensional Scaling of Multivariate Linear Models.

ERIC Educational Resources Information Center

Poole, Keith T.

1990-01-01

A general approach to least-squares unidimensional scaling is presented. Ordering information contained in the parameters is used to transform the standard squared error loss function into a discrete rather than continuous form. Monte Carlo tests with 38,094 ratings of 261 senators, and 1,258 representatives demonstrate the procedure's…

Cross-correlation least-squares reverse time migration in the pseudo-time domain

NASA Astrophysics Data System (ADS)

Li, Qingyang; Huang, Jianping; Li, Zhenchun

2017-08-01

The least-squares reverse time migration (LSRTM) method with higher image resolution and amplitude is becoming increasingly popular. However, the LSRTM is not widely used in field land data processing because of its sensitivity to the initial migration velocity model, large computational cost and mismatch of amplitudes between the synthetic and observed data. To overcome the shortcomings of the conventional LSRTM, we propose a cross-correlation least-squares reverse time migration algorithm in pseudo-time domain (PTCLSRTM). Our algorithm not only reduces the depth/velocity ambiguities, but also reduces the effect of velocity error on the imaging results. It relieves the accuracy requirements on the migration velocity model of least-squares migration (LSM). The pseudo-time domain algorithm eliminates the irregular wavelength sampling in the vertical direction, thus it can reduce the vertical grid points and memory requirements used during computation, which makes our method more computationally efficient than the standard implementation. Besides, for field data applications, matching the recorded amplitudes is a very difficult task because of the viscoelastic nature of the Earth and inaccuracies in the estimation of the source wavelet. To relax the requirement for strong amplitude matching of LSM, we extend the normalized cross-correlation objective function to the pseudo-time domain. Our method is only sensitive to the similarity between the predicted and the observed data. Numerical tests on synthetic and land field data confirm the effectiveness of our method and its adaptability for complex models.

From direct-space discrepancy functions to crystallographic least squares.

PubMed

Giacovazzo, Carmelo

2015-01-01

Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron-density maps. The new approach leads also to modifications of the standard least-squares procedures, potentially able to improve their efficiency. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least-squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so-called vector refinement, used when accurate estimates of the target phases are available.

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.

Control system estimation and design for aerospace vehicles

NASA Technical Reports Server (NTRS)

Stefani, R. T.; Williams, T. L.; Yakowitz, S. J.

1972-01-01

The selection of an estimator which is unbiased when applied to structural parameter estimation is discussed. The mathematical relationships for structural parameter estimation are defined. It is shown that a conventional weighted least squares (CWLS) estimate is biased when applied to structural parameter estimation. Two approaches to bias removal are suggested: (1) change the CWLS estimator or (2) change the objective function. The advantages of each approach are analyzed.

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; Grossman, B.

1991-01-01

A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.

Modified locally weighted--partial least squares regression improving clinical predictions from infrared spectra of human serum samples.

PubMed

Perez-Guaita, David; Kuligowski, Julia; Quintás, Guillermo; Garrigues, Salvador; Guardia, Miguel de la

2013-03-30

Locally weighted partial least squares regression (LW-PLSR) has been applied to the determination of four clinical parameters in human serum samples (total protein, triglyceride, glucose and urea contents) by Fourier transform infrared (FTIR) spectroscopy. Classical LW-PLSR models were constructed using different spectral regions. For the selection of parameters by LW-PLSR modeling, a multi-parametric study was carried out employing the minimum root-mean square error of cross validation (RMSCV) as objective function. In order to overcome the effect of strong matrix interferences on the predictive accuracy of LW-PLSR models, this work focuses on sample selection. Accordingly, a novel strategy for the development of local models is proposed. It was based on the use of: (i) principal component analysis (PCA) performed on an analyte specific spectral region for identifying most similar sample spectra and (ii) partial least squares regression (PLSR) constructed using the whole spectrum. Results found by using this strategy were compared to those provided by PLSR using the same spectral intervals as for LW-PLSR. Prediction errors found by both, classical and modified LW-PLSR improved those obtained by PLSR. Hence, both proposed approaches were useful for the determination of analytes present in a complex matrix as in the case of human serum samples. Copyright © 2013 Elsevier B.V. All rights reserved.

Effect of the curvature parameter on least-squares prediction within poor data coverage: case study for Africa

NASA Astrophysics Data System (ADS)

Abd-Elmotaal, Hussein; Kühtreiber, Norbert

2016-04-01

In the framework of the IAG African Geoid Project, there are a lot of large data gaps in its gravity database. These gaps are filled initially using unequal weight least-squares prediction technique. This technique uses a generalized Hirvonen covariance function model to replace the empirically determined covariance function. The generalized Hirvonen covariance function model has a sensitive parameter which is related to the curvature parameter of the covariance function at the origin. This paper studies the effect of the curvature parameter on the least-squares prediction results, especially in the large data gaps as appearing in the African gravity database. An optimum estimation of the curvature parameter has also been carried out. A wide comparison among the results obtained in this research along with their obtained accuracy is given and thoroughly discussed.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Alternating least squares with penalty functions.

PubMed

Gemperline, Paul J; Cash, Eric

2003-08-15

A new algorithm for self-modeling curve resolution (SMCR) that yields improved results by incorporating soft constraints is described. The method uses least squares penalty functions to implement constraints in an alternating least squares algorithm, including nonnegativity, unimodality, equality, and closure constraints. By using least squares penalty functions, soft constraints are formulated rather than hard constraints. Significant benefits are (obtained using soft constraints, especially in the form of fewer distortions due to noise in resolved profiles. Soft equality constraints can also be used to introduce incomplete or partial reference information into SMCR solutions. Four different examples demonstrating application of the new method are presented, including resolution of overlapped HPLC-DAD peaks, flow injection analysis data, and batch reaction data measured by UV/visible and near-infrared spectroscopy (NIR). Each example was selected to show one aspect of the significant advantages of soft constraints over traditionally used hard constraints. Incomplete or partial reference information into self-modeling curve resolution models is described. The method offers a substantial improvement in the ability to resolve time-dependent concentration profiles from mixture spectra recorded as a function of time.

A Christoffel function weighted least squares algorithm for collocation approximations

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

Narayan, Akil; Jakeman, John D.; Zhou, Tao

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

Narayan, Akil; Jakeman, John D.; Zhou, Tao

2016-11-28

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

[Locally weighted least squares estimation of DPOAE evoked by continuously sweeping primaries].

PubMed

Han, Xiaoli; Fu, Xinxing; Cui, Jie; Xiao, Ling

2013-12-01

Distortion product otoacoustic emission (DPOAE) signal can be used for diagnosis of hearing loss so that it has an important clinical value. Continuously using sweeping primaries to measure DPOAE provides an efficient tool to record DPOAE data rapidly when DPOAE is measured in a large frequency range. In this paper, locally weighted least squares estimation (LWLSE) of 2f1-f2 DPOAE is presented based on least-squares-fit (LSF) algorithm, in which DPOAE is evoked by continuously sweeping tones. In our study, we used a weighted error function as the loss function and the weighting matrixes in the local sense to obtain a smaller estimated variance. Firstly, ordinary least squares estimation of the DPOAE parameters was obtained. Then the error vectors were grouped and the different local weighting matrixes were calculated in each group. And finally, the parameters of the DPOAE signal were estimated based on least squares estimation principle using the local weighting matrixes. The simulation results showed that the estimate variance and fluctuation errors were reduced, so the method estimates DPOAE and stimuli more accurately and stably, which facilitates extraction of clearer DPOAE fine structure.

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems.

PubMed

Richards, Selena; Miller, Robert; Gemperline, Paul

2008-02-01

An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.

Full Waveform Inversion Using Student's t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method

NASA Astrophysics Data System (ADS)

Jeong, Woodon; Kang, Minji; Kim, Shinwoong; Min, Dong-Joo; Kim, Won-Ki

2015-06-01

Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l 1-norm-based objective functions. However, the l 1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student's t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student's t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student's t distribution for elastic FWI by comparing its basic properties with those of the l 2-norm and l 1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l 2-norm is sensitive to noise, whereas the l 1-norm and Student's t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student's t distribution gives better results than l 1- and l 2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student's t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student's t distribution. From our experiments, we conclude that FWI based on Student's t distribution can retrieve subsurface material properties with less distortion from noise than l 1- and l 2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student's t distribution.

Comparisons of a Constrained Least Squares Model versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

NASA Technical Reports Server (NTRS)

Abercromby, Kira J.; Rapp, Jason; Bedard, Donald; Seitzer, Patrick; Cardona, Tommaso; Cowardin, Heather; Barker, Ed; Lederer, Susan

2013-01-01

Constrained Linear Least Squares model is generally more accurate than the "human-in-the-loop". However, "human-in-the-loop" can remove materials that make no sense. The speed of the model in determining a "first cut" at the material ID makes it a viable option for spectral unmixing of debris objects.

Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

PubMed

Lu, Canyi; Lin, Zhouchen; Yan, Shuicheng

2015-02-01

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q ≥ 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

Reconstruction of internal density distributions in porous bodies from laser ultrasonic data

NASA Technical Reports Server (NTRS)

Lu, Yichi; Goldman, Jeffrey A.; Wadley, Haydn N. G.

1992-01-01

It is presently shown that, for density-reconstruction problems in which information about the inhomogeneity is known a priori, the nonlinear least-squares algorithm yields satisfactory results on the basis of limited projection data. The back-projection algorithm, which obviates assumptions about the objective function to be reconstructed, does not recover the boundary of the inhomogeneity when the number of projections is limited and ray-bending is ignored.

Three filters for visualization of phase objects with large variations of phase gradients

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

Sagan, Arkadiusz; Antosiewicz, Tomasz J.; Szoplik, Tomasz

2009-02-20

We propose three amplitude filters for visualization of phase objects. They interact with the spectra of pure-phase objects in the frequency plane and are based on tangent and error functions as well as antisymmetric combination of square roots. The error function is a normalized form of the Gaussian function. The antisymmetric square-root filter is composed of two square-root filters to widen its spatial frequency spectral range. Their advantage over other known amplitude frequency-domain filters, such as linear or square-root graded ones, is that they allow high-contrast visualization of objects with large variations of phase gradients.

Discordance between net analyte signal theory and practical multivariate calibration.

PubMed

Brown, Christopher D

2004-08-01

Lorber's concept of net analyte signal is reviewed in the context of classical and inverse least-squares approaches to multivariate calibration. It is shown that, in the presence of device measurement error, the classical and inverse calibration procedures have radically different theoretical prediction objectives, and the assertion that the popular inverse least-squares procedures (including partial least squares, principal components regression) approximate Lorber's net analyte signal vector in the limit is disproved. Exact theoretical expressions for the prediction error bias, variance, and mean-squared error are given under general measurement error conditions, which reinforce the very discrepant behavior between these two predictive approaches, and Lorber's net analyte signal theory. Implications for multivariate figures of merit and numerous recently proposed preprocessing treatments involving orthogonal projections are also discussed.

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

Prediction model of sinoatrial node field potential using high order partial least squares.

PubMed

Feng, Yu; Cao, Hui; Zhang, Yanbin

2015-01-01

High order partial least squares (HOPLS) is a novel data processing method. It is highly suitable for building prediction model which has tensor input and output. The objective of this study is to build a prediction model of the relationship between sinoatrial node field potential and high glucose using HOPLS. The three sub-signals of the sinoatrial node field potential made up the model's input. The concentration and the actuation duration of high glucose made up the model's output. The results showed that on the premise of predicting two dimensional variables, HOPLS had the same predictive ability and a lower dispersion degree compared with partial least squares (PLS).

Precision PEP-II optics measurement with an SVD-enhanced Least-Square fitting

NASA Astrophysics Data System (ADS)

Yan, Y. T.; Cai, Y.

2006-03-01

A singular value decomposition (SVD)-enhanced Least-Square fitting technique is discussed. By automatic identifying, ordering, and selecting dominant SVD modes of the derivative matrix that responds to the variations of the variables, the converging process of the Least-Square fitting is significantly enhanced. Thus the fitting speed can be fast enough for a fairly large system. This technique has been successfully applied to precision PEP-II optics measurement in which we determine all quadrupole strengths (both normal and skew components) and sextupole feed-downs as well as all BPM gains and BPM cross-plane couplings through Least-Square fitting of the phase advances and the Local Green's functions as well as the coupling ellipses among BPMs. The local Green's functions are specified by 4 local transfer matrix components R12, R34, R32, R14. These measurable quantities (the Green's functions, the phase advances and the coupling ellipse tilt angles and axis ratios) are obtained by analyzing turn-by-turn Beam Position Monitor (BPM) data with a high-resolution model-independent analysis (MIA). Once all of the quadrupoles and sextupole feed-downs are determined, we obtain a computer virtual accelerator which matches the real accelerator in linear optics. Thus, beta functions, linear coupling parameters, and interaction point (IP) optics characteristics can be measured and displayed.

Algorithms for Nonlinear Least-Squares Problems

DTIC Science & Technology

1988-09-01

O -,i(x) 2 , where each -,(x) is a smooth function mapping Rn to R. J - The m x n Jacobian matrix of f. ... x g - The gradient of the nonlinear least...V211f(X*)I112~ l~ l) J(xk)T J(xk) 2 + O(k - X*) For more convergence results and detailed convergence analysis for the Gauss-Newton method, see, e. g ...for a class of nonlinear least-squares problems that includes zero-residual prob- lems. The function Jt is the pseudo-inverse of Jk (see, e. g

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

Background Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual’s genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. Results We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. Conclusions The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate. PMID:23343408

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual's genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate.

Iterative reconstruction for x-ray computed tomography using prior-image induced nonlocal regularization.

PubMed

Zhang, Hua; Huang, Jing; Ma, Jianhua; Bian, Zhaoying; Feng, Qianjin; Lu, Hongbing; Liang, Zhengrong; Chen, Wufan

2014-09-01

Repeated X-ray computed tomography (CT) scans are often required in several specific applications such as perfusion imaging, image-guided biopsy needle, image-guided intervention, and radiotherapy with noticeable benefits. However, the associated cumulative radiation dose significantly increases as comparison with that used in the conventional CT scan, which has raised major concerns in patients. In this study, to realize radiation dose reduction by reducing the X-ray tube current and exposure time (mAs) in repeated CT scans, we propose a prior-image induced nonlocal (PINL) regularization for statistical iterative reconstruction via the penalized weighted least-squares (PWLS) criteria, which we refer to as "PWLS-PINL". Specifically, the PINL regularization utilizes the redundant information in the prior image and the weighted least-squares term considers a data-dependent variance estimation, aiming to improve current low-dose image quality. Subsequently, a modified iterative successive overrelaxation algorithm is adopted to optimize the associative objective function. Experimental results on both phantom and patient data show that the present PWLS-PINL method can achieve promising gains over the other existing methods in terms of the noise reduction, low-contrast object detection, and edge detail preservation.

Iterative Reconstruction for X-Ray Computed Tomography using Prior-Image Induced Nonlocal Regularization

PubMed Central

Ma, Jianhua; Bian, Zhaoying; Feng, Qianjin; Lu, Hongbing; Liang, Zhengrong; Chen, Wufan

2014-01-01

Repeated x-ray computed tomography (CT) scans are often required in several specific applications such as perfusion imaging, image-guided biopsy needle, image-guided intervention, and radiotherapy with noticeable benefits. However, the associated cumulative radiation dose significantly increases as comparison with that used in the conventional CT scan, which has raised major concerns in patients. In this study, to realize radiation dose reduction by reducing the x-ray tube current and exposure time (mAs) in repeated CT scans, we propose a prior-image induced nonlocal (PINL) regularization for statistical iterative reconstruction via the penalized weighted least-squares (PWLS) criteria, which we refer to as “PWLS-PINL”. Specifically, the PINL regularization utilizes the redundant information in the prior image and the weighted least-squares term considers a data-dependent variance estimation, aiming to improve current low-dose image quality. Subsequently, a modified iterative successive over-relaxation algorithm is adopted to optimize the associative objective function. Experimental results on both phantom and patient data show that the present PWLS-PINL method can achieve promising gains over the other existing methods in terms of the noise reduction, low-contrast object detection and edge detail preservation. PMID:24235272

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Least-squares luma-chroma demultiplexing algorithm for Bayer demosaicking.

PubMed

Leung, Brian; Jeon, Gwanggil; Dubois, Eric

2011-07-01

This paper addresses the problem of interpolating missing color components at the output of a Bayer color filter array (CFA), a process known as demosaicking. A luma-chroma demultiplexing algorithm is presented in detail, using a least-squares design methodology for the required bandpass filters. A systematic study of objective demosaicking performance and system complexity is carried out, and several system configurations are recommended. The method is compared with other benchmark algorithms in terms of CPSNR and S-CIELAB ∆E∗ objective quality measures and demosaicking speed. It was found to provide excellent performance and the best quality-speed tradeoff among the methods studied.

Low-mAs X-ray CT image reconstruction by adaptive-weighted TV-constrained penalized re-weighted least-squares

PubMed Central

Liu, Yan; Ma, Jianhua; Zhang, Hao; Wang, Jing; Liang, Zhengrong

2014-01-01

Background The negative effects of X-ray exposure, such as inducing genetic and cancerous diseases, has arisen more attentions. Objective This paper aims to investigate a penalized re-weighted least-square (PRWLS) strategy for low-mAs X-ray computed tomography image reconstruction by incorporating an adaptive weighted total variation (AwTV) penalty term and a noise variance model of projection data. Methods An AwTV penalty is introduced in the objective function by considering both piecewise constant property and local nearby intensity similarity of the desired image. Furthermore, the weight of data fidelity term in the objective function is determined by our recent study on modeling variance estimation of projection data in the presence of electronic background noise. Results The presented AwTV-PRWLS algorithm can achieve the highest full-width-at-half-maximum (FWHM) measurement, for data conditions of (1) full-view 10mA acquisition and (2) sparse-view 80mA acquisition. In comparison between the AwTV/TV-PRWLS strategies and the previous reported AwTV/TV-projection onto convex sets (AwTV/TV-POCS) approaches, the former can gain in terms of FWHM for data condition (1), but cannot gain for the data condition (2). Conclusions In the case of full-view 10mA projection data, the presented AwTV-PRWLS shows potential improvement. However, in the case of sparse-view 80mA projection data, the AwTV/TV-POCS shows advantage over the PRWLS strategies. PMID:25080113

A Genetic Algorithm Approach to Nonlinear Least Squares Estimation

ERIC Educational Resources Information Center

Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.

2004-01-01

A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…

Identification of Bouc-Wen hysteretic parameters based on enhanced response sensitivity approach

NASA Astrophysics Data System (ADS)

Wang, Li; Lu, Zhong-Rong

2017-05-01

This paper aims to identify parameters of Bouc-Wen hysteretic model using time-domain measured data. It follows a general inverse identification procedure, that is, identifying model parameters is treated as an optimization problem with the nonlinear least squares objective function. Then, the enhanced response sensitivity approach, which has been shown convergent and proper for such kind of problems, is adopted to solve the optimization problem. Numerical tests are undertaken to verify the proposed identification approach.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Multidimensional model of apathy in older adults using partial least squares--path modeling.

PubMed

Raffard, Stéphane; Bortolon, Catherine; Burca, Marianna; Gely-Nargeot, Marie-Christine; Capdevielle, Delphine

2016-06-01

Apathy defined as a mental state characterized by a lack of goal-directed behavior is prevalent and associated with poor functioning in older adults. The main objective of this study was to identify factors contributing to the distinct dimensions of apathy (cognitive, emotional, and behavioral) in older adults without dementia. One hundred and fifty participants (mean age, 80.42) completed self-rated questionnaires assessing apathy, emotional distress, anticipatory pleasure, motivational systems, physical functioning, quality of life, and cognitive functioning. Data were analyzed using partial least squares variance-based structural equation modeling in order to examine factors contributing to the three different dimensions of apathy in our sample. Overall, the different facets of apathy were associated with cognitive functioning, anticipatory pleasure, sensitivity to reward, and physical functioning, but the contribution of these different factors to the three dimensions of apathy differed significantly. More specifically, the impact of anticipatory pleasure and physical functioning was stronger for the cognitive than for emotional apathy. Conversely, the impact of sensibility to reward, although small, was slightly stronger on emotional apathy. Regarding behavioral apathy, again we found similar latent variables except for the cognitive functioning whose impact was not statistically significant. Our results highlight the need to take into account various mechanisms involved in the different facets of apathy in older adults without dementia, including not only cognitive factors but also motivational variables and aspects related to physical disability. Clinical implications are discussed.

Use of partial least squares regression to impute SNP genotypes in Italian cattle breeds.

PubMed

Dimauro, Corrado; Cellesi, Massimo; Gaspa, Giustino; Ajmone-Marsan, Paolo; Steri, Roberto; Marras, Gabriele; Macciotta, Nicolò P P

2013-06-05

The objective of the present study was to test the ability of the partial least squares regression technique to impute genotypes from low density single nucleotide polymorphisms (SNP) panels i.e. 3K or 7K to a high density panel with 50K SNP. No pedigree information was used. Data consisted of 2093 Holstein, 749 Brown Swiss and 479 Simmental bulls genotyped with the Illumina 50K Beadchip. First, a single-breed approach was applied by using only data from Holstein animals. Then, to enlarge the training population, data from the three breeds were combined and a multi-breed analysis was performed. Accuracies of genotypes imputed using the partial least squares regression method were compared with those obtained by using the Beagle software. The impact of genotype imputation on breeding value prediction was evaluated for milk yield, fat content and protein content. In the single-breed approach, the accuracy of imputation using partial least squares regression was around 90 and 94% for the 3K and 7K platforms, respectively; corresponding accuracies obtained with Beagle were around 85% and 90%. Moreover, computing time required by the partial least squares regression method was on average around 10 times lower than computing time required by Beagle. Using the partial least squares regression method in the multi-breed resulted in lower imputation accuracies than using single-breed data. The impact of the SNP-genotype imputation on the accuracy of direct genomic breeding values was small. The correlation between estimates of genetic merit obtained by using imputed versus actual genotypes was around 0.96 for the 7K chip. Results of the present work suggested that the partial least squares regression imputation method could be useful to impute SNP genotypes when pedigree information is not available.

Influence of the least-squares phase on optical vortices in strongly scintillated beams

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

Chen Mingzhou; Roux, Filippus S.; National Laser Centre, CSIR, P.O. Box 395, Pretoria 0001

2009-07-15

The optical vortices that exist in strongly scintillated beams make it difficult for conventional adaptive optics systems to remove the phase distortions. When the least-squares reconstructed phase is removed, the vortices still remain. However, we found that the removal of the least-squares phase induces a portion of the vortices to be annihilated during subsequent propagation, causing a reduction in the total number of vortices. This can be understood in terms of the restoration of equilibrium between explicit vortices, which are visible in the phase function, and vortex bound states, which are somehow encoded in the continuous phase fluctuations. Numerical simulationsmore » are provided to show that the total number of optical vortices in a strongly scintillated beam can be reduced significantly after a few steps of least-squares phase corrections.« less

Fast and accurate fitting and filtering of noisy exponentials in Legendre space.

PubMed

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters.

Calculation of Hammett Equation parameters for some N,N‧-bis (substituted-phenyl)-1,4-quinonediimines by density functional theory

NASA Astrophysics Data System (ADS)

Sein, Lawrence T.

2011-08-01

Hammett parameters σ' were determined from vertical ionization potentials, vertical electron affinities, adiabatic ionization potentials, adiabatic electron affinities, HOMO, and LUMO energies of a series of N, N' -bis (3',4'-substituted-phenyl)-1,4-quinonediimines computed at the B3LYP/6-311+G(2d,p) level on B3LYP/6-31G ∗ molecular geometries. These parameters were then least squares fit as a function of literature Hammett parameters. For N, N' -bis (4'-substituted-phenyl)-1,4-quinonediimines, the least squares fits demonstrated excellent linearity, with the square of Pearson's correlation coefficient ( r2) greater than 0.98 for all isomers. For N, N' -bis (3'-substituted-3'-aminophenyl)-1,4-quinonediimines, the least squares fits were less nearly linear, with r2 approximately 0.70 for all isomers when derived from calculated vertical ionization potentials, but those from calculated vertical electron affinities usually greater than 0.90.

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

The Least-Squares Estimation of Latent Trait Variables.

ERIC Educational Resources Information Center

Tatsuoka, Kikumi

This paper presents a new method for estimating a given latent trait variable by the least-squares approach. The beta weights are obtained recursively with the help of Fourier series and expressed as functions of item parameters of response curves. The values of the latent trait variable estimated by this method and by maximum likelihood method…

Quantized kernel least mean square algorithm.

PubMed

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

Multi-objective aerodynamic shape optimization of small livestock trailers

NASA Astrophysics Data System (ADS)

Gilkeson, C. A.; Toropov, V. V.; Thompson, H. M.; Wilson, M. C. T.; Foxley, N. A.; Gaskell, P. H.

2013-11-01

This article presents a formal optimization study of the design of small livestock trailers, within which the majority of animals are transported to market in the UK. The benefits of employing a headboard fairing to reduce aerodynamic drag without compromising the ventilation of the animals' microclimate are investigated using a multi-stage process involving computational fluid dynamics (CFD), optimal Latin hypercube (OLH) design of experiments (DoE) and moving least squares (MLS) metamodels. Fairings are parameterized in terms of three design variables and CFD solutions are obtained at 50 permutations of design variables. Both global and local search methods are employed to locate the global minimum from metamodels of the objective functions and a Pareto front is generated. The importance of carefully selecting an objective function is demonstrated and optimal fairing designs, offering drag reductions in excess of 5% without compromising animal ventilation, are presented.

Functional Generalized Structured Component Analysis.

PubMed

Suk, Hye Won; Hwang, Heungsun

2016-12-01

An extension of Generalized Structured Component Analysis (GSCA), called Functional GSCA, is proposed to analyze functional data that are considered to arise from an underlying smooth curve varying over time or other continua. GSCA has been geared for the analysis of multivariate data. Accordingly, it cannot deal with functional data that often involve different measurement occasions across participants and a large number of measurement occasions that exceed the number of participants. Functional GSCA addresses these issues by integrating GSCA with spline basis function expansions that represent infinite-dimensional curves onto a finite-dimensional space. For parameter estimation, functional GSCA minimizes a penalized least squares criterion by using an alternating penalized least squares estimation algorithm. The usefulness of functional GSCA is illustrated with gait data.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

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

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Least Squares Moving-Window Spectral Analysis.

PubMed

Lee, Young Jong

2017-08-01

Least squares regression is proposed as a moving-windows method for analysis of a series of spectra acquired as a function of external perturbation. The least squares moving-window (LSMW) method can be considered an extended form of the Savitzky-Golay differentiation for nonuniform perturbation spacing. LSMW is characterized in terms of moving-window size, perturbation spacing type, and intensity noise. Simulation results from LSMW are compared with results from other numerical differentiation methods, such as single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods. It is demonstrated that this simple LSMW method can be useful for quantitative analysis of nonuniformly spaced spectral data with high frequency noise.

Comparing least-squares and quantile regression approaches to analyzing median hospital charges.

PubMed

Olsen, Cody S; Clark, Amy E; Thomas, Andrea M; Cook, Lawrence J

2012-07-01

Emergency department (ED) and hospital charges obtained from administrative data sets are useful descriptors of injury severity and the burden to EDs and the health care system. However, charges are typically positively skewed due to costly procedures, long hospital stays, and complicated or prolonged treatment for few patients. The median is not affected by extreme observations and is useful in describing and comparing distributions of hospital charges. A least-squares analysis employing a log transformation is one approach for estimating median hospital charges, corresponding confidence intervals (CIs), and differences between groups; however, this method requires certain distributional properties. An alternate method is quantile regression, which allows estimation and inference related to the median without making distributional assumptions. The objective was to compare the log-transformation least-squares method to the quantile regression approach for estimating median hospital charges, differences in median charges between groups, and associated CIs. The authors performed simulations using repeated sampling of observed statewide ED and hospital charges and charges randomly generated from a hypothetical lognormal distribution. The median and 95% CI and the multiplicative difference between the median charges of two groups were estimated using both least-squares and quantile regression methods. Performance of the two methods was evaluated. In contrast to least squares, quantile regression produced estimates that were unbiased and had smaller mean square errors in simulations of observed ED and hospital charges. Both methods performed well in simulations of hypothetical charges that met least-squares method assumptions. When the data did not follow the assumed distribution, least-squares estimates were often biased, and the associated CIs had lower than expected coverage as sample size increased. Quantile regression analyses of hospital charges provide unbiased estimates even when lognormal and equal variance assumptions are violated. These methods may be particularly useful in describing and analyzing hospital charges from administrative data sets. © 2012 by the Society for Academic Emergency Medicine.

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Dynamic Reconstruction Algorithm of Three-Dimensional Temperature Field Measurement by Acoustic Tomography

PubMed Central

Li, Yanqiu; Liu, Shi; Inaki, Schlaberg H.

2017-01-01

Accuracy and speed of algorithms play an important role in the reconstruction of temperature field measurements by acoustic tomography. Existing algorithms are based on static models which only consider the measurement information. A dynamic model of three-dimensional temperature reconstruction by acoustic tomography is established in this paper. A dynamic algorithm is proposed considering both acoustic measurement information and the dynamic evolution information of the temperature field. An objective function is built which fuses measurement information and the space constraint of the temperature field with its dynamic evolution information. Robust estimation is used to extend the objective function. The method combines a tunneling algorithm and a local minimization technique to solve the objective function. Numerical simulations show that the image quality and noise immunity of the dynamic reconstruction algorithm are better when compared with static algorithms such as least square method, algebraic reconstruction technique and standard Tikhonov regularization algorithms. An effective method is provided for temperature field reconstruction by acoustic tomography. PMID:28895930

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

SU-F-18C-14: Hessian-Based Norm Penalty for Weighted Least-Square CBCT Reconstruction

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

Sun, T; Sun, N; Tan, S

Purpose: To develop a Hessian-based norm penalty for cone-beam CT (CBCT) reconstruction that has a similar ability in suppressing noise as the total variation (TV) penalty while avoiding the staircase effect and better preserving low-contrast objects. Methods: We extended the TV penalty to a Hessian-based norm penalty based on the Frobenius norm of the Hessian matrix of an image for CBCT reconstruction. The objective function was constructed using the penalized weighted least-square (PWLS) principle. An effective algorithm was developed to minimize the objective function using a majorization-minimization (MM) approach. We evaluated and compared the proposed penalty with the TV penaltymore » on a CatPhan 600 phantom and an anthropomorphic head phantom, each acquired at a low-dose protocol (10mA/10ms) and a high-dose protocol (80mA/12ms). For both penalties, contrast-to-noise (CNR) in four low-contrast regions-of-interest (ROIs) and the full-width-at-half-maximum (FWHM) of two point-like objects in constructed images were calculated and compared. Results: In the experiment of CatPhan 600 phantom, the Hessian-based norm penalty has slightly higher CNRs and approximately equivalent FWHM values compared with the TV penalty. In the experiment of the anthropomorphic head phantom at the low-dose protocol, the TV penalty result has several artificial piece-wise constant areas known as the staircase effect while in the Hessian-based norm penalty the image appears smoother and more similar to that of the FDK result using the high-dose protocol. Conclusion: The proposed Hessian-based norm penalty has a similar performance in suppressing noise to the TV penalty, but has a potential advantage in suppressing the staircase effect and preserving low-contrast objects. This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 60971112 and 61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086.« less

Phase aberration compensation of digital holographic microscopy based on least squares surface fitting

NASA Astrophysics Data System (ADS)

Di, Jianglei; Zhao, Jianlin; Sun, Weiwei; Jiang, Hongzhen; Yan, Xiaobo

2009-10-01

Digital holographic microscopy allows the numerical reconstruction of the complex wavefront of samples, especially biological samples such as living cells. In digital holographic microscopy, a microscope objective is introduced to improve the transverse resolution of the sample; however a phase aberration in the object wavefront is also brought along, which will affect the phase distribution of the reconstructed image. We propose here a numerical method to compensate for the phase aberration of thin transparent objects with a single hologram. The least squares surface fitting with points number less than the matrix of the original hologram is performed on the unwrapped phase distribution to remove the unwanted wavefront curvature. The proposed method is demonstrated with the samples of the cicada wings and epidermal cells of garlic, and the experimental results are consistent with that of the double exposure method.

Peelle's pertinent puzzle using the Monte Carlo technique

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

Kawano, Toshihiko; Talou, Patrick; Burr, Thomas

2009-01-01

We try to understand the long-standing problem of the Peelle's Pertinent Puzzle (PPP) using the Monte Carlo technique. We allow the probability density functions to be any kind of form to assume the impact of distribution, and obtain the least-squares solution directly from numerical simulations. We found that the standard least squares method gives the correct answer if a weighting function is properly provided. Results from numerical simulations show that the correct answer of PPP is 1.1 {+-} 0.25 if the common error is multiplicative. The thought-provoking answer of 0.88 is also correct, if the common error is additive, andmore » if the error is proportional to the measured values. The least squares method correctly gives us the most probable case, where the additive component has a negative value. Finally, the standard method fails for PPP due to a distorted (non Gaussian) joint distribution.« less

An iterative algorithm for calculating stylus radius unambiguously

NASA Astrophysics Data System (ADS)

Vorburger, T. V.; Zheng, A.; Renegar, T. B.; Song, J.-F.; Ma, L.

2011-08-01

The stylus radius is an important specification for stylus instruments and is commonly provided by instrument manufacturers. However, it is difficult to measure the stylus radius unambiguously. Accurate profiles of the stylus tip may be obtained by profiling over an object sharper than itself, such as a razor blade. However, the stylus profile thus obtained is a partial arc, and unless the shape of the stylus tip is a perfect sphere or circle, the effective value of the radius depends on the length of the tip profile over which the radius is determined. We have developed an iterative, least squares algorithm aimed to determine the effective least squares stylus radius unambiguously. So far, the algorithm converges to reasonable results for the least squares stylus radius. We suggest that the algorithm be considered for adoption in documentary standards describing the properties of stylus instruments.

Approximating a retarded-advanced differential equation that models human phonation

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2017-11-01

In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.

Least squares regression methods for clustered ROC data with discrete covariates.

PubMed

Tang, Liansheng Larry; Zhang, Wei; Li, Qizhai; Ye, Xuan; Chan, Leighton

2016-07-01

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

An Analysis of Advertising Effectiveness for U.S. Navy Recruiting

DTIC Science & Technology

1997-09-01

This thesis estimates the effect of Navy television advertising on enlistment rates of high quality male recruits (Armed Forces Qualification Test...Joint advertising is for all Armed Forces), Joint journal, and Joint direct mail advertising are explored. Enlistments are modeled as a function of...several factors including advertising , recruiters, and economic. Regression analyses (Ordinary Least Squares and Two Stage Least Squares) explore the

Interpreting the Results of Weighted Least-Squares Regression: Caveats for the Statistical Consumer.

ERIC Educational Resources Information Center

Willett, John B.; Singer, Judith D.

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

Generalized Least Squares Estimators in the Analysis of Covariance Structures.

ERIC Educational Resources Information Center

Browne, Michael W.

This paper concerns situations in which a p x p covariance matrix is a function of an unknown q x 1 parameter vector y-sub-o. Notation is defined in the second section, and some algebraic results used in subsequent sections are given. Section 3 deals with asymptotic properties of generalized least squares (G.L.S.) estimators of y-sub-o. Section 4…

Objective scatterometer wind ambiguity removal using smoothness and dynamical constraints

NASA Technical Reports Server (NTRS)

Hoffman, R. N.

1984-01-01

In the present investigation, a variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. At each SASS data point, two, three, or four wind vectors (termed ambiguities) are retrieved. It is pointed out that the VAM is basically a least squares method for fitting data. The problem may be nonlinear. The best fit to the data and constraints is obtained on the basis of a minimization of the objective function. The VAM was tested and tuned at 12 h GMT Sept. 10, 1978. Attention is given to a case study involving an intense cyclone centered south of Japan at 138 deg E.

Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space

PubMed Central

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. PMID:24603904

Model-Based Least Squares Reconstruction of Coded Source Neutron Radiographs: Integrating the ORNL HFIR CG1D Source Model

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

Santos-Villalobos, Hector J; Gregor, Jens; Bingham, Philip R

2014-01-01

At the present, neutron sources cannot be fabricated small and powerful enough in order to achieve high resolution radiography while maintaining an adequate flux. One solution is to employ computational imaging techniques such as a Magnified Coded Source Imaging (CSI) system. A coded-mask is placed between the neutron source and the object. The system resolution is increased by reducing the size of the mask holes and the flux is increased by increasing the size of the coded-mask and/or the number of holes. One limitation of such system is that the resolution of current state-of-the-art scintillator-based detectors caps around 50um. Tomore » overcome this challenge, the coded-mask and object are magnified by making the distance from the coded-mask to the object much smaller than the distance from object to detector. In previous work, we have shown via synthetic experiments that our least squares method outperforms other methods in image quality and reconstruction precision because of the modeling of the CSI system components. However, the validation experiments were limited to simplistic neutron sources. In this work, we aim to model the flux distribution of a real neutron source and incorporate such a model in our least squares computational system. We provide a full description of the methodology used to characterize the neutron source and validate the method with synthetic experiments.« less

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

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

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standardmore » least squares.« less

Landsat-4 (TDRSS-user) orbit determination using batch least-squares and sequential methods

NASA Technical Reports Server (NTRS)

Oza, D. H.; Jones, T. L.; Hakimi, M.; Samii, M. V.; Doll, C. E.; Mistretta, G. D.; Hart, R. C.

1992-01-01

TDRSS user orbit determination is analyzed using a batch least-squares method and a sequential estimation method. It was found that in the batch least-squares method analysis, the orbit determination consistency for Landsat-4, which was heavily tracked by TDRSS during January 1991, was about 4 meters in the rms overlap comparisons and about 6 meters in the maximum position differences in overlap comparisons. The consistency was about 10 to 30 meters in the 3 sigma state error covariance function in the sequential method analysis. As a measure of consistency, the first residual of each pass was within the 3 sigma bound in the residual space.

Parameter estimation for groundwater models under uncertain irrigation data

USGS Publications Warehouse

Demissie, Yonas; Valocchi, Albert J.; Cai, Ximing; Brozovic, Nicholas; Senay, Gabriel; Gebremichael, Mekonnen

2015-01-01

The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression-based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least-squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least-squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least-squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P. D.; Marini, J. W.

1977-01-01

A test for ambiguity resolution was derived which was the most powerful in the sense that it maximized the probability of a correct decision. When systematic error sources were properly included in the least squares reduction process to yield an optimal solution, the test reduced to choosing the solution which provided the smaller valuation of the least squares loss function. When systematic error sources were ignored in the least squares reduction, the most powerful test was a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudo-inverse of a reduced rank square matrix. A formula is presented for computing the power of the most powerful test. A numerical example is included in which the power of the test is computed for a situation which may occur during an actual satellite aided search and rescue mission.

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

Robust Joint Graph Sparse Coding for Unsupervised Spectral Feature Selection.

PubMed

Zhu, Xiaofeng; Li, Xuelong; Zhang, Shichao; Ju, Chunhua; Wu, Xindong

2017-06-01

In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of k -nearest neighbor classification performance.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Distributed least-squares estimation of a remote chemical source via convex combination in wireless sensor networks.

PubMed

Cao, Meng-Li; Meng, Qing-Hao; Zeng, Ming; Sun, Biao; Li, Wei; Ding, Cheng-Jun

2014-06-27

This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN). Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE) method to solve the chemical source localization (CSL) problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source.

Edge-Preserving Image Smoothing Constraint in Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) of Hyperspectral Data.

PubMed

Hugelier, Siewert; Vitale, Raffaele; Ruckebusch, Cyril

2018-03-01

This article explores smoothing with edge-preserving properties as a spatial constraint for the resolution of hyperspectral images with multivariate curve resolution-alternating least squares (MCR-ALS). For each constrained component image (distribution map), irrelevant spatial details and noise are smoothed applying an L 1 - or L 0 -norm penalized least squares regression, highlighting in this way big changes in intensity of adjacent pixels. The feasibility of the constraint is demonstrated on three different case studies, in which the objects under investigation are spatially clearly defined, but have significant spectral overlap. This spectral overlap is detrimental for obtaining a good resolution and additional spatial information should be provided. The final results show that the spatial constraint enables better image (map) abstraction, artifact removal, and better interpretation of the results obtained, compared to a classical MCR-ALS analysis of hyperspectral images.

Coded-Aperture X- or gamma -ray telescope with Least- squares image reconstruction. III. Data acquisition and analysis enhancements

NASA Astrophysics Data System (ADS)

Kohman, T. P.

1995-05-01

The design of a cosmic X- or gamma -ray telescope with least- squares image reconstruction and its simulated operation have been described (Rev. Sci. Instrum. 60, 3396 and 3410 (1989)). Use of an auxiliary open aperture ("limiter") ahead of the coded aperture limits the object field to fewer pixels than detector elements, permitting least-squares reconstruction with improved accuracy in the imaged field; it also yields a uniformly sensitive ("flat") central field. The design has been enhanced to provide for mask-antimask operation. This cancels and eliminates uncertainties in the detector background, and the simulated results have virtually the same statistical accuracy (pixel-by-pixel output-input RMSD) as with a single mask alone. The simulations have been made more realistic by incorporating instrumental blurring of sources. A second-stage least-squares procedure had been developed to determine the precise positions and total fluxes of point sources responsible for clusters of above-background pixels in the field resulting from the first-stage reconstruction. Another program converts source positions in the image plane to celestial coordinates and vice versa, the image being a gnomic projection of a region of the sky.

Contrast improvement of continuous wave diffuse optical tomography reconstruction by hybrid approach using least square and genetic algorithm

NASA Astrophysics Data System (ADS)

Patra, Rusha; Dutta, Pranab K.

2015-07-01

Reconstruction of the absorption coefficient of tissue with good contrast is of key importance in functional diffuse optical imaging. A hybrid approach using model-based iterative image reconstruction and a genetic algorithm is proposed to enhance the contrast of the reconstructed image. The proposed method yields an observed contrast of 98.4%, mean square error of 0.638×10-3, and object centroid error of (0.001 to 0.22) mm. Experimental validation of the proposed method has also been provided with tissue-like phantoms which shows a significant improvement in image quality and thus establishes the potential of the method for functional diffuse optical tomography reconstruction with continuous wave setup. A case study of finger joint imaging is illustrated as well to show the prospect of the proposed method in clinical diagnosis. The method can also be applied to the concentration measurement of a region of interest in a turbid medium.

Local classification: Locally weighted-partial least squares-discriminant analysis (LW-PLS-DA).

PubMed

Bevilacqua, Marta; Marini, Federico

2014-08-01

The possibility of devising a simple, flexible and accurate non-linear classification method, by extending the locally weighted partial least squares (LW-PLS) approach to the cases where the algorithm is used in a discriminant way (partial least squares discriminant analysis, PLS-DA), is presented. In particular, to assess which category an unknown sample belongs to, the proposed algorithm operates by identifying which training objects are most similar to the one to be predicted and building a PLS-DA model using these calibration samples only. Moreover, the influence of the selected training samples on the local model can be further modulated by adopting a not uniform distance-based weighting scheme which allows the farthest calibration objects to have less impact than the closest ones. The performances of the proposed locally weighted-partial least squares-discriminant analysis (LW-PLS-DA) algorithm have been tested on three simulated data sets characterized by a varying degree of non-linearity: in all cases, a classification accuracy higher than 99% on external validation samples was achieved. Moreover, when also applied to a real data set (classification of rice varieties), characterized by a high extent of non-linearity, the proposed method provided an average correct classification rate of about 93% on the test set. By the preliminary results, showed in this paper, the performances of the proposed LW-PLS-DA approach have proved to be comparable and in some cases better than those obtained by other non-linear methods (k nearest neighbors, kernel-PLS-DA and, in the case of rice, counterpropagation neural networks). Copyright © 2014 Elsevier B.V. All rights reserved.

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, X. R.; Wang, X.

2016-03-01

When using the genetic algorithm to solve the problem of too-short-arc (TSA) determination, due to the difference of computing processes between the genetic algorithm and classical method, the methods for outliers editing are no longer applicable. In the genetic algorithm, the robust estimation is acquired by means of using different loss functions in the fitness function, then the outlier problem of TSAs is solved. Compared with the classical method, the application of loss functions in the genetic algorithm is greatly simplified. Through the comparison of results of different loss functions, it is clear that the methods of least median square and least trimmed square can greatly improve the robustness of TSAs, and have a high breakdown point.

Degradation trend estimation of slewing bearing based on LSSVM model

NASA Astrophysics Data System (ADS)

Lu, Chao; Chen, Jie; Hong, Rongjing; Feng, Yang; Li, Yuanyuan

2016-08-01

A novel prediction method is proposed based on least squares support vector machine (LSSVM) to estimate the slewing bearing's degradation trend with small sample data. This method chooses the vibration signal which contains rich state information as the object of the study. Principal component analysis (PCA) was applied to fuse multi-feature vectors which could reflect the health state of slewing bearing, such as root mean square, kurtosis, wavelet energy entropy, and intrinsic mode function (IMF) energy. The degradation indicator fused by PCA can reflect the degradation more comprehensively and effectively. Then the degradation trend of slewing bearing was predicted by using the LSSVM model optimized by particle swarm optimization (PSO). The proposed method was demonstrated to be more accurate and effective by the whole life experiment of slewing bearing. Therefore, it can be applied in engineering practice.

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

NASA Astrophysics Data System (ADS)

Wu, Yanqiang; Jiang, Zaisen; Liu, Xiaoxia; Wei, Wenxin; Zhu, Shuang; Zhang, Long; Zou, Zhenyu; Xiong, Xiaohui; Wang, Qixin; Du, Jiliang

2017-03-01

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P.; Marini, J.

1979-01-01

The implementation of satellite-based Doppler positioning systems frequently requires the recovery of transmitter position from a single pass of Doppler data. The least-squares approach to the problem yields conjugate solutions on either side of the satellite subtrack. It is important to develop a procedure for choosing the proper solution which is correct in a high percentage of cases. A test for ambiguity resolution which is the most powerful in the sense that it maximizes the probability of a correct decision is derived. When systematic error sources are properly included in the least-squares reduction process to yield an optimal solution the test reduces to choosing the solution which provides the smaller valuation of the least-squares loss function. When systematic error sources are ignored in the least-squares reduction, the most powerful test is a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudoinverse of a reduced-rank square matrix. A formula for computing the power of the most powerful test is provided. Numerical examples are included in which the power of the test is computed for situations that are relevant to the design of a satellite-aided search and rescue system.

A component prediction method for flue gas of natural gas combustion based on nonlinear partial least squares method.

PubMed

Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun

2014-01-01

Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.

NLINEAR - NONLINEAR CURVE FITTING PROGRAM

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1994-01-01

A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.

Comment on "Fringe projection profilometry with nonparallel illumination: a least-squares approach"

NASA Astrophysics Data System (ADS)

Wang, Zhaoyang; Bi, Hongbo

2006-07-01

We comment on the recent Letter by Chen and Quan [Opt. Lett.30, 2101 (2005)] in which a least-squares approach was proposed to cope with the nonparallel illumination in fringe projection profilometry. It is noted that the previous mathematical derivations of the fringe pitch and carrier phase functions on the reference plane were incorrect. In addition, we suggest that the variation of carrier phase along the vertical direction should be considered.

Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N{sub 4}

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

Bender, Jason D.; Doraiswamy, Sriram; Candler, Graham V., E-mail: truhlar@umn.edu, E-mail: candler@aem.umn.edu

2014-02-07

Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with amore » review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N{sub 4}. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.« less

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, Xin-ran; Wang, Xin

2017-04-01

When the genetic algorithm is used to solve the problem of too short-arc (TSA) orbit determination, due to the difference of computing process between the genetic algorithm and the classical method, the original method for outlier deletion is no longer applicable. In the genetic algorithm, the robust estimation is realized by introducing different loss functions for the fitness function, then the outlier problem of the TSA orbit determination is solved. Compared with the classical method, the genetic algorithm is greatly simplified by introducing in different loss functions. Through the comparison on the calculations of multiple loss functions, it is found that the least median square (LMS) estimation and least trimmed square (LTS) estimation can greatly improve the robustness of the TSA orbit determination, and have a high breakdown point.

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Parameterisation of rainfall-runoff models for forecasting low and average flows, I: Conceptual modelling

NASA Astrophysics Data System (ADS)

Castiglioni, S.; Toth, E.

2009-04-01

In the calibration procedure of continuously-simulating models, the hydrologist has to choose which part of the observed hydrograph is most important to fit, either implicitly, through the visual agreement in manual calibration, or explicitly, through the choice of the objective function(s). Changing the objective functions it is in fact possible to emphasise different kind of errors, giving them more weight in the calibration phase. The objective functions used for calibrating hydrological models are generally of the quadratic type (mean squared error, correlation coefficient, coefficient of determination, etc) and are therefore oversensitive to high and extreme error values, that typically correspond to high and extreme streamflow values. This is appropriate when, like in the majority of streamflow forecasting applications, the focus is on the ability to reproduce potentially dangerous flood events; on the contrary, if the aim of the modelling is the reproduction of low and average flows, as it is the case in water resource management problems, this may result in a deterioration of the forecasting performance. This contribution presents the results of a series of automatic calibration experiments of a continuously-simulating rainfall-runoff model applied over several real-world case-studies, where the objective function is chosen so to highlight the fit of average and low flows. In this work a simple conceptual model will be used, of the lumped type, with a relatively low number of parameters to be calibrated. The experiments will be carried out for a set of case-study watersheds in Central Italy, covering an extremely wide range of geo-morphologic conditions and for whom at least five years of contemporary daily series of streamflow, precipitation and evapotranspiration estimates are available. Different objective functions will be tested in calibration and the results will be compared, over validation data, against those obtained with traditional squared functions. A companion work presents the results, over the same case-study watersheds and observation periods, of a system-theoretic model, again calibrated for reproducing average and low streamflows.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

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

Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weightedmore » $$\\ell^2$$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $$\\ell^2$$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.« less

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

NASA Astrophysics Data System (ADS)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Estimating gene function with least squares nonnegative matrix factorization.

PubMed

Wang, Guoli; Ochs, Michael F

2007-01-01

Nonnegative matrix factorization is a machine learning algorithm that has extracted information from data in a number of fields, including imaging and spectral analysis, text mining, and microarray data analysis. One limitation with the method for linking genes through microarray data in order to estimate gene function is the high variance observed in transcription levels between different genes. Least squares nonnegative matrix factorization uses estimates of the uncertainties on the mRNA levels for each gene in each condition, to guide the algorithm to a local minimum in normalized chi2, rather than a Euclidean distance or divergence between the reconstructed data and the data itself. Herein, application of this method to microarray data is demonstrated in order to predict gene function.

Assessment of Gait Characteristics in Total Knee Arthroplasty Patients Using a Hierarchical Partial Least Squares Method.

PubMed

Wang, Wei; Ackland, David C; McClelland, Jodie A; Webster, Kate E; Halgamuge, Saman

2018-01-01

Quantitative gait analysis is an important tool in objective assessment and management of total knee arthroplasty (TKA) patients. Studies evaluating gait patterns in TKA patients have tended to focus on discrete data such as spatiotemporal information, joint range of motion and peak values of kinematics and kinetics, or consider selected principal components of gait waveforms for analysis. These strategies may not have the capacity to capture small variations in gait patterns associated with each joint across an entire gait cycle, and may ultimately limit the accuracy of gait classification. The aim of this study was to develop an automatic feature extraction method to analyse patterns from high-dimensional autocorrelated gait waveforms. A general linear feature extraction framework was proposed and a hierarchical partial least squares method derived for discriminant analysis of multiple gait waveforms. The effectiveness of this strategy was verified using a dataset of joint angle and ground reaction force waveforms from 43 patients after TKA surgery and 31 healthy control subjects. Compared with principal component analysis and partial least squares methods, the hierarchical partial least squares method achieved generally better classification performance on all possible combinations of waveforms, with the highest classification accuracy . The novel hierarchical partial least squares method proposed is capable of capturing virtually all significant differences between TKA patients and the controls, and provides new insights into data visualization. The proposed framework presents a foundation for more rigorous classification of gait, and may ultimately be used to evaluate the effects of interventions such as surgery and rehabilitation.

The Impact of Financial Incentives on Physician Productivity in Medical Groups

PubMed Central

Conrad, Douglas A; Sales, Anne; Liang, Su-Ying; Chaudhuri, Anoshua; Maynard, Charles; Pieper, Lisa; Weinstein, Laurel; Gans, David; Piland, Neill

2002-01-01

Objective To estimate the effect of financial incentives in medical groups—both at the level of individual physician and collectively—on individual physician productivity. Data Sources/Study Setting Secondary data from 1997 on individual physician and group characteristics from two surveys: Medical Group Management Association (MGMA) Physician Compensation and Production Survey and the Cost Survey; Area Resource File data on market characteristics, and various sources of state regulatory data. Study Design Cross-sectional estimation of individual physician production function models, using ordinary least squares and two-stage least squares regression. Data Collection Data from respondents completing all items required for the two stages of production function estimation on both MGMA surveys (with RBRVS units as production measure: 102 groups, 2,237 physicians; and with charges as the production measure: 383 groups, 6,129 physicians). The 102 groups with complete data represent 1.8 percent of the 5,725 MGMA member groups. Principal Findings Individual production-based physician compensation leads to increased productivity, as expected (elasticity=.07, p<.05). The productivity effects of compensation methods based on equal shares of group net income and incentive bonuses are significantly positive (p<.05) and smaller in magnitude. The group-levelfinancial incentive does not appear to be significantly related to physician productivity. Conclusions Individual physician incentives based on own production do increase physician productivity. PMID:12236389

Application of Least-Squares Adjustment Technique to Geometric Camera Calibration and Photogrammetric Flow Visualization

NASA Technical Reports Server (NTRS)

Chen, Fang-Jenq

1997-01-01

Flow visualization produces data in the form of two-dimensional images. If the optical components of a camera system are perfect, the transformation equations between the two-dimensional image and the three-dimensional object space are linear and easy to solve. However, real camera lenses introduce nonlinear distortions that affect the accuracy of transformation unless proper corrections are applied. An iterative least-squares adjustment algorithm is developed to solve the nonlinear transformation equations incorporated with distortion corrections. Experimental applications demonstrate that a relative precision on the order of 40,000 is achievable without tedious laboratory calibrations of the camera.

Visual features as stepping stones toward semantics: Explaining object similarity in IT and perception with non-negative least squares

PubMed Central

Jozwik, Kamila M.; Kriegeskorte, Nikolaus; Mur, Marieke

2016-01-01

Object similarity, in brain representations and conscious perception, must reflect a combination of the visual appearance of the objects on the one hand and the categories the objects belong to on the other. Indeed, visual object features and category membership have each been shown to contribute to the object representation in human inferior temporal (IT) cortex, as well as to object-similarity judgments. However, the explanatory power of features and categories has not been directly compared. Here, we investigate whether the IT object representation and similarity judgments are best explained by a categorical or a feature-based model. We use rich models (>100 dimensions) generated by human observers for a set of 96 real-world object images. The categorical model consists of a hierarchically nested set of category labels (such as “human”, “mammal”, and “animal”). The feature-based model includes both object parts (such as “eye”, “tail”, and “handle”) and other descriptive features (such as “circular”, “green”, and “stubbly”). We used non-negative least squares to fit the models to the brain representations (estimated from functional magnetic resonance imaging data) and to similarity judgments. Model performance was estimated on held-out images not used in fitting. Both models explained significant variance in IT and the amounts explained were not significantly different. The combined model did not explain significant additional IT variance, suggesting that it is the shared model variance (features correlated with categories, categories correlated with features) that best explains IT. The similarity judgments were almost fully explained by the categorical model, which explained significantly more variance than the feature-based model. The combined model did not explain significant additional variance in the similarity judgments. Our findings suggest that IT uses features that help to distinguish categories as stepping stones toward a semantic representation. Similarity judgments contain additional categorical variance that is not explained by visual features, reflecting a higher-level more purely semantic representation. PMID:26493748

Visual features as stepping stones toward semantics: Explaining object similarity in IT and perception with non-negative least squares.

PubMed

Jozwik, Kamila M; Kriegeskorte, Nikolaus; Mur, Marieke

2016-03-01

Object similarity, in brain representations and conscious perception, must reflect a combination of the visual appearance of the objects on the one hand and the categories the objects belong to on the other. Indeed, visual object features and category membership have each been shown to contribute to the object representation in human inferior temporal (IT) cortex, as well as to object-similarity judgments. However, the explanatory power of features and categories has not been directly compared. Here, we investigate whether the IT object representation and similarity judgments are best explained by a categorical or a feature-based model. We use rich models (>100 dimensions) generated by human observers for a set of 96 real-world object images. The categorical model consists of a hierarchically nested set of category labels (such as "human", "mammal", and "animal"). The feature-based model includes both object parts (such as "eye", "tail", and "handle") and other descriptive features (such as "circular", "green", and "stubbly"). We used non-negative least squares to fit the models to the brain representations (estimated from functional magnetic resonance imaging data) and to similarity judgments. Model performance was estimated on held-out images not used in fitting. Both models explained significant variance in IT and the amounts explained were not significantly different. The combined model did not explain significant additional IT variance, suggesting that it is the shared model variance (features correlated with categories, categories correlated with features) that best explains IT. The similarity judgments were almost fully explained by the categorical model, which explained significantly more variance than the feature-based model. The combined model did not explain significant additional variance in the similarity judgments. Our findings suggest that IT uses features that help to distinguish categories as stepping stones toward a semantic representation. Similarity judgments contain additional categorical variance that is not explained by visual features, reflecting a higher-level more purely semantic representation. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Inverse determination of the penalty parameter in penalized weighted least-squares algorithm for noise reduction of low-dose CBCT

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

Wang, Jing; Guan, Huaiqun; Solberg, Timothy

2011-07-15

Purpose: A statistical projection restoration algorithm based on the penalized weighted least-squares (PWLS) criterion can substantially improve the image quality of low-dose CBCT images. The performance of PWLS is largely dependent on the choice of the penalty parameter. Previously, the penalty parameter was chosen empirically by trial and error. In this work, the authors developed an inverse technique to calculate the penalty parameter in PWLS for noise suppression of low-dose CBCT in image guided radiotherapy (IGRT). Methods: In IGRT, a daily CBCT is acquired for the same patient during a treatment course. In this work, the authors acquired the CBCTmore » with a high-mAs protocol for the first session and then a lower mAs protocol for the subsequent sessions. The high-mAs projections served as the goal (ideal) toward, which the low-mAs projections were to be smoothed by minimizing the PWLS objective function. The penalty parameter was determined through an inverse calculation of the derivative of the objective function incorporating both the high and low-mAs projections. Then the parameter obtained can be used for PWLS to smooth the noise in low-dose projections. CBCT projections for a CatPhan 600 and an anthropomorphic head phantom, as well as for a brain patient, were used to evaluate the performance of the proposed technique. Results: The penalty parameter in PWLS was obtained for each CBCT projection using the proposed strategy. The noise in the low-dose CBCT images reconstructed from the smoothed projections was greatly suppressed. Image quality in PWLS-processed low-dose CBCT was comparable to its corresponding high-dose CBCT. Conclusions: A technique was proposed to estimate the penalty parameter for PWLS algorithm. It provides an objective and efficient way to obtain the penalty parameter for image restoration algorithms that require predefined smoothing parameters.« less

Constrained Low-Rank Learning Using Least Squares-Based Regularization.

PubMed

Li, Ping; Yu, Jun; Wang, Meng; Zhang, Luming; Cai, Deng; Li, Xuelong

2017-12-01

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. Moreover, the low-dimensional representation of original data can be paired with some informative structure by imposing an appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a novel constrained LRR method. The objective function is formulated as a constrained nuclear norm minimization problem, which can be solved by the inexact augmented Lagrange multiplier algorithm. Extensive experiments on image classification, human pose estimation, and robust face recovery have confirmed the superiority of our method.

Prediction of pH of cola beverage using Vis/NIR spectroscopy and least squares-support vector machine

NASA Astrophysics Data System (ADS)

Liu, Fei; He, Yong

2008-02-01

Visible and near infrared (Vis/NIR) transmission spectroscopy and chemometric methods were utilized to predict the pH values of cola beverages. Five varieties of cola were prepared and 225 samples (45 samples for each variety) were selected for the calibration set, while 75 samples (15 samples for each variety) for the validation set. The smoothing way of Savitzky-Golay and standard normal variate (SNV) followed by first-derivative were used as the pre-processing methods. Partial least squares (PLS) analysis was employed to extract the principal components (PCs) which were used as the inputs of least squares-support vector machine (LS-SVM) model according to their accumulative reliabilities. Then LS-SVM with radial basis function (RBF) kernel function and a two-step grid search technique were applied to build the regression model with a comparison of PLS regression. The correlation coefficient (r), root mean square error of prediction (RMSEP) and bias were 0.961, 0.040 and 0.012 for PLS, while 0.975, 0.031 and 4.697x10 -3 for LS-SVM, respectively. Both methods obtained a satisfying precision. The results indicated that Vis/NIR spectroscopy combined with chemometric methods could be applied as an alternative way for the prediction of pH of cola beverages.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Aerodynamic parameter estimation via Fourier modulating function techniques

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1995-01-01

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Methods of Fitting a Straight Line to Data: Examples in Water Resources

USGS Publications Warehouse

Hirsch, Robert M.; Gilroy, Edward J.

1984-01-01

Three methods of fitting straight lines to data are described and their purposes are discussed and contrasted in terms of their applicability in various water resources contexts. The three methods are ordinary least squares (OLS), least normal squares (LNS), and the line of organic correlation (OC). In all three methods the parameters are based on moment statistics of the data. When estimation of an individual value is the objective, OLS is the most appropriate. When estimation of many values is the objective and one wants the set of estimates to have the appropriate variance, then OC is most appropriate. When one wishes to describe the relationship between two variables and measurement error is unimportant, then OC is most appropriate. Where the error is important in descriptive problems or in calibration problems, then structural analysis techniques may be most appropriate. Finally, if the problem is one of describing some geographic trajectory, then LNS is most appropriate.

Edge Extraction by an Exponential Function Considering X-ray Transmission Characteristics

NASA Astrophysics Data System (ADS)

Kim, Jong Hyeong; Youp Synn, Sang; Cho, Sung Man; Jong Joo, Won

2011-04-01

3-D radiographic methodology has been into the spotlight for quality inspection of mass product or in-service inspection of aging product. To locate a target object in 3-D space, its characteristic contours such as edge length, edge angle, and vertices are very important. In spite of a simple geometry product, it is very difficult to get clear shape contours from a single radiographic image. The image contains scattering noise at the edges and ambiguity coming from X-Ray absorption within the body. This article suggests a concise method to extract whole edges from a single X-ray image. At the edge point of the object, the intensity of the X-ray decays exponentially as the X-ray penetrates the object. Considering this X-Ray decaying property, edges are extracted by using the least square fitting with the control of Coefficient of Determination.

Orthogonalizing EM: A design-based least squares algorithm.

PubMed

Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z G

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p . Supplementary materials for this article are available online.

Hybrid robust model based on an improved functional link neural network integrating with partial least square (IFLNN-PLS) and its application to predicting key process variables.

PubMed

He, Yan-Lin; Xu, Yuan; Geng, Zhi-Qiang; Zhu, Qun-Xiong

2016-03-01

In this paper, a hybrid robust model based on an improved functional link neural network integrating with partial least square (IFLNN-PLS) is proposed. Firstly, an improved functional link neural network with small norm of expanded weights and high input-output correlation (SNEWHIOC-FLNN) was proposed for enhancing the generalization performance of FLNN. Unlike the traditional FLNN, the expanded variables of the original inputs are not directly used as the inputs in the proposed SNEWHIOC-FLNN model. The original inputs are attached to some small norm of expanded weights. As a result, the correlation coefficient between some of the expanded variables and the outputs is enhanced. The larger the correlation coefficient is, the more relevant the expanded variables tend to be. In the end, the expanded variables with larger correlation coefficient are selected as the inputs to improve the performance of the traditional FLNN. In order to test the proposed SNEWHIOC-FLNN model, three UCI (University of California, Irvine) regression datasets named Housing, Concrete Compressive Strength (CCS), and Yacht Hydro Dynamics (YHD) are selected. Then a hybrid model based on the improved FLNN integrating with partial least square (IFLNN-PLS) was built. In IFLNN-PLS model, the connection weights are calculated using the partial least square method but not the error back propagation algorithm. Lastly, IFLNN-PLS was developed as an intelligent measurement model for accurately predicting the key variables in the Purified Terephthalic Acid (PTA) process and the High Density Polyethylene (HDPE) process. Simulation results illustrated that the IFLNN-PLS could significant improve the prediction performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Body composition explains sex differential in physical performance among older adults.

PubMed

Tseng, Lisa A; Delmonico, Matthew J; Visser, Marjolein; Boudreau, Robert M; Goodpaster, Bret H; Schwartz, Ann V; Simonsick, Eleanor M; Satterfield, Suzanne; Harris, Tamara; Newman, Anne B

2014-01-01

Older women have higher percent body fat, poorer physical function, lower strength, and higher rates of nonfatal chronic conditions than men. We sought to determine whether these differences explained physical performance differences between men and women. Physical performance was assessed in the Health, Aging and Body Composition study in 2,863 men and women aged 70-79 with a composite 0-4 point score consisting of chair stands, standing balance including one-leg stand, and 6-m usual and narrow walk tests. Total body composition was measured by dual x-ray absorptiometry, thigh composition by computed tomography, and knee extensor strength by isokinetic dynamometer. Analysis of covariance estimated least square mean performance scores for men and women. Men had higher performance scores than women (least square means: 2.33±0.02 vs 2.03±0.02, p < .0001), adjusted for race, study site, age, and height. Body composition measures (total body fat and thigh muscle area, muscle density, subcutaneous fat, and intermuscular fat) accounted for differences between men and women (least square means: 2.15±0.02 vs 2.17±0.02, p = .53). Higher strength in men partly explained the sex difference (least square means: 2.28±0.02 vs 2.12±0.02, p < .0001). Strength attenuated the association of thigh muscle mass with performance. Chronic health conditions did not explain the sex difference. In a well-functioning cohort, poorer physical function in women compared with men can be explained predominantly by their higher fat mass, but also by other body composition differences. The higher proportion of body fat in women may put them at significant biomechanical disadvantage for greater disability in old age.

Combining Approach in Stages with Least Squares for fits of data in hyperelasticity

NASA Astrophysics Data System (ADS)

Beda, Tibi

2006-10-01

The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Using Remote Sensing Data to Evaluate Surface Soil Properties in Alabama Ultisols

NASA Technical Reports Server (NTRS)

Sullivan, Dana G.; Shaw, Joey N.; Rickman, Doug; Mask, Paul L.; Luvall, Jeff

2005-01-01

Evaluation of surface soil properties via remote sensing could facilitate soil survey mapping, erosion prediction and allocation of agrochemicals for precision management. The objective of this study was to evaluate the relationship between soil spectral signature and surface soil properties in conventionally managed row crop systems. High-resolution RS data were acquired over bare fields in the Coastal Plain, Appalachian Plateau, and Ridge and Valley provinces of Alabama using the Airborne Terrestrial Applications Sensor multispectral scanner. Soils ranged from sandy Kandiudults to fine textured Rhodudults. Surface soil samples (0-1 cm) were collected from 163 sampling points for soil organic carbon, particle size distribution, and citrate dithionite extractable iron content. Surface roughness, soil water content, and crusting were also measured during sampling. Two methods of analysis were evaluated: 1) multiple linear regression using common spectral band ratios, and 2) partial least squares regression. Our data show that thermal infrared spectra are highly, linearly related to soil organic carbon, sand and clay content. Soil organic carbon content was the most difficult to quantify in these highly weathered systems, where soil organic carbon was generally less than 1.2%. Estimates of sand and clay content were best using partial least squares regression at the Valley site, explaining 42-59% of the variability. In the Coastal Plain, sandy surfaces prone to crusting limited estimates of sand and clay content via partial least squares and regression with common band ratios. Estimates of iron oxide content were a function of mineralogy and best accomplished using specific band ratios, with regression explaining 36-65% of the variability at the Valley and Coastal Plain sites, respectively.

The use of least squares methods in functional optimization of energy use prediction models

NASA Astrophysics Data System (ADS)

Bourisli, Raed I.; Al-Shammeri, Basma S.; AlAnzi, Adnan A.

2012-06-01

The least squares method (LSM) is used to optimize the coefficients of a closed-form correlation that predicts the annual energy use of buildings based on key envelope design and thermal parameters. Specifically, annual energy use is related to a number parameters like the overall heat transfer coefficients of the wall, roof and glazing, glazing percentage, and building surface area. The building used as a case study is a previously energy-audited mosque in a suburb of Kuwait City, Kuwait. Energy audit results are used to fine-tune the base case mosque model in the VisualDOE{trade mark, serif} software. Subsequently, 1625 different cases of mosques with varying parameters were developed and simulated in order to provide the training data sets for the LSM optimizer. Coefficients of the proposed correlation are then optimized using multivariate least squares analysis. The objective is to minimize the difference between the correlation-predicted results and the VisualDOE-simulation results. It was found that the resulting correlation is able to come up with coefficients for the proposed correlation that reduce the difference between the simulated and predicted results to about 0.81%. In terms of the effects of the various parameters, the newly-defined weighted surface area parameter was found to have the greatest effect on the normalized annual energy use. Insulating the roofs and walls also had a major effect on the building energy use. The proposed correlation and methodology can be used during preliminary design stages to inexpensively assess the impacts of various design variables on the expected energy use. On the other hand, the method can also be used by municipality officials and planners as a tool for recommending energy conservation measures and fine-tuning energy codes.

A reconstruction algorithm for three-dimensional object-space data using spatial-spectral multiplexing

NASA Astrophysics Data System (ADS)

Wu, Zhejun; Kudenov, Michael W.

2017-05-01

This paper presents a reconstruction algorithm for the Spatial-Spectral Multiplexing (SSM) optical system. The goal of this algorithm is to recover the three-dimensional spatial and spectral information of a scene, given that a one-dimensional spectrometer array is used to sample the pupil of the spatial-spectral modulator. The challenge of the reconstruction is that the non-parametric representation of the three-dimensional spatial and spectral object requires a large number of variables, thus leading to an underdetermined linear system that is hard to uniquely recover. We propose to reparameterize the spectrum using B-spline functions to reduce the number of unknown variables. Our reconstruction algorithm then solves the improved linear system via a least- square optimization of such B-spline coefficients with additional spatial smoothness regularization. The ground truth object and the optical model for the measurement matrix are simulated with both spatial and spectral assumptions according to a realistic field of view. In order to test the robustness of the algorithm, we add Poisson noise to the measurement and test on both two-dimensional and three-dimensional spatial and spectral scenes. Our analysis shows that the root mean square error of the recovered results can be achieved within 5.15%.

Probability distribution functions for unit hydrographs with optimization using genetic algorithm

NASA Astrophysics Data System (ADS)

Ghorbani, Mohammad Ali; Singh, Vijay P.; Sivakumar, Bellie; H. Kashani, Mahsa; Atre, Atul Arvind; Asadi, Hakimeh

2017-05-01

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

A new method for gravity field recovery based on frequency analysis of spherical harmonics

NASA Astrophysics Data System (ADS)

Cai, Lin; Zhou, Zebing

2017-04-01

All existing methods for gravity field recovery are mostly based on the space-wise and time-wise approach, whose core processes are constructing the observation equations and solving them by the least square method. It's should be pointed that the least square method means the approximation. On the other hand, we can directly and precisely obtain the coefficients of harmonics by computing the Fast Fourier Transform (FFT) when we do 1-D data (time series) analysis. So the question whether we directly and precisely obtain the coefficients of spherical harmonic by computing 2-D FFT of measurements of satellite gravity mission is of great significance, since this may guide us to a new understanding of the signal components of gravity field and make us determine it quickly by taking advantage of FFT. Like the 1-D data analysis, the 2-D FFT of measurements of satellite can be computed rapidly. If we can determine the relationship between spherical harmonics and 2-D Fourier frequencies and the transfer function from measurements to spherical coefficients, the question mentioned above can be solved. So the objective of this research project is to establish a new method based on frequency analysis of spherical harmonic, which directly compute the confidents of spherical harmonic of gravity field, which is differ from recovery by least squares. There is a one to one correspondence between frequency spectrum and the time series in 1-D FFT. The 2-D FFT has a similar relationship to 1-D FFT. Owing to the fact that any degree or order (higher than one) of spherical function has multi frequencies and these frequencies may be aliased. Fortunately, the elements and ratio of these frequencies of spherical function can be determined, and we can compute the coefficients of spherical function from 2-D FFT. This relationship can be written as equations and equivalent to a matrix, which is solid and can be derived in advance. Until now the relationship has be determined. Some preliminary results, which only compute lower degree spherical harmonics, indicates that the difference between the input (EGM2008) and output (coefficients from recovery) is smaller than 5E-17, while the minimal precision of computer software (Matlab) is 2.2204E-16.

Quantitative Modelling of Trace Elements in Hard Coal.

PubMed

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross-validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment.

Quantitative Modelling of Trace Elements in Hard Coal

PubMed Central

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross–validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment. PMID:27438794

Orthogonalizing EM: A design-based least squares algorithm

PubMed Central

Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z. G.

2016-01-01

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online. PMID:27499558

Curve Fitting via the Criterion of Least Squares. Applications of Algebra and Elementary Calculus to Curve Fitting. [and] Linear Programming in Two Dimensions: I. Applications of High School Algebra to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 321, 453.

ERIC Educational Resources Information Center

Alexander, John W., Jr.; Rosenberg, Nancy S.

This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest

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

Chaudhry, Jehanzeb Hameed; Cyr, Eric C.; Liu, Kuo

2014-12-18

Here, we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-of-interest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-of-interest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to supportmore » the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost.« less

Least-Squares Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Kantak, Anil V.

1990-01-01

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

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.

Accumulated energy norm for full waveform inversion of marine data

NASA Astrophysics Data System (ADS)

Shin, Changsoo; Ha, Wansoo

2017-12-01

Macro-velocity models are important for imaging the subsurface structure. However, the conventional objective functions of full waveform inversion in the time and the frequency domain have a limited ability to recover the macro-velocity model because of the absence of low-frequency information. In this study, we propose new objective functions that can recover the macro-velocity model by minimizing the difference between the zero-frequency components of the square of seismic traces. Instead of the seismic trace itself, we use the square of the trace, which contains low-frequency information. We apply several time windows to the trace and obtain zero-frequency information of the squared trace for each time window. The shape of the new objective functions shows that they are suitable for local optimization methods. Since we use the acoustic wave equation in this study, this method can be used for deep-sea marine data, in which elastic effects can be ignored. We show that the zero-frequency components of the square of the seismic traces can be used to recover macro-velocities from synthetic and field data.

Fast function-on-scalar regression with penalized basis expansions.

PubMed

Reiss, Philip T; Huang, Lei; Mennes, Maarten

2010-01-01

Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990 s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals for the coefficient functions, simultaneous inference by permutation tests, and model selection, including a novel notion of pointwise model selection. P-OLS and P-GLS are compared in a simulation study. Our methods are illustrated with an analysis of age effects in a functional magnetic resonance imaging data set, as well as a reanalysis of a now-classic Canadian weather data set. An R package implementing the methods is publicly available.

Nusinersen versus Sham Control in Later-Onset Spinal Muscular Atrophy.

PubMed

Mercuri, Eugenio; Darras, Basil T; Chiriboga, Claudia A; Day, John W; Campbell, Craig; Connolly, Anne M; Iannaccone, Susan T; Kirschner, Janbernd; Kuntz, Nancy L; Saito, Kayoko; Shieh, Perry B; Tulinius, Már; Mazzone, Elena S; Montes, Jacqueline; Bishop, Kathie M; Yang, Qingqing; Foster, Richard; Gheuens, Sarah; Bennett, C Frank; Farwell, Wildon; Schneider, Eugene; De Vivo, Darryl C; Finkel, Richard S

2018-02-15

Nusinersen is an antisense oligonucleotide drug that modulates pre-messenger RNA splicing of the survival motor neuron 2 ( SMN2) gene. It has been developed for the treatment of spinal muscular atrophy (SMA). We conducted a multicenter, double-blind, sham-controlled, phase 3 trial of nusinersen in 126 children with SMA who had symptom onset after 6 months of age. The children were randomly assigned, in a 2:1 ratio, to undergo intrathecal administration of nusinersen at a dose of 12 mg (nusinersen group) or a sham procedure (control group) on days 1, 29, 85, and 274. The primary end point was the least-squares mean change from baseline in the Hammersmith Functional Motor Scale-Expanded (HFMSE) score at 15 months of treatment; HFMSE scores range from 0 to 66, with higher scores indicating better motor function. Secondary end points included the percentage of children with a clinically meaningful increase from baseline in the HFMSE score (≥3 points), an outcome that indicates improvement in at least two motor skills. In the prespecified interim analysis, there was a least-squares mean increase from baseline to month 15 in the HFMSE score in the nusinersen group (by 4.0 points) and a least-squares mean decrease in the control group (by -1.9 points), with a significant between-group difference favoring nusinersen (least-squares mean difference in change, 5.9 points; 95% confidence interval, 3.7 to 8.1; P<0.001). This result prompted early termination of the trial. Results of the final analysis were consistent with results of the interim analysis. In the final analysis, 57% of the children in the nusinersen group as compared with 26% in the control group had an increase from baseline to month 15 in the HFMSE score of at least 3 points (P<0.001), and the overall incidence of adverse events was similar in the nusinersen group and the control group (93% and 100%, respectively). Among children with later-onset SMA, those who received nusinersen had significant and clinically meaningful improvement in motor function as compared with those in the control group. (Funded by Biogen and Ionis Pharmaceuticals; CHERISH ClinicalTrials.gov number, NCT02292537 .).

Female disability disadvantage: a global perspective on sex differences in physical function and disability.

PubMed

Wheaton, Felicia V; Crimmins, Eileen M

2016-07-01

The objectives were to determine whether women always fare more poorly in terms of physical function and disability across countries that vary widely in terms of their level of development, epidemiologic context and level of gender equality. Sex differences in self-reported and objective measures of disability and physical function were compared among older adults aged 55-85 in the United States of America, Taiwan, Korea, Mexico, China, Indonesia and among the Tsimane of Bolivia using population-based studies collected between 2001 and 2011. Data were analysed using logistic and ordinary least-squares regression. Confidence intervals were examined to see whether the effect of being female differed significantly between countries. In all countries, women had consistently worse physical functioning (both self-reported and objectively measured). Women also tended to report more difficulty with activities of daily living (ADL), although differences were not always significant. In general, sex differences across measures were less pronounced in China. In Korea, women had significantly lower grip strength, but sex differences in ADL difficulty were non-significant or even reversed. Education and marital status helped explain sex differences. Overall, there was striking similarity in the magnitude and direction of sex differences across countries despite considerable differences in context, although modest variations in the effect of sex were observed.

Sparse partial least squares regression for simultaneous dimension reduction and variable selection

PubMed Central

Chun, Hyonho; Keleş, Sündüz

2010-01-01

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data. PMID:20107611

Online Least Squares One-Class Support Vector Machines-Based Abnormal Visual Event Detection

PubMed Central

Wang, Tian; Chen, Jie; Zhou, Yi; Snoussi, Hichem

2013-01-01

The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method. PMID:24351629

The relationship between air pollution, fossil fuel energy consumption, and water resources in the panel of selected Asia-Pacific countries.

PubMed

Rafindadi, Abdulkadir Abdulrashid; Yusof, Zarinah; Zaman, Khalid; Kyophilavong, Phouphet; Akhmat, Ghulam

2014-10-01

The objective of the study is to examine the relationship between air pollution, fossil fuel energy consumption, water resources, and natural resource rents in the panel of selected Asia-Pacific countries, over a period of 1975-2012. The study includes number of variables in the model for robust analysis. The results of cross-sectional analysis show that there is a significant relationship between air pollution, energy consumption, and water productivity in the individual countries of Asia-Pacific. However, the results of each country vary according to the time invariant shocks. For this purpose, the study employed the panel least square technique which includes the panel least square regression, panel fixed effect regression, and panel two-stage least square regression. In general, all the panel tests indicate that there is a significant and positive relationship between air pollution, energy consumption, and water resources in the region. The fossil fuel energy consumption has a major dominating impact on the changes in the air pollution in the region.

Online least squares one-class support vector machines-based abnormal visual event detection.

PubMed

Wang, Tian; Chen, Jie; Zhou, Yi; Snoussi, Hichem

2013-12-12

The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method.

An Aggregated Method for Determining Railway Defects and Obstacle Parameters

NASA Astrophysics Data System (ADS)

Loktev, Daniil; Loktev, Alexey; Stepanov, Roman; Pevzner, Viktor; Alenov, Kanat

2018-03-01

The method of combining algorithms of image blur analysis and stereo vision to determine the distance to objects (including external defects of railway tracks) and the speed of moving objects-obstacles is proposed. To estimate the deviation of the distance depending on the blur a statistical approach, logarithmic, exponential and linear standard functions are used. The statistical approach includes a method of estimating least squares and the method of least modules. The accuracy of determining the distance to the object, its speed and direction of movement is obtained. The paper develops a method of determining distances to objects by analyzing a series of images and assessment of depth using defocusing using its aggregation with stereoscopic vision. This method is based on a physical effect of dependence on the determined distance to the object on the obtained image from the focal length or aperture of the lens. In the calculation of the blur spot diameter it is assumed that blur occurs at the point equally in all directions. According to the proposed approach, it is possible to determine the distance to the studied object and its blur by analyzing a series of images obtained using the video detector with different settings. The article proposes and scientifically substantiates new and improved existing methods for detecting the parameters of static and moving objects of control, and also compares the results of the use of various methods and the results of experiments. It is shown that the aggregate method gives the best approximation to the real distances.

Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation

NASA Astrophysics Data System (ADS)

Li, T.; Griffiths, W. D.; Chen, J.

2017-11-01

The Maximum Likelihood method and the Linear Least Squares (LLS) method have been widely used to estimate Weibull parameters for reliability of brittle and metal materials. In the last 30 years, many researchers focused on the bias of Weibull modulus estimation, and some improvements have been achieved, especially in the case of the LLS method. However, there is a shortcoming in these methods for a specific type of data, where the lower tail deviates dramatically from the well-known linear fit in a classic LLS Weibull analysis. This deviation can be commonly found from the measured properties of materials, and previous applications of the LLS method on this kind of dataset present an unreliable linear regression. This deviation was previously thought to be due to physical flaws ( i.e., defects) contained in materials. However, this paper demonstrates that this deviation can also be caused by the linear transformation of the Weibull function, occurring in the traditional LLS method. Accordingly, it may not be appropriate to carry out a Weibull analysis according to the linearized Weibull function, and the Non-linear Least Squares method (Non-LS) is instead recommended for the Weibull modulus estimation of casting properties.

A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression

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

Mizukami, Wataru, E-mail: wataru.mizukami@bristol.ac.uk; Tew, David P., E-mail: david.tew@bristol.ac.uk; Habershon, Scott, E-mail: S.Habershon@warwick.ac.uk

2014-10-14

We present a new approach to semi-global potential energy surface fitting that uses the least absolute shrinkage and selection operator (LASSO) constrained least squares procedure to exploit an extremely flexible form for the potential function, while at the same time controlling the risk of overfitting and avoiding the introduction of unphysical features such as divergences or high-frequency oscillations. Drawing from a massively redundant set of overlapping distributed multi-dimensional Gaussian functions of inter-atomic separations we build a compact full-dimensional surface for malonaldehyde, fit to explicitly correlated coupled cluster CCSD(T)(F12*) energies with a root mean square deviations accuracy of 0.3%–0.5% up tomore » 25 000 cm{sup −1} above equilibrium. Importance-sampled diffusion Monte Carlo calculations predict zero point energies for malonaldehyde and its deuterated isotopologue of 14 715.4(2) and 13 997.9(2) cm{sup −1} and hydrogen transfer tunnelling splittings of 21.0(4) and 3.2(4) cm{sup −1}, respectively, which are in excellent agreement with the experimental values of 21.583 and 2.915(4) cm{sup −1}.« less

A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM.

PubMed

Li, Ji; Hu, Guoqing; Zhou, Yonghong; Zou, Chong; Peng, Wei; Alam Sm, Jahangir

2016-10-14

A piezo-resistive pressure sensor is made of silicon, the nature of which is considerably influenced by ambient temperature. The effect of temperature should be eliminated during the working period in expectation of linear output. To deal with this issue, an approach consists of a hybrid kernel Least Squares Support Vector Machine (LSSVM) optimized by a chaotic ions motion algorithm presented. To achieve the learning and generalization for excellent performance, a hybrid kernel function, constructed by a local kernel as Radial Basis Function (RBF) kernel, and a global kernel as polynomial kernel is incorporated into the Least Squares Support Vector Machine. The chaotic ions motion algorithm is introduced to find the best hyper-parameters of the Least Squares Support Vector Machine. The temperature data from a calibration experiment is conducted to validate the proposed method. With attention on algorithm robustness and engineering applications, the compensation result shows the proposed scheme outperforms other compared methods on several performance measures as maximum absolute relative error, minimum absolute relative error mean and variance of the averaged value on fifty runs. Furthermore, the proposed temperature compensation approach lays a foundation for more extensive research.

nmrfit

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

2017-09-01

Nmrfit reads the output from a nuclear magnetic resonance (NMR) experiment and, through a number of intuitive API calls, produces a least-squares fit of Voigt-function approximations via particle swarm optimization.

Functional Relationships and Regression Analysis.

ERIC Educational Resources Information Center

Preece, Peter F. W.

1978-01-01

Using a degenerate multivariate normal model for the distribution of organismic variables, the form of least-squares regression analysis required to estimate a linear functional relationship between variables is derived. It is suggested that the two conventional regression lines may be considered to describe functional, not merely statistical,…

Objective-subjective disparity in cancer-related cognitive impairment: does the use of change measures help reconcile the difference?

PubMed

O'Farrell, Erin; Smith, Andra; Collins, Barbara

2017-10-01

Studies to date have found little correlation between subjective and objective measures of cognitive function in cancer patients, making it difficult to interpret the significance of their cognitive complaints. The purpose of this study was to determine if a stronger correlation would be obtained using measures of cognitive change rather than static scores. Sixty women with early stage breast cancer underwent repeated cognitive assessment over the course of chemotherapy with a neuropsychological test battery (objective measure) and with the FACT-Cog (subjective measure). Their results were compared to 60 healthy women matched on age and education and assessed at similar intervals. We used multilevel modeling, with FACT-Cog as the dependent measure and ordinary least squares slopes of a neuropsychological summary score as the independent variable, to evaluate the co-variation between the subjective and objective measures over time RESULTS: Measures of both objective and subjective cognitive function declined over the course of chemotherapy in the breast cancer patients but there was no significant relationship between them, even when using change measures. Change in objective cognitive function was not related to change in anxiety or fatigue scores but the decline in perceived cognitive function was associated with greater anxiety and fatigue. The discrepancy in objective and subjective measures of cognition in breast cancer patients cannot be accounted for in terms of a failure to use change measures. Although the results are negative, we contend that this is the more appropriate methodology for analyzing cancer-related changes in cognition. Copyright © 2016 John Wiley & Sons, Ltd.

Least-Squares Models to Correct for Rater Effects in Performance Assessment.

ERIC Educational Resources Information Center

Raymond, Mark R.; Viswesvaran, Chockalingam

This study illustrates the use of three least-squares models to control for rater effects in performance evaluation: (1) ordinary least squares (OLS); (2) weighted least squares (WLS); and (3) OLS subsequent to applying a logistic transformation to observed ratings (LOG-OLS). The three models were applied to ratings obtained from four…

On one-sided filters for spectral Fourier approximations of discontinuous functions

NASA Technical Reports Server (NTRS)

Wei, Cai; Gottlieb, David; Shu, Chi-Wang

1991-01-01

The existence of one-sided filters, for spectral Fourier approximations of discontinuous functions, which can recover spectral accuracy up to discontinuity from one side, was proved. A least square procedure was also used to construct such a filter and test it on several discontinuous functions numerically.

Processing of fetal heart rate through non-invasive adaptive system based on recursive least squares algorithm

NASA Astrophysics Data System (ADS)

Fajkus, Marcel; Nedoma, Jan; Martinek, Radek; Vasinek, Vladimir

2017-10-01

In this article, we describe an innovative non-invasive method of Fetal Phonocardiography (fPCG) using fiber-optic sensors and adaptive algorithm for the measurement of fetal heart rate (fHR). Conventional PCG is based on a noninvasive scanning of acoustic signals by means of a microphone placed on the thorax. As for fPCG, the microphone is placed on the maternal abdomen. Our solution is based on patent pending non-invasive scanning of acoustic signals by means of a fiber-optic interferometer. Fiber-optic sensors are resistant to technical artifacts such as electromagnetic interferences (EMI), thus they can be used in situations where it is impossible to use conventional EFM methods, e.g. during Magnetic Resonance Imaging (MRI) examination or in case of delivery in water. The adaptive evaluation system is based on Recursive least squares (RLS) algorithm. Based on real measurements provided on five volunteers with their written consent, we created a simplified dynamic signal model of a distribution of heartbeat sounds (HS) through the human body. Our created model allows us to verification of the proposed adaptive system RLS algorithm. The functionality of the proposed non-invasive adaptive system was verified by objective parameters such as Sensitivity (S+) and Signal to Noise Ratio (SNR).

Penalized weighted least-squares approach for multienergy computed tomography image reconstruction via structure tensor total variation regularization.

PubMed

Zeng, Dong; Gao, Yuanyuan; Huang, Jing; Bian, Zhaoying; Zhang, Hua; Lu, Lijun; Ma, Jianhua

2016-10-01

Multienergy computed tomography (MECT) allows identifying and differentiating different materials through simultaneous capture of multiple sets of energy-selective data belonging to specific energy windows. However, because sufficient photon counts are not available in each energy window compared with that in the whole energy window, the MECT images reconstructed by the analytical approach often suffer from poor signal-to-noise and strong streak artifacts. To address the particular challenge, this work presents a penalized weighted least-squares (PWLS) scheme by incorporating the new concept of structure tensor total variation (STV) regularization, which is henceforth referred to as 'PWLS-STV' for simplicity. Specifically, the STV regularization is derived by penalizing higher-order derivatives of the desired MECT images. Thus it could provide more robust measures of image variation, which can eliminate the patchy artifacts often observed in total variation (TV) regularization. Subsequently, an alternating optimization algorithm was adopted to minimize the objective function. Extensive experiments with a digital XCAT phantom and meat specimen clearly demonstrate that the present PWLS-STV algorithm can achieve more gains than the existing TV-based algorithms and the conventional filtered backpeojection (FBP) algorithm in terms of both quantitative and visual quality evaluations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Optimally weighted least-squares steganalysis

NASA Astrophysics Data System (ADS)

Ker, Andrew D.

2007-02-01

Quantitative steganalysis aims to estimate the amount of payload in a stego object, and such estimators seem to arise naturally in steganalysis of Least Significant Bit (LSB) replacement in digital images. However, as with all steganalysis, the estimators are subject to errors, and their magnitude seems heavily dependent on properties of the cover. In very recent work we have given the first derivation of estimation error, for a certain method of steganalysis (the Least-Squares variant of Sample Pairs Analysis) of LSB replacement steganography in digital images. In this paper we make use of our theoretical results to find an improved estimator and detector. We also extend the theoretical analysis to another (more accurate) steganalysis estimator (Triples Analysis) and hence derive an improved version of that estimator too. Experimental results show that the new steganalyzers have improved accuracy, particularly in the difficult case of never-compressed covers.

Regression Analysis: Instructional Resource for Cost/Managerial Accounting

ERIC Educational Resources Information Center

Stout, David E.

2015-01-01

This paper describes a classroom-tested instructional resource, grounded in principles of active learning and a constructivism, that embraces two primary objectives: "demystify" for accounting students technical material from statistics regarding ordinary least-squares (OLS) regression analysis--material that students may find obscure or…

Effective Algorithm for Detection and Correction of the Wave Reconstruction Errors Caused by the Tilt of Reference Wave in Phase-shifting Interferometry

NASA Astrophysics Data System (ADS)

Xu, Xianfeng; Cai, Luzhong; Li, Dailin; Mao, Jieying

2010-04-01

In phase-shifting interferometry (PSI) the reference wave is usually supposed to be an on-axis plane wave. But in practice a slight tilt of reference wave often occurs, and this tilt will introduce unexpected errors of the reconstructed object wave-front. Usually the least-square method with iterations, which is time consuming, is employed to analyze the phase errors caused by the tilt of reference wave. Here a simple effective algorithm is suggested to detect and then correct this kind of errors. In this method, only some simple mathematic operation is used, avoiding using least-square equations as needed in most methods reported before. It can be used for generalized phase-shifting interferometry with two or more frames for both smooth and diffusing objects, and the excellent performance has been verified by computer simulations. The numerical simulations show that the wave reconstruction errors can be reduced by 2 orders of magnitude.

[Spectral quantitative analysis by nonlinear partial least squares based on neural network internal model for flue gas of thermal power plant].

PubMed

Cao, Hui; Li, Yao-Jiang; Zhou, Yan; Wang, Yan-Xia

2014-11-01

To deal with nonlinear characteristics of spectra data for the thermal power plant flue, a nonlinear partial least square (PLS) analysis method with internal model based on neural network is adopted in the paper. The latent variables of the independent variables and the dependent variables are extracted by PLS regression firstly, and then they are used as the inputs and outputs of neural network respectively to build the nonlinear internal model by train process. For spectra data of flue gases of the thermal power plant, PLS, the nonlinear PLS with the internal model of back propagation neural network (BP-NPLS), the non-linear PLS with the internal model of radial basis function neural network (RBF-NPLS) and the nonlinear PLS with the internal model of adaptive fuzzy inference system (ANFIS-NPLS) are compared. The root mean square error of prediction (RMSEP) of sulfur dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 16.96%, 16.60% and 19.55% than that of PLS, respectively. The RMSEP of nitric oxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 8.60%, 8.47% and 10.09% than that of PLS, respectively. The RMSEP of nitrogen dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 2.11%, 3.91% and 3.97% than that of PLS, respectively. Experimental results show that the nonlinear PLS is more suitable for the quantitative analysis of glue gas than PLS. Moreover, by using neural network function which can realize high approximation of nonlinear characteristics, the nonlinear partial least squares method with internal model mentioned in this paper have well predictive capabilities and robustness, and could deal with the limitations of nonlinear partial least squares method with other internal model such as polynomial and spline functions themselves under a certain extent. ANFIS-NPLS has the best performance with the internal model of adaptive fuzzy inference system having ability to learn more and reduce the residuals effectively. Hence, ANFIS-NPLS is an accurate and useful quantitative thermal power plant flue gas analysis method.

Triangulation of multistation camera data to locate a curved line in space

NASA Technical Reports Server (NTRS)

Fricke, C. L.

1974-01-01

A method is described for finding the location of a curved line in space from local azimuth as a function of elevation data obtained at several observation sites. A least-squares criterion is used to insure the best fit to the data. The method is applicable to the triangulation of an object having no identifiable structural features, provided its width is very small compared with its length so as to approximate a line in space. The method was implemented with a digital computer program and was successfully applied to data obtained from photographs of a barium ion cloud which traced out the earth's magnetic field line at very high altitudes.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Improvements on a non-invasive, parameter-free approach to inverse form finding

NASA Astrophysics Data System (ADS)

Landkammer, P.; Caspari, M.; Steinmann, P.

2017-08-01

Our objective is to determine the optimal undeformed workpiece geometry (material configuration) within forming processes when the prescribed deformed geometry (spatial configuration) is given. For solving the resulting shape optimization problem—also denoted as inverse form finding—we use a novel parameter-free approach, which relocates in each iteration the material nodal positions as design variables. The spatial nodal positions computed by an elasto-plastic finite element (FE) forming simulation are compared with their prescribed values. The objective function expresses a least-squares summation of the differences between the computed and the prescribed nodal positions. Here, a recently developed shape optimization approach (Landkammer and Steinmann in Comput Mech 57(2):169-191, 2016) is investigated with a view to enhance its stability and efficiency. Motivated by nonlinear optimization theory a detailed justification of the algorithm is given. Furthermore, a classification according to shape changing design, fixed and controlled nodal coordinates is introduced. Two examples with large elasto-plastic strains demonstrate that using a superconvergent patch recovery technique instead of a least-squares (L2 )-smoothing improves the efficiency. Updating the interior discretization nodes by solving a fictitious elastic problem also reduces the number of required FE iterations and avoids severe mesh distortions. Furthermore, the impact of the inclusion of the second deformation gradient in the Hessian of the Quasi-Newton approach is analyzed. Inverse form finding is a crucial issue in metal forming applications. As a special feature, the approach is designed to be coupled in a non-invasive fashion to arbitrary FE software.

Improvements on a non-invasive, parameter-free approach to inverse form finding

NASA Astrophysics Data System (ADS)

Landkammer, P.; Caspari, M.; Steinmann, P.

2018-04-01

Our objective is to determine the optimal undeformed workpiece geometry (material configuration) within forming processes when the prescribed deformed geometry (spatial configuration) is given. For solving the resulting shape optimization problem—also denoted as inverse form finding—we use a novel parameter-free approach, which relocates in each iteration the material nodal positions as design variables. The spatial nodal positions computed by an elasto-plastic finite element (FE) forming simulation are compared with their prescribed values. The objective function expresses a least-squares summation of the differences between the computed and the prescribed nodal positions. Here, a recently developed shape optimization approach (Landkammer and Steinmann in Comput Mech 57(2):169-191, 2016) is investigated with a view to enhance its stability and efficiency. Motivated by nonlinear optimization theory a detailed justification of the algorithm is given. Furthermore, a classification according to shape changing design, fixed and controlled nodal coordinates is introduced. Two examples with large elasto-plastic strains demonstrate that using a superconvergent patch recovery technique instead of a least-squares (L2)-smoothing improves the efficiency. Updating the interior discretization nodes by solving a fictitious elastic problem also reduces the number of required FE iterations and avoids severe mesh distortions. Furthermore, the impact of the inclusion of the second deformation gradient in the Hessian of the Quasi-Newton approach is analyzed. Inverse form finding is a crucial issue in metal forming applications. As a special feature, the approach is designed to be coupled in a non-invasive fashion to arbitrary FE software.

Automatic evaluation of interferograms

NASA Technical Reports Server (NTRS)

Becker, F.

1982-01-01

A system for the evaluation of interference patterns was developed. For digitizing and processing of the interferograms from classical and holographic interferometers a picture analysis system based upon a computer with a television digitizer was installed. Depending on the quality of the interferograms, four different picture enhancement operations may be used: Signal averaging; spatial smoothing, subtraction of the overlayed intensity function and the removal of distortion-patterns using a spatial filtering technique in the frequency spectrum of the interferograms. The extraction of fringe loci from the digitized interferograms is performed by a foating-threshold method. The fringes are numbered using a special scheme after the removal of any fringe disconnections which appeared if there was insufficient contrast in the holograms. The reconstruction of the object function from the fringe field uses least squares approximation with spline fit. Applications are given.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

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

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Simultaneous spectrophotometric determination of four metals by two kinds of partial least squares methods

NASA Astrophysics Data System (ADS)

Gao, Ling; Ren, Shouxin

2005-10-01

Simultaneous determination of Ni(II), Cd(II), Cu(II) and Zn(II) was studied by two methods, kernel partial least squares (KPLS) and wavelet packet transform partial least squares (WPTPLS), with xylenol orange and cetyltrimethyl ammonium bromide as reagents in the medium pH = 9.22 borax-hydrochloric acid buffer solution. Two programs, PKPLS and PWPTPLS, were designed to perform the calculations. Data reduction was performed using kernel matrices and wavelet packet transform, respectively. In the KPLS method, the size of the kernel matrix is only dependent on the number of samples, thus the method was suitable for the data matrix with many wavelengths and fewer samples. Wavelet packet representations of signals provide a local time-frequency description, thus in the wavelet packet domain, the quality of the noise removal can be improved. In the WPTPLS by optimization, wavelet function and decomposition level were selected as Daubeches 12 and 5, respectively. Experimental results showed both methods to be successful even where there was severe overlap of spectra.

Development of Jet Noise Power Spectral Laws Using SHJAR Data

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James

2009-01-01

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.

Least Square Fast Learning Network for modeling the combustion efficiency of a 300WM coal-fired boiler.

PubMed

Li, Guoqiang; Niu, Peifeng; Wang, Huaibao; Liu, Yongchao

2014-03-01

This paper presents a novel artificial neural network with a very fast learning speed, all of whose weights and biases are determined by the twice Least Square method, so it is called Least Square Fast Learning Network (LSFLN). In addition, there is another difference from conventional neural networks, which is that the output neurons of LSFLN not only receive the information from the hidden layer neurons, but also receive the external information itself directly from the input neurons. In order to test the validity of LSFLN, it is applied to 6 classical regression applications, and also employed to build the functional relation between the combustion efficiency and operating parameters of a 300WM coal-fired boiler. Experimental results show that, compared with other methods, LSFLN with very less hidden neurons could achieve much better regression precision and generalization ability at a much faster learning speed. Copyright © 2013 Elsevier Ltd. All rights reserved.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Least-squares dual characterization for ROI assessment in emission tomography

NASA Astrophysics Data System (ADS)

Ben Bouallègue, F.; Crouzet, J. F.; Dubois, A.; Buvat, I.; Mariano-Goulart, D.

2013-06-01

Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff.

Fast Algorithms for Structured Least Squares and Total Least Squares Problems

PubMed Central

Kalsi, Anoop; O’Leary, Dianne P.

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z1 and Z2. We develop formulas for the generators of the matrix M HM in terms of the generators of M and show that the Cholesky factorization of the matrix M HM can be computed quickly if Z1 is close to unitary and Z2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices. PMID:27274922

Fast Algorithms for Structured Least Squares and Total Least Squares Problems.

PubMed

Kalsi, Anoop; O'Leary, Dianne P

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary and Z 2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices.

CAP: A Computer Code for Generating Tabular Thermodynamic Functions from NASA Lewis Coefficients. Revised

NASA Technical Reports Server (NTRS)

Zehe, Michael J.; Gordon, Sanford; McBride, Bonnie J.

2002-01-01

For several decades the NASA Glenn Research Center has been providing a file of thermodynamic data for use in several computer programs. These data are in the form of least-squares coefficients that have been calculated from tabular thermodynamic data by means of the NASA Properties and Coefficients (PAC) program. The source thermodynamic data are obtained from the literature or from standard compilations. Most gas-phase thermodynamic functions are calculated by the authors from molecular constant data using ideal gas partition functions. The Coefficients and Properties (CAP) program described in this report permits the generation of tabulated thermodynamic functions from the NASA least-squares coefficients. CAP provides considerable flexibility in the output format, the number of temperatures to be tabulated, and the energy units of the calculated properties. This report provides a detailed description of input preparation, examples of input and output for several species, and a listing of all species in the current NASA Glenn thermodynamic data file.

CAP: A Computer Code for Generating Tabular Thermodynamic Functions from NASA Lewis Coefficients

NASA Technical Reports Server (NTRS)

Zehe, Michael J.; Gordon, Sanford; McBride, Bonnie J.

2001-01-01

For several decades the NASA Glenn Research Center has been providing a file of thermodynamic data for use in several computer programs. These data are in the form of least-squares coefficients that have been calculated from tabular thermodynamic data by means of the NASA Properties and Coefficients (PAC) program. The source thermodynamic data are obtained from the literature or from standard compilations. Most gas-phase thermodynamic functions are calculated by the authors from molecular constant data using ideal gas partition functions. The Coefficients and Properties (CAP) program described in this report permits the generation of tabulated thermodynamic functions from the NASA least-squares coefficients. CAP provides considerable flexibility in the output format, the number of temperatures to be tabulated, and the energy units of the calculated properties. This report provides a detailed description of input preparation, examples of input and output for several species, and a listing of all species in the current NASA Glenn thermodynamic data file.

a Transplantable Compensation Scheme for the Effect of the Radiance from the Interior of a Camera on the Accuracy of Temperature Measurement

NASA Astrophysics Data System (ADS)

Dong, Shidu; Yang, Xiaofan; He, Bo; Liu, Guojin

2006-11-01

Radiance coming from the interior of an uncooled infrared camera has a significant effect on the measured value of the temperature of the object. This paper presents a three-phase compensation scheme for coping with this effect. The first phase acquires the calibration data and forms the calibration function by least square fitting. Likewise, the second phase obtains the compensation data and builds the compensation function by fitting. With the aid of these functions, the third phase determines the temperature of the object in concern from any given ambient temperature. It is known that acquiring the compensation data of a camera is very time-consuming. For the purpose of getting the compensation data at a reasonable time cost, we propose a transplantable scheme. The idea of this scheme is to calculate the ratio between the central pixel’s responsivity of the child camera to the radiance from the interior and that of the mother camera, followed by determining the compensation data of the child camera using this ratio and the compensation data of the mother camera Experimental results show that either of the child camera and the mother camera can measure the temperature of the object with an error of no more than 2°C.

Principal components and iterative regression analysis of geophysical series: Application to Sunspot number (1750 2004)

NASA Astrophysics Data System (ADS)

Nordemann, D. J. R.; Rigozo, N. R.; de Souza Echer, M. P.; Echer, E.

2008-11-01

We present here an implementation of a least squares iterative regression method applied to the sine functions embedded in the principal components extracted from geophysical time series. This method seems to represent a useful improvement for the non-stationary time series periodicity quantitative analysis. The principal components determination followed by the least squares iterative regression method was implemented in an algorithm written in the Scilab (2006) language. The main result of the method is to obtain the set of sine functions embedded in the series analyzed in decreasing order of significance, from the most important ones, likely to represent the physical processes involved in the generation of the series, to the less important ones that represent noise components. Taking into account the need of a deeper knowledge of the Sun's past history and its implication to global climate change, the method was applied to the Sunspot Number series (1750-2004). With the threshold and parameter values used here, the application of the method leads to a total of 441 explicit sine functions, among which 65 were considered as being significant and were used for a reconstruction that gave a normalized mean squared error of 0.146.

Multivariate fMRI and Eye Tracking Reveal Differential Effects of Visual Interference on Recognition Memory Judgments for Objects and Scenes.

PubMed

O'Neil, Edward B; Watson, Hilary C; Dhillon, Sonya; Lobaugh, Nancy J; Lee, Andy C H

2015-09-01

Recent work has demonstrated that the perirhinal cortex (PRC) supports conjunctive object representations that aid object recognition memory following visual object interference. It is unclear, however, how these representations interact with other brain regions implicated in mnemonic retrieval and how congruent and incongruent interference influences the processing of targets and foils during object recognition. To address this, multivariate partial least squares was applied to fMRI data acquired during an interference match-to-sample task, in which participants made object or scene recognition judgments after object or scene interference. This revealed a pattern of activity sensitive to object recognition following congruent (i.e., object) interference that included PRC, prefrontal, and parietal regions. Moreover, functional connectivity analysis revealed a common pattern of PRC connectivity across interference and recognition conditions. Examination of eye movements during the same task in a separate study revealed that participants gazed more at targets than foils during correct object recognition decisions, regardless of interference congruency. By contrast, participants viewed foils more than targets for incorrect object memory judgments, but only after congruent interference. Our findings suggest that congruent interference makes object foils appear familiar and that a network of regions, including PRC, is recruited to overcome the effects of interference.

Simultaneous determination of penicillin G salts by infrared spectroscopy: Evaluation of combining orthogonal signal correction with radial basis function-partial least squares regression

NASA Astrophysics Data System (ADS)

Talebpour, Zahra; Tavallaie, Roya; Ahmadi, Seyyed Hamid; Abdollahpour, Assem

2010-09-01

In this study, a new method for the simultaneous determination of penicillin G salts in pharmaceutical mixture via FT-IR spectroscopy combined with chemometrics was investigated. The mixture of penicillin G salts is a complex system due to similar analytical characteristics of components. Partial least squares (PLS) and radial basis function-partial least squares (RBF-PLS) were used to develop the linear and nonlinear relation between spectra and components, respectively. The orthogonal signal correction (OSC) preprocessing method was used to correct unexpected information, such as spectral overlapping and scattering effects. In order to compare the influence of OSC on PLS and RBF-PLS models, the optimal linear (PLS) and nonlinear (RBF-PLS) models based on conventional and OSC preprocessed spectra were established and compared. The obtained results demonstrated that OSC clearly enhanced the performance of both RBF-PLS and PLS calibration models. Also in the case of some nonlinear relation between spectra and component, OSC-RBF-PLS gave satisfactory results than OSC-PLS model which indicated that the OSC was helpful to remove extrinsic deviations from linearity without elimination of nonlinear information related to component. The chemometric models were tested on an external dataset and finally applied to the analysis commercialized injection product of penicillin G salts.

Classifying Physical Morphology of Cocoa Beans Digital Images using Multiclass Ensemble Least-Squares Support Vector Machine

NASA Astrophysics Data System (ADS)

Lawi, Armin; Adhitya, Yudhi

2018-03-01

The objective of this research is to determine the quality of cocoa beans through morphology of their digital images. Samples of cocoa beans were scattered on a bright white paper under a controlled lighting condition. A compact digital camera was used to capture the images. The images were then processed to extract their morphological parameters. Classification process begins with an analysis of cocoa beans image based on morphological feature extraction. Parameters for extraction of morphological or physical feature parameters, i.e., Area, Perimeter, Major Axis Length, Minor Axis Length, Aspect Ratio, Circularity, Roundness, Ferret Diameter. The cocoa beans are classified into 4 groups, i.e.: Normal Beans, Broken Beans, Fractured Beans, and Skin Damaged Beans. The model of classification used in this paper is the Multiclass Ensemble Least-Squares Support Vector Machine (MELS-SVM), a proposed improvement model of SVM using ensemble method in which the separate hyperplanes are obtained by least square approach and the multiclass procedure uses One-Against- All method. The result of our proposed model showed that the classification with morphological feature input parameters were accurately as 99.705% for the four classes, respectively.

Development of a Low-Cost Attitude Sensor for Agricultural Vehicles

USDA-ARS?s Scientific Manuscript database

The objective of this research was to develop a low-cost attitude sensor for agricultural vehicles. The attitude sensor was composed of three vibratory gyroscopes and two inclinometers. A sensor fusion algorithm was developed to estimate tilt angles (roll and pitch) by least-squares method. In the a...

Effect of trial-to-trial variability on optimal event-related fMRI design: Implications for Beta-series correlation and multi-voxel pattern analysis

PubMed Central

Abdulrahman, Hunar; Henson, Richard N.

2016-01-01

Functional magnetic resonance imaging (fMRI) studies typically employ rapid, event-related designs for behavioral reasons and for reasons associated with statistical efficiency. Efficiency is calculated from the precision of the parameters (Betas) estimated from a General Linear Model (GLM) in which trial onsets are convolved with a Hemodynamic Response Function (HRF). However, previous calculations of efficiency have ignored likely variability in the neural response from trial to trial, for example due to attentional fluctuations, or different stimuli across trials. Here we compare three GLMs in their efficiency for estimating average and individual Betas across trials as a function of trial variability, scan noise and Stimulus Onset Asynchrony (SOA): “Least Squares All” (LSA), “Least Squares Separate” (LSS) and “Least Squares Unitary” (LSU). Estimation of responses to individual trials in particular is important for both functional connectivity using “Beta-series correlation” and “multi-voxel pattern analysis” (MVPA). Our simulations show that the ratio of trial-to-trial variability to scan noise impacts both the optimal SOA and optimal GLM, especially for short SOAs < 5 s: LSA is better when this ratio is high, whereas LSS and LSU are better when the ratio is low. For MVPA, the consistency across voxels of trial variability and of scan noise is also critical. These findings not only have important implications for design of experiments using Beta-series regression and MVPA, but also statistical parametric mapping studies that seek only efficient estimation of the mean response across trials. PMID:26549299

Basic Scientific Subroutines, Volume II.

ERIC Educational Resources Information Center

Ruckdeschel, F. R.

This book, second in a series dealing with scientific programing in the BASIC language, provides students, engineers, and scientists with a documented library of subroutines for scientific applications. Subjects of the eight chapters include: (1) least-squares approximation of functions and smoothing of data; (2) approximating functions by series…

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Vision System Measures Motions of Robot and External Objects

NASA Technical Reports Server (NTRS)

Talukder, Ashit; Matthies, Larry

2008-01-01

A prototype of an advanced robotic vision system both (1) measures its own motion with respect to a stationary background and (2) detects other moving objects and estimates their motions, all by use of visual cues. Like some prior robotic and other optoelectronic vision systems, this system is based partly on concepts of optical flow and visual odometry. Whereas prior optoelectronic visual-odometry systems have been limited to frame rates of no more than 1 Hz, a visual-odometry subsystem that is part of this system operates at a frame rate of 60 to 200 Hz, given optical-flow estimates. The overall system operates at an effective frame rate of 12 Hz. Moreover, unlike prior machine-vision systems for detecting motions of external objects, this system need not remain stationary: it can detect such motions while it is moving (even vibrating). The system includes a stereoscopic pair of cameras mounted on a moving robot. The outputs of the cameras are digitized, then processed to extract positions and velocities. The initial image-data-processing functions of this system are the same as those of some prior systems: Stereoscopy is used to compute three-dimensional (3D) positions for all pixels in the camera images. For each pixel of each image, optical flow between successive image frames is used to compute the two-dimensional (2D) apparent relative translational motion of the point transverse to the line of sight of the camera. The challenge in designing this system was to provide for utilization of the 3D information from stereoscopy in conjunction with the 2D information from optical flow to distinguish between motion of the camera pair and motions of external objects, compute the motion of the camera pair in all six degrees of translational and rotational freedom, and robustly estimate the motions of external objects, all in real time. To meet this challenge, the system is designed to perform the following image-data-processing functions: The visual-odometry subsystem (the subsystem that estimates the motion of the camera pair relative to the stationary background) utilizes the 3D information from stereoscopy and the 2D information from optical flow. It computes the relationship between the 3D and 2D motions and uses a least-mean-squares technique to estimate motion parameters. The least-mean-squares technique is suitable for real-time implementation when the number of external-moving-object pixels is smaller than the number of stationary-background pixels.

Synthesis and optimization of four bar mechanism with six design parameters

NASA Astrophysics Data System (ADS)

Jaiswal, Ankur; Jawale, H. P.

2018-04-01

Function generation is synthesis of mechanism for specific task, involves complexity for specially synthesis above five precision of coupler points. Thus pertains to large structural error. The methodology for arriving to better precision solution is to use the optimization technique. Work presented herein considers methods of optimization of structural error in closed kinematic chain with single degree of freedom, for generating functions like log(x), ex, tan(x), sin(x) with five precision points. The equation in Freudenstein-Chebyshev method is used to develop five point synthesis of mechanism. The extended formulation is proposed and results are obtained to verify existing results in literature. Optimization of structural error is carried out using least square approach. Comparative structural error analysis is presented on optimized error through least square method and extended Freudenstein-Chebyshev method.

NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species

NASA Technical Reports Server (NTRS)

McBride, Bonnie J.; Zehe, Michael J.; Gordon, Sanford

2002-01-01

This report documents the library of thermodynamic data used with the NASA Glenn computer program CEA (Chemical Equilibrium with Applications). This library, containing data for over 2000 solid, liquid, and gaseous chemical species for temperatures ranging from 200 to 20,000 K, is available for use with other computer codes as well. The data are expressed as least-squares coefficients to a seven-term functional form for C((sup o)(sub p)) (T) / R with integration constants for H (sup o) (T) / RT and S(sup o) (T) / R. The NASA Glenn computer program PAC (Properties and Coefficients) was used to calculate thermodynamic functions and to generate the least-squares coefficients. PAC input was taken from a variety of sources. A complete listing of the database is given along with a summary of thermodynamic properties at 0 and 298.15 K.

Understanding Least Squares through Monte Carlo Calculations

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2005-01-01

The method of least squares (LS) is considered as an important data analysis tool available to physical scientists. The mathematics of linear least squares(LLS) is summarized in a very compact matrix rotation that renders it practically "formulaic".

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, Dennis C.; Romero, Louis A.

1995-01-01

Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals.

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, D.C.; Romero, L.A.

1995-06-13

Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals. 6 figs.

Parameter identification for nonlinear aerodynamic systems

NASA Technical Reports Server (NTRS)

Pearson, Allan E.

1992-01-01

Continuing work on frequency analysis for transfer function identification is discussed. A new study was initiated into a 'weighted' least squares algorithm within the context of the Fourier modulating function approach. The first phase of applying these techniques to the F-18 flight data is nearing completion, and these results are summarized.

Photogrammetry Toolbox Reference Manual

NASA Technical Reports Server (NTRS)

Liu, Tianshu; Burner, Alpheus W.

2014-01-01

Specialized photogrammetric and image processing MATLAB functions useful for wind tunnel and other ground-based testing of aerospace structures are described. These functions include single view and multi-view photogrammetric solutions, basic image processing to determine image coordinates, 2D and 3D coordinate transformations and least squares solutions, spatial and radiometric camera calibration, epipolar relations, and various supporting utility functions.

Eddy current nondestructive testing device for measuring variable characteristics of a sample utilizing Walsh functions

DOEpatents

Libby, Hugo L.; Hildebrand, Bernard P.

1978-01-01

An eddy current testing device for measuring variable characteristics of a sample generates a signal which varies with variations in such characteristics. A signal expander samples at least a portion of this generated signal and expands the sampled signal on a selected basis of square waves or Walsh functions to produce a plurality of signal components representative of the sampled signal. A network combines these components to provide a display of at least one of the characteristics of the sample.

Convergence and objective functions of some fault/noise-injection-based online learning algorithms for RBF networks.

PubMed

Ho, Kevin I-J; Leung, Chi-Sing; Sum, John

2010-06-01

In the last two decades, many online fault/noise injection algorithms have been developed to attain a fault tolerant neural network. However, not much theoretical works related to their convergence and objective functions have been reported. This paper studies six common fault/noise-injection-based online learning algorithms for radial basis function (RBF) networks, namely 1) injecting additive input noise, 2) injecting additive/multiplicative weight noise, 3) injecting multiplicative node noise, 4) injecting multiweight fault (random disconnection of weights), 5) injecting multinode fault during training, and 6) weight decay with injecting multinode fault. Based on the Gladyshev theorem, we show that the convergence of these six online algorithms is almost sure. Moreover, their true objective functions being minimized are derived. For injecting additive input noise during training, the objective function is identical to that of the Tikhonov regularizer approach. For injecting additive/multiplicative weight noise during training, the objective function is the simple mean square training error. Thus, injecting additive/multiplicative weight noise during training cannot improve the fault tolerance of an RBF network. Similar to injective additive input noise, the objective functions of other fault/noise-injection-based online algorithms contain a mean square error term and a specialized regularization term.

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Phasing via pure crystallographic least squares: an unexpected feature.

PubMed

Burla, Maria Cristina; Carrozzini, Benedetta; Cascarano, Giovanni Luca; Giacovazzo, Carmelo; Polidori, Giampiero

2018-03-01

Crystallographic least-squares techniques, the main tool for crystal structure refinement of small and medium-size molecules, are for the first time used for ab initio phasing. It is shown that the chief obstacle to such use, the least-squares severe convergence limits, may be overcome by a multi-solution procedure able to progressively recognize and discard model atoms in false positions and to include in the current model new atoms sufficiently close to correct positions. The applications show that the least-squares procedure is able to solve many small structures without the use of important ancillary tools: e.g. no electron-density map is calculated as a support for the least-squares procedure.

On the application of the partition of unity method for nonlocal response of low-dimensional structures

NASA Astrophysics Data System (ADS)

Natarajan, Sundararajan

2014-12-01

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

The covariance matrix for the solution vector of an equality-constrained least-squares problem

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'

Confirmatory Factor Analysis of the Elementary School Success Profile for Teachers

ERIC Educational Resources Information Center

Webber, Kristina C.; Rizo, Cynthia F.; Bowen, Natasha K.

2012-01-01

Objectives: This study examines the factor structure and scale quality of data collected with the online Elementary School Success Profile (ESSP) for Teachers from a sample of teachers of 1,145 third through fifth graders. Methods: Confirmatory factor analysis (CFA) using Mplus and weighted least squares means and variances adjusted (WLSMV)…

Modelling Demand for Higher Education: A Partial Least-Squares Analysis of Portugal

ERIC Educational Resources Information Center

Oliveira, Manuela; Vieira, Carlos; Vieira, Isabel

2015-01-01

Recognizing the strategic relevance of higher education, various countries have established ambitious objectives for the percentage of graduates in their population by 2020. In some cases, without effective policies aimed at increasing domestic rates of participation in higher education, such goals will not be met. However, successful measures are…

Head Start Impact on Social-Emotional Outcomes for Children with Disabilities

ERIC Educational Resources Information Center

Lee, Kyunghee; Calkins, Andrea; Shin, Tae Seob

2016-01-01

Objective: Using the Head Start Impact Study data, this study examines Head Start's impacts on social-emotional outcomes for children with disabilities. Method: Among 4,442 children, 570 children were reported to have disabilities. Ordinary least squares regression was used to determine whether the number of disabilities, having an individualized…

Image interpolation via regularized local linear regression.

PubMed

Liu, Xianming; Zhao, Debin; Xiong, Ruiqin; Ma, Siwei; Gao, Wen; Sun, Huifang

2011-12-01

The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the l(2)-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation. © 2011 IEEE

A deconvolution extraction method for 2D multi-object fibre spectroscopy based on the regularized least-squares QR-factorization algorithm

NASA Astrophysics Data System (ADS)

Yu, Jian; Yin, Qian; Guo, Ping; Luo, A.-li

2014-09-01

This paper presents an efficient method for the extraction of astronomical spectra from two-dimensional (2D) multifibre spectrographs based on the regularized least-squares QR-factorization (LSQR) algorithm. We address two issues: we propose a modified Gaussian point spread function (PSF) for modelling the 2D PSF from multi-emission-line gas-discharge lamp images (arc images), and we develop an efficient deconvolution method to extract spectra in real circumstances. The proposed modified 2D Gaussian PSF model can fit various types of 2D PSFs, including different radial distortion angles and ellipticities. We adopt the regularized LSQR algorithm to solve the sparse linear equations constructed from the sparse convolution matrix, which we designate the deconvolution spectrum extraction method. Furthermore, we implement a parallelized LSQR algorithm based on graphics processing unit programming in the Compute Unified Device Architecture to accelerate the computational processing. Experimental results illustrate that the proposed extraction method can greatly reduce the computational cost and memory use of the deconvolution method and, consequently, increase its efficiency and practicability. In addition, the proposed extraction method has a stronger noise tolerance than other methods, such as the boxcar (aperture) extraction and profile extraction methods. Finally, we present an analysis of the sensitivity of the extraction results to the radius and full width at half-maximum of the 2D PSF.

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.

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

Least Squares Procedures.

ERIC Educational Resources Information Center

Hester, Yvette

Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

Regional regression of flood characteristics employing historical information

USGS Publications Warehouse

Tasker, Gary D.; Stedinger, J.R.

1987-01-01

Streamflow gauging networks provide hydrologic information for use in estimating the parameters of regional regression models. The regional regression models can be used to estimate flood statistics, such as the 100 yr peak, at ungauged sites as functions of drainage basin characteristics. A recent innovation in regional regression is the use of a generalized least squares (GLS) estimator that accounts for unequal station record lengths and sample cross correlation among the flows. However, this technique does not account for historical flood information. A method is proposed here to adjust this generalized least squares estimator to account for possible information about historical floods available at some stations in a region. The historical information is assumed to be in the form of observations of all peaks above a threshold during a long period outside the systematic record period. A Monte Carlo simulation experiment was performed to compare the GLS estimator adjusted for historical floods with the unadjusted GLS estimator and the ordinary least squares estimator. Results indicate that using the GLS estimator adjusted for historical information significantly improves the regression model. ?? 1987.

Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi; Balasiddamuni, P.

2017-11-01

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work “Tutorial on maximum likelihood estimation

Partial least squares density modeling (PLS-DM) - a new class-modeling strategy applied to the authentication of olives in brine by near-infrared spectroscopy.

PubMed

Oliveri, Paolo; López, M Isabel; Casolino, M Chiara; Ruisánchez, Itziar; Callao, M Pilar; Medini, Luca; Lanteri, Silvia

2014-12-03

A new class-modeling method, referred to as partial least squares density modeling (PLS-DM), is presented. The method is based on partial least squares (PLS), using a distance-based sample density measurement as the response variable. Potential function probability density is subsequently calculated on PLS scores and used, jointly with residual Q statistics, to develop efficient class models. The influence of adjustable model parameters on the resulting performances has been critically studied by means of cross-validation and application of the Pareto optimality criterion. The method has been applied to verify the authenticity of olives in brine from cultivar Taggiasca, based on near-infrared (NIR) spectra recorded on homogenized solid samples. Two independent test sets were used for model validation. The final optimal model was characterized by high efficiency and equilibrate balance between sensitivity and specificity values, if compared with those obtained by application of well-established class-modeling methods, such as soft independent modeling of class analogy (SIMCA) and unequal dispersed classes (UNEQ). Copyright © 2014 Elsevier B.V. All rights reserved.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm.

PubMed

Jafari, Masoumeh; Salimifard, Maryam; Dehghani, Maryam

2014-07-01

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-07-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

NASA Astrophysics Data System (ADS)

Cheng, Jian; Zhang, Fan; Liu, Tiegang

2018-06-01

In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.

SOM-based nonlinear least squares twin SVM via active contours for noisy image segmentation

NASA Astrophysics Data System (ADS)

Xie, Xiaomin; Wang, Tingting

2017-02-01

In this paper, a nonlinear least square twin support vector machine (NLSTSVM) with the integration of active contour model (ACM) is proposed for noisy image segmentation. Efforts have been made to seek the kernel-generated surfaces instead of hyper-planes for the pixels belonging to the foreground and background, respectively, using the kernel trick to enhance the performance. The concurrent self organizing maps (SOMs) are applied to approximate the intensity distributions in a supervised way, so as to establish the original training sets for the NLSTSVM. Further, the two sets are updated by adding the global region average intensities at each iteration. Moreover, a local variable regional term rather than edge stop function is adopted in the energy function to ameliorate the noise robustness. Experiment results demonstrate that our model holds the higher segmentation accuracy and more noise robustness.

Least square regularized regression in sum space.

PubMed

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Facial Age Synthesis Using Sparse Partial Least Squares (The Case of Ben Needham).

PubMed

Bukar, Ali M; Ugail, Hassan

2017-09-01

Automatic facial age progression (AFAP) has been an active area of research in recent years. This is due to its numerous applications which include searching for missing. This study presents a new method of AFAP. Here, we use an active appearance model (AAM) to extract facial features from available images. An aging function is then modelled using sparse partial least squares regression (sPLS). Thereafter, the aging function is used to render new faces at different ages. To test the accuracy of our algorithm, extensive evaluation is conducted using a database of 500 face images with known ages. Furthermore, the algorithm is used to progress Ben Needham's facial image that was taken when he was 21 months old to the ages of 6, 14, and 22 years. The algorithm presented in this study could potentially be used to enhance the search for missing people worldwide. © 2017 American Academy of Forensic Sciences.

Prediction of clinical depression scores and detection of changes in whole-brain using resting-state functional MRI data with partial least squares regression

PubMed Central

Shimizu, Yu; Yoshimoto, Junichiro; Takamura, Masahiro; Okada, Go; Okamoto, Yasumasa; Yamawaki, Shigeto; Doya, Kenji

2017-01-01

In diagnostic applications of statistical machine learning methods to brain imaging data, common problems include data high-dimensionality and co-linearity, which often cause over-fitting and instability. To overcome these problems, we applied partial least squares (PLS) regression to resting-state functional magnetic resonance imaging (rs-fMRI) data, creating a low-dimensional representation that relates symptoms to brain activity and that predicts clinical measures. Our experimental results, based upon data from clinically depressed patients and healthy controls, demonstrated that PLS and its kernel variants provided significantly better prediction of clinical measures than ordinary linear regression. Subsequent classification using predicted clinical scores distinguished depressed patients from healthy controls with 80% accuracy. Moreover, loading vectors for latent variables enabled us to identify brain regions relevant to depression, including the default mode network, the right superior frontal gyrus, and the superior motor area. PMID:28700672

Detection of Glutamic Acid in Oilseed Rape Leaves Using Near Infrared Spectroscopy and the Least Squares-Support Vector Machine

PubMed Central

Bao, Yidan; Kong, Wenwen; Liu, Fei; Qiu, Zhengjun; He, Yong

2012-01-01

Amino acids are quite important indices to indicate the growth status of oilseed rape under herbicide stress. Near infrared (NIR) spectroscopy combined with chemometrics was applied for fast determination of glutamic acid in oilseed rape leaves. The optimal spectral preprocessing method was obtained after comparing Savitzky-Golay smoothing, standard normal variate, multiplicative scatter correction, first and second derivatives, detrending and direct orthogonal signal correction. Linear and nonlinear calibration methods were developed, including partial least squares (PLS) and least squares-support vector machine (LS-SVM). The most effective wavelengths (EWs) were determined by the successive projections algorithm (SPA), and these wavelengths were used as the inputs of PLS and LS-SVM model. The best prediction results were achieved by SPA-LS-SVM (Raw) model with correlation coefficient r = 0.9943 and root mean squares error of prediction (RMSEP) = 0.0569 for prediction set. These results indicated that NIR spectroscopy combined with SPA-LS-SVM was feasible for the fast and effective detection of glutamic acid in oilseed rape leaves. The selected EWs could be used to develop spectral sensors, and the important and basic amino acid data were helpful to study the function mechanism of herbicide. PMID:23203052

Calibration of Lévy Processes with American Options

NASA Astrophysics Data System (ADS)

Achdou, Yves

We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

[Study on the detection of active ingredient contents of Paecilomyces hepiali mycelium via near infrared spectroscopy].

PubMed

Teng, Wei-Zhuo; Song, Jia; Meng, Fan-Xin; Meng, Qing-Fan; Lu, Jia-Hui; Hu, Shuang; Teng, Li-Rong; Wang, Di; Xie, Jing

2014-10-01

Partial least squares (PLS) and radial basis function neural network (RBFNN) combined with near infrared spectros- copy (NIR) were applied to develop models for cordycepic acid, polysaccharide and adenosine analysis in Paecilomyces hepialid fermentation mycelium. The developed models possess well generalization and predictive ability which can be applied for crude drugs and related productions determination. During the experiment, 214 Paecilomyces hepialid mycelium samples were obtained via chemical mutagenesis combined with submerged fermentation. The contents of cordycepic acid, polysaccharide and adenosine were determined via traditional methods and the near infrared spectroscopy data were collected. The outliers were removed and the numbers of calibration set were confirmed via Monte Carlo partial least square (MCPLS) method. Based on the values of degree of approach (Da), both moving window partial least squares (MWPLS) and moving window radial basis function neural network (MWRBFNN) were applied to optimize characteristic wavelength variables, optimum preprocessing methods and other important variables in the models. After comparison, the RBFNN, RBFNN and PLS models were developed successfully for cordycepic acid, polysaccharide and adenosine detection, and the correlation between reference values and predictive values in both calibration set (R2c) and validation set (R2p) of optimum models was 0.9417 and 0.9663, 0.9803 and 0.9850, and 0.9761 and 0.9728, respectively. All the data suggest that these models possess well fitness and predictive ability.

Three Perspectives on Teaching Least Squares

ERIC Educational Resources Information Center

Scariano, Stephen M.; Calzada, Maria

2004-01-01

The method of Least Squares is the most widely used technique for fitting a straight line to data, and it is typically discussed in several undergraduate courses. This article focuses on three developmentally different approaches for solving the Least Squares problem that are suitable for classroom exposition.

Estimating errors in least-squares fitting

NASA Technical Reports Server (NTRS)

Richter, P. H.

1995-01-01

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Development of New Methods for Predicting the Bistatic Electromagnetic Scattering from Absorbing Shapes

DTIC Science & Technology

1990-01-01

least-squares sense by adding a penalty term proportional to the square of the divergence to the variational principle At the start of this project... principle required for stable solutions of the electromagnetic field: It must be possible to express the basis functions used in the finite element method as... principle to derive several different methods for computing stable solutions to electromagnetic field problems. To understand above principle , notice that

A novel approach to the experimental study on methane/steam reforming kinetics using the Orthogonal Least Squares method

NASA Astrophysics Data System (ADS)

Sciazko, Anna; Komatsu, Yosuke; Brus, Grzegorz; Kimijima, Shinji; Szmyd, Janusz S.

2014-09-01

For a mathematical model based on the result of physical measurements, it becomes possible to determine their influence on the final solution and its accuracy. However, in classical approaches, the influence of different model simplifications on the reliability of the obtained results are usually not comprehensively discussed. This paper presents a novel approach to the study of methane/steam reforming kinetics based on an advanced methodology called the Orthogonal Least Squares method. The kinetics of the reforming process published earlier are divergent among themselves. To obtain the most probable values of kinetic parameters and enable direct and objective model verification, an appropriate calculation procedure needs to be proposed. The applied Generalized Least Squares (GLS) method includes all the experimental results into the mathematical model which becomes internally contradicted, as the number of equations is greater than number of unknown variables. The GLS method is adopted to select the most probable values of results and simultaneously determine the uncertainty coupled with all the variables in the system. In this paper, the evaluation of the reaction rate after the pre-determination of the reaction rate, which was made by preliminary calculation based on the obtained experimental results over a Nickel/Yttria-stabilized Zirconia catalyst, was performed.

Spectroscopic Determination of Aboveground Biomass in Grasslands Using Spectral Transformations, Support Vector Machine and Partial Least Squares Regression

PubMed Central

Marabel, Miguel; Alvarez-Taboada, Flor

2013-01-01

Aboveground biomass (AGB) is one of the strategic biophysical variables of interest in vegetation studies. The main objective of this study was to evaluate the Support Vector Machine (SVM) and Partial Least Squares Regression (PLSR) for estimating the AGB of grasslands from field spectrometer data and to find out which data pre-processing approach was the most suitable. The most accurate model to predict the total AGB involved PLSR and the Maximum Band Depth index derived from the continuum removed reflectance in the absorption features between 916–1,120 nm and 1,079–1,297 nm (R2 = 0.939, RMSE = 7.120 g/m2). Regarding the green fraction of the AGB, the Area Over the Minimum index derived from the continuum removed spectra provided the most accurate model overall (R2 = 0.939, RMSE = 3.172 g/m2). Identifying the appropriate absorption features was proved to be crucial to improve the performance of PLSR to estimate the total and green aboveground biomass, by using the indices derived from those spectral regions. Ordinary Least Square Regression could be used as a surrogate for the PLSR approach with the Area Over the Minimum index as the independent variable, although the resulting model would not be as accurate. PMID:23925082

Improved methods to estimate the effective impervious area in urban catchments using rainfall-runoff data

NASA Astrophysics Data System (ADS)

Ebrahimian, Ali; Wilson, Bruce N.; Gulliver, John S.

2016-05-01

Impervious surfaces are useful indicators of the urbanization impacts on water resources. Effective impervious area (EIA), which is the portion of total impervious area (TIA) that is hydraulically connected to the drainage system, is a better catchment parameter in the determination of actual urban runoff. Development of reliable methods for quantifying EIA rather than TIA is currently one of the knowledge gaps in the rainfall-runoff modeling context. The objective of this study is to improve the rainfall-runoff data analysis method for estimating EIA fraction in urban catchments by eliminating the subjective part of the existing method and by reducing the uncertainty of EIA estimates. First, the theoretical framework is generalized using a general linear least square model and using a general criterion for categorizing runoff events. Issues with the existing method that reduce the precision of the EIA fraction estimates are then identified and discussed. Two improved methods, based on ordinary least square (OLS) and weighted least square (WLS) estimates, are proposed to address these issues. The proposed weighted least squares method is then applied to eleven urban catchments in Europe, Canada, and Australia. The results are compared to map measured directly connected impervious area (DCIA) and are shown to be consistent with DCIA values. In addition, both of the improved methods are applied to nine urban catchments in Minnesota, USA. Both methods were successful in removing the subjective component inherent in the analysis of rainfall-runoff data of the current method. The WLS method is more robust than the OLS method and generates results that are different and more precise than the OLS method in the presence of heteroscedastic residuals in our rainfall-runoff data.

Two-way and three-way approaches to ultra high performance liquid chromatography-photodiode array dataset for the quantitative resolution of a two-component mixture containing ciprofloxacin and ornidazole.

PubMed

Dinç, Erdal; Ertekin, Zehra Ceren; Büker, Eda

2016-09-01

Two-way and three-way calibration models were applied to ultra high performance liquid chromatography with photodiode array data with coeluted peaks in the same wavelength and time regions for the simultaneous quantitation of ciprofloxacin and ornidazole in tablets. The chromatographic data cube (tensor) was obtained by recording chromatographic spectra of the standard and sample solutions containing ciprofloxacin and ornidazole with sulfadiazine as an internal standard as a function of time and wavelength. Parallel factor analysis and trilinear partial least squares were used as three-way calibrations for the decomposition of the tensor, whereas three-way unfolded partial least squares was applied as a two-way calibration to the unfolded dataset obtained from the data array of ultra high performance liquid chromatography with photodiode array detection. The validity and ability of two-way and three-way analysis methods were tested by analyzing validation samples: synthetic mixture, interday and intraday samples, and standard addition samples. Results obtained from two-way and three-way calibrations were compared to those provided by traditional ultra high performance liquid chromatography. The proposed methods, parallel factor analysis, trilinear partial least squares, unfolded partial least squares, and traditional ultra high performance liquid chromatography were successfully applied to the quantitative estimation of the solid dosage form containing ciprofloxacin and ornidazole. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonicwaves

NASA Astrophysics Data System (ADS)

Ogam, Erick; Fellah, Z. E. A.; Sebaa, Naima; Groby, J.-P.

2011-03-01

The inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range ofstudy.

A wavelet and least square filter based spatial-spectral denoising approach of hyperspectral imagery

NASA Astrophysics Data System (ADS)

Li, Ting; Chen, Xiao-Mei; Chen, Gang; Xue, Bo; Ni, Guo-Qiang

2009-11-01

Noise reduction is a crucial step in hyperspectral imagery pre-processing. Based on sensor characteristics, the noise of hyperspectral imagery represents in both spatial and spectral domain. However, most prevailing denosing techniques process the imagery in only one specific domain, which have not utilized multi-domain nature of hyperspectral imagery. In this paper, a new spatial-spectral noise reduction algorithm is proposed, which is based on wavelet analysis and least squares filtering techniques. First, in the spatial domain, a new stationary wavelet shrinking algorithm with improved threshold function is utilized to adjust the noise level band-by-band. This new algorithm uses BayesShrink for threshold estimation, and amends the traditional soft-threshold function by adding shape tuning parameters. Comparing with soft or hard threshold function, the improved one, which is first-order derivable and has a smooth transitional region between noise and signal, could save more details of image edge and weaken Pseudo-Gibbs. Then, in the spectral domain, cubic Savitzky-Golay filter based on least squares method is used to remove spectral noise and artificial noise that may have been introduced in during the spatial denoising. Appropriately selecting the filter window width according to prior knowledge, this algorithm has effective performance in smoothing the spectral curve. The performance of the new algorithm is experimented on a set of Hyperion imageries acquired in 2007. The result shows that the new spatial-spectral denoising algorithm provides more significant signal-to-noise-ratio improvement than traditional spatial or spectral method, while saves the local spectral absorption features better.

Collinearity in Least-Squares Analysis

ERIC Educational Resources Information Center

de Levie, Robert

2012-01-01

How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions…

Using Weighted Least Squares Regression for Obtaining Langmuir Sorption Constants

USDA-ARS?s Scientific Manuscript database

One of the most commonly used models for describing phosphorus (P) sorption to soils is the Langmuir model. To obtain model parameters, the Langmuir model is fit to measured sorption data using least squares regression. Least squares regression is based on several assumptions including normally dist...

The crux of the method: assumptions in ordinary least squares and logistic regression.

PubMed

Long, Rebecca G

2008-10-01

Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

Adaptive Modal Identification for Flutter Suppression Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Drew, Michael; Swei, Sean S.

2016-01-01

In this paper, we will develop an adaptive modal identification method for identifying the frequencies and damping of a flutter mode based on model-reference adaptive control (MRAC) and least-squares methods. The least-squares parameter estimation will achieve parameter convergence in the presence of persistent excitation whereas the MRAC parameter estimation does not guarantee parameter convergence. Two adaptive flutter suppression control approaches are developed: one based on MRAC and the other based on the least-squares method. The MRAC flutter suppression control is designed as an integral part of the parameter estimation where the feedback signal is used to estimate the modal information. On the other hand, the separation principle of control and estimation is applied to the least-squares method. The least-squares modal identification is used to perform parameter estimation.

Improvement of depth resolution in depth-resolved wavenumber-scanning interferometry using wavenumber-domain least-squares algorithm: comparison and experiment.

PubMed

Bai, Yulei; Jia, Quanjie; Zhang, Yun; Huang, Qiquan; Yang, Qiyu; Ye, Shuangli; He, Zhaoshui; Zhou, Yanzhou; Xie, Shengli

2016-05-01

It is important to improve the depth resolution in depth-resolved wavenumber-scanning interferometry (DRWSI) owing to the limited range of wavenumber scanning. In this work, a new nonlinear iterative least-squares algorithm called the wavenumber-domain least-squares algorithm (WLSA) is proposed for evaluating the phase of DRWSI. The simulated and experimental results of the Fourier transform (FT), complex-number least-squares algorithm (CNLSA), eigenvalue-decomposition and least-squares algorithm (EDLSA), and WLSA were compared and analyzed. According to the results, the WLSA is less dependent on the initial values, and the depth resolution δz is approximately changed from δz to δz/6. Thus, the WLSA exhibits a better performance than the FT, CNLSA, and EDLSA.

Evaluation of Available Software for Reconstruction of a Structure from its Imagery

DTIC Science & Technology

2017-04-01

Math . 2, 164–168. Lowe, D. G. (1999) Object recognition from local scale-invariant features, in Proc. Int. Conf. Computer Vision, Vol. 2, pp. 1150–1157...Marquardt, D. (1963) An algorithm for least-squares estimation of nonlinear parameters, SIAM J. Appl. Math . 11(2), 431–441. UNCLASSIFIED 11 DST-Group–TR

Male-Female Wage Differentials in the United States.

ERIC Educational Resources Information Center

Kiker, B. F.; Crouch, Henry L.

The primary objective of this paper is to describe a method of estimating female-male wage ratios. The estimating technique presented is two stage least squares (2SLS), in which equations are estimated for both men and women. After specifying and estimating the wage equations, the male-female wage differential is calculated that would remain if…

An improved algorithm for the determination of the system paramters of a visual binary by least squares

NASA Astrophysics Data System (ADS)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered. The definition of efficiency is revised.

A User's Version View of a Robustified, Bayesian Weighted Least-Squares Recursive Algorithm for Interpolating AVHRR-NDVI Data: Applications to an Animated Visualization of the Phenology of a Semi-Arid Study Area

NASA Astrophysics Data System (ADS)

Hermance, J. F.; Jacob, R. W.; Bradley, B. A.; Mustard, J. F.

2005-12-01

In studying vegetation patterns remotely, the objective is to draw inferences on the development of specific or general land surface phenology (LSP) as a function of space and time by determining the behavior of a parameter (in our case NDVI), when the parameter estimate may be biased by noise, data dropouts and obfuscations from atmospheric and other effects. We describe the underpinning concepts of a procedure for a robust interpolation of NDVI data that does not have the limitations of other mathematical approaches which require orthonormal basis functions (e.g. Fourier analysis). In this approach, data need not be uniformly sampled in time, nor do we expect noise to be Gaussian-distributed. Our approach is intuitive and straightforward, and is applied here to the refined modeling of LSP using 7 years of weekly and biweekly AVHRR NDVI data for a 150 x 150 km study area in central Nevada. This site is a microcosm of a broad range of vegetation classes, from irrigated agriculture with annual NDVIvalues of up to 0.7 to playas and alkali salt flats with annual NDVI values of only 0.07. Our procedure involves a form of parameter estimation employing Bayesian statistics. In utilitarian terms, the latter procedure is a method of statistical analysis (in our case, robustified, weighted least-squares recursive curve-fitting) that incorporates a variety of prior knowledge when forming current estimates of a particular process or parameter. In addition to the standard Bayesian approach, we account for outliers due to data dropouts or obfuscations because of clouds and snow cover. An initial "starting model" for the average annual cycle and long term (7 year) trend is determined by jointly fitting a common set of complex annual harmonics and a low order polynomial to an entire multi-year time series in one step. This is not a formal Fourier series in the conventional sense, but rather a set of 4 cosine and 4 sine coefficients with fundamental periods of 12, 6, 3 and 1.5 months. Instabilities during large time gaps in the data are suppressed by introducing an expectation of minimum roughness on the fitted time series. Our next significant computational step involves a constrained least squares fit to the observed NDVI data. Residuals between the observed NDVI value and the predicted starting model are computed, and the inverse of these residuals provide the weights for a weighted least squares analysis whereby a set of annual eighth-order splines are fit to the 7 years of NDVI data. Although a series of independent 8-th order annual functionals over a period of 7 years is intrinsically unstable when there are significant data gaps, the splined versions for this specific application are quite stable due to explicit continuity conditions on the values and derivatives of the functionals across contiguous years, as well as a priori constraints on the predicted values vis-a-vis the assumed initial model. Our procedure allows us to robustly interpolate original unequally-spaced NDVI data with a new time series having the most-appropriate, user-defined time base. We apply this approach to the temporal behavior of vegetation in our 150 x 150 km study area. Such a small area, being so rich in vegetation diversity, is particularly useful to view in map form and by animated annual and multi-year time sequences, since the interrelation between phenology, topography and specific usage patterns becomes clear.

Object matching using a locally affine invariant and linear programming techniques.

PubMed

Li, Hongsheng; Huang, Xiaolei; He, Lei

2013-02-01

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method.

PubMed

Natarajan, Logesh Kumar; Wu, Sean F

2012-06-01

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

A Comparison of Nonlinear Filters for Orbit Determination and Estimation

DTIC Science & Technology

1986-06-01

Com- mand uses a nonlinear least squares filter for element set maintenance for all objects orbiting the Earth (3). These objects, including active...initial state vector is the singularly averaged classical orbital element set provided by SPACECOM/DOA. The state vector in this research consists of...GSF (G) - - 26.0 36.7 GSF(A) 32.1 77.4 38.8 59.6 The Air Force Space Command is responsible for main- taining current orbital element sets for about

Full Waveform Inversion for Seismic Velocity And Anelastic Losses in Heterogeneous Structures

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

Askan, A.; /Carnegie Mellon U.; Akcelik, V.

2009-04-30

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the inverse problem is to reconstruct the anelastic properties of a heterogeneous medium with possibly discontinuous wave velocities. The inverse problem is formulated as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers in the time domain. This leads to amore » variational formulation in terms of the material model plus the state variables and their adjoints. We employ a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. The least-squares optimization approach to inverse wave propagation presents the well-known difficulties of ill posedness and multiple minima. To overcome ill posedness, we include a total variation regularization functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multiple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to remain within the basin of attraction of the global minimum. We illustrate the methodology with high-resolution inversions for two-dimensional sedimentary models of the San Fernando Valley, under SH-wave excitation. We perform inversions for both the seismic velocity and the intrinsic attenuation using synthetic waveforms at the observer locations as pseudoobserved data.« less

Modal characterization of the ASCIE segmented optics testbed: New algorithms and experimental results

NASA Technical Reports Server (NTRS)

Carrier, Alain C.; Aubrun, Jean-Noel

1993-01-01

New frequency response measurement procedures, on-line modal tuning techniques, and off-line modal identification algorithms are developed and applied to the modal identification of the Advanced Structures/Controls Integrated Experiment (ASCIE), a generic segmented optics telescope test-bed representative of future complex space structures. The frequency response measurement procedure uses all the actuators simultaneously to excite the structure and all the sensors to measure the structural response so that all the transfer functions are measured simultaneously. Structural responses to sinusoidal excitations are measured and analyzed to calculate spectral responses. The spectral responses in turn are analyzed as the spectral data become available and, which is new, the results are used to maintain high quality measurements. Data acquisition, processing, and checking procedures are fully automated. As the acquisition of the frequency response progresses, an on-line algorithm keeps track of the actuator force distribution that maximizes the structural response to automatically tune to a structural mode when approaching a resonant frequency. This tuning is insensitive to delays, ill-conditioning, and nonproportional damping. Experimental results show that is useful for modal surveys even in high modal density regions. For thorough modeling, a constructive procedure is proposed to identify the dynamics of a complex system from its frequency response with the minimization of a least-squares cost function as a desirable objective. This procedure relies on off-line modal separation algorithms to extract modal information and on least-squares parameter subset optimization to combine the modal results and globally fit the modal parameters to the measured data. The modal separation algorithms resolved modal density of 5 modes/Hz in the ASCIE experiment. They promise to be useful in many challenging applications.

Generalized Partial Least Squares Approach for Nominal Multinomial Logit Regression Models with a Functional Covariate

ERIC Educational Resources Information Center

Albaqshi, Amani Mohammed H.

2017-01-01

Functional Data Analysis (FDA) has attracted substantial attention for the last two decades. Within FDA, classifying curves into two or more categories is consistently of interest to scientists, but multi-class prediction within FDA is challenged in that most classification tools have been limited to binary response applications. The functional…

Sparse and stable Markowitz portfolios.

PubMed

Brodie, Joshua; Daubechies, Ingrid; De Mol, Christine; Giannone, Domenico; Loris, Ignace

2009-07-28

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e., portfolios with only few active positions), and allows accounting for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naïve evenly weighted portfolio.

Application of least median of squared orthogonal distance (LMD) and LMD-based reweighted least squares (RLS) methods on the stock-recruitment relationship

NASA Astrophysics Data System (ADS)

Wang, Yan-Jun; Liu, Qun

1999-03-01

Analysis of stock-recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD-based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

A class of least-squares filtering and identification algorithms with systolic array architectures

NASA Technical Reports Server (NTRS)

Kalson, Seth Z.; Yao, Kung

1991-01-01

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Multi-element array signal reconstruction with adaptive least-squares algorithms

NASA Technical Reports Server (NTRS)

Kumar, R.

1992-01-01

Two versions of the adaptive least-squares algorithm are presented for combining signals from multiple feeds placed in the focal plane of a mechanical antenna whose reflector surface is distorted due to various deformations. Coherent signal combining techniques based on the adaptive least-squares algorithm are examined for nearly optimally and adaptively combining the outputs of the feeds. The performance of the two versions is evaluated by simulations. It is demonstrated for the example considered that both of the adaptive least-squares algorithms are capable of offsetting most of the loss in the antenna gain incurred due to reflector surface deformations.

PRIM: An Efficient Preconditioning Iterative Reweighted Least Squares Method for Parallel Brain MRI Reconstruction.

PubMed

Xu, Zheng; Wang, Sheng; Li, Yeqing; Zhu, Feiyun; Huang, Junzhou

2018-02-08

The most recent history of parallel Magnetic Resonance Imaging (pMRI) has in large part been devoted to finding ways to reduce acquisition time. While joint total variation (JTV) regularized model has been demonstrated as a powerful tool in increasing sampling speed for pMRI, however, the major bottleneck is the inefficiency of the optimization method. While all present state-of-the-art optimizations for the JTV model could only reach a sublinear convergence rate, in this paper, we squeeze the performance by proposing a linear-convergent optimization method for the JTV model. The proposed method is based on the Iterative Reweighted Least Squares algorithm. Due to the complexity of the tangled JTV objective, we design a novel preconditioner to further accelerate the proposed method. Extensive experiments demonstrate the superior performance of the proposed algorithm for pMRI regarding both accuracy and efficiency compared with state-of-the-art methods.

Estimating Relative Positions of Outer-Space Structures

NASA Technical Reports Server (NTRS)

Balian, Harry; Breckenridge, William; Brugarolas, Paul

2009-01-01

A computer program estimates the relative position and orientation of two structures from measurements, made by use of electronic cameras and laser range finders on one structure, of distances and angular positions of fiducial objects on the other structure. The program was written specifically for use in determining errors in the alignment of large structures deployed in outer space from a space shuttle. The program is based partly on equations for transformations among the various coordinate systems involved in the measurements and on equations that account for errors in the transformation operators. It computes a least-squares estimate of the relative position and orientation. Sequential least-squares estimates, acquired at a measurement rate of 4 Hz, are averaged by passing them through a fourth-order Butterworth filter. The program is executed in a computer aboard the space shuttle, and its position and orientation estimates are displayed to astronauts on a graphical user interface.

Quantification of brain lipids by FTIR spectroscopy and partial least squares regression

NASA Astrophysics Data System (ADS)

Dreissig, Isabell; Machill, Susanne; Salzer, Reiner; Krafft, Christoph

2009-01-01

Brain tissue is characterized by high lipid content. Its content decreases and the lipid composition changes during transformation from normal brain tissue to tumors. Therefore, the analysis of brain lipids might complement the existing diagnostic tools to determine the tumor type and tumor grade. Objective of this work is to extract lipids from gray matter and white matter of porcine brain tissue, record infrared (IR) spectra of these extracts and develop a quantification model for the main lipids based on partial least squares (PLS) regression. IR spectra of the pure lipids cholesterol, cholesterol ester, phosphatidic acid, phosphatidylcholine, phosphatidylethanolamine, phosphatidylserine, phosphatidylinositol, sphingomyelin, galactocerebroside and sulfatide were used as references. Two lipid mixtures were prepared for training and validation of the quantification model. The composition of lipid extracts that were predicted by the PLS regression of IR spectra was compared with lipid quantification by thin layer chromatography.

Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions

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

Laboure, Vincent M.; Wang, Yaqi; DeHart, Mark D.

In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids [1] in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment [2], in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework [3] using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutionsmore » (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.« less

Least-Squares PN Formulation of the Transport Equation Using Self-Adjoint-Angular-Flux Consistent Boundary Conditions.

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

Vincent M. Laboure; Yaqi Wang; Mark D. DeHart

In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and findmore » the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.« less

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2012 CFR

2012-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2010 CFR

2010-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2011 CFR

2011-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2013 CFR

2013-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2014 CFR

2014-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

Visual Tracking via Sparse and Local Linear Coding.

PubMed

Wang, Guofeng; Qin, Xueying; Zhong, Fan; Liu, Yue; Li, Hongbo; Peng, Qunsheng; Yang, Ming-Hsuan

2015-11-01

The state search is an important component of any object tracking algorithm. Numerous algorithms have been proposed, but stochastic sampling methods (e.g., particle filters) are arguably one of the most effective approaches. However, the discretization of the state space complicates the search for the precise object location. In this paper, we propose a novel tracking algorithm that extends the state space of particle observations from discrete to continuous. The solution is determined accurately via iterative linear coding between two convex hulls. The algorithm is modeled by an optimal function, which can be efficiently solved by either convex sparse coding or locality constrained linear coding. The algorithm is also very flexible and can be combined with many generic object representations. Thus, we first use sparse representation to achieve an efficient searching mechanism of the algorithm and demonstrate its accuracy. Next, two other object representation models, i.e., least soft-threshold squares and adaptive structural local sparse appearance, are implemented with improved accuracy to demonstrate the flexibility of our algorithm. Qualitative and quantitative experimental results demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods in dynamic scenes.

Solution of a Complex Least Squares Problem with Constrained Phase.

PubMed

Bydder, Mark

2010-12-30

The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.

A one-year randomized trial of lorcaserin for weight loss in obese and overweight adults: the BLOSSOM trial.

PubMed

Fidler, Meredith C; Sanchez, Matilde; Raether, Brian; Weissman, Neil J; Smith, Steven R; Shanahan, William R; Anderson, Christen M

2011-10-01

Lorcaserin is a novel selective agonist of the serotonin 2C receptor. Our objective was to evaluate the effects of lorcaserin on body weight, cardiovascular risk factors, and safety in obese and overweight patients. This randomized, placebo-controlled, double-blind, parallel arm trial took place at 97 U.S. research centers. Patients included 4008 patients, aged 18-65 yr, with a body mass index between 30 and 45 kg/m(2) or between 27 and 29.9 kg/m(2) with an obesity-related comorbid condition. Patients were randomly assigned in a 2:1:2 ratio to receive lorcaserin 10 mg twice daily (BID), lorcaserin 10 mg once daily (QD), or placebo. All patients received diet and exercise counseling. The ordered primary endpoints were proportion of patients achieving at least 5% reduction in body weight, mean change in body weight, and proportion of patients achieving at least 10% reduction in body weight at 1 yr. Serial echocardiograms monitored heart valve function. Significantly more patients treated with lorcaserin 10 mg BID and QD lost at least 5% of baseline body weight (47.2 and 40.2%, respectively) as compared with placebo (25.0%, P < 0.001 vs. lorcaserin BID). Least squares mean (95% confidence interval) weight loss with lorcaserin BID and QD was 5.8% (5.5-6.2%) and 4.7% (4.3-5.2%), respectively, compared with 2.8% (2.5-3.2%) with placebo (P < 0.001 vs. lorcaserin BID; least squares mean difference, 3.0%). Weight loss of at least 10% was achieved by 22.6 and 17.4% of patients receiving lorcaserin 10 mg BID and QD, respectively, and 9.7% of patients in the placebo group (P < 0.001 vs. lorcaserin BID). Headache, nausea, and dizziness were the most common lorcaserin-related adverse events. U.S. Food and Drug Administration-defined echocardiographic valvulopathy occurred in 2.0% of patients on placebo and 2.0% on lorcaserin 10 mg BID. Lorcaserin administered in conjunction with a lifestyle modification program was associated with dose-dependent weight loss that was significantly greater than with placebo.

A Cubic Radial Basis Function in the MLPG Method for Beam Problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.

2002-01-01

A non-compactly supported cubic radial basis function implementation of the MLPG method for beam problems is presented. The evaluation of the derivatives of the shape functions obtained from the radial basis function interpolation is much simpler than the evaluation of the moving least squares shape function derivatives. The radial basis MLPG yields results as accurate or better than those obtained by the conventional MLPG method for problems with discontinuous and other complex loading conditions.

A hybrid framework for quantifying the influence of data in hydrological model calibration

NASA Astrophysics Data System (ADS)

Wright, David P.; Thyer, Mark; Westra, Seth; McInerney, David

2018-06-01

Influence diagnostics aim to identify a small number of influential data points that have a disproportionate impact on the model parameters and/or predictions. The key issues with current influence diagnostic techniques are that the regression-theory approaches do not provide hydrologically relevant influence metrics, while the case-deletion approaches are computationally expensive to calculate. The main objective of this study is to introduce a new two-stage hybrid framework that overcomes these challenges, by delivering hydrologically relevant influence metrics in a computationally efficient manner. Stage one uses computationally efficient regression-theory influence diagnostics to identify the most influential points based on Cook's distance. Stage two then uses case-deletion influence diagnostics to quantify the influence of points using hydrologically relevant metrics. To illustrate the application of the hybrid framework, we conducted three experiments on 11 hydro-climatologically diverse Australian catchments using the GR4J hydrological model. The first experiment investigated how many data points from stage one need to be retained in order to reliably identify those points that have the hightest influence on hydrologically relevant metrics. We found that a choice of 30-50 is suitable for hydrological applications similar to those explored in this study (30 points identified the most influential data 98% of the time and reduced the required recalibrations by 99% for a 10 year calibration period). The second experiment found little evidence of a change in the magnitude of influence with increasing calibration period length from 1, 2, 5 to 10 years. Even for 10 years the impact of influential points can still be high (>30% influence on maximum predicted flows). The third experiment compared the standard least squares (SLS) objective function with the weighted least squares (WLS) objective function on a 10 year calibration period. In two out of three flow metrics there was evidence that SLS, with the assumption of homoscedastic residual error, identified data points with higher influence (largest changes of 40%, 10%, and 44% for the maximum, mean, and low flows, respectively) than WLS, with the assumption of heteroscedastic residual errors (largest changes of 26%, 6%, and 6% for the maximum, mean, and low flows, respectively). The hybrid framework complements existing model diagnostic tools and can be applied to a wide range of hydrological modelling scenarios.

On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction.

PubMed

Crop, F; Van Rompaye, B; Paelinck, L; Vakaet, L; Thierens, H; De Wagter, C

2008-07-21

The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry.

Adaptive slab laser beam quality improvement using a weighted least-squares reconstruction algorithm.

PubMed

Chen, Shanqiu; Dong, LiZhi; Chen, XiaoJun; Tan, Yi; Liu, Wenjin; Wang, Shuai; Yang, Ping; Xu, Bing; Ye, YuTang

2016-04-10

Adaptive optics is an important technology for improving beam quality in solid-state slab lasers. However, there are uncorrectable aberrations in partial areas of the beam. In the criterion of the conventional least-squares reconstruction method, it makes the zones with small aberrations nonsensitive and hinders this zone from being further corrected. In this paper, a weighted least-squares reconstruction method is proposed to improve the relative sensitivity of zones with small aberrations and to further improve beam quality. Relatively small weights are applied to the zones with large residual aberrations. Comparisons of results show that peak intensity in the far field improved from 1242 analog digital units (ADU) to 2248 ADU, and beam quality β improved from 2.5 to 2.0. This indicates the weighted least-squares method has better performance than the least-squares reconstruction method when there are large zonal uncorrectable aberrations in the slab laser system.

Two-dimensional wavefront reconstruction based on double-shearing and least squares fitting

NASA Astrophysics Data System (ADS)

Liang, Peiying; Ding, Jianping; Zhu, Yangqing; Dong, Qian; Huang, Yuhua; Zhu, Zhen

2017-06-01

The two-dimensional wavefront reconstruction method based on double-shearing and least squares fitting is proposed in this paper. Four one-dimensional phase estimates of the measured wavefront, which correspond to the two shears and the two orthogonal directions, could be calculated from the differential phase, which solves the problem of the missing spectrum, and then by using the least squares method the two-dimensional wavefront reconstruction could be done. The numerical simulations of the proposed algorithm are carried out to verify the feasibility of this method. The influence of noise generated from different shear amount and different intensity on the accuracy of the reconstruction is studied and compared with the results from the algorithm based on single-shearing and least squares fitting. Finally, a two-grating lateral shearing interference experiment is carried out to verify the wavefront reconstruction algorithm based on doubleshearing and least squares fitting.

New method for calculating a mathematical expression for streamflow recession

USGS Publications Warehouse

Rutledge, Albert T.

1991-01-01

An empirical method has been devised to calculate the master recession curve, which is a mathematical expression for streamflow recession during times of negligible direct runoff. The method is based on the assumption that the storage-delay factor, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of streamflow. The resulting master recession curve can be nonlinear. The method can be executed by a computer program that reads a data file of daily mean streamflow, then allows the user to select several near-linear segments of streamflow recession. The storage-delay factor for each segment is one of the coefficients of the equation that results from linear least-squares regression. Using results for each recession segment, a mathematical expression of the storage-delay factor as a function of the log of streamflow is determined by linear least-squares regression. The master recession curve, which is a second-order polynomial expression for time as a function of log of streamflow, is then derived using the coefficients of this function.

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

Optimal apodization design for medical ultrasound using constrained least squares part I: theory.

PubMed

Guenther, Drake A; Walker, William F

2007-02-01

Aperture weighting functions are critical design parameters in the development of ultrasound systems because beam characteristics affect the contrast and point resolution of the final output image. In previous work by our group, we developed a metric that quantifies a broadband imaging system's contrast resolution performance. We now use this metric to formulate a novel general ultrasound beamformer design method. In our algorithm, we use constrained least squares (CLS) techniques and a linear algebra formulation to describe the system point spread function (PSF) as a function of the aperture weightings. In one approach, we minimize the energy of the PSF outside a certain boundary and impose a linear constraint on the aperture weights. In a second approach, we minimize the energy of the PSF outside a certain boundary while imposing a quadratic constraint on the energy of the PSF inside the boundary. We present detailed analysis for an arbitrary ultrasound imaging system and discuss several possible applications of the CLS techniques, such as designing aperture weightings to maximize contrast resolution and improve the system depth of field.

Matched Field Processing Based on Least Squares with a Small Aperture Hydrophone Array.

PubMed

Wang, Qi; Wang, Yingmin; Zhu, Guolei

2016-12-30

The receiver hydrophone array is the signal front-end and plays an important role in matched field processing, which usually covers the whole water column from the sea surface to the bottom. Such a large aperture array is very difficult to realize. To solve this problem, an approach called matched field processing based on least squares with a small aperture hydrophone array is proposed, which decomposes the received acoustic fields into depth function matrix and amplitudes of the normal modes at the beginning. Then all the mode amplitudes are estimated using the least squares in the sense of minimum norm, and the amplitudes estimated are used to recalculate the received acoustic fields of the small aperture array, which means the recalculated ones contain more environmental information. In the end, lots of numerical experiments with three small aperture arrays are processed in the classical shallow water, and the performance of matched field passive localization is evaluated. The results show that the proposed method can make the recalculated fields contain more acoustic information of the source, and the performance of matched field passive localization with small aperture array is improved, so the proposed algorithm is proved to be effective.

Matched Field Processing Based on Least Squares with a Small Aperture Hydrophone Array

PubMed Central

Wang, Qi; Wang, Yingmin; Zhu, Guolei

2016-01-01

The receiver hydrophone array is the signal front-end and plays an important role in matched field processing, which usually covers the whole water column from the sea surface to the bottom. Such a large aperture array is very difficult to realize. To solve this problem, an approach called matched field processing based on least squares with a small aperture hydrophone array is proposed, which decomposes the received acoustic fields into depth function matrix and amplitudes of the normal modes at the beginning. Then all the mode amplitudes are estimated using the least squares in the sense of minimum norm, and the amplitudes estimated are used to recalculate the received acoustic fields of the small aperture array, which means the recalculated ones contain more environmental information. In the end, lots of numerical experiments with three small aperture arrays are processed in the classical shallow water, and the performance of matched field passive localization is evaluated. The results show that the proposed method can make the recalculated fields contain more acoustic information of the source, and the performance of matched field passive localization with small aperture array is improved, so the proposed algorithm is proved to be effective. PMID:28042828

Applying ISO 11929:2010 Standard to detection limit calculation in least-squares based multi-nuclide gamma-ray spectrum evaluation

NASA Astrophysics Data System (ADS)

Kanisch, G.

2017-05-01

The concepts of ISO 11929 (2010) are applied to evaluation of radionuclide activities from more complex multi-nuclide gamma-ray spectra. From net peak areas estimated by peak fitting, activities and their standard uncertainties are calculated by weighted linear least-squares method with an additional step, where uncertainties of the design matrix elements are taken into account. A numerical treatment of the standard's uncertainty function, based on ISO 11929 Annex C.5, leads to a procedure for deriving decision threshold and detection limit values. The methods shown allow resolving interferences between radionuclide activities also in case of calculating detection limits where they can improve the latter by including more than one gamma line per radionuclide. The co"mmon single nuclide weighted mean is extended to an interference-corrected (generalized) weighted mean, which, combined with the least-squares method, allows faster detection limit calculations. In addition, a new grouped uncertainty budget was inferred, which for each radionuclide gives uncertainty budgets from seven main variables, such as net count rates, peak efficiencies, gamma emission intensities and others; grouping refers to summation over lists of peaks per radionuclide.

Experiments of multichannel least-square methods for sound field reproduction inside aircraft mock-up: Objective evaluations

NASA Astrophysics Data System (ADS)

Gauthier, P.-A.; Camier, C.; Lebel, F.-A.; Pasco, Y.; Berry, A.; Langlois, J.; Verron, C.; Guastavino, C.

2016-08-01

Sound environment reproduction of various flight conditions in aircraft mock-ups is a valuable tool for the study, prediction, demonstration and jury testing of interior aircraft sound quality and annoyance. To provide a faithful reproduced sound environment, time, frequency and spatial characteristics should be preserved. Physical sound field reproduction methods for spatial sound reproduction are mandatory to immerse the listener's body in the proper sound fields so that localization cues are recreated at the listener's ears. Vehicle mock-ups pose specific problems for sound field reproduction. Confined spaces, needs for invisible sound sources and very specific acoustical environment make the use of open-loop sound field reproduction technologies such as wave field synthesis (based on free-field models of monopole sources) not ideal. In this paper, experiments in an aircraft mock-up with multichannel least-square methods and equalization are reported. The novelty is the actual implementation of sound field reproduction with 3180 transfer paths and trim panel reproduction sources in laboratory conditions with a synthetic target sound field. The paper presents objective evaluations of reproduced sound fields using various metrics as well as sound field extrapolation and sound field characterization.

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Optimisation of chromatographic resolution using objective functions including both time and spectral information.

PubMed

Torres-Lapasió, J R; Pous-Torres, S; Ortiz-Bolsico, C; García-Alvarez-Coque, M C

2015-01-16

The optimisation of the resolution in high-performance liquid chromatography is traditionally performed attending only to the time information. However, even in the optimal conditions, some peak pairs may remain unresolved. Such incomplete resolution can be still accomplished by deconvolution, which can be carried out with more guarantees of success by including spectral information. In this work, two-way chromatographic objective functions (COFs) that incorporate both time and spectral information were tested, based on the peak purity (analyte peak fraction free of overlapping) and the multivariate selectivity (figure of merit derived from the net analyte signal) concepts. These COFs are sensitive to situations where the components that coelute in a mixture show some spectral differences. Therefore, they are useful to find out experimental conditions where the spectrochromatograms can be recovered by deconvolution. Two-way multivariate selectivity yielded the best performance and was applied to the separation using diode-array detection of a mixture of 25 phenolic compounds, which remained unresolved in the chromatographic order using linear and multi-linear gradients of acetonitrile-water. Peak deconvolution was carried out using the combination of orthogonal projection approach and alternating least squares. Copyright © 2014 Elsevier B.V. All rights reserved.

Low-dose dynamic myocardial perfusion CT image reconstruction using pre-contrast normal-dose CT scan induced structure tensor total variation regularization

NASA Astrophysics Data System (ADS)

Gong, Changfei; Han, Ce; Gan, Guanghui; Deng, Zhenxiang; Zhou, Yongqiang; Yi, Jinling; Zheng, Xiaomin; Xie, Congying; Jin, Xiance

2017-04-01

Dynamic myocardial perfusion CT (DMP-CT) imaging provides quantitative functional information for diagnosis and risk stratification of coronary artery disease by calculating myocardial perfusion hemodynamic parameter (MPHP) maps. However, the level of radiation delivered by dynamic sequential scan protocol can be potentially high. The purpose of this work is to develop a pre-contrast normal-dose scan induced structure tensor total variation regularization based on the penalized weighted least-squares (PWLS) criteria to improve the image quality of DMP-CT with a low-mAs CT acquisition. For simplicity, the present approach was termed as ‘PWLS-ndiSTV’. Specifically, the ndiSTV regularization takes into account the spatial-temporal structure information of DMP-CT data and further exploits the higher order derivatives of the objective images to enhance denoising performance. Subsequently, an effective optimization algorithm based on the split-Bregman approach was adopted to minimize the associative objective function. Evaluations with modified dynamic XCAT phantom and preclinical porcine datasets have demonstrated that the proposed PWLS-ndiSTV approach can achieve promising gains over other existing approaches in terms of noise-induced artifacts mitigation, edge details preservation, and accurate MPHP maps calculation.

Fruit fly optimization based least square support vector regression for blind image restoration

NASA Astrophysics Data System (ADS)

Zhang, Jiao; Wang, Rui; Li, Junshan; Yang, Yawei

2014-11-01

The goal of image restoration is to reconstruct the original scene from a degraded observation. It is a critical and challenging task in image processing. Classical restorations require explicit knowledge of the point spread function and a description of the noise as priors. However, it is not practical for many real image processing. The recovery processing needs to be a blind image restoration scenario. Since blind deconvolution is an ill-posed problem, many blind restoration methods need to make additional assumptions to construct restrictions. Due to the differences of PSF and noise energy, blurring images can be quite different. It is difficult to achieve a good balance between proper assumption and high restoration quality in blind deconvolution. Recently, machine learning techniques have been applied to blind image restoration. The least square support vector regression (LSSVR) has been proven to offer strong potential in estimating and forecasting issues. Therefore, this paper proposes a LSSVR-based image restoration method. However, selecting the optimal parameters for support vector machine is essential to the training result. As a novel meta-heuristic algorithm, the fruit fly optimization algorithm (FOA) can be used to handle optimization problems, and has the advantages of fast convergence to the global optimal solution. In the proposed method, the training samples are created from a neighborhood in the degraded image to the central pixel in the original image. The mapping between the degraded image and the original image is learned by training LSSVR. The two parameters of LSSVR are optimized though FOA. The fitness function of FOA is calculated by the restoration error function. With the acquired mapping, the degraded image can be recovered. Experimental results show the proposed method can obtain satisfactory restoration effect. Compared with BP neural network regression, SVR method and Lucy-Richardson algorithm, it speeds up the restoration rate and performs better. Both objective and subjective restoration performances are studied in the comparison experiments.

LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

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

Kirchhoff, William H.

2012-09-15

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton-Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals frommore » the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, 'Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,' and may also prove useful in applying ISO 18516: 2006, 'Surface chemical analysis-Auger electron spectroscopy and x-ray photoelectron spectroscopy-determination of lateral resolution.' Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.« less

Inference of reactive transport model parameters using a Bayesian multivariate approach

NASA Astrophysics Data System (ADS)

Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick

2014-08-01

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.

Full waveform inversion using envelope-based global correlation norm

NASA Astrophysics Data System (ADS)

Oh, Ju-Won; Alkhalifah, Tariq

2018-05-01

To increase the feasibility of full waveform inversion on real data, we suggest a new objective function, which is defined as the global correlation of the envelopes of modelled and observed data. The envelope-based global correlation norm has the advantage of the envelope inversion that generates artificial low-frequency information, which provides the possibility to recover long-wavelength structure in an early stage. In addition, the envelope-based global correlation norm maintains the advantage of the global correlation norm, which reduces the sensitivity of the misfit to amplitude errors so that the performance of inversion on real data can be enhanced when the exact source wavelet is not available and more complex physics are ignored. Through the synthetic example for 2-D SEG/EAGE overthrust model with inaccurate source wavelet, we compare the performance of four different approaches, which are the least-squares waveform inversion, least-squares envelope inversion, global correlation norm and envelope-based global correlation norm. Finally, we apply the envelope-based global correlation norm on the 3-D Ocean Bottom Cable (OBC) data from the North Sea. The envelope-based global correlation norm captures the strong reflections from the high-velocity caprock and generates artificial low-frequency reflection energy that helps us recover long-wavelength structure of the model domain in the early stages. From this long-wavelength model, the conventional global correlation norm is sequentially applied to invert for higher-resolution features of the model.

A Weighted Least Squares Approach To Robustify Least Squares Estimates.

ERIC Educational Resources Information Center

Lin, Chowhong; Davenport, Ernest C., Jr.

This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…

Domain Decomposition Algorithms for First-Order System Least Squares Methods

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Spacecraft inertia estimation via constrained least squares

NASA Technical Reports Server (NTRS)

Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.

2006-01-01

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

The dynamic relationships between economic status and health measures among working-age adults in the United States.

PubMed

Meraya, Abdulkarim M; Dwibedi, Nilanjana; Tan, Xi; Innes, Kim; Mitra, Sophie; Sambamoorthi, Usha

2018-04-18

We examine the dynamic relationships between economic status and health measures using data from 8 waves of the Panel Study of Income Dynamics from 1999 to 2013. Health measures are self-rated health (SRH) and functional limitations; economic status measures are labor income (earnings), family income, and net wealth. We use 3 different types of models: (a) ordinary least squares regression, (b) first-difference, and (c) system-generalized method of moment (GMM). Using ordinary least squares regression and first difference models, we find that higher levels of economic status are associated with better SRH and functional status among both men and women, although declines in income and wealth are associated with a decline in health for men only. Using system-GMM estimators, we find evidence of a causal link from labor income to SRH and functional status for both genders. Among men only, system-GMM results indicate that there is a causal link from net wealth to SRH and functional status. Results overall highlight the need for integrated economic and health policies, and for policies that mitigate the potential adverse health effects of short-term changes in economic status. Copyright © 2018 John Wiley & Sons, Ltd.

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 2. Numerical experiments

NASA Astrophysics Data System (ADS)

Akmaev, R. a.

1999-04-01

In Part 1 of this work ([Akmaev, 1999]), an overview of the theory of optimal interpolation (OI) ([Gandin, 1963]) and related techniques of data assimilation based on linear optimal estimation ([Liebelt, 1967]; [Catlin, 1989]; [Mendel, 1995]) is presented. The approach implies the use in data analysis of additional statistical information in the form of statistical moments, e.g., the mean and covariance (correlation). The a priori statistical characteristics, if available, make it possible to constrain expected errors and obtain optimal in some sense estimates of the true state from a set of observations in a given domain in space and/or time. The primary objective of OI is to provide estimates away from the observations, i.e., to fill in data voids in the domain under consideration. Additionally, OI performs smoothing suppressing the noise, i.e., the spectral components that are presumably not present in the true signal. Usually, the criterion of optimality is minimum variance of the expected errors and the whole approach may be considered constrained least squares or least squares with a priori information. Obviously, data assimilation techniques capable of incorporating any additional information are potentially superior to techniques that have no access to such information as, for example, the conventional least squares (e.g., [Liebelt, 1967]; [Weisberg, 1985]; [Press et al., 1992]; [Mendel, 1995]).

Nonlinear least-squares data fitting in Excel spreadsheets.

PubMed

Kemmer, Gerdi; Keller, Sandro

2010-02-01

We describe an intuitive and rapid procedure for analyzing experimental data by nonlinear least-squares fitting (NLSF) in the most widely used spreadsheet program. Experimental data in x/y form and data calculated from a regression equation are inputted and plotted in a Microsoft Excel worksheet, and the sum of squared residuals is computed and minimized using the Solver add-in to obtain the set of parameter values that best describes the experimental data. The confidence of best-fit values is then visualized and assessed in a generally applicable and easily comprehensible way. Every user familiar with the most basic functions of Excel will be able to implement this protocol, without previous experience in data fitting or programming and without additional costs for specialist software. The application of this tool is exemplified using the well-known Michaelis-Menten equation characterizing simple enzyme kinetics. Only slight modifications are required to adapt the protocol to virtually any other kind of dataset or regression equation. The entire protocol takes approximately 1 h.

Comparing implementations of penalized weighted least-squares sinogram restoration.

PubMed

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-11-01

A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors' previous penalized-likelihood implementation. Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes.

Space Object Maneuver Detection Algorithms Using TLE Data

NASA Astrophysics Data System (ADS)

Pittelkau, M.

2016-09-01

An important aspect of Space Situational Awareness (SSA) is detection of deliberate and accidental orbit changes of space objects. Although space surveillance systems detect orbit maneuvers within their tracking algorithms, maneuver data are not readily disseminated for general use. However, two-line element (TLE) data is available and can be used to detect maneuvers of space objects. This work is an attempt to improve upon existing TLE-based maneuver detection algorithms. Three adaptive maneuver detection algorithms are developed and evaluated: The first is a fading-memory Kalman filter, which is equivalent to the sliding-window least-squares polynomial fit, but computationally more efficient and adaptive to the noise in the TLE data. The second algorithm is based on a sample cumulative distribution function (CDF) computed from a histogram of the magnitude-squared |V|2 of change-in-velocity vectors (V), which is computed from the TLE data. A maneuver detection threshold is computed from the median estimated from the CDF, or from the CDF and a specified probability of false alarm. The third algorithm is a median filter. The median filter is the simplest of a class of nonlinear filters called order statistics filters, which is within the theory of robust statistics. The output of the median filter is practically insensitive to outliers, or large maneuvers. The median of the |V|2 data is proportional to the variance of the V, so the variance is estimated from the output of the median filter. A maneuver is detected when the input data exceeds a constant times the estimated variance.

Adaptive object tracking via both positive and negative models matching

NASA Astrophysics Data System (ADS)

Li, Shaomei; Gao, Chao; Wang, Yawen

2015-03-01

To improve tracking drift which often occurs in adaptive tracking, an algorithm based on the fusion of tracking and detection is proposed in this paper. Firstly, object tracking is posed as abinary classification problem and is modeled by partial least squares (PLS) analysis. Secondly, tracking object frame by frame via particle filtering. Thirdly, validating the tracking reliability based on both positive and negative models matching. Finally, relocating the object based on SIFT features matching and voting when drift occurs. Object appearance model is updated at the same time. The algorithm can not only sense tracking drift but also relocate the object whenever needed. Experimental results demonstrate that this algorithm outperforms state-of-the-art algorithms on many challenging sequences.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Scintillation Control for Adaptive Optical Sensors

DTIC Science & Technology

1999-09-21

defining where one influence function goes to zero fall directly under the peaks of the adjoining influcence functions. These actuators were fit to ^>gp(i...not orthogonal the influence function interaction matrix R must be computed with elements given by [3] rH = J dxPW(xp)e/b(xp)e,(xp). (22) In our...control signals can be found from the wave front phase by the least squares phase reconstruction technique [3]. An influence function and the

Design of vibration isolation systems using multiobjective optimization techniques

NASA Technical Reports Server (NTRS)

Rao, S. S.

1984-01-01

The design of vibration isolation systems is considered using multicriteria optimization techniques. The integrated values of the square of the force transmitted to the main mass and the square of the relative displacement between the main mass and the base are taken as the performance indices. The design of a three degrees-of-freedom isolation system with an exponentially decaying type of base disturbance is considered for illustration. Numerical results are obtained using the global criterion, utility function, bounded objective, lexicographic, goal programming, goal attainment and game theory methods. It is found that the game theory approach is superior in finding a better optimum solution with proper balance of the various objective functions.

Polymer tensiometer with ceramic cones: a case study for a Brazilian soil.

NASA Astrophysics Data System (ADS)

Durigon, A.; de Jong van Lier, Q.; van der Ploeg, M. J.; Gooren, H. P. A.; Metselaar, K.; de Rooij, G. H.

2009-04-01

Laboratory outflow experiments, in combination with inverse modeling techniques, allow to simultaneously determine retention and hydraulic conductivity functions. A numerical model solves the pressure-head-based form of the Richards' equation for unsaturated flow in a rigid porous medium. Applying adequate boundary conditions, the cumulative outflow is calculated at prescribed times, and as a function of the set of optimized parameters. These parameters are evaluated by nonlinear least-squares fitting of predicted to observed cumulative outflow with time. An objective function quantifies this difference between calculated and observed cumulative outflow and between predicted and measured soil water retention data. Using outflow data only in the objective function, the multistep outflow method results in unique estimates of the retention and hydraulic conductivity functions. To obtain more reliable estimates of the hydraulic conductivity as a function of the water content using the inverse method, the outflow data must be supplemented with soil retention data. To do so tensiometers filled with a polymer solution instead of water were used. The measurement range of these tensiometers is larger than that of the conventional tensiometers, being able to measure the entire pressure head range over which crops take up water, down to values in the order of -1.6 MPa. The objective of this study was to physically characterize a Brazilian red-yellow oxisol using measurements in outflow experiments by polymer tensiometers and processing these data with the inverse modeling technique for use in the analysis of a field experiment and in modeling. The soil was collected at an experimental site located in Piracicaba, Brazil, 22° 42 S, 47° 38 W, 550 m above sea level.

Concerning an application of the method of least squares with a variable weight matrix

NASA Technical Reports Server (NTRS)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

1976-01-01

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi

2018-01-01

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least-squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on an in-house object-oriented optimization tool. During the numerical optimization procedure, a design jig-shape is determined by the baseline jig-shape and basis functions. A total of 12 symmetric mode shapes of the cruise-weight configuration, rigid pitch shape, rigid left and right stabilator rotation shapes, and a residual shape are selected as sixteen basis functions. After three optimization runs, the trim shape error distribution is improved, and the maximum trim shape error of 0.9844 inches of the starting configuration becomes 0.00367 inch by the end of the third optimization run.

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

Neither fixed nor random: weighted least squares meta-analysis.

PubMed

Stanley, T D; Doucouliagos, Hristos

2015-06-15

This study challenges two core conventional meta-analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random-effects meta-analysis when there is publication (or small-sample) bias and better than a fixed-effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small-sample) bias and identical to fixed-effect meta-analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed-effect meta-analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects. Copyright © 2015 John Wiley & Sons, Ltd.

Combinatorics of least-squares trees.

PubMed

Mihaescu, Radu; Pachter, Lior

2008-09-09

A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least-squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four-point condition that the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss-Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution, and the taxon-weighted variance model. They also provide a time-optimal algorithm for computation.

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)

2003-01-01

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

Hessian-based norm regularization for image restoration with biomedical applications.

PubMed

Lefkimmiatis, Stamatios; Bourquard, Aurélien; Unser, Michael

2012-03-01

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.

Growth curves for ostriches (Struthio camelus) in a Brazilian population.

PubMed

Ramos, S B; Caetano, S L; Savegnago, R P; Nunes, B N; Ramos, A A; Munari, D P

2013-01-01

The objective of this study was to fit growth curves using nonlinear and linear functions to describe the growth of ostriches in a Brazilian population. The data set consisted of 112 animals with BW measurements from hatching to 383 d of age. Two nonlinear growth functions (Gompertz and logistic) and a third-order polynomial function were applied. The parameters for the models were estimated using the least-squares method and Gauss-Newton algorithm. The goodness-of-fit of the models was assessed using R(2) and the Akaike information criterion. The R(2) calculated for the logistic growth model was 0.945 for hens and 0.928 for cockerels and for the Gompertz growth model, 0.938 for hens and 0.924 for cockerels. The third-order polynomial fit gave R(2) of 0.938 for hens and 0.924 for cockerels. Among the Akaike information criterion calculations, the logistic growth model presented the lowest values in this study, both for hens and for cockerels. Nonlinear models are more appropriate for describing the sigmoid nature of ostrich growth.

Correlated Noise: How it Breaks NMF, and What to Do About It.

PubMed

Plis, Sergey M; Potluru, Vamsi K; Lane, Terran; Calhoun, Vince D

2011-01-12

Non-negative matrix factorization (NMF) is a problem of decomposing multivariate data into a set of features and their corresponding activations. When applied to experimental data, NMF has to cope with noise, which is often highly correlated. We show that correlated noise can break the Donoho and Stodden separability conditions of a dataset and a regular NMF algorithm will fail to decompose it, even when given freedom to be able to represent the noise as a separate feature. To cope with this issue, we present an algorithm for NMF with a generalized least squares objective function (glsNMF) and derive multiplicative updates for the method together with proving their convergence. The new algorithm successfully recovers the true representation from the noisy data. Robust performance can make glsNMF a valuable tool for analyzing empirical data.

Correlated Noise: How it Breaks NMF, and What to Do About It

PubMed Central

Plis, Sergey M.; Potluru, Vamsi K.; Lane, Terran; Calhoun, Vince D.

2010-01-01

Non-negative matrix factorization (NMF) is a problem of decomposing multivariate data into a set of features and their corresponding activations. When applied to experimental data, NMF has to cope with noise, which is often highly correlated. We show that correlated noise can break the Donoho and Stodden separability conditions of a dataset and a regular NMF algorithm will fail to decompose it, even when given freedom to be able to represent the noise as a separate feature. To cope with this issue, we present an algorithm for NMF with a generalized least squares objective function (glsNMF) and derive multiplicative updates for the method together with proving their convergence. The new algorithm successfully recovers the true representation from the noisy data. Robust performance can make glsNMF a valuable tool for analyzing empirical data. PMID:23750288

Sparse and stable Markowitz portfolios

PubMed Central

Brodie, Joshua; Daubechies, Ingrid; De Mol, Christine; Giannone, Domenico; Loris, Ignace

2009-01-01

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e., portfolios with only few active positions), and allows accounting for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naïve evenly weighted portfolio. PMID:19617537

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Application of recursive approaches to differential orbit correction of near Earth asteroids

NASA Astrophysics Data System (ADS)

Dmitriev, Vasily; Lupovka, Valery; Gritsevich, Maria

2016-10-01

Comparison of three approaches to the differential orbit correction of celestial bodies was performed: batch least squares fitting, Kalman filter, and recursive least squares filter. The first two techniques are well known and widely used (Montenbruck, O. & Gill, E., 2000). The most attention is paid to the algorithm and details of program realization of recursive least squares filter. The filter's algorithm was derived based on recursive least squares technique that are widely used in data processing applications (Simon, D, 2006). Usage recursive least squares filter, makes possible to process a new set of observational data, without reprocessing data, which has been processed before. Specific feature of such approach is that number of observation in data set may be variable. This feature makes recursive least squares filter more flexible approach compare to batch least squares (process complete set of observations in each iteration) and Kalman filtering (suppose updating state vector on each epoch with measurements).Advantages of proposed approach are demonstrated by processing of real astrometric observations of near Earth asteroids. The case of 2008 TC3 was studied. 2008 TC3 was discovered just before its impact with Earth. There are a many closely spaced observations of 2008 TC3 on the interval between discovering and impact, which creates favorable conditions for usage of recursive approaches. Each of approaches has very similar precision in case of 2008 TC3. At the same time, recursive least squares approaches have much higher performance. Thus, this approach more favorable for orbit fitting of a celestial body, which was detected shortly before the collision or close approach to the Earth.This work was carried out at MIIGAiK and supported by the Russian Science Foundation, Project no. 14-22-00197.References:O. Montenbruck and E. Gill, "Satellite Orbits, Models, Methods and Applications," Springer-Verlag, 2000, pp. 1-369.D. Simon, "Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches",1 edition. Hoboken, N.J.: Wiley-Interscience, 2006.

Comparisons of a Constrained Least Squares Model versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

NASA Technical Reports Server (NTRS)

Abercromby, Kira J.; Rapp, Jason; Bedard, Donald; Seitzer, Patrick; Cardona, Tommaso; Cowardin, Heather; Barker, Ed; Lederer, Susan

2013-01-01

Spectral reflectance data through the visible regime was collected at Las Campanas Observatory in Chile using an imaging spectrograph on one of the twin 6.5-m Magellan telescopes. The data were obtained on 1-2 May 2012 on the 'Landon Clay' telescope with the LDSS3 (Low Dispersion Survey Spectrograph 3). Five pieces of Geosynchronous Orbit (GEO) or near-GEO debris were identified and observed with an exposure time of 30 seconds on average. In addition, laboratory spectral reflectance data was collected using an Analytical Spectral Device (ASD) field spectrometer at California Polytechnic State University (Cal Poly) in San Luis Obispo on several typical common spacecraft materials including solar cells, circuit boards, various Kapton materials used for multi-layer insulation, and various paints. The remotely collected data and the laboratory-acquired data were then incorporated in a newly developed model that uses a constrained least squares method to unmix the spectrum in specific material components. The results of this model are compared to the previous method of a human-in-the-loop (considered here the traditional method) that identifies possible material components by varying the materials and percentages until a spectral match is obtained. The traditional model was found to match the remotely collected spectral data after it had been divided by the continuum to remove the space weathering effects, or a reddening of the materials. The constrained least-squares model also used the de-reddened spectra as inputs and the results were consistent with those obtained through the traditional method. For comparison, a first-order examination of including reddening effects into the constrained least-squares model will be explored and comparisons to the remotely collected data will be examined. The identification of each object s suspected material component will be discussed herein.

Comparisons of a Constrained Least Squares Model Versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

NASA Technical Reports Server (NTRS)

Rapp, Jason; Abercromby, Kira J.; Bedard, Donald; Seitzer, Patrick; Cardona, Tommaso; Cowardin, Heather; Barker, Ed; Lederer, Susan

2012-01-01

Spectral reflectance data through the visible regime was collected at Las Campanas Observatory in Chile using an imaging spectrograph on one of the twin 6.5-m Magellan telescopes. The data were obtained on 1-2 May 2012 on the 'Landon Clay' telescope with the LDSS3 (Low Dispersion Survey Spectrograph 3). Five pieces of Geosynchronous Orbit (GEO) or near-GEO debris were identified and observed with an exposure time of 30 seconds on average. In addition, laboratory spectral reflectance data was collected using an Analytical Spectral Device (ASD) field spectrometer at California Polytechnic State University in San Luis Obispo on several typical common spacecraft materials including solar cells, circuit boards, various Kapton materials used for multi-layer insulation, and various paints. The remotely collected data and the laboratory-acquired data were then incorporated in a newly developed model that uses a constrained least squares method to unmix the spectrum in specific material components. The results of this model are compared to the previous method of a human-in-the-loop (considered here the traditional method) that identifies possible material components by varying the materials and percentages until a spectral match is obtained. The traditional model was found to match the remotely collected spectral data after it had been divided by the continuum to remove the space weathering effects, or a "reddening" of the materials. The constrained least-squares model also used the de-reddened spectra as inputs and the results were consistent with those obtained through the traditional method. For comparison, a first-order examination of including reddening effects into the constrained least-squares model will be explored and comparisons to the remotely collected data will be examined. The identification of each object's suspected material component will be discussed herein.

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Experimental Determination of the 1 Sigma(+) State Electric-Dipole-Moment Function of Carbon Monoxide up to a Large Internuclear Separation

NASA Technical Reports Server (NTRS)

Chackerian, C., Jr.; Farreng, R.; Guelachvili, G.; Rossetti, C.; Urban, W.

1984-01-01

Experimental intensity information is combined with numerically obtained vibrational wave functions in a nonlinear least squares fitting procedure to obtain the ground electronic state electric-dipole-moment function of carbon monoxide valid in the range of nuclear oscillation (0.87 to 1.01 A) of about the V = 38th vibrational level. Mechanical anharmonicity intensity factors, H, are computed from this function for delta V + = 1, 2, 3, with or = to 38.

Experimental determination of the 1 Sigma(+) state electric dipole moment function of carbon monoxide up to a large internuclear separation

NASA Technical Reports Server (NTRS)

Chackerian, C., Jr.; Farrenq, R.; Guelachvili, G.; Rossetti, C.; Urban, W.

1984-01-01

Experimental intensity information is combined with numerically obtained vibrational wave functions in a nonlinear least-squares fitting procedure to obtain the ground electronic state electric dipole moment function of carbon monoxide valid in the range of nuclear oscillation (0.87-1.91 A) of about the V = 38th vibrational level. Vibrational transition matrix elements are computed from this function for Delta V = 1, 2, 3 with V not more than 38.

Comparison of beam position calculation methods for application in digital acquisition systems

NASA Astrophysics Data System (ADS)

Reiter, A.; Singh, R.

2018-05-01

Different approaches to the data analysis of beam position monitors in hadron accelerators are compared adopting the perspective of an analog-to-digital converter in a sampling acquisition system. Special emphasis is given to position uncertainty and robustness against bias and interference that may be encountered in an accelerator environment. In a time-domain analysis of data in the presence of statistical noise, the position calculation based on the difference-over-sum method with algorithms like signal integral or power can be interpreted as a least-squares analysis of a corresponding fit function. This link to the least-squares method is exploited in the evaluation of analysis properties and in the calculation of position uncertainty. In an analytical model and experimental evaluations the positions derived from a straight line fit or equivalently the standard deviation are found to be the most robust and to offer the least variance. The measured position uncertainty is consistent with the model prediction in our experiment, and the results of tune measurements improve significantly.

M-estimation for robust sparse unmixing of hyperspectral images

NASA Astrophysics Data System (ADS)

Toomik, Maria; Lu, Shijian; Nelson, James D. B.

2016-10-01

Hyperspectral unmixing methods often use a conventional least squares based lasso which assumes that the data follows the Gaussian distribution. The normality assumption is an approximation which is generally invalid for real imagery data. We consider a robust (non-Gaussian) approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers and relaxes the linearity assumption. The method consists of several appropriate penalties. We propose to use an lp norm with 0 < p < 1 in the sparse regression problem, which induces more sparsity in the results, but makes the problem non-convex. On the other hand, the problem, though non-convex, can be solved quite straightforwardly with an extensible algorithm based on iteratively reweighted least squares. To deal with the huge size of modern spectral libraries we introduce a library reduction step, similar to the multiple signal classification (MUSIC) array processing algorithm, which not only speeds up unmixing but also yields superior results. In the hyperspectral setting we extend the traditional least squares method to the robust heavy-tailed case and propose a generalised M-lasso solution. M-estimation replaces the Gaussian likelihood with a fixed function ρ(e) that restrains outliers. The M-estimate function reduces the effect of errors with large amplitudes or even assigns the outliers zero weights. Our experimental results on real hyperspectral data show that noise with large amplitudes (outliers) often exists in the data. This ability to mitigate the influence of such outliers can therefore offer greater robustness. Qualitative hyperspectral unmixing results on real hyperspectral image data corroborate the efficacy of the proposed method.

Speckle noise removal applied to ultrasound image of carotid artery based on total least squares model.

PubMed

Yang, Lei; Lu, Jun; Dai, Ming; Ren, Li-Jie; Liu, Wei-Zong; Li, Zhen-Zhou; Gong, Xue-Hao

2016-10-06

An ultrasonic image speckle noise removal method by using total least squares model is proposed and applied onto images of cardiovascular structures such as the carotid artery. On the basis of the least squares principle, the related principle of minimum square method is applied to cardiac ultrasound image speckle noise removal process to establish the model of total least squares, orthogonal projection transformation processing is utilized for the output of the model, and the denoising processing for the cardiac ultrasound image speckle noise is realized. Experimental results show that the improved algorithm can greatly improve the resolution of the image, and meet the needs of clinical medical diagnosis and treatment of the cardiovascular system for the head and neck. Furthermore, the success in imaging of carotid arteries has strong implications in neurological complications such as stroke.

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

NASA Technical Reports Server (NTRS)

Brozenec, Thomas F.; Bender, Douglas J.

1994-01-01

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

On the accuracy of least squares methods in the presence of corner singularities

NASA Technical Reports Server (NTRS)

Cox, C. L.; Fix, G. J.

1985-01-01

Elliptic problems with corner singularities are discussed. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. It is shown that if the least squares formulation is done in appropriately weighted space, then optimal convergence results in unweighted spaces like L(2).

Avoiding Communication in the Lanczos Bidiagonalization Routine and Associated Least Squares QR Solver

DTIC Science & Technology

2015-04-12

Avoiding communication in the Lanczos bidiagonalization routine and associated Least Squares QR solver Erin Carson Electrical Engineering and...Bidiagonalization Routine and Associated Least Squares QR Solver 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...throughout scienti c codes , are often the bottlenecks in application perfor- mance due to a low computation/communication ratio. In this paper we develop

Speckle evolution with multiple steps of least-squares phase removal

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

Chen Mingzhou; Dainty, Chris; Roux, Filippus S.

2011-08-15

We study numerically the evolution of speckle fields due to the annihilation of optical vortices after the least-squares phase has been removed. A process with multiple steps of least-squares phase removal is carried out to minimize both vortex density and scintillation index. Statistical results show that almost all the optical vortices can be removed from a speckle field, which finally decays into a quasiplane wave after such an iterative process.

Use of inequality constrained least squares estimation in small area estimation

NASA Astrophysics Data System (ADS)

Abeygunawardana, R. A. B.; Wickremasinghe, W. N.

2017-05-01

Traditional surveys provide estimates that are based only on the sample observations collected for the population characteristic of interest. However, these estimates may have unacceptably large variance for certain domains. Small Area Estimation (SAE) deals with determining precise and accurate estimates for population characteristics of interest for such domains. SAE usually uses least squares or maximum likelihood procedures incorporating prior information and current survey data. Many available methods in SAE use constraints in equality form. However there are practical situations where certain inequality restrictions on model parameters are more realistic. It will lead to Inequality Constrained Least Squares (ICLS) estimates if the method used is least squares. In this study ICLS estimation procedure is applied to many proposed small area estimates.

On the nullspace of TLS multi-station adjustment

NASA Astrophysics Data System (ADS)

Sterle, Oskar; Kogoj, Dušan; Stopar, Bojan; Kregar, Klemen

2018-07-01

In the article we present an analytic aspect of TLS multi-station least-squares adjustment with the main focus on the datum problem. The datum problem is, compared to previously published researches, theoretically analyzed and solved, where the solution is based on nullspace derivation of the mathematical model. The importance of datum problem solution is seen in a complete description of TLS multi-station adjustment solutions from a set of all minimally constrained least-squares solutions. On a basis of known nullspace, estimable parameters are described and the geometric interpretation of all minimally constrained least squares solutions is presented. At the end a simulated example is used to analyze the results of TLS multi-station minimally constrained and inner constrained least-squares adjustment solutions.

A note on implementation of decaying product correlation structures for quasi-least squares.

PubMed

Shults, Justine; Guerra, Matthew W

2014-08-30

This note implements an unstructured decaying product matrix via the quasi-least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations. The structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix. It is straightforward to show that the quasi-least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure. Furthermore, subject to conditions that are easily checked, the quasi-least squares estimators are valid for longitudinal Bernoulli data. We demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable. Copyright © 2014 John Wiley & Sons, Ltd.

Partial Least Squares for Discrimination in fMRI Data

PubMed Central

Andersen, Anders H.; Rayens, William S.; Liu, Yushu; Smith, Charles D.

2011-01-01

Multivariate methods for discrimination were used in the comparison of brain activation patterns between groups of cognitively normal women who are at either high or low Alzheimer's disease risk based on family history and apolipoprotein-E4 status. Linear discriminant analysis (LDA) was preceded by dimension reduction using either principal component analysis (PCA), partial least squares (PLS), or a new oriented partial least squares (OrPLS) method. The aim was to identify a spatial pattern of functionally connected brain regions that was differentially expressed by the risk groups and yielded optimal classification accuracy. Multivariate dimension reduction is required prior to LDA when the data contains more feature variables than there are observations on individual subjects. Whereas PCA has been commonly used to identify covariance patterns in neuroimaging data, this approach only identifies gross variability and is not capable of distinguishing among-groups from within-groups variability. PLS and OrPLS provide a more focused dimension reduction by incorporating information on class structure and therefore lead to more parsimonious models for discrimination. Performance was evaluated in terms of the cross-validated misclassification rates. The results support the potential of using fMRI as an imaging biomarker or diagnostic tool to discriminate individuals with disease or high risk. PMID:22227352

Using Quantile and Asymmetric Least Squares Regression for Optimal Risk Adjustment.

PubMed

Lorenz, Normann

2017-06-01

In this paper, we analyze optimal risk adjustment for direct risk selection (DRS). Integrating insurers' activities for risk selection into a discrete choice model of individuals' health insurance choice shows that DRS has the structure of a contest. For the contest success function (csf) used in most of the contest literature (the Tullock-csf), optimal transfers for a risk adjustment scheme have to be determined by means of a restricted quantile regression, irrespective of whether insurers are primarily engaged in positive DRS (attracting low risks) or negative DRS (repelling high risks). This is at odds with the common practice of determining transfers by means of a least squares regression. However, this common practice can be rationalized for a new csf, but only if positive and negative DRSs are equally important; if they are not, optimal transfers have to be calculated by means of a restricted asymmetric least squares regression. Using data from German and Swiss health insurers, we find considerable differences between the three types of regressions. Optimal transfers therefore critically depend on which csf represents insurers' incentives for DRS and, if it is not the Tullock-csf, whether insurers are primarily engaged in positive or negative DRS. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Identification of Reliable Components in Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS): a Data-Driven Approach across Metabolic Processes.

PubMed

Motegi, Hiromi; Tsuboi, Yuuri; Saga, Ayako; Kagami, Tomoko; Inoue, Maki; Toki, Hideaki; Minowa, Osamu; Noda, Tetsuo; Kikuchi, Jun

2015-11-04

There is an increasing need to use multivariate statistical methods for understanding biological functions, identifying the mechanisms of diseases, and exploring biomarkers. In addition to classical analyses such as hierarchical cluster analysis, principal component analysis, and partial least squares discriminant analysis, various multivariate strategies, including independent component analysis, non-negative matrix factorization, and multivariate curve resolution, have recently been proposed. However, determining the number of components is problematic. Despite the proposal of several different methods, no satisfactory approach has yet been reported. To resolve this problem, we implemented a new idea: classifying a component as "reliable" or "unreliable" based on the reproducibility of its appearance, regardless of the number of components in the calculation. Using the clustering method for classification, we applied this idea to multivariate curve resolution-alternating least squares (MCR-ALS). Comparisons between conventional and modified methods applied to proton nuclear magnetic resonance ((1)H-NMR) spectral datasets derived from known standard mixtures and biological mixtures (urine and feces of mice) revealed that more plausible results are obtained by the modified method. In particular, clusters containing little information were detected with reliability. This strategy, named "cluster-aided MCR-ALS," will facilitate the attainment of more reliable results in the metabolomics datasets.

[The research on separating and extracting overlapping spectral feature lines in LIBS using damped least squares method].

PubMed

Wang, Yin; Zhao, Nan-jing; Liu, Wen-qing; Yu, Yang; Fang, Li; Meng, De-shuo; Hu, Li; Zhang, Da-hai; Ma, Min-jun; Xiao, Xue; Wang, Yu; Liu, Jian-guo

2015-02-01

In recent years, the technology of laser induced breakdown spectroscopy has been developed rapidly. As one kind of new material composition detection technology, laser induced breakdown spectroscopy can simultaneously detect multi elements fast and simply without any complex sample preparation and realize field, in-situ material composition detection of the sample to be tested. This kind of technology is very promising in many fields. It is very important to separate, fit and extract spectral feature lines in laser induced breakdown spectroscopy, which is the cornerstone of spectral feature recognition and subsequent elements concentrations inversion research. In order to realize effective separation, fitting and extraction of spectral feature lines in laser induced breakdown spectroscopy, the original parameters for spectral lines fitting before iteration were analyzed and determined. The spectral feature line of' chromium (Cr I : 427.480 nm) in fly ash gathered from a coal-fired power station, which was overlapped with another line(FeI: 427.176 nm), was separated from the other one and extracted by using damped least squares method. Based on Gauss-Newton iteration, damped least squares method adds damping factor to step and adjust step length dynamically according to the feedback information after each iteration, in order to prevent the iteration from diverging and make sure that the iteration could converge fast. Damped least squares method helps to obtain better results of separating, fitting and extracting spectral feature lines and give more accurate intensity values of these spectral feature lines: The spectral feature lines of chromium in samples which contain different concentrations of chromium were separated and extracted. And then, the intensity values of corresponding spectral lines were given by using damped least squares method and least squares method separately. The calibration curves were plotted, which showed the relationship between spectral line intensity values and chromium concentrations in different samples. And then their respective linear correlations were compared. The experimental results showed that the linear correlation of the intensity values of spectral feature lines and the concentrations of chromium in different samples, which was obtained by damped least squares method, was better than that one obtained by least squares method. And therefore, damped least squares method was stable, reliable and suitable for separating, fitting and extracting spectral feature lines in laser induced breakdown spectroscopy.

Numerical Technique for Analyzing Rotating Rake Mode Measurements in a Duct With Passive Treatment and Shear Flow

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Sutliff, Daniel L.

2007-01-01

A technique is presented for the analysis of measured data obtained from a rotating microphone rake system. The system is designed to measure the interaction modes of ducted fans. A Fourier analysis of the data from the rotating system results in a set of circumferential mode levels at each radial location of a microphone inside the duct. Radial basis functions are then least-squares fit to this data to obtain the radial mode amplitudes. For ducts with soft walls and mean flow, the radial basis functions must be numerically computed. The linear companion matrix method is used to obtain both the eigenvalues of interest, without an initial guess, and the radial basis functions. The governing equations allow for the mean flow to have a boundary layer at the wall. In addition, a nonlinear least-squares method is used to adjust the wall impedance to best fit the data in an attempt to use the rotating system as an in-duct wall impedance measurement tool. Simulated and measured data are used to show the effects of wall impedance and mean flow on the computed results.

Artificial neural network and classical least-squares methods for neurotransmitter mixture analysis.

PubMed

Schulze, H G; Greek, L S; Gorzalka, B B; Bree, A V; Blades, M W; Turner, R F

1995-02-01

Identification of individual components in biological mixtures can be a difficult problem regardless of the analytical method employed. In this work, Raman spectroscopy was chosen as a prototype analytical method due to its inherent versatility and applicability to aqueous media, making it useful for the study of biological samples. Artificial neural networks (ANNs) and the classical least-squares (CLS) method were used to identify and quantify the Raman spectra of the small-molecule neurotransmitters and mixtures of such molecules. The transfer functions used by a network, as well as the architecture of a network, played an important role in the ability of the network to identify the Raman spectra of individual neurotransmitters and the Raman spectra of neurotransmitter mixtures. Specifically, networks using sigmoid and hyperbolic tangent transfer functions generalized better from the mixtures in the training data set to those in the testing data sets than networks using sine functions. Networks with connections that permit the local processing of inputs generally performed better than other networks on all the testing data sets. and better than the CLS method of curve fitting, on novel spectra of some neurotransmitters. The CLS method was found to perform well on noisy, shifted, and difference spectra.

Quantitative hard x-ray phase contrast imaging of micropipes in SiC

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

Kohn, V. G.; Argunova, T. S.; Je, J. H., E-mail: jhje@postech.ac.kr

2013-12-15

Peculiarities of quantitative hard x-ray phase contrast imaging of micropipes in SiC are discussed. The micropipe is assumed as a hollow cylinder with an elliptical cross section. The major and minor diameters can be restored using the least square fitting procedure by comparing the experimental data, i.e. the profile across the micropipe axis, with those calculated based on phase contrast theory. It is shown that one projection image gives an information which does not allow a complete determination of the elliptical cross section, if an orientation of micropipe is not known. Another problem is a weak accuracy in estimating themore » diameters, partly because of using pink synchrotron radiation, which is necessary because a monochromatic beam intensity is not sufficient to reveal the weak contrast from a very small object. The general problems of accuracy in estimating the two diameters using the least square procedure are discussed. Two experimental examples are considered to demonstrate small as well as modest accuracies in estimating the diameters.« less

Development of predictive models for total phenolics and free p-coumaric acid contents in barley grain by near-infrared spectroscopy.

PubMed

Han, Zhigang; Cai, Shengguan; Zhang, Xuelei; Qian, Qiufeng; Huang, Yuqing; Dai, Fei; Zhang, Guoping

2017-07-15

Barley grains are rich in phenolic compounds, which are associated with reduced risk of chronic diseases. Development of barley cultivars with high phenolic acid content has become one of the main objectives in breeding programs. A rapid and accurate method for measuring phenolic compounds would be helpful for crop breeding. We developed predictive models for both total phenolics (TPC) and p-coumaric acid (PA), based on near-infrared spectroscopy (NIRS) analysis. Regressions of partial least squares (PLS) and least squares support vector machine (LS-SVM) were compared for improving the models, and Monte Carlo-Uninformative Variable Elimination (MC-UVE) was applied to select informative wavelengths. The optimal calibration models generated high coefficients of correlation (r pre ) and ratio performance deviation (RPD) for TPC and PA. These results indicated the models are suitable for rapid determination of phenolic compounds in barley grains. Copyright © 2017 Elsevier Ltd. All rights reserved.

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

NASA Technical Reports Server (NTRS)

Ulbrich, N.; Volden, T.

2017-01-01

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

The Use of Alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient

ERIC Educational Resources Information Center

Coskuntuncel, Orkun

2013-01-01

The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

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

Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.

Coupled Research in Ocean Acoustics and Signal Processing for the Next Generation of Underwater Acoustic Communication Systems

DTIC Science & Technology

2016-08-05

technique which used unobserved ”intermediate” variables to break a high-dimensional estimation problem such as least- squares (LS) optimization of a large...Least Squares (GEM-LS). The estimator is iterative and the work in this time period focused on characterizing the convergence properties of this...ap- proach by relaxing the statistical assumptions which is termed the Relaxed Approximate Graph-Structured Recursive Least Squares (RAGS-RLS). This

Intrinsic random functions for mitigation of atmospheric effects in terrestrial radar interferometry

NASA Astrophysics Data System (ADS)

Butt, Jemil; Wieser, Andreas; Conzett, Stefan

2017-06-01

The benefits of terrestrial radar interferometry (TRI) for deformation monitoring are restricted by the influence of changing meteorological conditions contaminating the potentially highly precise measurements with spurious deformations. This is especially the case when the measurement setup includes long distances between instrument and objects of interest and the topography affecting atmospheric refraction is complex. These situations are typically encountered with geo-monitoring in mountainous regions, e.g. with glaciers, landslides or volcanoes. We propose and explain an approach for the mitigation of atmospheric influences based on the theory of intrinsic random functions of order k (IRF-k) generalizing existing approaches based on ordinary least squares estimation of trend functions. This class of random functions retains convenient computational properties allowing for rigorous statistical inference while still permitting to model stochastic spatial phenomena which are non-stationary in mean and variance. We explore the correspondence between the properties of the IRF-k and the properties of the measurement process. In an exemplary case study, we find that our method reduces the time needed to obtain reliable estimates of glacial movements from 12 h down to 0.5 h compared to simple temporal averaging procedures.

Weight Vector Fluctuations in Adaptive Antenna Arrays Tuned Using the Least-Mean-Square Error Algorithm with Quadratic Constraint

NASA Astrophysics Data System (ADS)

Zimina, S. V.

2015-06-01

We present the results of statistical analysis of an adaptive antenna array tuned using the least-mean-square error algorithm with quadratic constraint on the useful-signal amplification with allowance for the weight-coefficient fluctuations. Using the perturbation theory, the expressions for the correlation function and power of the output signal of the adaptive antenna array, as well as the formula for the weight-vector covariance matrix are obtained in the first approximation. The fluctuations are shown to lead to the signal distortions at the antenna-array output. The weight-coefficient fluctuations result in the appearance of additional terms in the statistical characteristics of the antenna array. It is also shown that the weight-vector fluctuations are isotropic, i.e., identical in all directions of the weight-coefficient space.

A Simulated Annealing based Optimization Algorithm for Automatic Variogram Model Fitting

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Safa, Mohammad

2016-09-01

Fitting a theoretical model to an experimental variogram is an important issue in geostatistical studies because if the variogram model parameters are tainted with uncertainty, the latter will spread in the results of estimations and simulations. Although the most popular fitting method is fitting by eye, in some cases use is made of the automatic fitting method on the basis of putting together the geostatistical principles and optimization techniques to: 1) provide a basic model to improve fitting by eye, 2) fit a model to a large number of experimental variograms in a short time, and 3) incorporate the variogram related uncertainty in the model fitting. Effort has been made in this paper to improve the quality of the fitted model by improving the popular objective function (weighted least squares) in the automatic fitting. Also, since the variogram model function (£) and number of structures (m) too affect the model quality, a program has been provided in the MATLAB software that can present optimum nested variogram models using the simulated annealing method. Finally, to select the most desirable model from among the single/multi-structured fitted models, use has been made of the cross-validation method, and the best model has been introduced to the user as the output. In order to check the capability of the proposed objective function and the procedure, 3 case studies have been presented.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra

NASA Astrophysics Data System (ADS)

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-04-01

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models’ performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra.

PubMed

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-03-13

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models' performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Least-squares model-based halftoning

NASA Astrophysics Data System (ADS)

Pappas, Thrasyvoulos N.; Neuhoff, David L.

1992-08-01

A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach permits the halftoner to be tuned to the individual printer, whose characteristics may vary considerably from those of other printers, for example, write-black vs. write-white laser printers.

Robust Least-Squares Support Vector Machine With Minimization of Mean and Variance of Modeling Error.

PubMed

Lu, Xinjiang; Liu, Wenbo; Zhou, Chuang; Huang, Minghui

2017-06-13

The least-squares support vector machine (LS-SVM) is a popular data-driven modeling method and has been successfully applied to a wide range of applications. However, it has some disadvantages, including being ineffective at handling non-Gaussian noise as well as being sensitive to outliers. In this paper, a robust LS-SVM method is proposed and is shown to have more reliable performance when modeling a nonlinear system under conditions where Gaussian or non-Gaussian noise is present. The construction of a new objective function allows for a reduction of the mean of the modeling error as well as the minimization of its variance, and it does not constrain the mean of the modeling error to zero. This differs from the traditional LS-SVM, which uses a worst-case scenario approach in order to minimize the modeling error and constrains the mean of the modeling error to zero. In doing so, the proposed method takes the modeling error distribution information into consideration and is thus less conservative and more robust in regards to random noise. A solving method is then developed in order to determine the optimal parameters for the proposed robust LS-SVM. An additional analysis indicates that the proposed LS-SVM gives a smaller weight to a large-error training sample and a larger weight to a small-error training sample, and is thus more robust than the traditional LS-SVM. The effectiveness of the proposed robust LS-SVM is demonstrated using both artificial and real life cases.

An Alternating Least Squares Method for the Weighted Approximation of a Symmetric Matrix.

ERIC Educational Resources Information Center

ten Berge, Jos M. F.; Kiers, Henk A. L.

1993-01-01

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

Maximum likelihood estimation in calibrating a stereo camera setup.

PubMed

Muijtjens, A M; Roos, J M; Arts, T; Hasman, A

1999-02-01

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x-ray cameras simultaneously. Regularly, calibration of the position measurement system is obtained by registration of the images of a calibration object, containing 10-20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measured image positions of stereo pairs can be used for calibration. Thus, a separate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensionless parameters. Maximum Likelihood (ML) estimates of these parameters were obtained in an error analysis. It is shown that the ML estimates can be found by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in more accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction problem appeared well conditioned as long as the object aperture is larger than 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstruction of the 3-D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error in this parameter.

An analysis of the least-squares problem for the DSN systematic pointing error model

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Superresolution restoration of an image sequence: adaptive filtering approach.

PubMed

Elad, M; Feuer, A

1999-01-01

This paper presents a new method based on adaptive filtering theory for superresolution restoration of continuous image sequences. The proposed methodology suggests least squares (LS) estimators which adapt in time, based on adaptive filters, least mean squares (LMS) or recursive least squares (RLS). The adaptation enables the treatment of linear space and time-variant blurring and arbitrary motion, both of them assumed known. The proposed new approach is shown to be of relatively low computational requirements. Simulations demonstrating the superresolution restoration algorithms are presented.

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2013 CFR

2013-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2010 CFR

2010-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2012 CFR

2012-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2011 CFR

2011-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2014 CFR

2014-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

Fast global image smoothing based on weighted least squares.

PubMed

Min, Dongbo; Choi, Sunghwan; Lu, Jiangbo; Ham, Bumsub; Sohn, Kwanghoon; Do, Minh N

2014-12-01

This paper presents an efficient technique for performing a spatially inhomogeneous edge-preserving image smoothing, called fast global smoother. Focusing on sparse Laplacian matrices consisting of a data term and a prior term (typically defined using four or eight neighbors for 2D image), our approach efficiently solves such global objective functions. In particular, we approximate the solution of the memory-and computation-intensive large linear system, defined over a d-dimensional spatial domain, by solving a sequence of 1D subsystems. Our separable implementation enables applying a linear-time tridiagonal matrix algorithm to solve d three-point Laplacian matrices iteratively. Our approach combines the best of two paradigms, i.e., efficient edge-preserving filters and optimization-based smoothing. Our method has a comparable runtime to the fast edge-preserving filters, but its global optimization formulation overcomes many limitations of the local filtering approaches. Our method also achieves high-quality results as the state-of-the-art optimization-based techniques, but runs ∼10-30 times faster. Besides, considering the flexibility in defining an objective function, we further propose generalized fast algorithms that perform Lγ norm smoothing (0 < γ < 2) and support an aggregated (robust) data term for handling imprecise data constraints. We demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications.

Total variation-based method for radar coincidence imaging with model mismatch for extended target

NASA Astrophysics Data System (ADS)

Cao, Kaicheng; Zhou, Xiaoli; Cheng, Yongqiang; Fan, Bo; Qin, Yuliang

2017-11-01

Originating from traditional optical coincidence imaging, radar coincidence imaging (RCI) is a staring/forward-looking imaging technique. In RCI, the reference matrix must be computed precisely to reconstruct the image as preferred; unfortunately, such precision is almost impossible due to the existence of model mismatch in practical applications. Although some conventional sparse recovery algorithms are proposed to solve the model-mismatch problem, they are inapplicable to nonsparse targets. We therefore sought to derive the signal model of RCI with model mismatch by replacing the sparsity constraint item with total variation (TV) regularization in the sparse total least squares optimization problem; in this manner, we obtain the objective function of RCI with model mismatch for an extended target. A more robust and efficient algorithm called TV-TLS is proposed, in which the objective function is divided into two parts and the perturbation matrix and scattering coefficients are updated alternately. Moreover, due to the ability of TV regularization to recover sparse signal or image with sparse gradient, TV-TLS method is also applicable to sparse recovering. Results of numerical experiments demonstrate that, for uniform extended targets, sparse targets, and real extended targets, the algorithm can achieve preferred imaging performance both in suppressing noise and in adapting to model mismatch.

Racial and ethnic differences in cognitive function among older adults in the USA

PubMed Central

Díaz-Venegas, Carlos; Downer, Brian; Langa, Kenneth M.; Wong, Rebeca

2016-01-01

Objective Examine differences in cognition between Hispanic, non-Hispanic black (NHB), and non-Hispanic white (NHW) older adults in the United States. Data/Methods The final sample includes 18 982 participants aged 51 or older who received a modified version of the Telephone Interview for Cognitive Status during the 2010 Health and Retirement Study follow-up. Ordinary least squares will be used to examine differences in overall cognition according to race/ethnicity. Results Hispanics and NHB had lower cognition than NHW for all age groups (51–59, 60–69, 70–79, 80+). Hispanics had higher cognition than NHB for all age groups but these differences were all within one point. The lower cognition among NHB compared to NHW remained significant after controlling for age, gender, and education, whereas the differences in cognition between Hispanics and NHW were no longer significant after controlling for these covariates. Cognitive scores increased with greater educational attainment for all race/ethnic groups, but Hispanics exhibited the least benefit. Discussion Our results highlight the role of education in race/ethnic differences in cognitive function during old age. Education seems beneficial for cognition in old age for all race/ethnic groups, but Hispanics appear to receive a lower benefit compared to other race/ethnic groups. Further research is needed on the racial and ethnic differences in the pathways of the benefits of educational attainment for late-life cognitive function. PMID:26766788

A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants

ERIC Educational Resources Information Center

Cooper, Paul D.

2010-01-01

A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…

Deriving the Quadratic Regression Equation Using Algebra

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…

A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

NASA Astrophysics Data System (ADS)

Salama, Paul

2008-02-01

Multi-photon microscopy has provided biologists with unprecedented opportunities for high resolution imaging deep into tissues. Unfortunately deep tissue multi-photon microscopy images are in general noisy since they are acquired at low photon counts. To aid in the analysis and segmentation of such images it is sometimes necessary to initially enhance the acquired images. One way to enhance an image is to find the maximum a posteriori (MAP) estimate of each pixel comprising an image, which is achieved by finding a constrained least squares estimate of the unknown distribution. In arriving at the distribution it is assumed that the noise is Poisson distributed, the true but unknown pixel values assume a probability mass function over a finite set of non-negative values, and since the observed data also assumes finite values because of low photon counts, the sum of the probabilities of the observed pixel values (obtained from the histogram of the acquired pixel values) is less than one. Experimental results demonstrate that it is possible to closely estimate the unknown probability mass function with these assumptions.

A Generic Nonlinear Aerodynamic Model for Aircraft

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2014-01-01

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

On the log-normality of historical magnetic-storm intensity statistics: implications for extreme-event probabilities

USGS Publications Warehouse

Love, Jeffrey J.; Rigler, E. Joshua; Pulkkinen, Antti; Riley, Pete

2015-01-01

An examination is made of the hypothesis that the statistics of magnetic-storm-maximum intensities are the realization of a log-normal stochastic process. Weighted least-squares and maximum-likelihood methods are used to fit log-normal functions to −Dst storm-time maxima for years 1957-2012; bootstrap analysis is used to established confidence limits on forecasts. Both methods provide fits that are reasonably consistent with the data; both methods also provide fits that are superior to those that can be made with a power-law function. In general, the maximum-likelihood method provides forecasts having tighter confidence intervals than those provided by weighted least-squares. From extrapolation of maximum-likelihood fits: a magnetic storm with intensity exceeding that of the 1859 Carrington event, −Dst≥850 nT, occurs about 1.13 times per century and a wide 95% confidence interval of [0.42,2.41] times per century; a 100-yr magnetic storm is identified as having a −Dst≥880 nT (greater than Carrington) but a wide 95% confidence interval of [490,1187] nT.

On the equivalence of spherical splines with least-squares collocation and Stokes's formula for regional geoid computation

NASA Astrophysics Data System (ADS)

Ophaug, Vegard; Gerlach, Christian

2017-11-01

This work is an investigation of three methods for regional geoid computation: Stokes's formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223-232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes's formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes's formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

NASA Technical Reports Server (NTRS)

Tiffany, S. H.; Adams, W. M., Jr.

1984-01-01

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Fuzzy support vector machines for adaptive Morse code recognition.

PubMed

Yang, Cheng-Hong; Jin, Li-Cheng; Chuang, Li-Yeh

2006-11-01

Morse code is now being harnessed for use in rehabilitation applications of augmentative-alternative communication and assistive technology, facilitating mobility, environmental control and adapted worksite access. In this paper, Morse code is selected as a communication adaptive device for persons who suffer from muscle atrophy, cerebral palsy or other severe handicaps. A stable typing rate is strictly required for Morse code to be effective as a communication tool. Therefore, an adaptive automatic recognition method with a high recognition rate is needed. The proposed system uses both fuzzy support vector machines and the variable-degree variable-step-size least-mean-square algorithm to achieve these objectives. We apply fuzzy memberships to each point, and provide different contributions to the decision learning function for support vector machines. Statistical analyses demonstrated that the proposed method elicited a higher recognition rate than other algorithms in the literature.

Image reconstruction of IRAS survey scans

NASA Technical Reports Server (NTRS)

Bontekoe, Tj. Romke

1990-01-01

The IRAS survey data can be used successfully to produce images of extended objects. The major difficulties, viz. non-uniform sampling, different response functions for each detector, and varying signal-to-noise levels for each detector for each scan, were resolved. The results of three different image construction techniques are compared: co-addition, constrained least squares, and maximum entropy. The maximum entropy result is superior. An image of the galaxy M51 with an average spatial resolution of 45 arc seconds is presented, using 60 micron survey data. This exceeds the telescope diffraction limit of 1 minute of arc, at this wavelength. Data fusion is a proposed method for combining data from different instruments, with different spacial resolutions, at different wavelengths. Data estimates of the physical parameters, temperature, density and composition, can be made from the data without prior image (re-)construction. An increase in the accuracy of these parameters is expected as the result of this more systematic approach.

Application of principal component analysis (PCA) as a sensory assessment tool for fermented food products.

PubMed

Ghosh, Debasree; Chattopadhyay, Parimal

2012-06-01

The objective of the work was to use the method of quantitative descriptive analysis (QDA) to describe the sensory attributes of the fermented food products prepared with the incorporation of lactic cultures. Panellists were selected and trained to evaluate various attributes specially color and appearance, body texture, flavor, overall acceptability and acidity of the fermented food products like cow milk curd and soymilk curd, idli, sauerkraut and probiotic ice cream. Principal component analysis (PCA) identified the six significant principal components that accounted for more than 90% of the variance in the sensory attribute data. Overall product quality was modelled as a function of principal components using multiple least squares regression (R (2) = 0.8). The result from PCA was statistically analyzed by analysis of variance (ANOVA). These findings demonstrate the utility of quantitative descriptive analysis for identifying and measuring the fermented food product attributes that are important for consumer acceptability.

A method for the microlensed flux variance of QSOs

NASA Astrophysics Data System (ADS)

Goodman, Jeremy; Sun, Ai-Lei

2014-06-01

A fast and practical method is described for calculating the microlensed flux variance of an arbitrary source by uncorrelated stars. The required inputs are the mean convergence and shear due to the smoothed potential of the lensing galaxy, the stellar mass function, and the absolute square of the Fourier transform of the surface brightness in the source plane. The mathematical approach follows previous authors but has been generalized, streamlined, and implemented in publicly available code. Examples of its application are given for Dexter and Agol's inhomogeneous-disc models as well as the usual Gaussian sources. Since the quantity calculated is a second moment of the magnification, it is only logarithmically sensitive to the sizes of very compact sources. However, for the inferred sizes of actual quasi-stellar objects (QSOs), it has some discriminatory power and may lend itself to simple statistical tests. At the very least, it should be useful for testing the convergence of microlensing simulations.

A Nonlinear Least Squares Approach to Time of Death Estimation Via Body Cooling.

PubMed

Rodrigo, Marianito R

2016-01-01

The problem of time of death (TOD) estimation by body cooling is revisited by proposing a nonlinear least squares approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall-Hoare double exponential formula and a technique for reducing the dimension of the state space, an error function that depends on the two cooling rates is constructed, with the aim of minimizing this function. Standard nonlinear optimization methods that are used to minimize the bivariate error function require an initial guess for these unknown rates. Hence, a systematic procedure based on the given temperature data is also proposed to determine an initial estimate for the rates. Then, an explicit formula for the TOD is given. Results of numerical simulations using both theoretical and experimental data are presented, both yielding reasonable estimates. The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact, the method allows the estimation of the temperature at death once the cooling rates and the TOD have been calculated. The procedure requires at least three temperature readings, although more measured readings could improve the estimates. With the aid of computerized recording and thermocouple detectors, temperature readings spaced 10-15 min apart, for example, can be taken. The formulas can be straightforwardly programmed and installed on a hand-held device for field use. © 2015 American Academy of Forensic Sciences.

System identification and model reduction using modulating function techniques

NASA Technical Reports Server (NTRS)

Shen, Yan

1993-01-01

Weighted least squares (WLS) and adaptive weighted least squares (AWLS) algorithms are initiated for continuous-time system identification using Fourier type modulating function techniques. Two stochastic signal models are examined using the mean square properties of the stochastic calculus: an equation error signal model with white noise residuals, and a more realistic white measurement noise signal model. The covariance matrices in each model are shown to be banded and sparse, and a joint likelihood cost function is developed which links the real and imaginary parts of the modulated quantities. The superior performance of above algorithms is demonstrated by comparing them with the LS/MFT and popular predicting error method (PEM) through 200 Monte Carlo simulations. A model reduction problem is formulated with the AWLS/MFT algorithm, and comparisons are made via six examples with a variety of model reduction techniques, including the well-known balanced realization method. Here the AWLS/MFT algorithm manifests higher accuracy in almost all cases, and exhibits its unique flexibility and versatility. Armed with this model reduction, the AWLS/MFT algorithm is extended into MIMO transfer function system identification problems. The impact due to the discrepancy in bandwidths and gains among subsystem is explored through five examples. Finally, as a comprehensive application, the stability derivatives of the longitudinal and lateral dynamics of an F-18 aircraft are identified using physical flight data provided by NASA. A pole-constrained SIMO and MIMO AWLS/MFT algorithm is devised and analyzed. Monte Carlo simulations illustrate its high-noise rejecting properties. Utilizing the flight data, comparisons among different MFT algorithms are tabulated and the AWLS is found to be strongly favored in almost all facets.

Irradiation dose detection of irradiated milk powder using visible and near-infrared spectroscopy and chemometrics.

PubMed

Kong, W W; Zhang, C; Liu, F; Gong, A P; He, Y

2013-08-01

The objective of this study was to examine the possibility of applying visible and near-infrared spectroscopy to the quantitative detection of irradiation dose of irradiated milk powder. A total of 150 samples were used: 100 for the calibration set and 50 for the validation set. The samples were irradiated at 5 different dose levels in the dose range 0 to 6.0 kGy. Six different pretreatment methods were compared. The prediction results of full spectra given by linear and nonlinear calibration methods suggested that Savitzky-Golay smoothing and first derivative were suitable pretreatment methods in this study. Regression coefficient analysis was applied to select effective wavelengths (EW). Less than 10 EW were selected and they were useful for portable detection instrument or sensor development. Partial least squares, extreme learning machine, and least squares support vector machine were used. The best prediction performance was achieved by the EW-extreme learning machine model with first-derivative spectra, and correlation coefficients=0.97 and root mean square error of prediction=0.844. This study provided a new approach for the fast detection of irradiation dose of milk powder. The results could be helpful for quality detection and safety monitoring of milk powder. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

An on-line modified least-mean-square algorithm for training neurofuzzy controllers.

PubMed

Tan, Woei Wan

2007-04-01

The problem hindering the use of data-driven modelling methods for training controllers on-line is the lack of control over the amount by which the plant is excited. As the operating schedule determines the information available on-line, the knowledge of the process may degrade if the setpoint remains constant for an extended period. This paper proposes an identification algorithm that alleviates "learning interference" by incorporating fuzzy theory into the normalized least-mean-square update rule. The ability of the proposed methodology to achieve faster learning is examined by employing the algorithm to train a neurofuzzy feedforward controller for controlling a liquid level process. Since the proposed identification strategy has similarities with the normalized least-mean-square update rule and the recursive least-square estimator, the on-line learning rates of these algorithms are also compared.

An algorithm for surface smoothing with rational splines

NASA Technical Reports Server (NTRS)

Schiess, James R.

1987-01-01

Discussed is an algorithm for smoothing surfaces with spline functions containing tension parameters. The bivariate spline functions used are tensor products of univariate rational-spline functions. A distinct tension parameter corresponds to each rectangular strip defined by a pair of consecutive spline knots along either axis. Equations are derived for writing the bivariate rational spline in terms of functions and derivatives at the knots. Estimates of these values are obtained via weighted least squares subject to continuity constraints at the knots. The algorithm is illustrated on a set of terrain elevation data.

Multiway analysis methods applied to the fluorescence excitation-emission dataset for the simultaneous quantification of valsartan and amlodipine in tablets

NASA Astrophysics Data System (ADS)

Dinç, Erdal; Ertekin, Zehra Ceren; Büker, Eda

2017-09-01

In this study, excitation-emission matrix datasets, which have strong overlapping bands, were processed by using four different chemometric calibration algorithms consisting of parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares for the simultaneous quantitative estimation of valsartan and amlodipine besylate in tablets. In analyses, preliminary separation step was not used before the application of parallel factor analysis Tucker3, three-way partial least squares and unfolded partial least squares approaches for the analysis of the related drug substances in samples. Three-way excitation-emission matrix data array was obtained by concatenating excitation-emission matrices of the calibration set, validation set, and commercial tablet samples. The excitation-emission matrix data array was used to get parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares calibrations and to predict the amounts of valsartan and amlodipine besylate in samples. For all the methods, calibration and prediction of valsartan and amlodipine besylate were performed in the working concentration ranges of 0.25-4.50 μg/mL. The validity and the performance of all the proposed methods were checked by using the validation parameters. From the analysis results, it was concluded that the described two-way and three-way algorithmic methods were very useful for the simultaneous quantitative resolution and routine analysis of the related drug substances in marketed samples.

Addressing the identification problem in age-period-cohort analysis: a tutorial on the use of partial least squares and principal components analysis.

PubMed

Tu, Yu-Kang; Krämer, Nicole; Lee, Wen-Chung

2012-07-01

In the analysis of trends in health outcomes, an ongoing issue is how to separate and estimate the effects of age, period, and cohort. As these 3 variables are perfectly collinear by definition, regression coefficients in a general linear model are not unique. In this tutorial, we review why identification is a problem, and how this problem may be tackled using partial least squares and principal components regression analyses. Both methods produce regression coefficients that fulfill the same collinearity constraint as the variables age, period, and cohort. We show that, because the constraint imposed by partial least squares and principal components regression is inherent in the mathematical relation among the 3 variables, this leads to more interpretable results. We use one dataset from a Taiwanese health-screening program to illustrate how to use partial least squares regression to analyze the trends in body heights with 3 continuous variables for age, period, and cohort. We then use another dataset of hepatocellular carcinoma mortality rates for Taiwanese men to illustrate how to use partial least squares regression to analyze tables with aggregated data. We use the second dataset to show the relation between the intrinsic estimator, a recently proposed method for the age-period-cohort analysis, and partial least squares regression. We also show that the inclusion of all indicator variables provides a more consistent approach. R code for our analyses is provided in the eAppendix.

Feature Detection and Curve Fitting Using Fast Walsh Transforms for Shock Tracking: Applications

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2017-01-01

Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it has been proven that the inner product of the Walsh Root function for group p with every polynomial of degree < or = (p - 1) across the element is identically zero. It has also been proven that the magnitude and location of a discontinuous jump, as represented by a Heaviside function, are explicitly identified by its Fast Walsh Transform (FWT) coefficients. These two proofs enable an algorithm that quickly provides a Weighted Least Squares fit to distributions across the element that include a discontinuity. The detection of a discontinuity enables analytic relations to locally describe its evolution and provide increased accuracy. Time accurate examples are provided for advection, Burgers equation, and Riemann problems (diaphragm burst) in closed tubes and de Laval nozzles. New algorithms to detect up to two C0 and/or C1 discontinuities within a single element are developed for application to the Riemann problem, in which a contact discontinuity and shock wave form after the diaphragm bursts.

Application of time transfer functions to Gaia's global astrometry. Validation on DPAC simulated Gaia-like observations

NASA Astrophysics Data System (ADS)

Bertone, Stefano; Vecchiato, Alberto; Bucciarelli, Beatrice; Crosta, Mariateresa; Lattanzi, Mario G.; Bianchi, Luca; Angonin, Marie-Christine; Le Poncin-Lafitte, Christophe

2017-12-01

Context. A key objective of the ESA Gaia satellite is the realization of a quasi-inertial reference frame at visual wavelengths by means of global astrometric techniques. This requires accurate mathematical and numerical modeling of relativistic light propagation, as well as double-blind-like procedures for the internal validation of the results, before they are released to the scientific community at large. Aims: We aim to specialize the time transfer functions (TTF) formalism to the case of the Gaia observer and prove its applicability to the task of global sphere reconstruction (GSR), in anticipation of its inclusion in the GSR system, already featuring the Relativistic Astrometric MODel (RAMOD) suite, as an additional semi-external validation of the forthcoming Gaia baseline astrometric solutions. Methods: We extended the current GSR framework and software infrastructure (GSR2) to include TTF relativistic observation equations compatible with Gaia's operations. We used simulated data generated by the Gaia Data Processing and Analysis Consortium (DPAC) to obtain different least-squares estimations of the full (five-parameter) stellar spheres and gauge results. These were compared to analogous solutions obtained with the current RAMOD model in GSR2 (RAMOD@GSR2) and to the catalog generated with the Gaia RElativistic Model (GREM), the model baselined for Gaia and used to generate the DPAC synthetic data. Results: Linearized least-squares TTF solutions are based on spheres of about 132 000 primary stars uniformly distributed on the sky and simulated observations spanning the entire 5 yr range of Gaia's nominal operational lifetime. The statistical properties of the results compare well with those of GREM. Finally, comparisons to RAMOD@GSR2 solutions confirmed the known lower accuracy of that model and allowed us to establish firm limits on the quality of the linearization point outside of which an iteration for non-linearity is required for its proper convergence. This has proved invaluable as RAMOD@GSR2 is prepared to go into operations on real satellite data.

Comparing implementations of penalized weighted least-squares sinogram restoration

PubMed Central

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-01-01

Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. Results: All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors’ previous penalized-likelihood implementation. Conclusions: Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes. PMID:21158306

Difficulty Factors, Distribution Effects, and the Least Squares Simplex Data Matrix Solution

ERIC Educational Resources Information Center

Ten Berge, Jos M. F.

1972-01-01

In the present article it is argued that the Least Squares Simplex Data Matrix Solution does not deal adequately with difficulty factors inasmuch as the theoretical foundation is insufficient. (Author/CB)

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

An Empirical Method for Determining the Lunar Gravity Field. Ph.D. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Ferrari, A. J.

1971-01-01

A method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Customer demand prediction of service-oriented manufacturing using the least square support vector machine optimized by particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Cao, Jin; Jiang, Zhibin; Wang, Kangzhou

2017-07-01

Many nonlinear customer satisfaction-related factors significantly influence the future customer demand for service-oriented manufacturing (SOM). To address this issue and enhance the prediction accuracy, this article develops a novel customer demand prediction approach for SOM. The approach combines the phase space reconstruction (PSR) technique with the optimized least square support vector machine (LSSVM). First, the prediction sample space is reconstructed by the PSR to enrich the time-series dynamics of the limited data sample. Then, the generalization and learning ability of the LSSVM are improved by the hybrid polynomial and radial basis function kernel. Finally, the key parameters of the LSSVM are optimized by the particle swarm optimization algorithm. In a real case study, the customer demand prediction of an air conditioner compressor is implemented. Furthermore, the effectiveness and validity of the proposed approach are demonstrated by comparison with other classical predication approaches.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

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

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Diagnosis of the Ill-condition of the RFM Based on Condition Index and Variance Decomposition Proportion (CIVDP)

NASA Astrophysics Data System (ADS)

Qing, Zhou; Weili, Jiao; Tengfei, Long

2014-03-01

The Rational Function Model (RFM) is a new generalized sensor model. It does not need the physical parameters of sensors to achieve a high accuracy that is compatible to the rigorous sensor models. At present, the main method to solve RPCs is the Least Squares Estimation. But when coefficients has a large number or the distribution of the control points is not even, the classical least square method loses its superiority due to the ill-conditioning problem of design matrix. Condition Index and Variance Decomposition Proportion (CIVDP) is a reliable method for diagnosing the multicollinearity among the design matrix. It can not only detect the multicollinearity, but also can locate the parameters and show the corresponding columns in the design matrix. In this paper, the CIVDP method is used to diagnose the ill-condition problem of the RFM and to find the multicollinearity in the normal matrix.

Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction

PubMed Central

Gregor, Jens; Fessler, Jeffrey A.

2015-01-01

Tomographic image reconstruction is often formulated as a regularized weighted least squares (RWLS) problem optimized by iterative algorithms that are either inherently algebraic or derived from a statistical point of view. This paper compares a modified version of SIRT (Simultaneous Iterative Reconstruction Technique), which is of the former type, with a version of SQS (Separable Quadratic Surrogates), which is of the latter type. We show that the two algorithms minimize the same criterion function using similar forms of preconditioned gradient descent. We present near-optimal relaxation for both based on eigenvalue bounds and include a heuristic extension for use with ordered subsets. We provide empirical evidence that SIRT and SQS converge at the same rate for all intents and purposes. For context, we compare their performance with an implementation of preconditioned conjugate gradient. The illustrative application is X-ray CT of luggage for aviation security. PMID:26478906

Simultaneous determination of three herbicides by differential pulse voltammetry and chemometrics.

PubMed

Ni, Yongnian; Wang, Lin; Kokot, Serge

2011-01-01

A novel differential pulse voltammetry method (DPV) was researched and developed for the simultaneous determination of Pendimethalin, Dinoseb and sodium 5-nitroguaiacolate (5NG) with the aid of chemometrics. The voltammograms of these three compounds overlapped significantly, and to facilitate the simultaneous determination of the three analytes, chemometrics methods were applied. These included classical least squares (CLS), principal component regression (PCR), partial least squares (PLS) and radial basis function-artificial neural networks (RBF-ANN). A separately prepared verification data set was used to confirm the calibrations, which were built from the original and first derivative data matrices of the voltammograms. On the basis relative prediction errors and recoveries of the analytes, the RBF-ANN and the DPLS (D - first derivative spectra) models performed best and are particularly recommended for application. The DPLS calibration model was applied satisfactorily for the prediction of the three analytes from market vegetables and lake water samples.

Complementary effect of patient volume and quality of care on hospital cost efficiency.

PubMed

Choi, Jeong Hoon; Park, Imsu; Jung, Ilyoung; Dey, Asoke

2017-06-01

This study explores the direct effect of an increase in patient volume in a hospital and the complementary effect of quality of care on the cost efficiency of U.S. hospitals in terms of patient volume. The simultaneous equation model with three-stage least squares is used to measure the direct effect of patient volume and the complementary effect of quality of care and volume. Cost efficiency is measured with a data envelopment analysis method. Patient volume has a U-shaped relationship with hospital cost efficiency and an inverted U-shaped relationship with quality of care. Quality of care functions as a moderator for the relationship between patient volume and efficiency. This paper addresses the economically important question of the relationship of volume with quality of care and hospital cost efficiency. The three-stage least square simultaneous equation model captures the simultaneous effects of patient volume on hospital quality of care and cost efficiency.

The Mean Life Squared Relationship for Abundances of Extinct Radioactivities

NASA Technical Reports Server (NTRS)

Lodders, K.; Cameron, A. G. W.

2004-01-01

We discovered that the abundances of now extinct radioactivities (relative to stable reference isotopes) in meteorites vary as a function of their mean lifetimes squared. This relationship applies to chondrites, achondrites, and irons but to calcium-aluminum inclusions (CAIs). Certain meteorites contain excesses in isotopic abundances from the decay of radioactive isotopes with half-lives much less than the age of the solar system. These short-lived radioactivities are now extinct, but they were alive when meteorites assembled in the early solar system. The origin of these radioactivities and the processes which control their abundances in the solar nebula are still not well understood. Some clues may come from our finding that the meteoritic abundances of now extinct radioactivities (relative to stable reference isotopes) vary as a function of their mean lifetimes squared. This relationship applies to chondrites, achondrites, and irons, but not to CAIs. This points to at least two different processes establishing the abundances of short-lived isotopes found in the meteoritic record.

Online Pairwise Learning Algorithms.

PubMed

Ying, Yiming; Zhou, Ding-Xuan

2016-04-01

Pairwise learning usually refers to a learning task that involves a loss function depending on pairs of examples, among which the most notable ones are bipartite ranking, metric learning, and AUC maximization. In this letter we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS) that we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works (Kar, Sriperumbudur, Jain, & Karnick, 2013 ; Wang, Khardon, Pechyony, & Jones, 2012 ), which require that the iterates are restricted to a bounded domain or the loss function is strongly convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem that guarantees the almost sure convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely used kernels in the setting of pairwise learning and illustrate the convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.

49 CFR 172.327 - Petroleum sour crude oil in bulk packaging.

Code of Federal Regulations, 2014 CFR

2014-10-01

... least 100 mm (3.9 inches). The width of the border forming the square-on-point marking must be at least... hydrogen sulfide vapors may occur. (b) The border of the square-on-point must be black or red on a white or other suitable contrasting background. The symbol must be black and located in the center of the square...

Validation of Core Temperature Estimation Algorithm

DTIC Science & Technology

2016-01-29

plot of observed versus estimated core temperature with the line of identity (dashed) and the least squares regression line (solid) and line equation...estimated PSI with the line of identity (dashed) and the least squares regression line (solid) and line equation in the top left corner. (b) Bland...for comparison. The root mean squared error (RMSE) was also computed, as given by Equation 2.

Least-Squares Analysis of Data with Uncertainty in "y" and "x": Algorithms in Excel and KaleidaGraph

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2018-01-01

For the least-squares analysis of data having multiple uncertain variables, the generally accepted best solution comes from minimizing the sum of weighted squared residuals over all uncertain variables, with, for example, weights in x[subscript i] taken as inversely proportional to the variance [delta][subscript xi][superscript 2]. A complication…

Linear Least Squares for Correlated Data

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

Throughout the literature authors have consistently discussed the suspicion that regression results were less than satisfactory when the independent variables were correlated. Camm, Gulledge, and Womer, and Womer and Marcotte provide excellent applied examples of these concerns. Many authors have obtained partial solutions for this problem as discussed by Womer and Marcotte and Wonnacott and Wonnacott, which result in generalized least squares algorithms to solve restrictive cases. This paper presents a simple but relatively general multivariate method for obtaining linear least squares coefficients which are free of the statistical distortion created by correlated independent variables.

A Simple Formula to Calculate Shallow-Water Transmission Loss by Means of a Least-Squares Surface Fit Technique.

DTIC Science & Technology

1980-09-01

HASTRUP , T REAL UNCLASSIFIED SACLAATCEN- SM-139 N SACLANTCEN Memorandum SM -139 -LEFW SACLANT ASW RESEARCH CENTRE ~ MEMORANDUM A SIMPLE FORMULA TO...CALCULATE SHALLOW-WATER TRANSMISSION LOSS BY MEANS OF A LEAST- SQUARES SURFACE FIT TECHNIQUE 7-sallby OLE F. HASTRUP and TUNCAY AKAL I SEPTEMBER 1980 NORTH...JRANSi4ISSION LOSS/ BY MEANS OF A LEAST-SQUARES SURFACE fIT TECHNIQUE, C T ~e F./ Hastrup .0TnaAa ()1 Sep 8 This memorandum has been prepared within the

The least-squares mixing models to generate fraction images derived from remote sensing multispectral data

NASA Technical Reports Server (NTRS)

Shimabukuro, Yosio Edemir; Smith, James A.

1991-01-01

Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.

Application of multispectral reflectance for early detection of tomato disease

NASA Astrophysics Data System (ADS)

Xu, Huirong; Zhu, Shengpan; Ying, Yibin; Jiang, Huanyu

2006-10-01

Automatic diagnosis of plant disease is important for plant management and environmental preservation in the future. The objective of this study is to use multispectral reflectance measurements to make an early discrimination between the healthy and infected plants by the strain of tobacco mosaic virus (TMV-U1) infection. There were reflectance changes in the visible (VIS) and near infrared spectroscopy (NIR) between the healthy and infected plants. Discriminant models were developed using discriminant partial least squares (DPLS) and Mahalanobis distance (MD). The DPLS models had a root mean square error of calibration (RMSEC) of 0.397 and correlation coefficient (r) of 0.59 and the MD model correctly classified 86.7% healthy plants and up to 91.7% infected plants.

Identification and compensation of the temperature influences in a miniature three-axial accelerometer based on the least squares method

NASA Astrophysics Data System (ADS)

Grigorie, Teodor Lucian; Corcau, Ileana Jenica; Tudosie, Alexandru Nicolae

2017-06-01

The paper presents a way to obtain an intelligent miniaturized three-axial accelerometric sensor, based on the on-line estimation and compensation of the sensor errors generated by the environmental temperature variation. Taking into account that this error's value is a strongly nonlinear complex function of the values of environmental temperature and of the acceleration exciting the sensor, its correction may not be done off-line and it requires the presence of an additional temperature sensor. The proposed identification methodology for the error model is based on the least square method which process off-line the numerical values obtained from the accelerometer experimental testing for different values of acceleration applied to its axes of sensitivity and for different values of operating temperature. A final analysis of the error level after the compensation highlights the best variant for the matrix in the error model. In the sections of the paper are shown the results of the experimental testing of the accelerometer on all the three sensitivity axes, the identification of the error models on each axis by using the least square method, and the validation of the obtained models with experimental values. For all of the three detection channels was obtained a reduction by almost two orders of magnitude of the acceleration absolute maximum error due to environmental temperature variation.

Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients

NASA Astrophysics Data System (ADS)

Steinbock, Michael J.; Hyde, Milo W.

2012-10-01

Adaptive optics is used in applications such as laser communication, remote sensing, and laser weapon systems to estimate and correct for atmospheric distortions of propagated light in real-time. Within an adaptive optics system, a reconstruction process interprets the raw wavefront sensor measurements and calculates an estimate for the unwrapped phase function to be sent through a control law and applied to a wavefront correction device. This research is focused on adaptive optics using a self-referencing interferometer wavefront sensor, which directly measures the wrapped wavefront phase. Therefore, its measurements must be reconstructed for use on a continuous facesheet deformable mirror. In testing and evaluating a novel class of branch-point- tolerant wavefront reconstructors based on the post-processing congruence operation technique, an increase in Strehl ratio compared to a traditional least squares reconstructor was noted even in non-scintillated fields. To investigate this further, this paper uses wave-optics simulations to eliminate many of the variables from a hardware adaptive optics system, so as to focus on the reconstruction techniques alone. The simulation results along with a discussion of the physical reasoning for this phenomenon are provided. For any applications using a self-referencing interferometer wavefront sensor with low signal levels or high localized wavefront gradients, understanding this phenomena is critical when applying a traditional least squares wavefront reconstructor.

Simple and Reliable Determination of Intravoxel Incoherent Motion Parameters for the Differential Diagnosis of Head and Neck Tumors

PubMed Central

Sasaki, Miho; Sumi, Misa; Eida, Sato; Katayama, Ikuo; Hotokezaka, Yuka; Nakamura, Takashi

2014-01-01

Intravoxel incoherent motion (IVIM) imaging can characterize diffusion and perfusion of normal and diseased tissues, and IVIM parameters are authentically determined by using cumbersome least-squares method. We evaluated a simple technique for the determination of IVIM parameters using geometric analysis of the multiexponential signal decay curve as an alternative to the least-squares method for the diagnosis of head and neck tumors. Pure diffusion coefficients (D), microvascular volume fraction (f), perfusion-related incoherent microcirculation (D*), and perfusion parameter that is heavily weighted towards extravascular space (P) were determined geometrically (Geo D, Geo f, and Geo P) or by least-squares method (Fit D, Fit f, and Fit D*) in normal structures and 105 head and neck tumors. The IVIM parameters were compared for their levels and diagnostic abilities between the 2 techniques. The IVIM parameters were not able to determine in 14 tumors with the least-squares method alone and in 4 tumors with the geometric and least-squares methods. The geometric IVIM values were significantly different (p<0.001) from Fit values (+2±4% and −7±24% for D and f values, respectively). Geo D and Fit D differentiated between lymphomas and SCCs with similar efficacy (78% and 80% accuracy, respectively). Stepwise approaches using combinations of Geo D and Geo P, Geo D and Geo f, or Fit D and Fit D* differentiated between pleomorphic adenomas, Warthin tumors, and malignant salivary gland tumors with the same efficacy (91% accuracy = 21/23). However, a stepwise differentiation using Fit D and Fit f was less effective (83% accuracy = 19/23). Considering cumbersome procedures with the least squares method compared with the geometric method, we concluded that the geometric determination of IVIM parameters can be an alternative to least-squares method in the diagnosis of head and neck tumors. PMID:25402436

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

Software For Least-Squares And Robust Estimation

NASA Technical Reports Server (NTRS)

Jeffreys, William H.; Fitzpatrick, Michael J.; Mcarthur, Barbara E.; Mccartney, James

1990-01-01

GAUSSFIT computer program includes full-featured programming language facilitating creation of mathematical models solving least-squares and robust-estimation problems. Programming language designed to make it easy to specify complex reduction models. Written in 100 percent C language.

Beyond Principal Component Analysis: A Trilinear Decomposition Model and Least Squares Estimation.

ERIC Educational Resources Information Center

Pham, Tuan Dinh; Mocks, Joachim

1992-01-01

Sufficient conditions are derived for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis. The limiting covariance matrix is computed. (Author/SLD)

Simultaneous quantitative analysis of olmesartan, amlodipine and hydrochlorothiazide in their combined dosage form utilizing classical and alternating least squares based chemometric methods.

PubMed

Darwish, Hany W; Bakheit, Ahmed H; Abdelhameed, Ali S

2016-03-01

Simultaneous spectrophotometric analysis of a multi-component dosage form of olmesartan, amlodipine and hydrochlorothiazide used for the treatment of hypertension has been carried out using various chemometric methods. Multivariate calibration methods include classical least squares (CLS) executed by net analyte processing (NAP-CLS), orthogonal signal correction (OSC-CLS) and direct orthogonal signal correction (DOSC-CLS) in addition to multivariate curve resolution-alternating least squares (MCR-ALS). Results demonstrated the efficiency of the proposed methods as quantitative tools of analysis as well as their qualitative capability. The three analytes were determined precisely using the aforementioned methods in an external data set and in a dosage form after optimization of experimental conditions. Finally, the efficiency of the models was validated via comparison with the partial least squares (PLS) method in terms of accuracy and precision.

Estimating the Extreme Behaviors of Students Performance Using Quantile Regression--Evidences from Taiwan

ERIC Educational Resources Information Center

Chen, Sheng-Tung; Kuo, Hsiao-I.; Chen, Chi-Chung

2012-01-01

The two-stage least squares approach together with quantile regression analysis is adopted here to estimate the educational production function. Such a methodology is able to capture the extreme behaviors of the two tails of students' performance and the estimation outcomes have important policy implications. Our empirical study is applied to the…

Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Greenberg, P. S.

1994-01-01

Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation

Workshop on Functional and Structural Relationships and Factor Analysis (1983). Summary of Research Interests of Participants.

DTIC Science & Technology

1983-01-01

J. Amer. Statist. Assoc. 75, 687-692. Dahm, P. F., Helton, B. and Fuller, W. A. (1983), Generalized least squares estimation of the genotypic ...with applications to -"insect development times". Austral. J. Statist. 23, 204-213. [2] Angus , J.F., R. Morton and C. Schafer. (1981). "Phasic

Lightweight In-Plane Actuated Deformable Mirrors for Space Telescopes

DTIC Science & Technology

2006-09-01

dimensional beam-string and axisymmetric plate-membrane. The beam-string (a clamped beam simultaneously under an axial load ) is an important...Tensile load versus radius. . . . . . . . . . . . . . . . . . . . . . 175 7.4. Actuation voltage functions. . . . . . . . . . . . . . . . . . . . 179...membrane Asymptotic finite element Flint and De- noyer [45] 2003 In-plane Circular membrane Numerical least squares fit Actuators modelled as line loads

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…

Modeling of mass transfer of Phospholipids in separation process with supercritical CO2 fluid by RBF artificial neural networks

USDA-ARS?s Scientific Manuscript database

An artificial Radial Basis Function (RBF) neural network model was developed for the prediction of mass transfer of the phospholipids from canola meal in supercritical CO2 fluid. The RBF kind of artificial neural networks (ANN) with orthogonal least squares (OLS) learning algorithm were used for mod...

The fundamentals of average local variance--Part II: Sampling simple regular patterns with optical imagery.

PubMed

Bøcher, Peder Klith; McCloy, Keith R

2006-02-01

In this investigation, the characteristics of the average local variance (ALV) function is investigated through the acquisition of images at different spatial resolutions of constructed scenes of regular patterns of black and white squares. It is shown that the ALV plot consistently peaks at a spatial resolution in which the pixels has a size corresponding to half the distance between scene objects, and that, under very specific conditions, it also peaks at a spatial resolution in which the pixel size corresponds to the whole distance between scene objects. It is argued that the peak at object distance when present is an expression of the Nyquist sample rate. The presence of this peak is, hence, shown to be a function of the matching between the phase of the scene pattern and the phase of the sample grid, i.e., the image. When these phases match, a clear and distinct peak is produced on the ALV plot. The fact that the peak at half the distance consistently occurs in the ALV plot is linked to the circumstance that the sampling interval (distance between pixels) and the extent of the sampling unit (size of pixels) are equal. Hence, at twice the Nyquist sampling rate, each fundamental period of the pattern is covered by four pixels; therefore, at least one pixel is always completely embedded within one pattern element, regardless of sample scene phase. If the objects in the scene are scattered with a distance larger than their extent, the peak will be related to the size by a factor larger than 1/2. This is suggested to be the explanation to the results presented by others that the ALV plot is related to scene-object size by a factor of 1/2-3/4.

Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction.

PubMed

Fessler, J A; Booth, S D

1999-01-01

Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant, i.e., for those with approximately block-Toeplitz or block-circulant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.

Equivalent orthotropic elastic moduli identification method for laminated electrical steel sheets

NASA Astrophysics Data System (ADS)

Saito, Akira; Nishikawa, Yasunari; Yamasaki, Shintaro; Fujita, Kikuo; Kawamoto, Atsushi; Kuroishi, Masakatsu; Nakai, Hideo

2016-05-01

In this paper, a combined numerical-experimental methodology for the identification of elastic moduli of orthotropic media is presented. Special attention is given to the laminated electrical steel sheets, which are modeled as orthotropic media with nine independent engineering elastic moduli. The elastic moduli are determined specifically for use with finite element vibration analyses. We propose a three-step methodology based on a conventional nonlinear least squares fit between measured and computed natural frequencies. The methodology consists of: (1) successive augmentations of the objective function by increasing the number of modes, (2) initial condition updates, and (3) appropriate selection of the natural frequencies based on their sensitivities on the elastic moduli. Using the results of numerical experiments, it is shown that the proposed method achieves more accurate converged solution than a conventional approach. Finally, the proposed method is applied to measured natural frequencies and mode shapes of the laminated electrical steel sheets. It is shown that the method can successfully identify the orthotropic elastic moduli that can reproduce the measured natural frequencies and frequency response functions by using finite element analyses with a reasonable accuracy.

Nonparametric methods for drought severity estimation at ungauged sites

NASA Astrophysics Data System (ADS)

Sadri, S.; Burn, D. H.

2012-12-01

The objective in frequency analysis is, given extreme events such as drought severity or duration, to estimate the relationship between that event and the associated return periods at a catchment. Neural networks and other artificial intelligence approaches in function estimation and regression analysis are relatively new techniques in engineering, providing an attractive alternative to traditional statistical models. There are, however, few applications of neural networks and support vector machines in the area of severity quantile estimation for drought frequency analysis. In this paper, we compare three methods for this task: multiple linear regression, radial basis function neural networks, and least squares support vector regression (LS-SVR). The area selected for this study includes 32 catchments in the Canadian Prairies. From each catchment drought severities are extracted and fitted to a Pearson type III distribution, which act as observed values. For each method-duration pair, we use a jackknife algorithm to produce estimated values at each site. The results from these three approaches are compared and analyzed, and it is found that LS-SVR provides the best quantile estimates and extrapolating capacity.

First and second order derivatives for optimizing parallel RF excitation waveforms.

PubMed

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. Copyright © 2015 Elsevier Inc. All rights reserved.

First and second order derivatives for optimizing parallel RF excitation waveforms

NASA Astrophysics Data System (ADS)

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

Point-spread function reconstruction in ground-based astronomy by l(1)-l(p) model.

PubMed

Chan, Raymond H; Yuan, Xiaoming; Zhang, Wenxing

2012-11-01

In ground-based astronomy, images of objects in outer space are acquired via ground-based telescopes. However, the imaging system is generally interfered by atmospheric turbulence, and hence images so acquired are blurred with unknown point-spread function (PSF). To restore the observed images, the wavefront of light at the telescope's aperture is utilized to derive the PSF. A model with the Tikhonov regularization has been proposed to find the high-resolution phase gradients by solving a least-squares system. Here we propose the l(1)-l(p) (p=1, 2) model for reconstructing the phase gradients. This model can provide sharper edges in the gradients while removing noise. The minimization models can easily be solved by the Douglas-Rachford alternating direction method of a multiplier, and the convergence rate is readily established. Numerical results are given to illustrate that the model can give better phase gradients and hence a more accurate PSF. As a result, the restored images are much more accurate when compared to the traditional Tikhonov regularization model.

'Where' depends on 'what': a differential functional anatomy for position discrimination in one- versus two-dimensions.

PubMed

Fink, G R; Marshall, J C; Weiss, P H; Shah, N J; Toni, I; Halligan, P W; Zilles, K

2000-01-01

Line bisection is widely used as a clinical test of spatial cognition in patients with left visuospatial neglect after right hemisphere lesion. Surprisingly, many neglect patients who show severe impairment on marking the center of horizontal lines can accurately mark the center of squares. That these patients with left neglect are also typically poor at judging whether lines are correctly prebisected implies that the deficit can be perceptual rather than motoric. These findings suggest a differential neural basis for one- and two-dimensional visual position discrimination that we investigated with functional neuroimaging (fMRI). Normal subjects judged whether, in premarked lines or squares, the mark was placed centrally. Line center judgements differentially activated right parietal cortex, while square center judgements differentially activated the lingual gyrus bilaterally. These distinct neural bases for one- and two-dimensional visuospatial judgements help explain the observed clinical dissociations by showing that as a stimulus becomes a better, more 'object-like' gestalt, the ventral visuoperceptive route assumes more responsibility for assessing position within the object.

Working set selection using functional gain for LS-SVM.

PubMed

Bo, Liefeng; Jiao, Licheng; Wang, Ling

2007-09-01

The efficiency of sequential minimal optimization (SMO) depends strongly on the working set selection. This letter shows how the improvement of SMO in each iteration, named the functional gain (FG), is used to select the working set for least squares support vector machine (LS-SVM). We prove the convergence of the proposed method and give some theoretical support for its performance. Empirical comparisons demonstrate that our method is superior to the maximum violating pair (MVP) working set selection.

Universal Approximation by Using the Correntropy Objective Function.

PubMed

Nayyeri, Mojtaba; Sadoghi Yazdi, Hadi; Maskooki, Alaleh; Rouhani, Modjtaba

2017-10-16

Several objective functions have been proposed in the literature to adjust the input parameters of a node in constructive networks. Furthermore, many researchers have focused on the universal approximation capability of the network based on the existing objective functions. In this brief, we use a correntropy measure based on the sigmoid kernel in the objective function to adjust the input parameters of a newly added node in a cascade network. The proposed network is shown to be capable of approximating any continuous nonlinear mapping with probability one in a compact input sample space. Thus, the convergence is guaranteed. The performance of our method was compared with that of eight different objective functions, as well as with an existing one hidden layer feedforward network on several real regression data sets with and without impulsive noise. The experimental results indicate the benefits of using a correntropy measure in reducing the root mean square error and increasing the robustness to noise.

Automatic correction of intensity nonuniformity from sparseness of gradient distribution in medical images.

PubMed

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P; Gee, James C

2009-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities.

Automatic Correction of Intensity Nonuniformity from Sparseness of Gradient Distribution in Medical Images

PubMed Central

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P.; Gee, James C.

2013-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities. PMID:20426191

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

NASA Technical Reports Server (NTRS)

Pak, Chan-gi

2018-01-01

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on in-house object-oriented optimization tool.

[CHARACTERIZATION OF VESTIBULAR DISORDERS IN THE INJURED PERSONS WITH THE BRAIN CONCUSSION IN ACUTE PERIOD].

PubMed

Skobska, O E; Kadzhaya, N V; Andreyev, O A; Potapov, E V

2015-04-01

There were examined 32 injured persons, ageing (34.1 ± 1.3) yrs at average, for the brain commotion (BC). The adopted protocol SCAT-3 (Standardized Concussion Assessment Tool, 3rd ed.), DHI (Dizziness Handicap Inventory questionnaire), computer stabilography (KS) were applied for the vestibular disorders diagnosis. There was established, that in acute period of BC a dyssociation between regression of objective neurological symptoms and permanence of the BC indices occurs, what confirms a latent disorder of the balance function. Changes of basic indices of statokinesiography, including increase of the vibration amplitude enhancement in general centre of pressure in a saggital square and the BC square (235.3 ± 13.7) mm2 in a modified functional test of Romberg with the closed eyes is possible to apply as objective criteria for the BC diagnosis.

Technique for estimating the 2- to 500-year flood discharges on unregulated streams in rural Missouri

USGS Publications Warehouse

Alexander, Terry W.; Wilson, Gary L.

1995-01-01

A generalized least-squares regression technique was used to relate the 2- to 500-year flood discharges from 278 selected streamflow-gaging stations to statistically significant basin characteristics. The regression relations (estimating equations) were defined for three hydrologic regions (I, II, and III) in rural Missouri. Ordinary least-squares regression analyses indicate that drainage area (Regions I, II, and III) and main-channel slope (Regions I and II) are the only basin characteristics needed for computing the 2- to 500-year design-flood discharges at gaged or ungaged stream locations. The resulting generalized least-squares regression equations provide a technique for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood discharges on unregulated streams in rural Missouri. The regression equations for Regions I and II were developed from stream-flow-gaging stations with drainage areas ranging from 0.13 to 11,500 square miles and 0.13 to 14,000 square miles, and main-channel slopes ranging from 1.35 to 150 feet per mile and 1.20 to 279 feet per mile. The regression equations for Region III were developed from streamflow-gaging stations with drainage areas ranging from 0.48 to 1,040 square miles. Standard errors of estimate for the generalized least-squares regression equations in Regions I, II, and m ranged from 30 to 49 percent.

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

NASA Technical Reports Server (NTRS)

Long, S. A. T.

1974-01-01

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

Statistical procedures for determination and verification of minimum reporting levels for drinking water methods.

PubMed

Winslow, Stephen D; Pepich, Barry V; Martin, John J; Hallberg, George R; Munch, David J; Frebis, Christopher P; Hedrick, Elizabeth J; Krop, Richard A

2006-01-01

The United States Environmental Protection Agency's Office of Ground Water and Drinking Water has developed a single-laboratory quantitation procedure: the lowest concentration minimum reporting level (LCMRL). The LCMRL is the lowest true concentration for which future recovery is predicted to fall, with high confidence (99%), between 50% and 150%. The procedure takes into account precision and accuracy. Multiple concentration replicates are processed through the entire analytical method and the data are plotted as measured sample concentration (y-axis) versus true concentration (x-axis). If the data support an assumption of constant variance over the concentration range, an ordinary least-squares regression line is drawn; otherwise, a variance-weighted least-squares regression is used. Prediction interval lines of 99% confidence are drawn about the regression. At the points where the prediction interval lines intersect with data quality objective lines of 50% and 150% recovery, lines are dropped to the x-axis. The higher of the two values is the LCMRL. The LCMRL procedure is flexible because the data quality objectives (50-150%) and the prediction interval confidence (99%) can be varied to suit program needs. The LCMRL determination is performed during method development only. A simpler procedure for verification of data quality objectives at a given minimum reporting level (MRL) is also presented. The verification procedure requires a single set of seven samples taken through the entire method procedure. If the calculated prediction interval is contained within data quality recovery limits (50-150%), the laboratory performance at the MRL is verified.

46 CFR 168.15-15 - Size.

Code of Federal Regulations, 2013 CFR

2013-10-01

... accommodate, must be marked outside the space. (b) Each room must be of such size that there is at least 1.8 square meters (20 square feet) of deck area and a volume of at least 4.2 cubic meters (150 cubic feet...

46 CFR 168.15-15 - Size.

Code of Federal Regulations, 2014 CFR

2014-10-01

... accommodate, must be marked outside the space. (b) Each room must be of such size that there is at least 1.8 square meters (20 square feet) of deck area and a volume of at least 4.2 cubic meters (150 cubic feet...

Constrained Least Squares Estimators of Oblique Common Factors.

ERIC Educational Resources Information Center

McDonald, Roderick P.

1981-01-01

An expression is given for weighted least squares estimators of oblique common factors of factor analyses, constrained to have the same covariance matrix as the factors they estimate. A proof of the uniqueness of the solution is given. (Author/JKS)

Areal Control Using Generalized Least Squares As An Alternative to Stratification

Treesearch

Raymond L. Czaplewski

2001-01-01

Stratification for both variance reduction and areal control proliferates the number of strata, which causes small sample sizes in many strata. This might compromise statistical efficiency. Generalized least squares can, in principle, replace stratification for areal control.

First-Order System Least-Squares for the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Bochev, P.; Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.

Least square neural network model of the crude oil blending process.

PubMed

Rubio, José de Jesús

2016-06-01

In this paper, the recursive least square algorithm is designed for the big data learning of a feedforward neural network. The proposed method as the combination of the recursive least square and feedforward neural network obtains four advantages over the alone algorithms: it requires less number of regressors, it is fast, it has the learning ability, and it is more compact. Stability, convergence, boundedness of parameters, and local minimum avoidance of the proposed technique are guaranteed. The introduced strategy is applied for the modeling of the crude oil blending process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Simulation of Foam Divot Weight on External Tank Utilizing Least Squares and Neural Network Methods

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Coroneos, Rula M.

2007-01-01

Simulation of divot weight in the insulating foam, associated with the external tank of the U.S. space shuttle, has been evaluated using least squares and neural network concepts. The simulation required models based on fundamental considerations that can be used to predict under what conditions voids form, the size of the voids, and subsequent divot ejection mechanisms. The quadratic neural networks were found to be satisfactory for the simulation of foam divot weight in various tests associated with the external tank. Both linear least squares method and the nonlinear neural network predicted identical results.

Error propagation of partial least squares for parameters optimization in NIR modeling.

PubMed

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-05

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models. Copyright © 2017. Published by Elsevier B.V.

Error propagation of partial least squares for parameters optimization in NIR modeling

NASA Astrophysics Data System (ADS)

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-01

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models.

Arrhenius time-scaled least squares: a simple, robust approach to accelerated stability data analysis for bioproducts.

PubMed

Rauk, Adam P; Guo, Kevin; Hu, Yanling; Cahya, Suntara; Weiss, William F

2014-08-01

Defining a suitable product presentation with an acceptable stability profile over its intended shelf-life is one of the principal challenges in bioproduct development. Accelerated stability studies are routinely used as a tool to better understand long-term stability. Data analysis often employs an overall mass action kinetics description for the degradation and the Arrhenius relationship to capture the temperature dependence of the observed rate constant. To improve predictive accuracy and precision, the current work proposes a least-squares estimation approach with a single nonlinear covariate and uses a polynomial to describe the change in a product attribute with respect to time. The approach, which will be referred to as Arrhenius time-scaled (ATS) least squares, enables accurate, precise predictions to be achieved for degradation profiles commonly encountered during bioproduct development. A Monte Carlo study is conducted to compare the proposed approach with the common method of least-squares estimation on the logarithmic form of the Arrhenius equation and nonlinear estimation of a first-order model. The ATS least squares method accommodates a range of degradation profiles, provides a simple and intuitive approach for data presentation, and can be implemented with ease. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.

Least-Squares Regression and Spectral Residual Augmented Classical Least-Squares Chemometric Models for Stability-Indicating Analysis of Agomelatine and Its Degradation Products: A Comparative Study.

PubMed

Naguib, Ibrahim A; Abdelrahman, Maha M; El Ghobashy, Mohamed R; Ali, Nesma A

2016-01-01

Two accurate, sensitive, and selective stability-indicating methods are developed and validated for simultaneous quantitative determination of agomelatine (AGM) and its forced degradation products (Deg I and Deg II), whether in pure forms or in pharmaceutical formulations. Partial least-squares regression (PLSR) and spectral residual augmented classical least-squares (SRACLS) are two chemometric models that are being subjected to a comparative study through handling UV spectral data in range (215-350 nm). For proper analysis, a three-factor, four-level experimental design was established, resulting in a training set consisting of 16 mixtures containing different ratios of interfering species. An independent test set consisting of eight mixtures was used to validate the prediction ability of the suggested models. The results presented indicate the ability of mentioned multivariate calibration models to analyze AGM, Deg I, and Deg II with high selectivity and accuracy. The analysis results of the pharmaceutical formulations were statistically compared to the reference HPLC method, with no significant differences observed regarding accuracy and precision. The SRACLS model gives comparable results to the PLSR model; however, it keeps the qualitative spectral information of the classical least-squares algorithm for analyzed components.

DIFFERENTIATION OF AURANTII FRUCTUS IMMATURUS AND FRUCTUS PONICIRI TRIFOLIATAE IMMATURUS BY FLOW-INJECTION WITH ULTRAVIOLET SPECTROSCOPIC DETECTION AND PROTON NUCLEAR MAGNETIC RESONANCE USING PARTIAL LEAST-SQUARES DISCRIMINANT ANALYSIS.

PubMed

Zhang, Mengliang; Zhao, Yang; Harrington, Peter de B; Chen, Pei

2016-03-01

Two simple fingerprinting methods, flow-injection coupled to ultraviolet spectroscopy and proton nuclear magnetic resonance, were used for discriminating between Aurantii fructus immaturus and Fructus poniciri trifoliatae immaturus . Both methods were combined with partial least-squares discriminant analysis. In the flow-injection method, four data representations were evaluated: total ultraviolet absorbance chromatograms, averaged ultraviolet spectra, absorbance at 193, 205, 225, and 283 nm, and absorbance at 225 and 283 nm. Prediction rates of 100% were achieved for all data representations by partial least-squares discriminant analysis using leave-one-sample-out cross-validation. The prediction rate for the proton nuclear magnetic resonance data by partial least-squares discriminant analysis with leave-one-sample-out cross-validation was also 100%. A new validation set of data was collected by flow-injection with ultraviolet spectroscopic detection two weeks later and predicted by partial least-squares discriminant analysis models constructed by the initial data representations with no parameter changes. The classification rates were 95% with the total ultraviolet absorbance chromatograms datasets and 100% with the other three datasets. Flow-injection with ultraviolet detection and proton nuclear magnetic resonance are simple, high throughput, and low-cost methods for discrimination studies.

Least squares reconstruction of non-linear RF phase encoded MR data.

PubMed

Salajeghe, Somaie; Babyn, Paul; Sharp, Jonathan C; Sarty, Gordon E

2016-09-01

The numerical feasibility of reconstructing MRI signals generated by RF coils that produce B1 fields with a non-linearly varying spatial phase is explored. A global linear spatial phase variation of B1 is difficult to produce from current confined to RF coils. Here we use regularized least squares inversion, in place of the usual Fourier transform, to reconstruct signals generated in B1 fields with non-linear phase variation. RF encoded signals were simulated for three RF coil configurations: ideal linear, parallel conductors and, circular coil pairs. The simulated signals were reconstructed by Fourier transform and by regularized least squares. The Fourier reconstruction of simulated RF encoded signals from the parallel conductor coil set showed minor distortions over the reconstruction of signals from the ideal linear coil set but the Fourier reconstruction of signals from the circular coil set produced severe geometric distortion. Least squares inversion in all cases produced reconstruction errors comparable to the Fourier reconstruction of the simulated signal from the ideal linear coil set. MRI signals encoded in B1 fields with non-linearly varying spatial phase may be accurately reconstructed using regularized least squares thus pointing the way to the use of simple RF coil designs for RF encoded MRI. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

Flu and Finances: Influenza Outbreaks and Loan Defaults in US Cities, 2004–2012

PubMed Central

Collins, J. Michael; Schmeiser, Maximilian D.

2015-01-01

Objectives. We examined the association between influenza outbreaks in 83 metropolitan areas and credit card and mortgage defaults, as measured in quarterly zip code–level credit data over the period of 2004 to 2012. Methods. We used ordinary least squares, fixed effects, and 2-stage least squares instrumental variables regression strategies to examine the relationship between influenza-related Google searches and 30-, 60-, and 90-day credit card and mortgage delinquency rates. Results. We found that a proxy for influenza outbreaks is associated with a small but statistically significant increase in credit card and mortgage default rates, net of other factors. These effects are largest for 90-day defaults, suggesting that influenza outbreaks have a disproportionate impact on vulnerable borrowers who are already behind on their payments. Conclusions. Overall, it appears there is a relationship between exogenous health shocks (such as influenza) and credit default. The results suggest that consumer finances could benefit from policies that aim to reduce the financial shocks of illness, particularly for vulnerable borrowers. PMID:26180971

Multicategory Composite Least Squares Classifiers

PubMed Central

Park, Seo Young; Liu, Yufeng; Liu, Dacheng; Scholl, Paul

2010-01-01

Classification is a very useful statistical tool for information extraction. In particular, multicategory classification is commonly seen in various applications. Although binary classification problems are heavily studied, extensions to the multicategory case are much less so. In view of the increased complexity and volume of modern statistical problems, it is desirable to have multicategory classifiers that are able to handle problems with high dimensions and with a large number of classes. Moreover, it is necessary to have sound theoretical properties for the multicategory classifiers. In the literature, there exist several different versions of simultaneous multicategory Support Vector Machines (SVMs). However, the computation of the SVM can be difficult for large scale problems, especially for problems with large number of classes. Furthermore, the SVM cannot produce class probability estimation directly. In this article, we propose a novel efficient multicategory composite least squares classifier (CLS classifier), which utilizes a new composite squared loss function. The proposed CLS classifier has several important merits: efficient computation for problems with large number of classes, asymptotic consistency, ability to handle high dimensional data, and simple conditional class probability estimation. Our simulated and real examples demonstrate competitive performance of the proposed approach. PMID:21218128

A CFD-based aerodynamic design procedure for hypersonic wind-tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.

1993-01-01

A new procedure which unifies the best of current classical design practices, computational fluid dynamics (CFD), and optimization procedures is demonstrated for designing the aerodynamic lines of hypersonic wind-tunnel nozzles. The new procedure can be used to design hypersonic wind tunnel nozzles with thick boundary layers where the classical design procedure has been shown to break down. An efficient CFD code, which solves the parabolized Navier-Stokes (PNS) equations using an explicit upwind algorithm, is coupled to a least-squares (LS) optimization procedure. A LS problem is formulated to minimize the difference between the computed flow field and the objective function, consisting of the centerline Mach number distribution and the exit Mach number and flow angle profiles. The aerodynamic lines of the nozzle are defined using a cubic spline, the slopes of which are optimized with the design procedure. The advantages of the new procedure are that it allows full use of powerful CFD codes in the design process, solves an optimization problem to determine the new contour, can be used to design new nozzles or improve sections of existing nozzles, and automatically compensates the nozzle contour for viscous effects as part of the unified design procedure. The new procedure is demonstrated by designing two Mach 15, a Mach 12, and a Mach 18 helium nozzles. The flexibility of the procedure is demonstrated by designing the two Mach 15 nozzles using different constraints, the first nozzle for a fixed length and exit diameter and the second nozzle for a fixed length and throat diameter. The computed flow field for the Mach 15 least squares parabolized Navier-Stokes (LS/PNS) designed nozzle is compared with the classically designed nozzle and demonstrates a significant improvement in the flow expansion process and uniform core region.

Long-term optical flux and colour variability in quasars

NASA Astrophysics Data System (ADS)

Sukanya, N.; Stalin, C. S.; Jeyakumar, S.; Praveen, D.; Dhani, Arnab; Damle, R.

2016-02-01

We have used optical V and R band observations from the Massive Compact Halo Object (MACHO) project on a sample of 59 quasars behind the Magellanic clouds to study their long term optical flux and colour variations. These quasars, lying in the redshift range of 0.2 < z < 2.8 and having apparent V band magnitudes between 16.6 and 20.1 mag, have observations ranging from 49 to 1353 epochs spanning over 7.5 yr with frequency of sampling between 2 to 10 days. All the quasars show variability during the observing period. The normalised excess variance (Fvar) in V and R bands are in the range 0.2% < FVvar < 1.6% and 0.1% < FRvar < 1.5% respectively. In a large fraction of the sources, Fvar is larger in the V band compared to the R band. From the z-transformed discrete cross-correlation function analysis, we find that there is no lag between the V and R band variations. Adopting the Markov Chain Monte Carlo (MCMC) approach, and properly taking into account the correlation between the errors in colours and magnitudes, it is found that the majority of sources show a bluer when brighter trend, while a minor fraction of quasars show the opposite behaviour. This is similar to the results obtained from another two independent algorithms, namely the weighted linear least squares fit (FITEXY) and the bivariate correlated errors and intrinsic scatter regression (BCES). However, the ordinary least squares (OLS) fit, normally used in the colour variability studies of quasars, indicates that all the quasars studied here show a bluer when brighter trend. It is therefore very clear that the OLS algorithm cannot be used for the study of colour variability in quasars.

Penalized Weighted Least-Squares Approach to Sinogram Noise Reduction and Image Reconstruction for Low-Dose X-Ray Computed Tomography

PubMed Central

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-01-01

Reconstructing low-dose X-ray CT (computed tomography) images is a noise problem. This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first- and second-order noise moments and the penalty models signal spatial correlations. Three different implementations were studied for the PWLS minimization. One utilizes a MRF (Markov random field) Gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the PWLS cost function by iterative Gauss-Seidel algorithm. Another employs Karhunen-Loève (KL) transform to de-correlate data signals among nearby views and minimizes the PWLS adaptively to each KL component by analytical calculation, where the spatial correlation among nearby bins is modeled by the same Gibbs functional. The third one models the spatial correlations among image pixels in image domain also by a MRF Gibbs functional and minimizes the PWLS by iterative successive over-relaxation algorithm. In these three implementations, a quadratic functional regularization was chosen for the MRF model. Phantom experiments showed a comparable performance of these three PWLS-based methods in terms of suppressing noise-induced streak artifacts and preserving resolution in the reconstructed images. Computer simulations concurred with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS implementation may have the advantage in terms of computation for high-resolution dynamic low-dose CT imaging. PMID:17024831

Navy Fuel Composition and Screening Tool (FCAST) v2.8

DTIC Science & Technology

2016-05-10

allowed us to develop partial least squares (PLS) models based on gas chromatography–mass spectrometry (GC-MS) data that predict fuel properties. The...Chemometric property modeling Partial least squares PLS Compositional profiler Naval Air Systems Command Air-4.4.5 Patuxent River Naval Air Station Patuxent...Cumulative predicted residual error sum of squares DiEGME Diethylene glycol monomethyl ether FCAST Fuel Composition and Screening Tool FFP Fit for

Development of a kernel function for clinical data.

PubMed

Daemen, Anneleen; De Moor, Bart

2009-01-01

For most diseases and examinations, clinical data such as age, gender and medical history guides clinical management, despite the rise of high-throughput technologies. To fully exploit such clinical information, appropriate modeling of relevant parameters is required. As the widely used linear kernel function has several disadvantages when applied to clinical data, we propose a new kernel function specifically developed for this data. This "clinical kernel function" more accurately represents similarities between patients. Evidently, three data sets were studied and significantly better performances were obtained with a Least Squares Support Vector Machine when based on the clinical kernel function compared to the linear kernel function.

Sensory Profile and Consumer Acceptability of Prebiotic White Chocolate with Sucrose Substitutes and the Addition of Goji Berry (Lycium barbarum).

PubMed

Morais Ferreira, Janaína Madruga; Azevedo, Bruna Marcacini; Luccas, Valdecir; Bolini, Helena Maria André

2017-03-01

Functional food is a product containing nutrients that provide health benefits beyond basic nutrition. The objective of the present study was to evaluate the descriptive sensory profile and consumers' acceptance of functional (prebiotic) white chocolates with and without the addition of an antioxidant source (goji berry [GB]) and sucrose replacement. The descriptive sensory profile was determined by quantitative descriptive analysis (QDA) with trained assessors (n = 12), and the acceptance test was performed with 120 consumers. The correlation of descriptive and hedonic data was determined by partial least squares (PLS). The results of QDA indicated that GB reduces the perception of most aroma and flavor attributes, and enhances the bitter taste, bitter aftertaste, astringency, and most of the texture attributes. The consumers' acceptance of the chocolates was positive for all sensory characteristics, with acceptance scores above 6 on a 9-point scale. According to the PLS regression analysis, the descriptors cream color and cocoa butter flavor contributed positively to the acceptance of functional white chocolates. Therefore, prebiotic white chocolate with or without the addition of GB is innovative and can attract consumers, due to its functional properties, being a promising alternative for the food industry. © 2017 Institute of Food Technologists®.

Functional unit, technological dynamics, and scaling properties for the life cycle energy of residences.

PubMed

Frijia, Stephane; Guhathakurta, Subhrajit; Williams, Eric

2012-02-07

Prior LCA studies take the operational phase to include all energy use within a residence, implying a functional unit of all household activities, but then exclude related supply chains such as production of food, appliances, and household chemicals. We argue that bounding the functional unit to provision of a climate controlled space better focuses the LCA on the building, rather than activities that occur within a building. The second issue explored in this article is how technological change in the operational phase affects life cycle energy. Heating and cooling equipment is replaced at least several times over the lifetime of a residence; improved efficiency of newer equipment affects life cycle energy use. The third objective is to construct parametric models to describe LCA results for a family of related products. We explore these three issues through a case study of energy use of residences: one-story and two-story detached homes, 1,500-3,500 square feet in area, located in Phoenix, Arizona, built in 2002 and retired in 2051. With a restricted functional unit and accounting for technological progress, approximately 30% of a building's life cycle energy can be attributed to materials and construction, compared to 0.4-11% in previous studies.

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

PubMed

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

Analysis of Lunar Seismic Signals: Determination of Instrumental Parameters and Seismic Velocity Distributions. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Horvath, P.

1979-01-01

Inverse filters were designed to correct the effect of instrumental response, coupling of the seismometer to the ground, and near surface structures. The least squares technique was used to determine the instrumental constants and the transfer functions of the long period lunar seismographs. The influence of noise and the results of these calculations are discussed.

Crown area equations for 13 species of trees and shrubs in northern California and southwestern Oregon

Treesearch

Fabian C.C. Uzoh; Martin W. Ritchie

1996-01-01

The equations presented predict crown area for 13 species of trees and shrubs which may be found growing in competition with commercial conifers during early stages of stand development. The equations express crown area as a function of basal area and height. Parameters were estimated for each species individually using weighted nonlinear least square regression.

Cluster Differences Scaling with a Within-Clusters Loss Component and a Fuzzy Successive Approximation Strategy To Avoid Local Minima.

ERIC Educational Resources Information Center

Heiser, Willem J.; And Others

1997-01-01

The least squares loss function of cluster differences scaling, originally defined only on residuals of pairs allocated to different clusters, is extended with a loss component for pairs allocated to the same cluster. Findings show that this makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates. (SLD)

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.

An Orbit And Dispersion Correction Scheme for the PEP II

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

Cai, Y.; Donald, M.; Shoaee, H.

2011-09-01

To achieve optimum luminosity in a storage ring it is vital to control the residual vertical dispersion. In the original PEP storage ring, a scheme to control the residual dispersion function was implemented using the ring orbit as the controlling element. The 'best' orbit not necessarily giving the lowest vertical dispersion. A similar scheme has been implemented in both the on-line control code and in the simulation code LEGO. The method involves finding the response matrices (sensitivity of orbit/dispersion at each Beam-Position-Monitor (BPM) to each orbit corrector) and solving in a least squares sense for minimum orbit, dispersion function ormore » both. The optimum solution is usually a subset of the full least squares solution. A scheme of simultaneously correcting the orbits and dispersion has been implemented in the simulation code and on-line control system for PEP-II. The scheme is based on the eigenvector decomposition method. An important ingredient of the scheme is to choose the optimum eigenvectors that minimize the orbit, dispersion and corrector strength. Simulations indicate this to be a very effective way to control the vertical residual dispersion.« less

Temperature dependence of emission measure in solar X-ray plasmas. 1: Non-flaring active regions

NASA Technical Reports Server (NTRS)

Phillips, K. J. H.

1974-01-01

X-ray and ultraviolet line emission from hot, optically thin material forming coronal active regions on the sun may be described in terms of an emission measure distribution function, Phi (T). A relationship is developed between line flux and Phi (T), a theory which assumes that the electron density is a single-valued function of temperature. The sources of error involved in deriving Phi (T) from a set of line fluxes are examined in some detail. These include errors in atomic data (collisional excitation rates, assessment of other mechanisms for populating excited states of transitions, element abundances, ion concentrations, oscillator strengths) and errors in observed line fluxes arising from poorly - known instrumental responses. Two previous analyses are discussed in which Phi (T) for a non-flaring active region is derived. A least squares method of Batstone uses X-ray data of low statistical significance, a fact which appears to influence the results considerably. Two methods for finding Phi (T) ab initio are developed. The coefficients are evaluated by least squares. These two methods should have application not only to active-region plasmas, but also to hot, flare-produced plasmas.

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard; Felus, Yaron A.

2008-06-01

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model ( Y- E Y = ( X- E X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E Y and E X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler-Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335-342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.

Mitigating Errors in External Respiratory Surrogate-Based Models of Tumor Position

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

Malinowski, Kathleen T.; Fischell Department of Bioengineering, University of Maryland, College Park, MD; McAvoy, Thomas J.

2012-04-01

Purpose: To investigate the effect of tumor site, measurement precision, tumor-surrogate correlation, training data selection, model design, and interpatient and interfraction variations on the accuracy of external marker-based models of tumor position. Methods and Materials: Cyberknife Synchrony system log files comprising synchronously acquired positions of external markers and the tumor from 167 treatment fractions were analyzed. The accuracy of Synchrony, ordinary-least-squares regression, and partial-least-squares regression models for predicting the tumor position from the external markers was evaluated. The quantity and timing of the data used to build the predictive model were varied. The effects of tumor-surrogate correlation and the precisionmore » in both the tumor and the external surrogate position measurements were explored by adding noise to the data. Results: The tumor position prediction errors increased during the duration of a fraction. Increasing the training data quantities did not always lead to more accurate models. Adding uncorrelated noise to the external marker-based inputs degraded the tumor-surrogate correlation models by 16% for partial-least-squares and 57% for ordinary-least-squares. External marker and tumor position measurement errors led to tumor position prediction changes 0.3-3.6 times the magnitude of the measurement errors, varying widely with model algorithm. The tumor position prediction errors were significantly associated with the patient index but not with the fraction index or tumor site. Partial-least-squares was as accurate as Synchrony and more accurate than ordinary-least-squares. Conclusions: The accuracy of surrogate-based inferential models of tumor position was affected by all the investigated factors, except for the tumor site and fraction index.« less

Child Maltreatment and Executive Functioning in Middle Adulthood: A Prospective Examination

PubMed Central

Nikulina, Valentina; Widom, Cathy Spatz

2013-01-01

Objective There is extensive evidence of negative consequences of childhood maltreatment for IQ, academic achievement, and post-traumatic stress disorder (PTSD) and increased attention to neurobiological consequences. However, few prospective studies have assessed the long-term effects of abuse and neglect on executive functioning. The current study examines whether childhood abuse and neglect predicts components of executive functioning and nonverbal reasoning ability in middle adulthood and whether PTSD moderates this relationship. Method Using a prospective cohort design, a large sample (N = 792) of court-substantiated cases of childhood physical and sexual abuse and neglect (ages 0-11) and matched controls were followed into adulthood (mean age = 41). Executive functioning was assessed with the Trail Making B test and non-verbal reasoning with Matrix Reasoning. PTSD (DSM-III-R lifetime diagnosis) was assessed at age 29. Data were analyzed using ordinary least squares regressions, controlling for age, sex, and race and possible confounds of IQ, depression, and excessive alcohol use. Results In multivariate analyses, childhood maltreatment overall and childhood neglect predicted poorer executive functioning and non-verbal reasoning at age 41, whereas physical and sexual abuse did not. A past history of PTSD did not mediate or moderate these relations. Conclusions Childhood maltreatment and neglect specifically have a significant long-term impact on important aspects of adult neuropsychological functioning. These findings suggest the need for targeted efforts dedicated to interventions for neglected children. PMID:23876115

Development of a partial least squares-artificial neural network (PLS-ANN) hybrid model for the prediction of consumer liking scores of ready-to-drink green tea beverages.

PubMed

Yu, Peigen; Low, Mei Yin; Zhou, Weibiao

2018-01-01

In order to develop products that would be preferred by consumers, the effects of the chemical compositions of ready-to-drink green tea beverages on consumer liking were studied through regression analyses. Green tea model systems were prepared by dosing solutions of 0.1% green tea extract with differing concentrations of eight flavour keys deemed to be important for green tea aroma and taste, based on a D-optimal experimental design, before undergoing commercial sterilisation. Sensory evaluation of the green tea model system was carried out using an untrained consumer panel to obtain hedonic liking scores of the samples. Regression models were subsequently trained to objectively predict the consumer liking scores of the green tea model systems. A linear partial least squares (PLS) regression model was developed to describe the effects of the eight flavour keys on consumer liking, with a coefficient of determination (R 2 ) of 0.733, and a root-mean-square error (RMSE) of 3.53%. The PLS model was further augmented with an artificial neural network (ANN) to establish a PLS-ANN hybrid model. The established hybrid model was found to give a better prediction of consumer liking scores, based on its R 2 (0.875) and RMSE (2.41%). Copyright © 2017 Elsevier Ltd. All rights reserved.

A Model and Simple Iterative Algorithm for Redundancy Analysis.

ERIC Educational Resources Information Center

Fornell, Claes; And Others

1988-01-01

This paper shows that redundancy maximization with J. K. Johansson's extension can be accomplished via a simple iterative algorithm based on H. Wold's Partial Least Squares. The model and the iterative algorithm for the least squares approach to redundancy maximization are presented. (TJH)

Generalized Structured Component Analysis

ERIC Educational Resources Information Center

Hwang, Heungsun; Takane, Yoshio

2004-01-01

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method…

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

NASA Astrophysics Data System (ADS)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

Correspondence and Least Squares Analyses of Soil and Rock Compositions for the Viking Lander 1 and Pathfinder Sites

NASA Technical Reports Server (NTRS)

Larsen, K. W.; Arvidson, R. E.; Jolliff, B. L.; Clark, B. C.

2000-01-01

Correspondence and Least Squares Mixing Analysis techniques are applied to the chemical composition of Viking 1 soils and Pathfinder rocks and soils. Implications for the parent composition of local and global materials are discussed.

Spectral analysis of GEOS-3 altimeter data and frequency domain collocation. [to estimate gravity anomalies

NASA Technical Reports Server (NTRS)

Eren, K.

1980-01-01

The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.

Growth kinetics of borided layers: Artificial neural network and least square approaches

NASA Astrophysics Data System (ADS)

Campos, I.; Islas, M.; Ramírez, G.; VillaVelázquez, C.; Mota, C.

2007-05-01

The present study evaluates the growth kinetics of the boride layer Fe 2B in AISI 1045 steel, by means of neural networks and the least square techniques. The Fe 2B phase was formed at the material surface using the paste boriding process. The surface boron potential was modified considering different boron paste thicknesses, with exposure times of 2, 4 and 6 h, and treatment temperatures of 1193, 1223 and 1273 K. The neural network and the least square models were set by the layer thickness of Fe 2B phase, and assuming that the growth of the boride layer follows a parabolic law. The reliability of the techniques used is compared with a set of experiments at a temperature of 1223 K with 5 h of treatment time and boron potentials of 2, 3, 4 and 5 mm. The results of the Fe 2B layer thicknesses show a mean error of 5.31% for the neural network and 3.42% for the least square method.

Measurement System Characterization in the Presence of Measurement Errors

NASA Technical Reports Server (NTRS)

Commo, Sean A.

2012-01-01

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

NASA Astrophysics Data System (ADS)

Olivares, A.; Górriz, J. M.; Ramírez, J.; Olivares, G.

2011-02-01

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed.

Operational Risk Measurement of Chinese Commercial Banks Based on Extreme Value Theory

NASA Astrophysics Data System (ADS)

Song, Jiashan; Li, Yong; Ji, Feng; Peng, Cheng

The financial institutions and supervision institutions have all agreed on strengthening the measurement and management of operational risks. This paper attempts to build a model on the loss of operational risks basing on Peak Over Threshold model, emphasizing on weighted least square, which improved Hill’s estimation method, while discussing the situation of small sample, and fix the sample threshold more objectively basing on the media-published data of primary banks loss on operational risk from 1994 to 2007.

Steady potential solver for unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Dan

1994-01-01

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Kernel machines for epilepsy diagnosis via EEG signal classification: a comparative study.

PubMed

Lima, Clodoaldo A M; Coelho, André L V

2011-10-01

We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely, Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality). Copyright © 2011 Elsevier B.V. All rights reserved.

Application of Partial Least Square (PLS) Analysis on Fluorescence Data of 8-Anilinonaphthalene-1-Sulfonic Acid, a Polarity Dye, for Monitoring Water Adulteration in Ethanol Fuel.

PubMed

Kumar, Keshav; Mishra, Ashok Kumar

2015-07-01

Fluorescence characteristic of 8-anilinonaphthalene-1-sulfonic acid (ANS) in ethanol-water mixture in combination with partial least square (PLS) analysis was used to propose a simple and sensitive analytical procedure for monitoring the adulteration of ethanol by water. The proposed analytical procedure was found to be capable of detecting even small adulteration level of ethanol by water. The robustness of the procedure is evident from the statistical parameters such as square of correlation coefficient (R(2)), root mean square of calibration (RMSEC) and root mean square of prediction (RMSEP) that were found to be well with in the acceptable limits.