Real-time simulation of large-scale floods

NASA Astrophysics Data System (ADS)

Liu, Q.; Qin, Y.; Li, G. D.; Liu, Z.; Cheng, D. J.; Zhao, Y. H.

2016-08-01

According to the complex real-time water situation, the real-time simulation of large-scale floods is very important for flood prevention practice. Model robustness and running efficiency are two critical factors in successful real-time flood simulation. This paper proposed a robust, two-dimensional, shallow water model based on the unstructured Godunov- type finite volume method. A robust wet/dry front method is used to enhance the numerical stability. An adaptive method is proposed to improve the running efficiency. The proposed model is used for large-scale flood simulation on real topography. Results compared to those of MIKE21 show the strong performance of the proposed model.

Robust phase retrieval of complex-valued object in phase modulation by hybrid Wirtinger flow method

NASA Astrophysics Data System (ADS)

Wei, Zhun; Chen, Wen; Yin, Tiantian; Chen, Xudong

2017-09-01

This paper presents a robust iterative algorithm, known as hybrid Wirtinger flow (HWF), for phase retrieval (PR) of complex objects from noisy diffraction intensities. Numerical simulations indicate that the HWF method consistently outperforms conventional PR methods in terms of both accuracy and convergence rate in multiple phase modulations. The proposed algorithm is also more robust to low oversampling ratios, loose constraints, and noisy environments. Furthermore, compared with traditional Wirtinger flow, sample complexity is largely reduced. It is expected that the proposed HWF method will find applications in the rapidly growing coherent diffractive imaging field for high-quality image reconstruction with multiple modulations, as well as other disciplines where PR is needed.

Five-equation and robust three-equation methods for solution verification of large eddy simulation

NASA Astrophysics Data System (ADS)

Dutta, Rabijit; Xing, Tao

2018-02-01

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations: A New Approach Based on the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Himansu, Ananda; Loh, Ching-Yuen; Wang, Xiao-Yen; Yu, Shang-Tao

2003-01-01

This paper reports on a significant advance in the area of non-reflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of the development of the space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics-based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains their unique robustness and accuracy in terms of the conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction

NASA Astrophysics Data System (ADS)

Kavetski, Dmitri; Clark, Martyn P.

2010-10-01

Despite the widespread use of conceptual hydrological models in environmental research and operations, they remain frequently implemented using numerically unreliable methods. This paper considers the impact of the time stepping scheme on model analysis (sensitivity analysis, parameter optimization, and Markov chain Monte Carlo-based uncertainty estimation) and prediction. It builds on the companion paper (Clark and Kavetski, 2010), which focused on numerical accuracy, fidelity, and computational efficiency. Empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions. (1) Unreliable time stepping schemes, in particular, fixed-step explicit methods, suffer from troublesome numerical artifacts that severely deform the objective function of the model. These deformations are not rare isolated instances but can arise in any model structure, in any catchment, and under common hydroclimatic conditions. (2) Sensitivity analysis can be severely contaminated by numerical errors, often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations. (3) Robust time stepping schemes generally produce "better behaved" objective functions, free of spurious local optima, and with sufficient numerical continuity to permit parameter optimization using efficient quasi Newton methods. When implemented within a multistart framework, modern Newton-type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers. (4) Unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states. (5) Even when interactions between hydrological parameters and numerical errors provide "the right result for the wrong reason" and the calibrated model performance appears adequate, unreliable time stepping schemes make the model unnecessarily fragile in predictive mode, undermining validation assessments and operational use. Erroneous or misleading conclusions of model analysis and prediction arising from numerical artifacts in hydrological models are intolerable, especially given that robust numerics are accepted as mainstream in other areas of science and engineering. We hope that the vivid empirical findings will encourage the conceptual hydrological community to close its Pandora's box of numerical problems, paving the way for more meaningful model application and interpretation.

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

A kriging metamodel-assisted robust optimization method based on a reverse model

NASA Astrophysics Data System (ADS)

Zhou, Hui; Zhou, Qi; Liu, Congwei; Zhou, Taotao

2018-02-01

The goal of robust optimization methods is to obtain a solution that is both optimum and relatively insensitive to uncertainty factors. Most existing robust optimization approaches use outer-inner nested optimization structures where a large amount of computational effort is required because the robustness of each candidate solution delivered from the outer level should be evaluated in the inner level. In this article, a kriging metamodel-assisted robust optimization method based on a reverse model (K-RMRO) is first proposed, in which the nested optimization structure is reduced into a single-loop optimization structure to ease the computational burden. Ignoring the interpolation uncertainties from kriging, K-RMRO may yield non-robust optima. Hence, an improved kriging-assisted robust optimization method based on a reverse model (IK-RMRO) is presented to take the interpolation uncertainty of kriging metamodel into consideration. In IK-RMRO, an objective switching criterion is introduced to determine whether the inner level robust optimization or the kriging metamodel replacement should be used to evaluate the robustness of design alternatives. The proposed criterion is developed according to whether or not the robust status of the individual can be changed because of the interpolation uncertainties from the kriging metamodel. Numerical and engineering cases are used to demonstrate the applicability and efficiency of the proposed approach.

Quantifying spatial distribution of spurious mixing in ocean models.

PubMed

Ilıcak, Mehmet

2016-12-01

Numerical mixing is inevitable for ocean models due to tracer advection schemes. Until now, there is no robust way to identify the regions of spurious mixing in ocean models. We propose a new method to compute the spatial distribution of the spurious diapycnic mixing in an ocean model. This new method is an extension of available potential energy density method proposed by Winters and Barkan (2013). We test the new method in lock-exchange and baroclinic eddies test cases. We can quantify the amount and the location of numerical mixing. We find high-shear areas are the main regions which are susceptible to numerical truncation errors. We also test the new method to quantify the numerical mixing in different horizontal momentum closures. We conclude that Smagorinsky viscosity has less numerical mixing than the Leith viscosity using the same non-dimensional constant.

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

Computational methods of robust controller design for aerodynamic flutter suppression

NASA Technical Reports Server (NTRS)

Anderson, L. R.

1981-01-01

The development of Riccati iteration, a tool for the design and analysis of linear control systems is examined. First, Riccati iteration is applied to the problem of pole placement and order reduction in two-time scale control systems. Order reduction, yielding a good approximation to the original system, is demonstrated using a 16th order linear model of a turbofan engine. Next, a numerical method for solving the Riccati equation is presented and demonstrated for a set of eighth order random examples. A literature review of robust controller design methods follows which includes a number of methods for reducing the trajectory and performance index sensitivity in linear regulators. Lastly, robust controller design for large parameter variations is discussed.

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 1; The Two Dimensional Time Marching Schemes

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1998-01-01

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Variable fidelity robust optimization of pulsed laser orbital debris removal under epistemic uncertainty

NASA Astrophysics Data System (ADS)

Hou, Liqiang; Cai, Yuanli; Liu, Jin; Hou, Chongyuan

2016-04-01

A variable fidelity robust optimization method for pulsed laser orbital debris removal (LODR) under uncertainty is proposed. Dempster-shafer theory of evidence (DST), which merges interval-based and probabilistic uncertainty modeling, is used in the robust optimization. The robust optimization method optimizes the performance while at the same time maximizing its belief value. A population based multi-objective optimization (MOO) algorithm based on a steepest descent like strategy with proper orthogonal decomposition (POD) is used to search robust Pareto solutions. Analytical and numerical lifetime predictors are used to evaluate the debris lifetime after the laser pulses. Trust region based fidelity management is designed to reduce the computational cost caused by the expensive model. When the solutions fall into the trust region, the analytical model is used to reduce the computational cost. The proposed robust optimization method is first tested on a set of standard problems and then applied to the removal of Iridium 33 with pulsed lasers. It will be shown that the proposed approach can identify the most robust solutions with minimum lifetime under uncertainty.

Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.

PubMed

Li, Ben; Stenstrom, M K

2014-01-01

One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

NASA Astrophysics Data System (ADS)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute fluxes - where Hydrus simulations may fail to converge - no numerical problem appears, and ii) accuracy of simulations even for loose spatial domain discretisations, which can only be obtained by Hydrus with fine discretisations.

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations - A New Approach based on the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Chang, S.-C.; Himansu, A.; Loh, C.-Y.; Wang, X.-Y.; Yu, S.-T.J.

2005-01-01

This paper reports on a significant advance in the area of nonreflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of t he development of t he space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics- based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains t heir unique robustness and accuracy in terms of t he conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Fast and robust reconstruction for fluorescence molecular tomography via a sparsity adaptive subspace pursuit method.

PubMed

Ye, Jinzuo; Chi, Chongwei; Xue, Zhenwen; Wu, Ping; An, Yu; Xu, Han; Zhang, Shuang; Tian, Jie

2014-02-01

Fluorescence molecular tomography (FMT), as a promising imaging modality, can three-dimensionally locate the specific tumor position in small animals. However, it remains challenging for effective and robust reconstruction of fluorescent probe distribution in animals. In this paper, we present a novel method based on sparsity adaptive subspace pursuit (SASP) for FMT reconstruction. Some innovative strategies including subspace projection, the bottom-up sparsity adaptive approach, and backtracking technique are associated with the SASP method, which guarantees the accuracy, efficiency, and robustness for FMT reconstruction. Three numerical experiments based on a mouse-mimicking heterogeneous phantom have been performed to validate the feasibility of the SASP method. The results show that the proposed SASP method can achieve satisfactory source localization with a bias less than 1mm; the efficiency of the method is much faster than mainstream reconstruction methods; and this approach is robust even under quite ill-posed condition. Furthermore, we have applied this method to an in vivo mouse model, and the results demonstrate the feasibility of the practical FMT application with the SASP method.

A Robust Shape Reconstruction Method for Facial Feature Point Detection.

PubMed

Tan, Shuqiu; Chen, Dongyi; Guo, Chenggang; Huang, Zhiqi

2017-01-01

Facial feature point detection has been receiving great research advances in recent years. Numerous methods have been developed and applied in practical face analysis systems. However, it is still a quite challenging task because of the large variability in expression and gestures and the existence of occlusions in real-world photo shoot. In this paper, we present a robust sparse reconstruction method for the face alignment problems. Instead of a direct regression between the feature space and the shape space, the concept of shape increment reconstruction is introduced. Moreover, a set of coupled overcomplete dictionaries termed the shape increment dictionary and the local appearance dictionary are learned in a regressive manner to select robust features and fit shape increments. Additionally, to make the learned model more generalized, we select the best matched parameter set through extensive validation tests. Experimental results on three public datasets demonstrate that the proposed method achieves a better robustness over the state-of-the-art methods.

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

Development of Numerical Methods to Estimate the Ohmic Breakdown Scenarios of a Tokamak

NASA Astrophysics Data System (ADS)

Yoo, Min-Gu; Kim, Jayhyun; An, Younghwa; Hwang, Yong-Seok; Shim, Seung Bo; Lee, Hae June; Na, Yong-Su

2011-10-01

The ohmic breakdown is a fundamental method to initiate the plasma in a tokamak. For the robust breakdown, ohmic breakdown scenarios have to be carefully designed by optimizing the magnetic field configurations to minimize the stray magnetic fields. This research focuses on development of numerical methods to estimate the ohmic breakdown scenarios by precise analysis of the magnetic field configurations. This is essential for the robust and optimal breakdown and start-up of fusion devices especially for ITER and its beyond equipped with low toroidal electric field (ET <= 0.3 V/m). A field-line-following analysis code based on the Townsend avalanche theory and a particle simulation code are developed to analyze the breakdown characteristics of actual complex magnetic field configurations including the stray magnetic fields in tokamaks. They are applied to the ohmic breakdown scenarios of tokamaks such as KSTAR and VEST and compared with experiments.

Robust recognition of handwritten numerals based on dual cooperative network

NASA Technical Reports Server (NTRS)

Lee, Sukhan; Choi, Yeongwoo

1992-01-01

An approach to robust recognition of handwritten numerals using two operating parallel networks is presented. The first network uses inputs in Cartesian coordinates, and the second network uses the same inputs transformed into polar coordinates. How the proposed approach realizes the robustness to local and global variations of input numerals by handling inputs both in Cartesian coordinates and in its transformed Polar coordinates is described. The required network structures and its learning scheme are discussed. Experimental results show that by tracking only a small number of distinctive features for each teaching numeral in each coordinate, the proposed system can provide robust recognition of handwritten numerals.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

A Gradient Taguchi Method for Engineering Optimization

NASA Astrophysics Data System (ADS)

Hwang, Shun-Fa; Wu, Jen-Chih; He, Rong-Song

2017-10-01

To balance the robustness and the convergence speed of optimization, a novel hybrid algorithm consisting of Taguchi method and the steepest descent method is proposed in this work. Taguchi method using orthogonal arrays could quickly find the optimum combination of the levels of various factors, even when the number of level and/or factor is quite large. This algorithm is applied to the inverse determination of elastic constants of three composite plates by combining numerical method and vibration testing. For these problems, the proposed algorithm could find better elastic constants in less computation cost. Therefore, the proposed algorithm has nice robustness and fast convergence speed as compared to some hybrid genetic algorithms.

Nonlinear robust control of hypersonic aircrafts with interactions between flight dynamics and propulsion systems.

PubMed

Li, Zhaoying; Zhou, Wenjie; Liu, Hao

2016-09-01

This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

NASA Astrophysics Data System (ADS)

Crevoisier, David; Chanzy, André; Voltz, Marc

2009-06-01

Ross [Ross PJ. Modeling soil water and solute transport - fast, simplified numerical solutions. Agron J 2003;95:1352-61] developed a fast, simplified method for solving Richards' equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988;3:1-15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D.

Tabu Search enhances network robustness under targeted attacks

NASA Astrophysics Data System (ADS)

Sun, Shi-wen; Ma, Yi-lin; Li, Rui-qi; Wang, Li; Xia, Cheng-yi

2016-03-01

We focus on the optimization of network robustness with respect to intentional attacks on high-degree nodes. Given an existing network, this problem can be considered as a typical single-objective combinatorial optimization problem. Based on the heuristic Tabu Search optimization algorithm, a link-rewiring method is applied to reconstruct the network while keeping the degree of every node unchanged. Through numerical simulations, BA scale-free network and two real-world networks are investigated to verify the effectiveness of the proposed optimization method. Meanwhile, we analyze how the optimization affects other topological properties of the networks, including natural connectivity, clustering coefficient and degree-degree correlation. The current results can help to improve the robustness of existing complex real-world systems, as well as to provide some insights into the design of robust networks.

Horsetail matching: a flexible approach to optimization under uncertainty

NASA Astrophysics Data System (ADS)

Cook, L. W.; Jarrett, J. P.

2018-04-01

It is important to design engineering systems to be robust with respect to uncertainties in the design process. Often, this is done by considering statistical moments, but over-reliance on statistical moments when formulating a robust optimization can produce designs that are stochastically dominated by other feasible designs. This article instead proposes a formulation for optimization under uncertainty that minimizes the difference between a design's cumulative distribution function and a target. A standard target is proposed that produces stochastically non-dominated designs, but the formulation also offers enough flexibility to recover existing approaches for robust optimization. A numerical implementation is developed that employs kernels to give a differentiable objective function. The method is applied to algebraic test problems and a robust transonic airfoil design problem where it is compared to multi-objective, weighted-sum and density matching approaches to robust optimization; several advantages over these existing methods are demonstrated.

A P-Norm Robust Feature Extraction Method for Identifying Differentially Expressed Genes

PubMed Central

Liu, Jian; Liu, Jin-Xing; Gao, Ying-Lian; Kong, Xiang-Zhen; Wang, Xue-Song; Wang, Dong

2015-01-01

In current molecular biology, it becomes more and more important to identify differentially expressed genes closely correlated with a key biological process from gene expression data. In this paper, based on the Schatten p-norm and Lp-norm, a novel p-norm robust feature extraction method is proposed to identify the differentially expressed genes. In our method, the Schatten p-norm is used as the regularization function to obtain a low-rank matrix and the Lp-norm is taken as the error function to improve the robustness to outliers in the gene expression data. The results on simulation data show that our method can obtain higher identification accuracies than the competitive methods. Numerous experiments on real gene expression data sets demonstrate that our method can identify more differentially expressed genes than the others. Moreover, we confirmed that the identified genes are closely correlated with the corresponding gene expression data. PMID:26201006

A P-Norm Robust Feature Extraction Method for Identifying Differentially Expressed Genes.

PubMed

Liu, Jian; Liu, Jin-Xing; Gao, Ying-Lian; Kong, Xiang-Zhen; Wang, Xue-Song; Wang, Dong

2015-01-01

In current molecular biology, it becomes more and more important to identify differentially expressed genes closely correlated with a key biological process from gene expression data. In this paper, based on the Schatten p-norm and Lp-norm, a novel p-norm robust feature extraction method is proposed to identify the differentially expressed genes. In our method, the Schatten p-norm is used as the regularization function to obtain a low-rank matrix and the Lp-norm is taken as the error function to improve the robustness to outliers in the gene expression data. The results on simulation data show that our method can obtain higher identification accuracies than the competitive methods. Numerous experiments on real gene expression data sets demonstrate that our method can identify more differentially expressed genes than the others. Moreover, we confirmed that the identified genes are closely correlated with the corresponding gene expression data.

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1993-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

A new unconditionally stable and consistent quasi-analytical in-stream water quality solution scheme for CSTR-based water quality simulators

NASA Astrophysics Data System (ADS)

Woldegiorgis, Befekadu Taddesse; van Griensven, Ann; Pereira, Fernando; Bauwens, Willy

2017-06-01

Most common numerical solutions used in CSTR-based in-stream water quality simulators are susceptible to instabilities and/or solution inconsistencies. Usually, they cope with instability problems by adopting computationally expensive small time steps. However, some simulators use fixed computation time steps and hence do not have the flexibility to do so. This paper presents a novel quasi-analytical solution for CSTR-based water quality simulators of an unsteady system. The robustness of the new method is compared with the commonly used fourth-order Runge-Kutta methods, the Euler method and three versions of the SWAT model (SWAT2012, SWAT-TCEQ, and ESWAT). The performance of each method is tested for different hypothetical experiments. Besides the hypothetical data, a real case study is used for comparison. The growth factors we derived as stability measures for the different methods and the R-factor—considered as a consistency measure—turned out to be very useful for determining the most robust method. The new method outperformed all the numerical methods used in the hypothetical comparisons. The application for the Zenne River (Belgium) shows that the new method provides stable and consistent BOD simulations whereas the SWAT2012 model is shown to be unstable for the standard daily computation time step. The new method unconditionally simulates robust solutions. Therefore, it is a reliable scheme for CSTR-based water quality simulators that use first-order reaction formulations.

Application of numerical grid generation for improved CFD analysis of multiphase screw machines

NASA Astrophysics Data System (ADS)

Rane, S.; Kovačević, A.

2017-08-01

Algebraic grid generation is widely used for discretization of the working domain of twin screw machines. Algebraic grid generation is fast and has good control over the placement of grid nodes. However, the desired qualities of grid which should be able to handle multiphase flows such as oil injection, may be difficult to achieve at times. In order to obtain fast solution of multiphase screw machines, it is important to further improve the quality and robustness of the computational grid. In this paper, a deforming grid of a twin screw machine is generated using algebraic transfinite interpolation to produce initial mesh upon which an elliptic partial differential equations (PDE) of the Poisson’s form is solved numerically to produce smooth final computational mesh. The quality of numerical cells and their distribution obtained by the differential method is greatly improved. In addition, a similar procedure was introduced to fully smoothen the transition of the partitioning rack curve between the rotors thus improving continuous movement of grid nodes and in turn improve robustness and speed of the Computational Fluid Dynamic (CFD) solver. Analysis of an oil injected twin screw compressor is presented to compare the improvements in grid quality factors in the regions of importance such as interlobe space, radial tip and the core of the rotor. The proposed method that combines algebraic and differential grid generation offer significant improvement in grid quality and robustness of numerical solution.

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

An improved, robust, axial line singularity method for bodies of revolution

NASA Technical Reports Server (NTRS)

Hemsch, Michael J.

1989-01-01

The failures encountered in attempts to increase the range of applicability of the axial line singularity method for representing incompressible, inviscid flow about an inclined and slender body-of-revolution are presently noted to be common to all efforts to solve Fredholm equations of the first kind. It is shown that a previously developed smoothing technique yields a robust method for numerical solution of the governing equations; this technique is easily retrofitted to existing codes, and allows the number of circularities to be increased until the most accurate line singularity solution is obtained.

Performance issues for iterative solvers in device simulation

NASA Technical Reports Server (NTRS)

Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai

1994-01-01

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations

DOE PAGES

Banerjee, Amartya S.; Suryanarayana, Phanish; Pask, John E.

2016-01-21

Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization of DIIS in which Pulay extrapolation is performed at periodic intervals rather than on every self-consistent field iteration, and linear mixing is performed on all other iterations. Lastly, we demonstrate through numerical tests on a wide variety of materials systems in the framework of density functional theory that the proposed generalization of Pulay's method significantly improves its robustness and efficiency.

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

Robust Inference of Risks of Large Portfolios

PubMed Central

Fan, Jianqing; Han, Fang; Liu, Han; Vickers, Byron

2016-01-01

We propose a bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios. The proposed approach exploits rank-based and quantile-based estimators, and can be viewed as a robust extension of the H-CLUB procedure (Fan et al., 2015). Such an extension allows us to handle possibly misspecified models and heavy-tailed data, which are stylized features in financial returns. Under mixing conditions, we analyze the proposed approach and demonstrate its advantage over H-CLUB. We further provide thorough numerical results to back up the developed theory, and also apply the proposed method to analyze a stock market dataset. PMID:27818569

Robust and fast-converging level set method for side-scan sonar image segmentation

NASA Astrophysics Data System (ADS)

Liu, Yan; Li, Qingwu; Huo, Guanying

2017-11-01

A robust and fast-converging level set method is proposed for side-scan sonar (SSS) image segmentation. First, the noise in each sonar image is removed using the adaptive nonlinear complex diffusion filter. Second, k-means clustering is used to obtain the initial presegmentation image from the denoised image, and then the distance maps of the initial contours are reinitialized to guarantee the accuracy of the numerical calculation used in the level set evolution. Finally, the satisfactory segmentation is achieved using a robust variational level set model, where the evolution control parameters are generated by the presegmentation. The proposed method is successfully applied to both synthetic image with speckle noise and real SSS images. Experimental results show that the proposed method needs much less iteration and therefore is much faster than the fuzzy local information c-means clustering method, the level set method using a gamma observation model, and the enhanced region-scalable fitting method. Moreover, the proposed method can usually obtain more accurate segmentation results compared with other methods.

Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1995-01-01

We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Feature selection methods for object-based classification of sub-decimeter resolution digital aerial imagery

USDA-ARS?s Scientific Manuscript database

Due to the availability of numerous spectral, spatial, and contextual features, the determination of optimal features and class separabilities can be a time consuming process in object-based image analysis (OBIA). While several feature selection methods have been developed to assist OBIA, a robust c...

A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.

PubMed

Ling, Hong; Luo, Ercang; Dai, Wei

2006-12-22

Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Robust numerical simulation of porosity evolution in chemical vapor infiltration III: three space dimension

NASA Astrophysics Data System (ADS)

Jin, Shi; Wang, Xuelei

2003-04-01

Chemical vapor infiltration (CVI) process is an important technology to fabricate ceramic matrix composites (CMC's). In this paper, a three-dimension numerical model is presented to describe pore microstructure evolution during the CVI process. We extend the two-dimension model proposed in [S. Jin, X.L. Wang, T.L. Starr, J. Mater. Res. 14 (1999) 3829; S. Jin. X.L. Wang, T.L. Starr, X.F. Chen, J. Comp. Phys. 162 (2000) 467], where the fiber surface is modeled as an evolving interface, to the three space dimension. The 3D method keeps all the virtue of the 2D model: robust numerical capturing of topological changes of the interface such as the merging, and fast detection of the inaccessible pores. For models in the kinetic limit, where the moving speed of the interface is constant, some numerical examples are presented to show that this three-dimension model will effectively track the change of porosity, close-off time, location and shape of all pores.

Robust Control Design for Systems With Probabilistic Uncertainty

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.

2005-01-01

This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.

Parameterized LMI Based Diagonal Dominance Compensator Study for Polynomial Linear Parameter Varying System

NASA Astrophysics Data System (ADS)

Han, Xiaobao; Li, Huacong; Jia, Qiusheng

2017-12-01

For dynamic decoupling of polynomial linear parameter varying(PLPV) system, a robust dominance pre-compensator design method is given. The parameterized precompensator design problem is converted into an optimal problem constrained with parameterized linear matrix inequalities(PLMI) by using the conception of parameterized Lyapunov function(PLF). To solve the PLMI constrained optimal problem, the precompensator design problem is reduced into a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a new constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator is achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation on a turbofan engine PLPV model.

RSRE: RNA structural robustness evaluator

PubMed Central

Shu, Wenjie; Zheng, Zhiqiang; Wang, Shengqi

2007-01-01

Biological robustness, defined as the ability to maintain stable functioning in the face of various perturbations, is an important and fundamental topic in current biology, and has become a focus of numerous studies in recent years. Although structural robustness has been explored in several types of RNA molecules, the origins of robustness are still controversial. Computational analysis results are needed to make up for the lack of evidence of robustness in natural biological systems. The RNA structural robustness evaluator (RSRE) web server presented here provides a freely available online tool to quantitatively evaluate the structural robustness of RNA based on the widely accepted definition of neutrality. Several classical structure comparison methods are employed; five randomization methods are implemented to generate control sequences; sub-optimal predicted structures can be optionally utilized to mitigate the uncertainty of secondary structure prediction. With a user-friendly interface, the web application is easy to use. Intuitive illustrations are provided along with the original computational results to facilitate analysis. The RSRE will be helpful in the wide exploration of RNA structural robustness and will catalyze our understanding of RNA evolution. The RSRE web server is freely available at http://biosrv1.bmi.ac.cn/RSRE/ or http://biotech.bmi.ac.cn/RSRE/. PMID:17567615

DNS of Supersonic Turbulent Flows in a DLR Scramjet Intake

NASA Astrophysics Data System (ADS)

Li, Xinliang; Yu, Changping

2014-11-01

Direct numerical simulation (DNS) of supersonic/hypersonic flow through a DLR scramjet intake GK01 is performed. The free stream Mach numbers are 3, 5 and 7, and the angle of attack is zero degree. The DNS cases are performed by using an optimized MP scheme with adaptive dissipation (OMP-AD) developed by the authors, and the blow-and-suction perturbations near the leading edge are used to trigger the transition. To stabilize the simulation, locally non-linear flittering is used in high-Mach-number case. The transition, separation, and shock-turbulent boundary layer interaction are studied by using both flow visualization and statistical analysis. A new method, OMP-AD, is also addressed in this paper. The OMP-AD scheme is developed by using joint MP method and optimized technique, and the coefficients in the scheme are flexible to show low dissipation in the smoothing region, and to show high robust (but high dissipation) in the large gradient region. Numerical tests show that the OMP-AD is more robust than the original MP schemes, and the numerical dissipation of OMP-AD is very low.

Efficient Variable Selection Method for Exposure Variables on Binary Data

NASA Astrophysics Data System (ADS)

Ohno, Manabu; Tarumi, Tomoyuki

In this paper, we propose a new variable selection method for "robust" exposure variables. We define "robust" as property that the same variable can select among original data and perturbed data. There are few studies of effective for the selection method. The problem that selects exposure variables is almost the same as a problem that extracts correlation rules without robustness. [Brin 97] is suggested that correlation rules are possible to extract efficiently using chi-squared statistic of contingency table having monotone property on binary data. But the chi-squared value does not have monotone property, so it's is easy to judge the method to be not independent with an increase in the dimension though the variable set is completely independent, and the method is not usable in variable selection for robust exposure variables. We assume anti-monotone property for independent variables to select robust independent variables and use the apriori algorithm for it. The apriori algorithm is one of the algorithms which find association rules from the market basket data. The algorithm use anti-monotone property on the support which is defined by association rules. But independent property does not completely have anti-monotone property on the AIC of independent probability model, but the tendency to have anti-monotone property is strong. Therefore, selected variables with anti-monotone property on the AIC have robustness. Our method judges whether a certain variable is exposure variable for the independent variable using previous comparison of the AIC. Our numerical experiments show that our method can select robust exposure variables efficiently and precisely.

Efficient and robust relaxation procedures for multi-component mixtures including phase transition

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

Han, Ee, E-mail: eehan@math.uni-bremen.de; Hantke, Maren, E-mail: maren.hantke@ovgu.de; Müller, Siegfried, E-mail: mueller@igpm.rwth-aachen.de

We consider a thermodynamic consistent multi-component model in multi-dimensions that is a generalization of the classical two-phase flow model of Baer and Nunziato. The exchange of mass, momentum and energy between the phases is described by additional source terms. Typically these terms are handled by relaxation procedures. Available relaxation procedures suffer from efficiency and robustness resulting in very costly computations that in general only allow for one-dimensional computations. Therefore we focus on the development of new efficient and robust numerical methods for relaxation processes. We derive exact procedures to determine mechanical and thermal equilibrium states. Further we introduce a novelmore » iterative method to treat the mass transfer for a three component mixture. All new procedures can be extended to an arbitrary number of inert ideal gases. We prove existence, uniqueness and physical admissibility of the resulting states and convergence of our new procedures. Efficiency and robustness of the procedures are verified by means of numerical computations in one and two space dimensions. - Highlights: • We develop novel relaxation procedures for a generalized, thermodynamically consistent Baer–Nunziato type model. • Exact procedures for mechanical and thermal relaxation procedures avoid artificial parameters. • Existence, uniqueness and physical admissibility of the equilibrium states are proven for special mixtures. • A novel iterative method for mass transfer is introduced for a three component mixture providing a unique and admissible equilibrium state.« less

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1992-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Inverse transport calculations in optical imaging with subspace optimization algorithms

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

Ding, Tian, E-mail: tding@math.utexas.edu; Ren, Kui, E-mail: ren@math.utexas.edu

2014-09-15

Inverse boundary value problems for the radiative transport equation play an important role in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years, developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic. We propose here a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknown transport solution (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analyticallymore » recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm.« less

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties.

PubMed

Song, Qiankun; Yu, Qinqin; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E

2018-07-01

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Novel Robust H∞ Filter Based on Krein Space Theory in the SINS/CNS Attitude Reference System.

PubMed

Yu, Fei; Lv, Chongyang; Dong, Qianhui

2016-03-18

Owing to their numerous merits, such as compact, autonomous and independence, the strapdown inertial navigation system (SINS) and celestial navigation system (CNS) can be used in marine applications. What is more, due to the complementary navigation information obtained from two different kinds of sensors, the accuracy of the SINS/CNS integrated navigation system can be enhanced availably. Thus, the SINS/CNS system is widely used in the marine navigation field. However, the CNS is easily interfered with by the surroundings, which will lead to the output being discontinuous. Thus, the uncertainty problem caused by the lost measurement will reduce the system accuracy. In this paper, a robust H∞ filter based on the Krein space theory is proposed. The Krein space theory is introduced firstly, and then, the linear state and observation models of the SINS/CNS integrated navigation system are established reasonably. By taking the uncertainty problem into account, in this paper, a new robust H∞ filter is proposed to improve the robustness of the integrated system. At last, this new robust filter based on the Krein space theory is estimated by numerical simulations and actual experiments. Additionally, the simulation and experiment results and analysis show that the attitude errors can be reduced by utilizing the proposed robust filter effectively when the measurements are missing discontinuous. Compared to the traditional Kalman filter (KF) method, the accuracy of the SINS/CNS integrated system is improved, verifying the robustness and the availability of the proposed robust H∞ filter.

Final Report of the Project "From the finite element method to the virtual element method"

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

Manzini, Gianmarco; Gyrya, Vitaliy

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for themore » numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.« less

Sliding mode control for generalized robust synchronization of mismatched fractional order dynamical systems and its application to secure transmission of voice messages.

PubMed

Muthukumar, P; Balasubramaniam, P; Ratnavelu, K

2017-07-26

This paper proposes a generalized robust synchronization method for different dimensional fractional order dynamical systems with mismatched fractional derivatives in the presence of function uncertainty and external disturbance by a designing sliding mode controller. Based on the proposed theory of generalized robust synchronization criterion, a novel audio cryptosystem is proposed for sending or sharing voice messages secretly via insecure channel. Numerical examples are given to verify the potency of the proposed theories. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Assessing the Robustness of Complete Bacterial Genome Segmentations

NASA Astrophysics Data System (ADS)

Devillers, Hugo; Chiapello, Hélène; Schbath, Sophie; El Karoui, Meriem

Comparison of closely related bacterial genomes has revealed the presence of highly conserved sequences forming a "backbone" that is interrupted by numerous, less conserved, DNA fragments. Segmentation of bacterial genomes into backbone and variable regions is particularly useful to investigate bacterial genome evolution. Several software tools have been designed to compare complete bacterial chromosomes and a few online databases store pre-computed genome comparisons. However, very few statistical methods are available to evaluate the reliability of these software tools and to compare the results obtained with them. To fill this gap, we have developed two local scores to measure the robustness of bacterial genome segmentations. Our method uses a simulation procedure based on random perturbations of the compared genomes. The scores presented in this paper are simple to implement and our results show that they allow to discriminate easily between robust and non-robust bacterial genome segmentations when using aligners such as MAUVE and MGA.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

NASA Astrophysics Data System (ADS)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

Shock capturing finite difference algorithms for supersonic flow past fighter and missile type configurations

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

A comparison of three feature selection methods for object-based classification of sub-decimeter resolution UltraCam-L imagery

USDA-ARS?s Scientific Manuscript database

The availability of numerous spectral, spatial, and contextual features with object-based image analysis (OBIA) renders the selection of optimal features a time consuming and subjective process. While several feature election methods have been used in conjunction with OBIA, a robust comparison of th...

A simple finite element method for linear hyperbolic problems

DOE PAGES

Mu, Lin; Ye, Xiu

2017-09-14

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for linear hyperbolic problems

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

Mu, Lin; Ye, Xiu

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

NASA Astrophysics Data System (ADS)

Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi

2010-08-01

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

A robust collagen scoring method for human liver fibrosis by second harmonic microscopy.

PubMed

Guilbert, Thomas; Odin, Christophe; Le Grand, Yann; Gailhouste, Luc; Turlin, Bruno; Ezan, Frédérick; Désille, Yoann; Baffet, Georges; Guyader, Dominique

2010-12-06

Second Harmonic Generation (SHG) microscopy offers the opportunity to image collagen of type I without staining. We recently showed that a simple scoring method, based on SHG images of histological human liver biopsies, correlates well with the Metavir assessment of fibrosis level (Gailhouste et al., J. Hepatol., 2010). In this article, we present a detailed study of this new scoring method with two different objective lenses. By using measurements of the objectives point spread functions and of the photomultiplier gain, and a simple model of the SHG intensity, we show that our scoring method, applied to human liver biopsies, is robust to the objective's numerical aperture (NA) for low NA, the choice of the reference sample and laser power, and the spatial sampling rate. The simplicity and robustness of our collagen scoring method may open new opportunities in the quantification of collagen content in different organs, which is of main importance in providing diagnostic information and evaluation of therapeutic efficiency.

Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments.

PubMed

Sainath, Kamalesh; Teixeira, Fernando L; Donderici, Burkay

2014-01-01

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both its (complex) permittivity and permeability tensors. Among the salient features of our formulation are (i) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (ii) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly evanescent spectra contributions, and (iii) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena (e.g., mode coupling at interfaces and nonreciprocal mode propagation). Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Numerical Algorithms for Acoustic Integrals - The Devil is in the Details

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1996-01-01

The accurate prediction of the aeroacoustic field generated by aerospace vehicles or nonaerospace machinery is necessary for designers to control and reduce source noise. Powerful computational aeroacoustic methods, based on various acoustic analogies (primarily the Lighthill acoustic analogy) and Kirchhoff methods, have been developed for prediction of noise from complicated sources, such as rotating blades. Both methods ultimately predict the noise through a numerical evaluation of an integral formulation. In this paper, we consider three generic acoustic formulations and several numerical algorithms that have been used to compute the solutions to these formulations. Algorithms for retarded-time formulations are the most efficient and robust, but they are difficult to implement for supersonic-source motion. Collapsing-sphere and emission-surface formulations are good alternatives when supersonic-source motion is present, but the numerical implementations of these formulations are more computationally demanding. New algorithms - which utilize solution adaptation to provide a specified error level - are needed.

A Semi-implicit Treatment of Porous Media in Steady-State CFD.

PubMed

Domaingo, Andreas; Langmayr, Daniel; Somogyi, Bence; Almbauer, Raimund

There are many situations in computational fluid dynamics which require the definition of source terms in the Navier-Stokes equations. These source terms not only allow to model the physics of interest but also have a strong impact on the reliability, stability, and convergence of the numerics involved. Therefore, sophisticated numerical approaches exist for the description of such source terms. In this paper, we focus on the source terms present in the Navier-Stokes or Euler equations due to porous media-in particular the Darcy-Forchheimer equation. We introduce a method for the numerical treatment of the source term which is independent of the spatial discretization and based on linearization. In this description, the source term is treated in a fully implicit way whereas the other flow variables can be computed in an implicit or explicit manner. This leads to a more robust description in comparison with a fully explicit approach. The method is well suited to be combined with coarse-grid-CFD on Cartesian grids, which makes it especially favorable for accelerated solution of coupled 1D-3D problems. To demonstrate the applicability and robustness of the proposed method, a proof-of-concept example in 1D, as well as more complex examples in 2D and 3D, is presented.

A robust ordering strategy for retailers facing a free shipping option.

PubMed

Meng, Qing-chun; Wan, Xiao-le; Rong, Xiao-xia

2015-01-01

Free shipping with conditions has become one of the most effective marketing tools available. An increasing number of companies, especially e-businesses, prefer to offer free shipping with some predetermined condition, such as a minimum purchase amount by the customer. However, in practice, the demands of buyers are uncertain; they are often affected by many factors, such as the weather and season. We begin by modeling the centralized ordering problem in which the supplier offers a free shipping service and retailers face stochastic demands. As these random data are considered, only partial information such as the known mean, support, and deviation is needed. The model is then analyzed via a robust optimization method, and the two types of equivalent sets of uncertainty constraints that are obtained provide good mathematical properties with consideration of the robustness of solutions. Subsequently, a numerical example is used to compare the results achieved from a robust optimization method and the linear decision rules. Additionally, the robustness of the optimal solution is discussed, as it is affected by the minimum quantity parameters. The increasing cost-threshold relationship is divided into three periods. In addition, the case study shows that the proposed method achieves better stability as well as computational complexity.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

A Novel Robust H∞ Filter Based on Krein Space Theory in the SINS/CNS Attitude Reference System

PubMed Central

Yu, Fei; Lv, Chongyang; Dong, Qianhui

2016-01-01

Owing to their numerous merits, such as compact, autonomous and independence, the strapdown inertial navigation system (SINS) and celestial navigation system (CNS) can be used in marine applications. What is more, due to the complementary navigation information obtained from two different kinds of sensors, the accuracy of the SINS/CNS integrated navigation system can be enhanced availably. Thus, the SINS/CNS system is widely used in the marine navigation field. However, the CNS is easily interfered with by the surroundings, which will lead to the output being discontinuous. Thus, the uncertainty problem caused by the lost measurement will reduce the system accuracy. In this paper, a robust H∞ filter based on the Krein space theory is proposed. The Krein space theory is introduced firstly, and then, the linear state and observation models of the SINS/CNS integrated navigation system are established reasonably. By taking the uncertainty problem into account, in this paper, a new robust H∞ filter is proposed to improve the robustness of the integrated system. At last, this new robust filter based on the Krein space theory is estimated by numerical simulations and actual experiments. Additionally, the simulation and experiment results and analysis show that the attitude errors can be reduced by utilizing the proposed robust filter effectively when the measurements are missing discontinuous. Compared to the traditional Kalman filter (KF) method, the accuracy of the SINS/CNS integrated system is improved, verifying the robustness and the availability of the proposed robust H∞ filter. PMID:26999153

A review of contemporary methods for the presentation of scientific uncertainty.

PubMed

Makinson, K A; Hamby, D M; Edwards, J A

2012-12-01

Graphic methods for displaying uncertainty are often the most concise and informative way to communicate abstract concepts. Presentation methods currently in use for the display and interpretation of scientific uncertainty are reviewed. Numerous subjective and objective uncertainty display methods are presented, including qualitative assessments, node and arrow diagrams, standard statistical methods, box-and-whisker plots,robustness and opportunity functions, contribution indexes, probability density functions, cumulative distribution functions, and graphical likelihood functions.

LOCAL ORTHOGONAL CUTTING METHOD FOR COMPUTING MEDIAL CURVES AND ITS BIOMEDICAL APPLICATIONS

PubMed Central

Einstein, Daniel R.; Dyedov, Vladimir

2010-01-01

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method called local orthogonal cutting (LOC) for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stability and consistency tests. These concepts lend themselves to robust numerical techniques and result in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods. PMID:20628546

An adaptive discontinuous Galerkin solver for aerodynamic flows

NASA Astrophysics Data System (ADS)

Burgess, Nicholas K.

This work considers the accuracy, efficiency, and robustness of an unstructured high-order accurate discontinuous Galerkin (DG) solver for computational fluid dynamics (CFD). Recently, there has been a drive to reduce the discretization error of CFD simulations using high-order methods on unstructured grids. However, high-order methods are often criticized for lacking robustness and having high computational cost. The goal of this work is to investigate methods that enhance the robustness of high-order discontinuous Galerkin (DG) methods on unstructured meshes, while maintaining low computational cost and high accuracy of the numerical solutions. This work investigates robustness enhancement of high-order methods by examining effective non-linear solvers, shock capturing methods, turbulence model discretizations and adaptive refinement techniques. The goal is to develop an all encompassing solver that can simulate a large range of physical phenomena, where all aspects of the solver work together to achieve a robust, efficient and accurate solution strategy. The components and framework for a robust high-order accurate solver that is capable of solving viscous, Reynolds Averaged Navier-Stokes (RANS) and shocked flows is presented. In particular, this work discusses robust discretizations of the turbulence model equation used to close the RANS equations, as well as stable shock capturing strategies that are applicable across a wide range of discretization orders and applicable to very strong shock waves. Furthermore, refinement techniques are considered as both efficiency and robustness enhancement strategies. Additionally, efficient non-linear solvers based on multigrid and Krylov subspace methods are presented. The accuracy, efficiency, and robustness of the solver is demonstrated using a variety of challenging aerodynamic test problems, which include turbulent high-lift and viscous hypersonic flows. Adaptive mesh refinement was found to play a critical role in obtaining a robust and efficient high-order accurate flow solver. A goal-oriented error estimation technique has been developed to estimate the discretization error of simulation outputs. For high-order discretizations, it is shown that functional output error super-convergence can be obtained, provided the discretization satisfies a property known as dual consistency. The dual consistency of the DG methods developed in this work is shown via mathematical analysis and numerical experimentation. Goal-oriented error estimation is also used to drive an hp-adaptive mesh refinement strategy, where a combination of mesh or h-refinement, and order or p-enrichment, is employed based on the smoothness of the solution. The results demonstrate that the combination of goal-oriented error estimation and hp-adaptation yield superior accuracy, as well as enhanced robustness and efficiency for a variety of aerodynamic flows including flows with strong shock waves. This work demonstrates that DG discretizations can be the basis of an accurate, efficient, and robust CFD solver. Furthermore, enhancing the robustness of DG methods does not adversely impact the accuracy or efficiency of the solver for challenging and complex flow problems. In particular, when considering the computation of shocked flows, this work demonstrates that the available shock capturing techniques are sufficiently accurate and robust, particularly when used in conjunction with adaptive mesh refinement . This work also demonstrates that robust solutions of the Reynolds Averaged Navier-Stokes (RANS) and turbulence model equations can be obtained for complex and challenging aerodynamic flows. In this context, the most robust strategy was determined to be a low-order turbulence model discretization coupled to a high-order discretization of the RANS equations. Although RANS solutions using high-order accurate discretizations of the turbulence model were obtained, the behavior of current-day RANS turbulence models discretized to high-order was found to be problematic, leading to solver robustness issues. This suggests that future work is warranted in the area of turbulence model formulation for use with high-order discretizations. Alternately, the use of Large-Eddy Simulation (LES) subgrid scale models with high-order DG methods offers the potential to leverage the high accuracy of these methods for very high fidelity turbulent simulations. This thesis has developed the algorithmic improvements that will lay the foundation for the development of a three-dimensional high-order flow solution strategy that can be used as the basis for future LES simulations.

Towards building a robust computational framework to simulate multi-physics problems - a solution technique for three-phase (gas-liquid-solid) interactions

NASA Astrophysics Data System (ADS)

Zhang, Lucy

In this talk, we show a robust numerical framework to model and simulate gas-liquid-solid three-phase flows. The overall algorithm adopts a non-boundary-fitted approach that avoids frequent mesh-updating procedures by defining independent meshes and explicit interfacial points to represent each phase. In this framework, we couple the immersed finite element method (IFEM) and the connectivity-free front tracking (CFFT) method that model fluid-solid and gas-liquid interactions, respectively, for the three-phase models. The CFFT is used here to simulate gas-liquid multi-fluid flows that uses explicit interfacial points to represent the gas-liquid interface and for its easy handling of interface topology changes. Instead of defining different levels simultaneously as used in level sets, an indicator function naturally couples the two methods together to represent and track each of the three phases. Several 2-D and 3-D testing cases are performed to demonstrate the robustness and capability of the coupled numerical framework in dealing with complex three-phase problems, in particular free surfaces interacting with deformable solids. The solution technique offers accuracy and stability, which provides a means to simulate various engineering applications. The author would like to acknowledge the supports from NIH/DHHS R01-2R01DC005642-10A1 and the National Natural Science Foundation of China (NSFC) 11550110185.

Robust Fault Detection for Switched Fuzzy Systems With Unknown Input.

PubMed

Han, Jian; Zhang, Huaguang; Wang, Yingchun; Sun, Xun

2017-10-03

This paper investigates the fault detection problem for a class of switched nonlinear systems in the T-S fuzzy framework. The unknown input is considered in the systems. A novel fault detection unknown input observer design method is proposed. Based on the proposed observer, the unknown input can be removed from the fault detection residual. The weighted H∞ performance level is considered to ensure the robustness. In addition, the weighted H₋ performance level is introduced, which can increase the sensibility of the proposed detection method. To verify the proposed scheme, a numerical simulation example and an electromechanical system simulation example are provided at the end of this paper.

Robust control for spacecraft rendezvous system with actuator unsymmetrical saturation: a gain scheduling approach

NASA Astrophysics Data System (ADS)

Wang, Qian; Xue, Anke

2018-06-01

This paper has proposed a robust control for the spacecraft rendezvous system by considering the parameter uncertainties and actuator unsymmetrical saturation based on the discrete gain scheduling approach. By changing of variables, we transform the actuator unsymmetrical saturation control problem into a symmetrical one. The main advantage of the proposed method is improving the dynamic performance of the closed-loop system with a region of attraction as large as possible. By the Lyapunov approach and the scheduling technology, the existence conditions for the admissible controller are formulated in the form of linear matrix inequalities. The numerical simulation illustrates the effectiveness of the proposed method.

Extension of CE/SE method to non-equilibrium dissociating flows

NASA Astrophysics Data System (ADS)

Wen, C. Y.; Saldivar Massimi, H.; Shen, H.

2018-03-01

In this study, the hypersonic non-equilibrium flows over rounded nose geometries are numerically investigated by a robust conservation element and solution element (CE/SE) code, which is based on hybrid meshes consisting of triangular and quadrilateral elements. The dissociating and recombination chemical reactions as well as the vibrational energy relaxation are taken into account. The stiff source terms are solved by an implicit trapezoidal method of integration. Comparison with laboratory and numerical cases are provided to demonstrate the accuracy and reliability of the present CE/SE code in simulating hypersonic non-equilibrium flows.

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

A weak Galerkin least-squares finite element method for div-curl systems

NASA Astrophysics Data System (ADS)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

DOE PAGES

Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...

1995-01-01

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less

A discontinuous Galerkin method for numerical pricing of European options under Heston stochastic volatility

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2016-12-01

The paper is based on the results from our recent research on multidimensional option pricing problems. We focus on European option valuation when the price movement of the underlying asset is driven by a stochastic volatility following a square root process proposed by Heston. The stochastic approach incorporates a new additional spatial variable into this model and makes it very robust, i.e. it provides a framework to price a variety of options that is closer to reality. The main topic is to present the numerical scheme arising from the concept of discontinuous Galerkin methods and applicable to the Heston option pricing model. The numerical results are presented on artificial benchmarks as well as on reference market data.

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Yu, Sheng-Tao

2001-01-01

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

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

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

DOE PAGES

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich; ...

2017-10-28

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.

PubMed

Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun

2016-05-09

The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers' misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise.

PubMed

Wang, Junxiang; Wang, Xianpeng; Xu, Dingjie; Bi, Guoan

2018-03-09

This paper deals with joint estimation of direction-of-departure (DOD) and direction-of- arrival (DOA) in bistatic multiple-input multiple-output (MIMO) radar with the coexistence of unknown mutual coupling and spatial colored noise by developing a novel robust covariance tensor-based angle estimation method. In the proposed method, a third-order tensor is firstly formulated for capturing the multidimensional nature of the received data. Then taking advantage of the temporal uncorrelated characteristic of colored noise and the banded complex symmetric Toeplitz structure of the mutual coupling matrices, a novel fourth-order covariance tensor is constructed for eliminating the influence of both spatial colored noise and mutual coupling. After a robust signal subspace estimation is obtained by using the higher-order singular value decomposition (HOSVD) technique, the rotational invariance technique is applied to achieve the DODs and DOAs. Compared with the existing HOSVD-based subspace methods, the proposed method can provide superior angle estimation performance and automatically jointly perform the DODs and DOAs. Results from numerical experiments are presented to verify the effectiveness of the proposed method.

Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise

PubMed Central

Wang, Junxiang; Wang, Xianpeng; Xu, Dingjie; Bi, Guoan

2018-01-01

This paper deals with joint estimation of direction-of-departure (DOD) and direction-of- arrival (DOA) in bistatic multiple-input multiple-output (MIMO) radar with the coexistence of unknown mutual coupling and spatial colored noise by developing a novel robust covariance tensor-based angle estimation method. In the proposed method, a third-order tensor is firstly formulated for capturing the multidimensional nature of the received data. Then taking advantage of the temporal uncorrelated characteristic of colored noise and the banded complex symmetric Toeplitz structure of the mutual coupling matrices, a novel fourth-order covariance tensor is constructed for eliminating the influence of both spatial colored noise and mutual coupling. After a robust signal subspace estimation is obtained by using the higher-order singular value decomposition (HOSVD) technique, the rotational invariance technique is applied to achieve the DODs and DOAs. Compared with the existing HOSVD-based subspace methods, the proposed method can provide superior angle estimation performance and automatically jointly perform the DODs and DOAs. Results from numerical experiments are presented to verify the effectiveness of the proposed method. PMID:29522499

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data.

PubMed

Zhou, Yunyi; Tao, Chenyang; Lu, Wenlian; Feng, Jianfeng

2018-04-20

Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis. Copyright © 2018. Published by Elsevier B.V.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Multiple attractors and critical parameters and how to find them numerically: the right, the wrong and the gambling way

NASA Astrophysics Data System (ADS)

True, Hans

2013-03-01

In recent years, several authors have proposed 'easier numerical methods' to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras are commented upon. I also address the questions when a linearisation is allowed and the curious fact that the hunting motion is more robust than the ideal stationary-state motion on the track. Concepts such as 'multiple attractors', 'subcritical and supercritical bifurcations', 'permitted linearisation', 'the danger of running at supercritical speeds' and 'chaotic motion' are addressed.

A Robust Ordering Strategy for Retailers Facing a Free Shipping Option

PubMed Central

Meng, Qing-chun; Wan, Xiao-le; Rong, Xiao-xia

2015-01-01

Free shipping with conditions has become one of the most effective marketing tools available. An increasing number of companies, especially e-businesses, prefer to offer free shipping with some predetermined condition, such as a minimum purchase amount by the customer. However, in practice, the demands of buyers are uncertain; they are often affected by many factors, such as the weather and season. We begin by modeling the centralized ordering problem in which the supplier offers a free shipping service and retailers face stochastic demands. As these random data are considered, only partial information such as the known mean, support, and deviation is needed. The model is then analyzed via a robust optimization method, and the two types of equivalent sets of uncertainty constraints that are obtained provide good mathematical properties with consideration of the robustness of solutions. Subsequently, a numerical example is used to compare the results achieved from a robust optimization method and the linear decision rules. Additionally, the robustness of the optimal solution is discussed, as it is affected by the minimum quantity parameters. The increasing cost-threshold relationship is divided into three periods. In addition, the case study shows that the proposed method achieves better stability as well as computational complexity. PMID:25993533

A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme

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

Kupferman, R.

The author presents a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.

Modified Method of Adaptive Artificial Viscosity for Solution of Gas Dynamics Problems on Parallel Computer Systems

NASA Astrophysics Data System (ADS)

Popov, Igor; Sukov, Sergey

2018-02-01

A modification of the adaptive artificial viscosity (AAV) method is considered. This modification is based on one stage time approximation and is adopted to calculation of gasdynamics problems on unstructured grids with an arbitrary type of grid elements. The proposed numerical method has simplified logic, better performance and parallel efficiency compared to the implementation of the original AAV method. Computer experiments evidence the robustness and convergence of the method to difference solution.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

Robust location of optical fiber modes via the argument principle method

NASA Astrophysics Data System (ADS)

Chen, Parry Y.; Sivan, Yonatan

2017-05-01

We implement a robust, globally convergent root search method for transcendental equations guaranteed to locate all complex roots within a specified search domain, based on Cauchy's residue theorem. Although several implementations of the argument principle already exist, ours has several advantages: it allows singularities within the search domain and branch points are not fatal to the method. Furthermore, our implementation is simple and is written in MATLAB, fulfilling the need for an easily integrated implementation which can be readily modified to accommodate the many variations of the argument principle method, each of which is suited to a different application. We apply the method to the step index fiber dispersion relation, which has become topical due to the recent proliferation of high index contrast fibers. We also find modes with permittivity as the eigenvalue, catering to recent numerical methods that expand the radiation of sources using eigenmodes.

A bi-objective model for robust yard allocation scheduling for outbound containers

NASA Astrophysics Data System (ADS)

Liu, Changchun; Zhang, Canrong; Zheng, Li

2017-01-01

This article examines the yard allocation problem for outbound containers, with consideration of uncertainty factors, mainly including the arrival and operation time of calling vessels. Based on the time buffer inserting method, a bi-objective model is constructed to minimize the total operational cost and to maximize the robustness of fighting against the uncertainty. Due to the NP-hardness of the constructed model, a two-stage heuristic is developed to solve the problem. In the first stage, initial solutions are obtained by a greedy algorithm that looks n-steps ahead with the uncertainty factors set as their respective expected values; in the second stage, based on the solutions obtained in the first stage and with consideration of uncertainty factors, a neighbourhood search heuristic is employed to generate robust solutions that can fight better against the fluctuation of uncertainty factors. Finally, extensive numerical experiments are conducted to test the performance of the proposed method.

Robust master-slave synchronization for general uncertain delayed dynamical model based on adaptive control scheme.

PubMed

Wang, Tianbo; Zhou, Wuneng; Zhao, Shouwei; Yu, Weiqin

2014-03-01

In this paper, the robust exponential synchronization problem for a class of uncertain delayed master-slave dynamical system is investigated by using the adaptive control method. Different from some existing master-slave models, the considered master-slave system includes bounded unmodeled dynamics. In order to compensate the effect of unmodeled dynamics and effectively achieve synchronization, a novel adaptive controller with simple updated laws is proposed. Moreover, the results are given in terms of LMIs, which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the method. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Stable and low diffusive hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1992-01-01

A new concept for upwinding is introduced, named the hybrid upwind splitting (HUS), which is achieved by combining the basically distinct flux vector splitting (FVS) and the flux difference splitting (FDS) approaches. The HUS approach yields upwind methods which share the robustness of the FVS schemes in the capture of nonlinear waves and the accuracy of some of the FDS schemes. Numerical illustrations are presented proving the relevance of the HUS methods for viscous calculations.

Numerical detection of the Gardner transition in a mean-field glass former.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Rainone, Corrado; Seoane, Beatriz; Zamponi, Francesco

2015-07-01

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

Robust stability of linear systems: Some computational considerations

NASA Technical Reports Server (NTRS)

Laub, A. J.

1979-01-01

The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter.

A two-dimensional, TVD numerical scheme for inviscid, high Mach number flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Eberhardt, S.; Palmer, G.

1986-01-01

A new algorithm has been developed for hypervelocity flows in chemical equilibrium. Solutions have been achieved for Mach numbers up to 15 with no adverse effect on convergence. Two methods of coupling an equilibrium chemistry package have been tested, with the simpler method proving to be more robust. Improvements in boundary conditions are still required for a production-quality code.

Multi-damage identification based on joint approximate diagonalisation and robust distance measure

NASA Astrophysics Data System (ADS)

Cao, S.; Ouyang, H.

2017-05-01

Mode shapes or operational deflection shapes are highly sensitive to damage and can be used for multi-damage identification. Nevertheless, one drawback of this kind of methods is that the extracted spatial shape features tend to be compromised by noise, which degrades their damage identification accuracy, especially for incipient damage. To overcome this, joint approximate diagonalisation (JAD) also known as simultaneous diagonalisation is investigated to estimate mode shapes (MS’s) statistically. The major advantage of JAD method is that it efficiently provides the common Eigen-structure of a set of power spectral density matrices. In this paper, a new criterion in terms of coefficient of variation (CV) is utilised to numerically demonstrate the better noise robustness and accuracy of JAD method over traditional frequency domain decomposition method (FDD). Another original contribution is that a new robust damage index (DI) is proposed, which is comprised of local MS distortions of several modes weighted by their associated vibration participation factors. The advantage of doing this is to include fair contributions from changes of all modes concerned. Moreover, the proposed DI provides a measure of damage-induced changes in ‘modal vibration energy’ in terms of the selected mode shapes. Finally, an experimental study is presented to verify the efficiency and noise robustness of JAD method and the proposed DI. The results show that the proposed DI is effective and robust under random vibration situations, which indicates that it has the potential to be applied to practical engineering structures with ambient excitations.

Robust Eye Center Localization through Face Alignment and Invariant Isocentric Patterns

PubMed Central

Teng, Dongdong; Chen, Dihu; Tan, Hongzhou

2015-01-01

The localization of eye centers is a very useful cue for numerous applications like face recognition, facial expression recognition, and the early screening of neurological pathologies. Several methods relying on available light for accurate eye-center localization have been exploited. However, despite the considerable improvements that eye-center localization systems have undergone in recent years, only few of these developments deal with the challenges posed by the profile (non-frontal face). In this paper, we first use the explicit shape regression method to obtain the rough location of the eye centers. Because this method extracts global information from the human face, it is robust against any changes in the eye region. We exploit this robustness and utilize it as a constraint. To locate the eye centers accurately, we employ isophote curvature features, the accuracy of which has been demonstrated in a previous study. By applying these features, we obtain a series of eye-center locations which are candidates for the actual position of the eye-center. Among these locations, the estimated locations which minimize the reconstruction error between the two methods mentioned above are taken as the closest approximation for the eye centers locations. Therefore, we combine explicit shape regression and isophote curvature feature analysis to achieve robustness and accuracy, respectively. In practical experiments, we use BioID and FERET datasets to test our approach to obtaining an accurate eye-center location while retaining robustness against changes in scale and pose. In addition, we apply our method to non-frontal faces to test its robustness and accuracy, which are essential in gaze estimation but have seldom been mentioned in previous works. Through extensive experimentation, we show that the proposed method can achieve a significant improvement in accuracy and robustness over state-of-the-art techniques, with our method ranking second in terms of accuracy. According to our implementation on a PC with a Xeon 2.5Ghz CPU, the frame rate of the eye tracking process can achieve 38 Hz. PMID:26426929

A conservative fully implicit algorithm for predicting slug flows

NASA Astrophysics Data System (ADS)

Krasnopolsky, Boris I.; Lukyanov, Alexander A.

2018-02-01

An accurate and predictive modelling of slug flows is required by many industries (e.g., oil and gas, nuclear engineering, chemical engineering) to prevent undesired events potentially leading to serious environmental accidents. For example, the hydrodynamic and terrain-induced slugging leads to unwanted unsteady flow conditions. This demands the development of fast and robust numerical techniques for predicting slug flows. The presented in this paper study proposes a multi-fluid model and its implementation method accounting for phase appearance and disappearance. The numerical modelling of phase appearance and disappearance presents a complex numerical challenge for all multi-component and multi-fluid models. Numerical challenges arise from the singular systems of equations when some phases are absent and from the solution discontinuity when some phases appear or disappear. This paper provides a flexible and robust solution to these issues. A fully implicit formulation described in this work enables to efficiently solve governing fluid flow equations. The proposed numerical method provides a modelling capability of phase appearance and disappearance processes, which is based on switching procedure between various sets of governing equations. These sets of equations are constructed using information about the number of phases present in the computational domain. The proposed scheme does not require an explicit truncation of solutions leading to a conservative scheme for mass and linear momentum. A transient two-fluid model is used to verify and validate the proposed algorithm for conditions of hydrodynamic and terrain-induced slug flow regimes. The developed modelling capabilities allow to predict all the major features of the experimental data, and are in a good quantitative agreement with them.

On numerical instabilities of Godunov-type schemes for strong shocks

NASA Astrophysics Data System (ADS)

Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha

2017-12-01

It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. Numerical results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed scheme.

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

NASA Astrophysics Data System (ADS)

Scovazzi, Guglielmo; Wheeler, Mary F.; Mikelić, Andro; Lee, Sanghyun

2017-04-01

The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns - referred to as viscous fingering - may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods.

Robust Unit Commitment Considering Uncertain Demand Response

DOE PAGES

Liu, Guodong; Tomsovic, Kevin

2014-09-28

Although price responsive demand response has been widely accepted as playing an important role in the reliable and economic operation of power system, the real response from demand side can be highly uncertain due to limited understanding of consumers' response to pricing signals. To model the behavior of consumers, the price elasticity of demand has been explored and utilized in both research and real practice. However, the price elasticity of demand is not precisely known and may vary greatly with operating conditions and types of customers. To accommodate the uncertainty of demand response, alternative unit commitment methods robust to themore » uncertainty of the demand response require investigation. In this paper, a robust unit commitment model to minimize the generalized social cost is proposed for the optimal unit commitment decision taking into account uncertainty of the price elasticity of demand. By optimizing the worst case under proper robust level, the unit commitment solution of the proposed model is robust against all possible realizations of the modeled uncertain demand response. Numerical simulations on the IEEE Reliability Test System show the e ectiveness of the method. Finally, compared to unit commitment with deterministic price elasticity of demand, the proposed robust model can reduce the average Locational Marginal Prices (LMPs) as well as the price volatility.« less

Conditioning and Robustness of RNA Boltzmann Sampling under Thermodynamic Parameter Perturbations.

PubMed

Rogers, Emily; Murrugarra, David; Heitsch, Christine

2017-07-25

Understanding how RNA secondary structure prediction methods depend on the underlying nearest-neighbor thermodynamic model remains a fundamental challenge in the field. Minimum free energy (MFE) predictions are known to be "ill conditioned" in that small changes to the thermodynamic model can result in significantly different optimal structures. Hence, the best practice is now to sample from the Boltzmann distribution, which generates a set of suboptimal structures. Although the structural signal of this Boltzmann sample is known to be robust to stochastic noise, the conditioning and robustness under thermodynamic perturbations have yet to be addressed. We present here a mathematically rigorous model for conditioning inspired by numerical analysis, and also a biologically inspired definition for robustness under thermodynamic perturbation. We demonstrate the strong correlation between conditioning and robustness and use its tight relationship to define quantitative thresholds for well versus ill conditioning. These resulting thresholds demonstrate that the majority of the sequences are at least sample robust, which verifies the assumption of sampling's improved conditioning over the MFE prediction. Furthermore, because we find no correlation between conditioning and MFE accuracy, the presence of both well- and ill-conditioned sequences indicates the continued need for both thermodynamic model refinements and alternate RNA structure prediction methods beyond the physics-based ones. Copyright © 2017. Published by Elsevier Inc.

An interface capturing scheme for modeling atomization in compressible flows

NASA Astrophysics Data System (ADS)

Garrick, Daniel P.; Hagen, Wyatt A.; Regele, Jonathan D.

2017-09-01

The study of atomization in supersonic flow is critical to ensuring reliable ignition of scramjet combustors under startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both shocks and material interfaces with high density ratios. In this work, a shock and interface capturing scheme is developed that uses the Harten-Lax-van Leer-Contact (HLLC) Riemann solver while a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme retains the fluid immiscibility condition in the volume fraction and phasic densities in the context of the five equation model. The approach includes the effects of compressibility, surface tension, and molecular viscosity. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Simulations of secondary atomization of a cylindrical water column after its interaction with a shockwave show good qualitative agreement with experimentally observed behavior. Three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow demonstrate the robustness of the method.

Evaluation of two outlier-detection-based methods for detecting tissue-selective genes from microarray data.

PubMed

Kadota, Koji; Konishi, Tomokazu; Shimizu, Kentaro

2007-05-01

Large-scale expression profiling using DNA microarrays enables identification of tissue-selective genes for which expression is considerably higher and/or lower in some tissues than in others. Among numerous possible methods, only two outlier-detection-based methods (an AIC-based method and Sprent's non-parametric method) can treat equally various types of selective patterns, but they produce substantially different results. We investigated the performance of these two methods for different parameter settings and for a reduced number of samples. We focused on their ability to detect selective expression patterns robustly. We applied them to public microarray data collected from 36 normal human tissue samples and analyzed the effects of both changing the parameter settings and reducing the number of samples. The AIC-based method was more robust in both cases. The findings confirm that the use of the AIC-based method in the recently proposed ROKU method for detecting tissue-selective expression patterns is correct and that Sprent's method is not suitable for ROKU.

A robust H∞-tracking design for uncertain Takagi-Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach

NASA Astrophysics Data System (ADS)

Hassan Asemani, Mohammad; Johari Majd, Vahid

2015-12-01

This paper addresses a robust H∞ fuzzy observer-based tracking design problem for uncertain Takagi-Sugeno fuzzy systems with external disturbances. To have a practical observer-based controller, the premise variables of the system are assumed to be not measurable in general, which leads to a more complex design process. The tracker is synthesised based on a fuzzy Lyapunov function approach and non-parallel distributed compensation (non-PDC) scheme. Using the descriptor redundancy approach, the robust stability conditions are derived in the form of strict linear matrix inequalities (LMIs) even in the presence of uncertainties in the system, input, and output matrices simultaneously. Numerical simulations are provided to show the effectiveness of the proposed method.

Communication: Analysing kinetic transition networks for rare events.

PubMed

Stevenson, Jacob D; Wales, David J

2014-07-28

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

Robust visual tracking via multiscale deep sparse networks

NASA Astrophysics Data System (ADS)

Wang, Xin; Hou, Zhiqiang; Yu, Wangsheng; Xue, Yang; Jin, Zefenfen; Dai, Bo

2017-04-01

In visual tracking, deep learning with offline pretraining can extract more intrinsic and robust features. It has significant success solving the tracking drift in a complicated environment. However, offline pretraining requires numerous auxiliary training datasets and is considerably time-consuming for tracking tasks. To solve these problems, a multiscale sparse networks-based tracker (MSNT) under the particle filter framework is proposed. Based on the stacked sparse autoencoders and rectifier linear unit, the tracker has a flexible and adjustable architecture without the offline pretraining process and exploits the robust and powerful features effectively only through online training of limited labeled data. Meanwhile, the tracker builds four deep sparse networks of different scales, according to the target's profile type. During tracking, the tracker selects the matched tracking network adaptively in accordance with the initial target's profile type. It preserves the inherent structural information more efficiently than the single-scale networks. Additionally, a corresponding update strategy is proposed to improve the robustness of the tracker. Extensive experimental results on a large scale benchmark dataset show that the proposed method performs favorably against state-of-the-art methods in challenging environments.

Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels

NASA Astrophysics Data System (ADS)

Qian, Shouguo; Li, Gang; Shao, Fengjing; Xing, Yulong

2018-05-01

We construct and study efficient high order discontinuous Galerkin methods for the shallow water flows in open channels with irregular geometry and a non-flat bottom topography in this paper. The proposed methods are well-balanced for the still water steady state solution, and can preserve the non-negativity of wet cross section numerically. The well-balanced property is obtained via a novel source term separation and discretization. A simple positivity-preserving limiter is employed to provide efficient and robust simulations near the wetting and drying fronts. Numerical examples are performed to verify the well-balanced property, the non-negativity of the wet cross section, and good performance for both continuous and discontinuous solutions.

Robust Feedback Control of Reconfigurable Multi-Agent Systems in Uncertain Adversarial Environments

DTIC Science & Technology

2015-07-09

R. G., Optimal Lunar Landing and Retargeting using a Hybrid Control Strategy. Proceedings of the 2013 AAS/AIAA Space Flight Mechanics Meeting (AAS...Furfaro, R. & Sanfelice, R. G., Switching System Model for Pinpoint Lunar Landing Guidance Using a Hybrid Control Strategy. Proceedings of the AIAA...methods in distributed settings and the design of numerical methods to properly compute their trajectories . We have generate results showing that

Developments in Cylindrical Shell Stability Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.; Starnes, James H., Jr.

1998-01-01

Today high-performance computing systems and new analytical and numerical techniques enable engineers to explore the use of advanced materials for shell design. This paper reviews some of the historical developments of shell buckling analysis and design. The paper concludes by identifying key research directions for reliable and robust methods development in shell stability analysis and design.

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

New methods in hydrologic modeling and decision support for culvert flood risk under climate change

NASA Astrophysics Data System (ADS)

Rosner, A.; Letcher, B. H.; Vogel, R. M.; Rees, P. S.

2015-12-01

Assessing culvert flood vulnerability under climate change poses an unusual combination of challenges. We seek a robust method of planning for an uncertain future, and therefore must consider a wide range of plausible future conditions. Culverts in our case study area, northwestern Massachusetts, USA, are predominantly found in small, ungaged basins. The need to predict flows both at numerous sites and under numerous plausible climate conditions requires a statistical model with low data and computational requirements. We present a statistical streamflow model that is driven by precipitation and temperature, allowing us to predict flows without reliance on reference gages of observed flows. The hydrological analysis is used to determine each culvert's risk of failure under current conditions. We also explore the hydrological response to a range of plausible future climate conditions. These results are used to determine the tolerance of each culvert to future increases in precipitation. In a decision support context, current flood risk as well as tolerance to potential climate changes are used to provide a robust assessment and prioritization for culvert replacements.

A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: Towards minimalism

NASA Astrophysics Data System (ADS)

Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi

2018-06-01

Developed is a high-order accurate shock-capturing scheme for the compressible Euler/Navier-Stokes equations; the formal accuracy is 5th order in space and 4th order in time. The performance and efficiency of the scheme are validated in various numerical tests. The main ingredients of the scheme are nothing special; they are variants of the standard numerical flux, MUSCL, the usual Lagrange's polynomial and the conventional Runge-Kutta method. The scheme can compute a boundary layer accurately with a rational resolution and capture a stationary contact discontinuity sharply without inner points. And yet it is endowed with high resistance against shock anomalies (carbuncle phenomenon, post-shock oscillations, etc.). A good balance between high robustness and low dissipation is achieved by blending three types of numerical fluxes according to physical situation in an intuitively easy-to-understand way. The performance of the scheme is largely comparable to that of WENO5-Rusanov, while its computational cost is 30-40% less than of that of the advanced scheme.

Gradient-based Electrical Properties Tomography (gEPT): a Robust Method for Mapping Electrical Properties of Biological Tissues In Vivo Using Magnetic Resonance Imaging

PubMed Central

Liu, Jiaen; Zhang, Xiaotong; Schmitter, Sebastian; Van de Moortele, Pierre-Francois; He, Bin

2014-01-01

Purpose To develop high-resolution electrical properties tomography (EPT) methods and investigate a gradient-based EPT (gEPT) approach which aims to reconstruct the electrical properties (EP), including conductivity and permittivity, of an imaged sample from experimentally measured B1 maps with improved boundary reconstruction and robustness against measurement noise. Theory and Methods Using a multi-channel transmit/receive stripline head coil, with acquired B1 maps for each coil element, by assuming negligible Bz component compared to transverse B1 components, a theory describing the relationship between B1 field, EP value and their spatial gradient has been proposed. The final EP images were obtained through spatial integration over the reconstructed EP gradient. Numerical simulation, physical phantom and in vivo human experiments at 7 T have been conducted to evaluate the performance of the proposed methods. Results Reconstruction results were compared with target EP values in both simulations and phantom experiments. Human experimental results were compared with EP values in literature. Satisfactory agreement was observed with improved boundary reconstruction. Importantly, the proposed gEPT method proved to be more robust against noise when compared to previously described non-gradient-based EPT approaches. Conclusion The proposed gEPT approach holds promises to improve EP mapping quality by recovering the boundary information and enhancing robustness against noise. PMID:25213371

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

NASA Astrophysics Data System (ADS)

Iwase, Shigeru; Futamura, Yasunori; Imakura, Akira; Sakurai, Tetsuya; Tsukamoto, Shigeru; Ono, Tomoya

2018-05-01

We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a contour integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve an exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite-difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the freestanding silicene with the line defect originating from the reversed buckled phases.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Clustering high dimensional data using RIA

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

Aziz, Nazrina

2015-05-15

Clustering may simply represent a convenient method for organizing a large data set so that it can easily be understood and information can efficiently be retrieved. However, identifying cluster in high dimensionality data sets is a difficult task because of the curse of dimensionality. Another challenge in clustering is some traditional functions cannot capture the pattern dissimilarity among objects. In this article, we used an alternative dissimilarity measurement called Robust Influence Angle (RIA) in the partitioning method. RIA is developed using eigenstructure of the covariance matrix and robust principal component score. We notice that, it can obtain cluster easily andmore » hence avoid the curse of dimensionality. It is also manage to cluster large data sets with mixed numeric and categorical value.« less

Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises.

PubMed

Chang, Wen-Jer; Huang, Bo-Jyun

2014-11-01

The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

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

A simple finite element method for non-divergence form elliptic equation

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-01

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for non-divergence form elliptic equation

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

Mu, Lin; Ye, Xiu

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

Progress in multirate digital control system design

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1991-01-01

A new methodology for multirate sampled-data control design based on a new generalized control law structure, two new parameter-optimization-based control law synthesis methods, and a new singular-value-based robustness analysis method are described. The control law structure can represent multirate sampled-data control laws of arbitrary structure and dynamic order, with arbitrarily prescribed sampling rates for all sensors and update rates for all processor states and actuators. The two control law synthesis methods employ numerical optimization to determine values for the control law parameters. The robustness analysis method is based on the multivariable Nyquist criterion applied to the loop transfer function for the sampling period equal to the period of repetition of the system's complete sampling/update schedule. The complete methodology is demonstrated by application to the design of a combination yaw damper and modal suppression system for a commercial aircraft.

The effect of numerical methods on the simulation of mid-ocean ridge hydrothermal models

NASA Astrophysics Data System (ADS)

Carpio, J.; Braack, M.

2012-01-01

This work considers the effect of the numerical method on the simulation of a 2D model of hydrothermal systems located in the high-permeability axial plane of mid-ocean ridges. The behavior of hot plumes, formed in a porous medium between volcanic lava and the ocean floor, is very irregular due to convective instabilities. Therefore, we discuss and compare two different numerical methods for solving the mathematical model of this system. In concrete, we consider two ways to treat the temperature equation of the model: a semi-Lagrangian formulation of the advective terms in combination with a Galerkin finite element method for the parabolic part of the equations and a stabilized finite element scheme. Both methods are very robust and accurate. However, due to physical instabilities in the system at high Rayleigh number, the effect of the numerical method is significant with regard to the temperature distribution at a certain time instant. The good news is that relevant statistical quantities remain relatively stable and coincide for the two numerical schemes. The agreement is larger in the case of a mathematical model with constant water properties. In the case of a model with nonlinear dependence of the water properties on the temperature and pressure, the agreement in the statistics is clearly less pronounced. Hence, the presented work accentuates the need for a strengthened validation of the compatibility between numerical scheme (accuracy/resolution) and complex (realistic/nonlinear) models.

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.

Doubly robust nonparametric inference on the average treatment effect.

PubMed

Benkeser, D; Carone, M; Laan, M J Van Der; Gilbert, P B

2017-12-01

Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.

Robust control of combustion instabilities

NASA Astrophysics Data System (ADS)

Hong, Boe-Shong

Several interactive dynamical subsystems, each of which has its own time-scale and physical significance, are decomposed to build a feedback-controlled combustion- fluid robust dynamics. On the fast-time scale, the phenomenon of combustion instability is corresponding to the internal feedback of two subsystems: acoustic dynamics and flame dynamics, which are parametrically dependent on the slow-time-scale mean-flow dynamics controlled for global performance by a mean-flow controller. This dissertation constructs such a control system, through modeling, analysis and synthesis, to deal with model uncertainties, environmental noises and time- varying mean-flow operation. Conservation law is decomposed as fast-time acoustic dynamics and slow-time mean-flow dynamics, served for synthesizing LPV (linear parameter varying)- L2-gain robust control law, in which a robust observer is embedded for estimating and controlling the internal status, while achieving trade- offs among robustness, performances and operation. The robust controller is formulated as two LPV-type Linear Matrix Inequalities (LMIs), whose numerical solver is developed by finite-element method. Some important issues related to physical understanding and engineering application are discussed in simulated results of the control system.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

An Extended Lagrangian Method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1995-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Fire metrology: Current and future directions in physics-based measurements

Treesearch

Robert L. Kremens; Alistair M.S. Smith; Matthew B. Dickinson

2010-01-01

The robust evaluation of fire impacts on the biota, soil, and atmosphere requires measurement and analysis methods that can characterize combustion processes across a range of temporal and spatial scales. Numerous challenges are apparent in the literature. These challenges have led to novel research to quantify the 1) structure and heterogeneity of the pre-fire...

Extended robust support vector machine based on financial risk minimization.

PubMed

Takeda, Akiko; Fujiwara, Shuhei; Kanamori, Takafumi

2014-11-01

Financial risk measures have been used recently in machine learning. For example, ν-support vector machine ν-SVM) minimizes the conditional value at risk (CVaR) of margin distribution. The measure is popular in finance because of the subadditivity property, but it is very sensitive to a few outliers in the tail of the distribution. We propose a new classification method, extended robust SVM (ER-SVM), which minimizes an intermediate risk measure between the CVaR and value at risk (VaR) by expecting that the resulting model becomes less sensitive than ν-SVM to outliers. We can regard ER-SVM as an extension of robust SVM, which uses a truncated hinge loss. Numerical experiments imply the ER-SVM's possibility of achieving a better prediction performance with proper parameter setting.

H∞ control of combustion in diesel engines using a discrete dynamics model

NASA Astrophysics Data System (ADS)

Hirata, Mitsuo; Ishizuki, Sota; Suzuki, Masayasu

2016-09-01

This paper proposes a control method for combustion in diesel engines using a discrete dynamics model. The proposed two-degree-of-freedom control scheme achieves not only good feedback properties such as disturbance suppression and robust stability but also a good transient response. The method includes a feedforward controller constructed from the inverse model of the plant, and a feedback controller designed by an Hcontrol method, which reduces the effect of the turbocharger lag. The effectiveness of the proposed method is evaluated via numerical simulations.

Exploring a potential energy surface by machine learning for characterizing atomic transport

NASA Astrophysics Data System (ADS)

Kanamori, Kenta; Toyoura, Kazuaki; Honda, Junya; Hattori, Kazuki; Seko, Atsuto; Karasuyama, Masayuki; Shitara, Kazuki; Shiga, Motoki; Kuwabara, Akihide; Takeuchi, Ichiro

2018-03-01

We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.

A positivity-preserving, implicit defect-correction multigrid method for turbulent combustion

NASA Astrophysics Data System (ADS)

Wasserman, M.; Mor-Yossef, Y.; Greenberg, J. B.

2016-07-01

A novel, robust multigrid method for the simulation of turbulent and chemically reacting flows is developed. A survey of previous attempts at implementing multigrid for the problems at hand indicated extensive use of artificial stabilization to overcome numerical instability arising from non-linearity of turbulence and chemistry model source-terms, small-scale physics of combustion, and loss of positivity. These issues are addressed in the current work. The highly stiff Reynolds-averaged Navier-Stokes (RANS) equations, coupled with turbulence and finite-rate chemical kinetics models, are integrated in time using the unconditionally positive-convergent (UPC) implicit method. The scheme is successfully extended in this work for use with chemical kinetics models, in a fully-coupled multigrid (FC-MG) framework. To tackle the degraded performance of multigrid methods for chemically reacting flows, two major modifications are introduced with respect to the basic, Full Approximation Storage (FAS) approach. First, a novel prolongation operator that is based on logarithmic variables is proposed to prevent loss of positivity due to coarse-grid corrections. Together with the extended UPC implicit scheme, the positivity-preserving prolongation operator guarantees unconditional positivity of turbulence quantities and species mass fractions throughout the multigrid cycle. Second, to improve the coarse-grid-correction obtained in localized regions of high chemical activity, a modified defect correction procedure is devised, and successfully applied for the first time to simulate turbulent, combusting flows. The proposed modifications to the standard multigrid algorithm create a well-rounded and robust numerical method that provides accelerated convergence, while unconditionally preserving the positivity of model equation variables. Numerical simulations of various flows involving premixed combustion demonstrate that the proposed MG method increases the efficiency by a factor of up to eight times with respect to an equivalent single-grid method, and by two times with respect to an artificially-stabilized MG method.

Unconstrained handwritten numeral recognition based on radial basis competitive and cooperative networks with spatio-temporal feature representation.

PubMed

Lee, S; Pan, J J

1996-01-01

This paper presents a new approach to representation and recognition of handwritten numerals. The approach first transforms a two-dimensional (2-D) spatial representation of a numeral into a three-dimensional (3-D) spatio-temporal representation by identifying the tracing sequence based on a set of heuristic rules acting as transformation operators. A multiresolution critical-point segmentation method is then proposed to extract local feature points, at varying degrees of scale and coarseness. A new neural network architecture, referred to as radial-basis competitive and cooperative network (RCCN), is presented especially for handwritten numeral recognition. RCCN is a globally competitive and locally cooperative network with the capability of self-organizing hidden units to progressively achieve desired network performance, and functions as a universal approximator of arbitrary input-output mappings. Three types of RCCNs are explored: input-space RCCN (IRCCN), output-space RCCN (ORCCN), and bidirectional RCCN (BRCCN). Experiments against handwritten zip code numerals acquired by the U.S. Postal Service indicated that the proposed method is robust in terms of variations, deformations, transformations, and corruption, achieving about 97% recognition rate.

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Golden angle based scanning for robust corneal topography with OCT

PubMed Central

Wagner, Joerg; Goldblum, David; Cattin, Philippe C.

2017-01-01

Corneal topography allows the assessment of the cornea’s refractive power which is crucial for diagnostics and surgical planning. The use of optical coherence tomography (OCT) for corneal topography is still limited. One limitation is the susceptibility to disturbances like blinking of the eye. This can result in partially corrupted scans that cannot be evaluated using common methods. We present a new scanning method for reliable corneal topography from partial scans. Based on the golden angle, the method features a balanced scan point distribution which refines over measurement time and remains balanced when part of the scan is removed. The performance of the method is assessed numerically and by measurements of test surfaces. The results confirm that the method enables numerically well-conditioned and reliable corneal topography from partially corrupted scans and reduces the need for repeated measurements in case of abrupt disturbances. PMID:28270961

Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

NASA Astrophysics Data System (ADS)

Li, G. Q.; Zhu, Z. H.

2015-12-01

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

A parallel direct-forcing fictitious domain method for simulating microswimmers

NASA Astrophysics Data System (ADS)

Gao, Tong; Lin, Zhaowu

2017-11-01

We present a 3D parallel direct-forcing fictitious domain method for simulating swimming micro-organisms at small Reynolds numbers. We treat the motile micro-swimmers as spherical rigid particles using the ``Squirmer'' model. The particle dynamics are solved on the moving Larangian meshes that overlay upon a fixed Eulerian mesh for solving the fluid motion, and the momentum exchange between the two phases is resolved by distributing pseudo body-forces over the particle interior regions which constrain the background fictitious fluids to follow the particle movement. While the solid and fluid subproblems are solved separately, no inner-iterations are required to enforce numerical convergence. We demonstrate the accuracy and robustness of the method by comparing our results with the existing analytical and numerical studies for various cases of single particle dynamics and particle-particle interactions. We also perform a series of numerical explorations to obtain statistical and rheological measurements to characterize the dynamics and structures of Squirmer suspensions. NSF DMS 1619960.

Myocardial strains from 3D displacement encoded magnetic resonance imaging

PubMed Central

2012-01-01

Background The ability to measure and quantify myocardial motion and deformation provides a useful tool to assist in the diagnosis, prognosis and management of heart disease. The recent development of magnetic resonance imaging methods, such as harmonic phase analysis of tagging and displacement encoding with stimulated echoes (DENSE), make detailed non-invasive 3D kinematic analyses of human myocardium possible in the clinic and for research purposes. A robust analysis method is required, however. Methods We propose to estimate strain using a polynomial function which produces local models of the displacement field obtained with DENSE. Given a specific polynomial order, the model is obtained as the least squares fit of the acquired displacement field. These local models are subsequently used to produce estimates of the full strain tensor. Results The proposed method is evaluated on a numerical phantom as well as in vivo on a healthy human heart. The evaluation showed that the proposed method produced accurate results and showed low sensitivity to noise in the numerical phantom. The method was also demonstrated in vivo by assessment of the full strain tensor and to resolve transmural strain variations. Conclusions Strain estimation within a 3D myocardial volume based on polynomial functions yields accurate and robust results when validated on an analytical model. The polynomial field is capable of resolving the measured material positions from the in vivo data, and the obtained in vivo strains values agree with previously reported myocardial strains in normal human hearts. PMID:22533791

Evaluation of Two Outlier-Detection-Based Methods for Detecting Tissue-Selective Genes from Microarray Data

PubMed Central

Kadota, Koji; Konishi, Tomokazu; Shimizu, Kentaro

2007-01-01

Large-scale expression profiling using DNA microarrays enables identification of tissue-selective genes for which expression is considerably higher and/or lower in some tissues than in others. Among numerous possible methods, only two outlier-detection-based methods (an AIC-based method and Sprent’s non-parametric method) can treat equally various types of selective patterns, but they produce substantially different results. We investigated the performance of these two methods for different parameter settings and for a reduced number of samples. We focused on their ability to detect selective expression patterns robustly. We applied them to public microarray data collected from 36 normal human tissue samples and analyzed the effects of both changing the parameter settings and reducing the number of samples. The AIC-based method was more robust in both cases. The findings confirm that the use of the AIC-based method in the recently proposed ROKU method for detecting tissue-selective expression patterns is correct and that Sprent’s method is not suitable for ROKU. PMID:19936074

Integrated approaches to the application of advanced modeling technology in process development and optimization

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

Allgor, R.J.; Feehery, W.F.; Tolsma, J.E.

The batch process development problem serves as good candidate to guide the development of process modeling environments. It demonstrates that very robust numerical techniques are required within an environment that can collect, organize, and maintain the data and models required to address the batch process development problem. This paper focuses on improving the robustness and efficiency of the numerical algorithms required in such a modeling environment through the development of hybrid numerical and symbolic strategies.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

Mixed Arlequin method for multiscale poromechanics problems: Mixed Arlequin method for multiscale poromechanics problems

DOE PAGES

Sun, WaiChing; Cai, Zhijun; Choo, Jinhyun

2016-11-18

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. Here, to examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space ofmore » the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Finally, through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model.« less

Taguchi Method Applied in Optimization of Shipley SJR 5740 Positive Resist Deposition

NASA Technical Reports Server (NTRS)

Hui, A.; Blosiu, J. O.; Wiberg, D. V.

1998-01-01

Taguchi Methods of Robust Design presents a way to optimize output process performance through an organized set of experiments by using orthogonal arrays. Analysis of variance and signal-to-noise ratio is used to evaluate the contribution of each of the process controllable parameters in the realization of the process optimization. In the photoresist deposition process, there are numerous controllable parameters that can affect the surface quality and thickness of the final photoresist layer.

Computation of diverging sums based on a finite number of terms

NASA Astrophysics Data System (ADS)

Lv, Q. Z.; Norris, S.; Pelphrey, R.; Su, Q.; Grobe, R.

2017-10-01

We propose a numerical method that permits us to compute the sum of a diverging series from only the first N terms by generalizing the traditional Borel technique. The method is rather robust and can be used to recover the ground state energy from the diverging perturbation theory for quantum field theoretical systems that are spatially constrained. Surprisingly, even the corresponding eigenvectors can be generated despite the intrinsic non-perturbative nature of bound state problems.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

NASA Astrophysics Data System (ADS)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Two-Phase Cryogenic Heat Exchanger for the Thermodynamic Vent System

NASA Technical Reports Server (NTRS)

Christie, Robert J.

2011-01-01

A two-phase cryogenic heat exchanger for a thermodynamic vent system was designed and analyzed, and the predicted performance was compared with test results. A method for determining the required size of the Joule-Thomson device was also developed. Numerous sensitivity studies were performed to show that the design was robust and possessed a comfortable capacity margin. The comparison with the test results showed very similar heat extraction performance for similar inlet conditions. It was also shown that estimates for Joule- Thomson device flow rates and exit quality can vary significantly and these need to be accommodated for with a robust system design.

The L sub 1 finite element method for pure convection problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1991-01-01

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

Constraining the thermal conditions of impact environments through integrated low-temperature thermochronometry and numerical modeling

NASA Astrophysics Data System (ADS)

Kelly, N. M.; Marchi, S.; Mojzsis, S. J.; Flowers, R. M.; Metcalf, J. R.; Bottke, W. F., Jr.

2017-12-01

Impacts have a significant physical and chemical influence on the surface conditions of a planet. The cratering record is used to understand a wide array of impact processes, such as the evolution of the impact flux through time. However, the relationship between impactor size and a resulting impact crater remains controversial (e.g., Bottke et al., 2016). Likewise, small variations in the impact velocity are known to significantly affect the thermal-mechanical disturbances in the aftermath of a collision. Development of more robust numerical models for impact cratering has implications for how we evaluate the disruptive capabilities of impact events, including the extent and duration of thermal anomalies, the volume of ejected material, and the resulting landscape of impacted environments. To address uncertainties in crater scaling relationships, we present an approach and methodology that integrates numerical modeling of the thermal evolution of terrestrial impact craters with low-temperature, (U-Th)/He thermochronometry. The approach uses time-temperature (t-T) paths of crust within an impact crater, generated from numerical simulations of an impact. These t-T paths are then used in forward models to predict the resetting behavior of (U-Th)/He ages in the mineral chronometers apatite and zircon. Differences between the predicted and measured (U-Th)/He ages from a modeled terrestrial impact crater can then be used to evaluate parameters in the original numerical simulations, and refine the crater scaling relationships. We expect our methodology to additionally inform our interpretation of impact products, such as lunar impact breccias and meteorites, providing robust constraints on their thermal histories. In addition, the method is ideal for sample return mission planning - robust "prediction" of ages we expect from a given impact environment enhances our ability to target sampling sites on the Moon, Mars or other solar system bodies where impacts have strongly shaped the surface. Bottke, W.F., Vokrouhlicky, D., Ghent, B., et al. (2016). 47th LPSC, Abstract #2036.

A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

PubMed

Khoram, Nafiseh; Zayane, Chadia; Djellouli, Rabia; Laleg-Kirati, Taous-Meriem

2016-03-15

The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages. We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data. Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method. We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods. We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%). Published by Elsevier B.V.

A new operational approach for solving fractional variational problems depending on indefinite integrals

NASA Astrophysics Data System (ADS)

Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

2018-04-01

In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

Essentially nonoscillatory postprocessing filtering methods

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1992-01-01

High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

A new look at the robust control of discrete-time Markov jump linear systems

NASA Astrophysics Data System (ADS)

Todorov, M. G.; Fragoso, M. D.

2016-03-01

In this paper, we make a foray in the role played by a set of four operators on the study of robust H2 and mixed H2/H∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H2 performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H2 controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H2/H∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.

Improved numerical methods for turbulent viscous recirculating flows

NASA Technical Reports Server (NTRS)

Turan, A.; Vandoormaal, J. P.

1988-01-01

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

A robust and contact resolving Riemann solver on unstructured mesh, Part I, Euler method

NASA Astrophysics Data System (ADS)

Shen, Zhijun; Yan, Wei; Yuan, Guangwei

2014-07-01

This article presents a new cell-centered numerical method for compressible flows on arbitrary unstructured meshes. A multi-dimensional Riemann solver based on the HLLC method (denoted by HLLC-2D solver) is established. The work is an extension from the cell-centered Lagrangian scheme of Maire et al. [27] to the Eulerian framework. Similarly to the work in [27], a two-dimensional contact velocity defined on a grid node is introduced, and the motivation is to keep an edge flux consistency with the node velocity connected to the edge intrinsically. The main new feature of the algorithm is to relax the condition that the contact pressures must be same in the traditional HLLC solver. The discontinuous fluxes are constructed across each wave sampling direction rather than only along the contact wave direction. The two-dimensional contact velocity of the grid node is determined via enforcing conservation of mass, momentum and total energy, and thus the new method satisfies these conservation properties at nodes rather than on grid edges. Other good properties of the HLLC-2d solver, such as the positivity and the contact preserving, are described, and the two-dimensional high-order extension is constructed employing MUSCL type reconstruction procedure. Numerical results based on both quadrilateral and triangular grids are presented to demonstrate the robustness and the accuracy of this new solver, which shows it has better performance than the existing HLLC method.

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

NASA Astrophysics Data System (ADS)

Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-12-01

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.

Direct numerical simulation of variable surface tension flows using a Volume-of-Fluid method

NASA Astrophysics Data System (ADS)

Seric, Ivana; Afkhami, Shahriar; Kondic, Lou

2018-01-01

We develop a general methodology for the inclusion of a variable surface tension coefficient into a Volume-of-Fluid based Navier-Stokes solver. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation is applicable to both temperature and concentration dependent surface tension coefficient, along with the setups involving a large jump in the temperature between the fluid and its surrounding, as well as the situations where the concentration should be strictly confined to the fluid domain, such as the mixing of fluids with different surface tension coefficients. We demonstrate the applicability of our method to the thermocapillary migration of bubbles and the coalescence of drops characterized by a different surface tension coefficient.

Computational methods for yeast prion curing curves.

PubMed

Ridout, Martin S

2008-10-01

If the chemical guanidine hydrochloride is added to a dividing culture of yeast cells in which some of the protein Sup35p is in its prion form, the proportion of cells that carry replicating units of the prion, termed propagons, decreases gradually over time. Stochastic models to describe this process of 'curing' have been developed in earlier work. The present paper investigates the use of numerical methods of Laplace transform inversion to calculate curing curves and contrasts this with an alternative, more direct, approach that involves numerical integration. Transform inversion is found to provide a much more efficient computational approach that allows different models to be investigated with minimal programming effort. The method is used to investigate the robustness of the curing curve to changes in the assumed distribution of cell generation times. Matlab code is available for carrying out the calculations.

The Superior Lambert Algorithm

NASA Astrophysics Data System (ADS)

der, G.

2011-09-01

Lambert algorithms are used extensively for initial orbit determination, mission planning, space debris correlation, and missile targeting, just to name a few applications. Due to the significance of the Lambert problem in Astrodynamics, Gauss, Battin, Godal, Lancaster, Gooding, Sun and many others (References 1 to 15) have provided numerous formulations leading to various analytic solutions and iterative methods. Most Lambert algorithms and their computer programs can only work within one revolution, break down or converge slowly when the transfer angle is near zero or 180 degrees, and their multi-revolution limitations are either ignored or barely addressed. Despite claims of robustness, many Lambert algorithms fail without notice, and the users seldom have a clue why. The DerAstrodynamics lambert2 algorithm, which is based on the analytic solution formulated by Sun, works for any number of revolutions and converges rapidly at any transfer angle. It provides significant capability enhancements over every other Lambert algorithm in use today. These include improved speed, accuracy, robustness, and multirevolution capabilities as well as implementation simplicity. Additionally, the lambert2 algorithm provides a powerful tool for solving the angles-only problem without artificial singularities (pointed out by Gooding in Reference 16), which involves 3 lines of sight captured by optical sensors, or systems such as the Air Force Space Surveillance System (AFSSS). The analytic solution is derived from the extended Godal’s time equation by Sun, while the iterative method of solution is that of Laguerre, modified for robustness. The Keplerian solution of a Lambert algorithm can be extended to include the non-Keplerian terms of the Vinti algorithm via a simple targeting technique (References 17 to 19). Accurate analytic non-Keplerian trajectories can be predicted for satellites and ballistic missiles, while performing at least 100 times faster in speed than most numerical integration methods.

Real-time PCR machine system modeling and a systematic approach for the robust design of a real-time PCR-on-a-chip system.

PubMed

Lee, Da-Sheng

2010-01-01

Chip-based DNA quantification systems are widespread, and used in many point-of-care applications. However, instruments for such applications may not be maintained or calibrated regularly. Since machine reliability is a key issue for normal operation, this study presents a system model of the real-time Polymerase Chain Reaction (PCR) machine to analyze the instrument design through numerical experiments. Based on model analysis, a systematic approach was developed to lower the variation of DNA quantification and achieve a robust design for a real-time PCR-on-a-chip system. Accelerated lift testing was adopted to evaluate the reliability of the chip prototype. According to the life test plan, this proposed real-time PCR-on-a-chip system was simulated to work continuously for over three years with similar reproducibility in DNA quantification. This not only shows the robustness of the lab-on-a-chip system, but also verifies the effectiveness of our systematic method for achieving a robust design.

An immersed boundary method for simulating vesicle dynamics in three dimensions

NASA Astrophysics Data System (ADS)

Seol, Yunchang; Hu, Wei-Fan; Kim, Yongsam; Lai, Ming-Chih

2016-10-01

We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows (Hu et al., 2014 [17]) to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric case, the fully 3D numerical implementation is much more complicated and is far from straightforward. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. As in 3D axisymmetric case, instead of keeping the vesicle locally incompressible, we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. The vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex (Lagrangian marker in the IB method) of the triangulation. A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method. We perform the convergence study for the immersed boundary forces and the fluid velocity field. We then study the vesicle dynamics in various flows such as quiescent, simple shear, and gravitational flows. Our numerical results show good agreements with those obtained in previous theoretical, experimental and numerical studies.

Numerically pricing American options under the generalized mixed fractional Brownian motion model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying

2016-06-01

In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-01-25

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effectivemore » to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a non-condensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. As a result, volume fraction of the absent phase can be calculated effectively as zero.« less

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.

PubMed

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

Implementation details of the coupled QMR algorithm

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1992-01-01

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

NASA Technical Reports Server (NTRS)

White, Jeffery A.; Baurle, Robert A.; Passe, Bradley J.; Spiegel, Seth C.; Nishikawa, Hiroaki

2017-01-01

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

Use of the parameterised finite element method to robustly and efficiently evolve the edge of a moving cell.

PubMed

Neilson, Matthew P; Mackenzie, John A; Webb, Steven D; Insall, Robert H

2010-11-01

In this paper we present a computational tool that enables the simulation of mathematical models of cell migration and chemotaxis on an evolving cell membrane. Recent models require the numerical solution of systems of reaction-diffusion equations on the evolving cell membrane and then the solution state is used to drive the evolution of the cell edge. Previous work involved moving the cell edge using a level set method (LSM). However, the LSM is computationally very expensive, which severely limits the practical usefulness of the algorithm. To address this issue, we have employed the parameterised finite element method (PFEM) as an alternative method for evolving a cell boundary. We show that the PFEM is far more efficient and robust than the LSM. We therefore suggest that the PFEM potentially has an essential role to play in computational modelling efforts towards the understanding of many of the complex issues related to chemotaxis.

Robust cooperation of connected vehicle systems with eigenvalue-bounded interaction topologies in the presence of uncertain dynamics

NASA Astrophysics Data System (ADS)

Li, Keqiang; Gao, Feng; Li, Shengbo Eben; Zheng, Yang; Gao, Hongbo

2017-12-01

This study presents a distributed H-infinity control method for uncertain platoons with dimensionally and structurally unknown interaction topologies provided that the associated topological eigenvalues are bounded by a predesigned range.With an inverse model to compensate for nonlinear powertrain dynamics, vehicles in a platoon are modeled by third-order uncertain systems with bounded disturbances. On the basis of the eigenvalue decomposition of topological matrices, we convert the platoon system to a norm-bounded uncertain part and a diagonally structured certain part by applying linear transformation. We then use a common Lyapunov method to design a distributed H-infinity controller. Numerically, two linear matrix inequalities corresponding to the minimum and maximum eigenvalues should be solved. The resulting controller can tolerate interaction topologies with eigenvalues located in a certain range. The proposed method can also ensure robustness performance and disturbance attenuation ability for the closed-loop platoon system. Hardware-in-the-loop tests are performed to validate the effectiveness of our method.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

SpeCond: a method to detect condition-specific gene expression

PubMed Central

2011-01-01

Transcriptomic studies routinely measure expression levels across numerous conditions. These datasets allow identification of genes that are specifically expressed in a small number of conditions. However, there are currently no statistically robust methods for identifying such genes. Here we present SpeCond, a method to detect condition-specific genes that outperforms alternative approaches. We apply the method to a dataset of 32 human tissues to determine 2,673 specifically expressed genes. An implementation of SpeCond is freely available as a Bioconductor package at http://www.bioconductor.org/packages/release/bioc/html/SpeCond.html. PMID:22008066

A free energy-based surface tension force model for simulation of multiphase flows by level-set method

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Chen, Z.; Shu, C.; Wang, Y.; Niu, X. D.; Shu, S.

2017-09-01

In this paper, a free energy-based surface tension force (FESF) model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method. By using the analytical form of order parameter along the normal direction to the interface in the phase-field method and the free energy principle, FESF model offers an explicit and analytical formulation for the surface tension force. The only variable in this formulation is the normal distance to the interface, which can be substituted by the distance function solved by the level set method. On one hand, as compared to conventional continuum surface force (CSF) model in the level set method, FESF model introduces no regularized delta function, due to which it suffers less from numerical diffusions and performs better in mass conservation. On the other hand, as compared to the phase field surface tension force (PFSF) model, the evaluation of surface tension force in FESF model is based on an analytical approach rather than numerical approximations of spatial derivatives. Therefore, better numerical stability and higher accuracy can be expected. Various numerical examples are tested to validate the robustness of the proposed FESF model. It turns out that FESF model performs better than CSF model and PFSF model in terms of accuracy, stability, convergence speed and mass conservation. It is also shown in numerical tests that FESF model can effectively simulate problems with high density/viscosity ratio, high Reynolds number and severe topological interfacial changes.

A robust sub-pixel edge detection method of infrared image based on tremor-based retinal receptive field model

NASA Astrophysics Data System (ADS)

Gao, Kun; Yang, Hu; Chen, Xiaomei; Ni, Guoqiang

2008-03-01

Because of complex thermal objects in an infrared image, the prevalent image edge detection operators are often suitable for a certain scene and extract too wide edges sometimes. From a biological point of view, the image edge detection operators work reliably when assuming a convolution-based receptive field architecture. A DoG (Difference-of- Gaussians) model filter based on ON-center retinal ganglion cell receptive field architecture with artificial eye tremors introduced is proposed for the image contour detection. Aiming at the blurred edges of an infrared image, the subsequent orthogonal polynomial interpolation and sub-pixel level edge detection in rough edge pixel neighborhood is adopted to locate the foregoing rough edges in sub-pixel level. Numerical simulations show that this method can locate the target edge accurately and robustly.

Scale-adaptive compressive tracking with feature integration

NASA Astrophysics Data System (ADS)

Liu, Wei; Li, Jicheng; Chen, Xiao; Li, Shuxin

2016-05-01

Numerous tracking-by-detection methods have been proposed for robust visual tracking, among which compressive tracking (CT) has obtained some promising results. A scale-adaptive CT method based on multifeature integration is presented to improve the robustness and accuracy of CT. We introduce a keypoint-based model to achieve the accurate scale estimation, which can additionally give a prior location of the target. Furthermore, by the high efficiency of data-independent random projection matrix, multiple features are integrated into an effective appearance model to construct the naïve Bayes classifier. At last, an adaptive update scheme is proposed to update the classifier conservatively. Experiments on various challenging sequences demonstrate substantial improvements by our proposed tracker over CT and other state-of-the-art trackers in terms of dealing with scale variation, abrupt motion, deformation, and illumination changes.

Numerical Predictions of Wind Turbine Power and Aerodynamic Loads for the NREL Phase II and IV Combined Experiment Rotor

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Johnson, Wayne; vanDam, C. P.; Chao, David D.; Cortes, Regina; Yee, Karen

1999-01-01

Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

Computational methods for reactive transport modeling: A Gibbs energy minimization approach for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg

2016-02-01

We present a numerical method for multiphase chemical equilibrium calculations based on a Gibbs energy minimization approach. The method can accurately and efficiently determine the stable phase assemblage at equilibrium independently of the type of phases and species that constitute the chemical system. We have successfully applied our chemical equilibrium algorithm in reactive transport simulations to demonstrate its effective use in computationally intensive applications. We used FEniCS to solve the governing partial differential equations of mass transport in porous media using finite element methods in unstructured meshes. Our equilibrium calculations were benchmarked with GEMS3K, the numerical kernel of the geochemical package GEMS. This allowed us to compare our results with a well-established Gibbs energy minimization algorithm, as well as their performance on every mesh node, at every time step of the transport simulation. The benchmark shows that our novel chemical equilibrium algorithm is accurate, robust, and efficient for reactive transport applications, and it is an improvement over the Gibbs energy minimization algorithm used in GEMS3K. The proposed chemical equilibrium method has been implemented in Reaktoro, a unified framework for modeling chemically reactive systems, which is now used as an alternative numerical kernel of GEMS.

Guide to NavyFOAM V1.0

DTIC Science & Technology

2011-04-01

NavyFOAM has been developed using an open-source CFD software tool-kit ( OpenFOAM ) that draws heavily upon object-oriented programming. The...numerical methods and the physical models in the original version of OpenFOAM have been upgraded in an effort to improve accuracy and robustness of...computational fluid dynamics OpenFOAM , Object Oriented Programming (OOP) (CFD), NavyFOAM, 16. SECURITY CLASSIFICATION OF: a. REPORT UNCLASSIFIED b

Robust Feature Selection Technique using Rank Aggregation.

PubMed

Sarkar, Chandrima; Cooley, Sarah; Srivastava, Jaideep

2014-01-01

Although feature selection is a well-developed research area, there is an ongoing need to develop methods to make classifiers more efficient. One important challenge is the lack of a universal feature selection technique which produces similar outcomes with all types of classifiers. This is because all feature selection techniques have individual statistical biases while classifiers exploit different statistical properties of data for evaluation. In numerous situations this can put researchers into dilemma as to which feature selection method and a classifiers to choose from a vast range of choices. In this paper, we propose a technique that aggregates the consensus properties of various feature selection methods to develop a more optimal solution. The ensemble nature of our technique makes it more robust across various classifiers. In other words, it is stable towards achieving similar and ideally higher classification accuracy across a wide variety of classifiers. We quantify this concept of robustness with a measure known as the Robustness Index (RI). We perform an extensive empirical evaluation of our technique on eight data sets with different dimensions including Arrythmia, Lung Cancer, Madelon, mfeat-fourier, internet-ads, Leukemia-3c and Embryonal Tumor and a real world data set namely Acute Myeloid Leukemia (AML). We demonstrate not only that our algorithm is more robust, but also that compared to other techniques our algorithm improves the classification accuracy by approximately 3-4% (in data set with less than 500 features) and by more than 5% (in data set with more than 500 features), across a wide range of classifiers.

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods

NASA Astrophysics Data System (ADS)

Maximov, Ivan I.; Vinding, Mads S.; Tse, Desmond H. Y.; Nielsen, Niels Chr.; Shah, N. Jon

2015-05-01

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

Predictive Lateral Logic for Numerical Entry Guidance Algorithms

NASA Technical Reports Server (NTRS)

Smith, Kelly M.

2016-01-01

Recent entry guidance algorithm development123 has tended to focus on numerical integration of trajectories onboard in order to evaluate candidate bank profiles. Such methods enjoy benefits such as flexibility to varying mission profiles and improved robustness to large dispersions. A common element across many of these modern entry guidance algorithms is a reliance upon the concept of Apollo heritage lateral error (or azimuth error) deadbands in which the number of bank reversals to be performed is non-deterministic. This paper presents a closed-loop bank reversal method that operates with a fixed number of bank reversals defined prior to flight. However, this number of bank reversals can be modified at any point, including in flight, based on contingencies such as fuel leaks where propellant usage must be minimized.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

Anderson acceleration and application to the three-temperature energy equations

NASA Astrophysics Data System (ADS)

An, Hengbin; Jia, Xiaowei; Walker, Homer F.

2017-10-01

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton-Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Generalized Ordinary Differential Equation Models 1

PubMed Central

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-01-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. PMID:25544787

Generalized Ordinary Differential Equation Models.

PubMed

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

The Contact Dynamics method: A nonsmooth story

NASA Astrophysics Data System (ADS)

Dubois, Frédéric; Acary, Vincent; Jean, Michel

2018-03-01

When velocity jumps are occurring, the dynamics is said to be nonsmooth. For instance, in collections of contacting rigid bodies, jumps are caused by shocks and dry friction. Without compliance at the interface, contact laws are not only non-differentiable in the usual sense but also multi-valued. Modeling contacting bodies is of interest in order to understand the behavior of numerous mechanical systems such as flexible multi-body systems, granular materials or masonry. These granular materials behave puzzlingly either like a solid or a fluid and a description in the frame of classical continuous mechanics would be welcome though far to be satisfactory nowadays. Jean-Jacques Moreau greatly contributed to convex analysis, functions of bounded variations, differential measure theory, sweeping process theory, definitive mathematical tools to deal with nonsmooth dynamics. He converted all these underlying theoretical ideas into an original nonsmooth implicit numerical method called Contact Dynamics (CD); a robust and efficient method to simulate large collections of bodies with frictional contacts and impacts. The CD method offers a very interesting complementary alternative to the family of smoothed explicit numerical methods, often called Distinct Elements Method (DEM). In this paper developments and improvements of the CD method are presented together with a critical comparative review of advantages and drawbacks of both approaches. xml:lang="fr"

Overview of computational control research at UT Austin

NASA Technical Reports Server (NTRS)

Bong, Wie

1989-01-01

An overview of current research activities at UT Austin is presented to discuss certain technical issues in the following areas: (1) Computer-Aided Nonlinear Control Design: In this project, the describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. INCA program has been enhanced to allow the numerical calculation of describing functions as well as the nonlinear limit cycle analysis capability in the frequency domain; (2) Robust Linear Quadratic Gaussian (LQG) Compensator Synthesis: Robust control design techniques and software tools are developed for flexible space structures with parameter uncertainty. In particular, an interactive, robust multivariable control design capability is being developed for INCA program; and (3) LQR-Based Autonomous Control System for the Space Station: In this project, real time implementation of LQR-based autonomous control system is investigated for the space station with time-varying inertias and with significant multibody dynamic interactions.

Structural damage detection based on stochastic subspace identification and statistical pattern recognition: I. Theory

NASA Astrophysics Data System (ADS)

Ren, W. X.; Lin, Y. Q.; Fang, S. E.

2011-11-01

One of the key issues in vibration-based structural health monitoring is to extract the damage-sensitive but environment-insensitive features from sampled dynamic response measurements and to carry out the statistical analysis of these features for structural damage detection. A new damage feature is proposed in this paper by using the system matrices of the forward innovation model based on the covariance-driven stochastic subspace identification of a vibrating system. To overcome the variations of the system matrices, a non-singularity transposition matrix is introduced so that the system matrices are normalized to their standard forms. For reducing the effects of modeling errors, noise and environmental variations on measured structural responses, a statistical pattern recognition paradigm is incorporated into the proposed method. The Mahalanobis and Euclidean distance decision functions of the damage feature vector are adopted by defining a statistics-based damage index. The proposed structural damage detection method is verified against one numerical signal and two numerical beams. It is demonstrated that the proposed statistics-based damage index is sensitive to damage and shows some robustness to the noise and false estimation of the system ranks. The method is capable of locating damage of the beam structures under different types of excitations. The robustness of the proposed damage detection method to the variations in environmental temperature is further validated in a companion paper by a reinforced concrete beam tested in the laboratory and a full-scale arch bridge tested in the field.

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

NASA Astrophysics Data System (ADS)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Global optimisation methods for poroelastic material characterisation using a clamped sample in a Kundt tube setup

NASA Astrophysics Data System (ADS)

Vanhuyse, Johan; Deckers, Elke; Jonckheere, Stijn; Pluymers, Bert; Desmet, Wim

2016-02-01

The Biot theory is commonly used for the simulation of the vibro-acoustic behaviour of poroelastic materials. However, it relies on a number of material parameters. These can be hard to characterize and require dedicated measurement setups, yielding a time-consuming and costly characterisation. This paper presents a characterisation method which is able to identify all material parameters using only an impedance tube. The method relies on the assumption that the sample is clamped within the tube, that the shear wave is excited and that the acoustic field is no longer one-dimensional. This paper numerically shows the potential of the developed method. It therefore performs a sensitivity analysis of the quantification parameters, i.e. reflection coefficients and relative pressures, and a parameter estimation using global optimisation methods. A 3-step procedure is developed and validated. It is shown that even in the presence of numerically simulated noise this procedure leads to a robust parameter estimation.

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1991-01-01

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

A compressible multiphase framework for simulating supersonic atomization

NASA Astrophysics Data System (ADS)

Regele, Jonathan D.; Garrick, Daniel P.; Hosseinzadeh-Nik, Zahra; Aslani, Mohamad; Owkes, Mark

2016-11-01

The study of atomization in supersonic combustors is critical in designing efficient and high performance scramjets. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in high speed compressible flow requires robust numerical methods that can handle discontinuities caused by both material interfaces and shocks. A shock capturing/diffused interface method is developed to simulate high-speed compressible gas-liquid flows with surface tension effects using the five-equation model. This includes developments that account for the interfacial pressure jump that occurs in the presence of surface tension. A simple and efficient method for computing local interface curvature is developed and an acoustic non-dimensional scaling for the surface tension force is proposed. The method successfully captures a variety of droplet breakup modes over a range of Weber numbers and demonstrates the impact of surface tension in countering droplet deformation in both subsonic and supersonic cross flows.

An efficient numerical method for solving the Boltzmann equation in multidimensions

NASA Astrophysics Data System (ADS)

Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

2018-01-01

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

A new approach of watermarking technique by means multichannel wavelet functions

NASA Astrophysics Data System (ADS)

Agreste, Santa; Puccio, Luigia

2012-12-01

The digital piracy involving images, music, movies, books, and so on, is a legal problem that has not found a solution. Therefore it becomes crucial to create and to develop methods and numerical algorithms in order to solve the copyright problems. In this paper we focus the attention on a new approach of watermarking technique applied to digital color images. Our aim is to describe the realized watermarking algorithm based on multichannel wavelet functions with multiplicity r = 3, called MCWM 1.0. We report a large experimentation and some important numerical results in order to show the robustness of the proposed algorithm to geometrical attacks.

An Energy Decaying Scheme for Nonlinear Dynamics of Shells

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

A frequency dependent preconditioned wavelet method for atmospheric tomography

NASA Astrophysics Data System (ADS)

Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny

2013-12-01

Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

NASA Astrophysics Data System (ADS)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

A study of method robustness for arsenic speciation in drinking water samples by anion exchange HPLC-ICP-MS.

PubMed

Day, Jason A; Montes-Bayón, María; Vonderheide, Anne P; Caruso, Joseph A

2002-08-01

Regulating arsenic species in drinking waters is a reasonable objective, since the various species have different toxicological impacts. However, developing robust and sensitive speciation methods is mandatory prior to any such regulations. Numerous arsenic speciation publications exist, but the question of robustness or ruggedness for a regulatory method has not been fully explored. The present work illustrates the use of anion exchange chromatography coupled to ICP-MS with a commercially available "speciation kit" option. The mobile phase containing 2 mM NaH(2)PO(4) and 0.2 mM EDTA at pH 6 allowed adequate separation of four As species (As(III), As(V), MMAA, DMAA) in less than 10 min. The analytical performance characteristics studied, including method detection limits (lower than 100 ng L(-1) for all the species evaluated), proved the suitability of the method to fulfill the current regulation. Other parameters evaluated such as laboratory fortified blanks, spiked recoveries, and reproducibility over a certain period of time produced adequate results. The samples analyzed were taken from water utilities in different areas of the United States and were provided by the U.S. EPA. The data suggests the speciation setup performs to U.S. EPA specifications but sample treatment and chemistry are also important factors for achieving good recoveries for samples spiked with As(III) as arsenite and As(V) as arsenate.

Robustness of high-fidelity Rydberg gates with single-site addressability

NASA Astrophysics Data System (ADS)

Goerz, Michael H.; Halperin, Eli J.; Aytac, Jon M.; Koch, Christiane P.; Whaley, K. Birgitta

2014-09-01

Controlled-phase (cphase) gates can be realized with trapped neutral atoms by making use of the Rydberg blockade. Achieving the ultrahigh fidelities required for quantum computation with such Rydberg gates, however, is compromised by experimental inaccuracies in pulse amplitudes and timings, as well as by stray fields that cause fluctuations of the Rydberg levels. We report here a comparative study of analytic and numerical pulse sequences for the Rydberg cphase gate that specifically examines the robustness of the gate fidelity with respect to such experimental perturbations. Analytical pulse sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP) are found to be at best moderately robust under these perturbations. In contrast, optimal control theory is seen to allow generation of numerical pulses that are inherently robust within a predefined tolerance window. The resulting numerical pulse shapes display simple modulation patterns and can be rationalized in terms of an interference between distinct two-photon Rydberg excitation pathways. Pulses of such low complexity should be experimentally feasible, allowing gate fidelities of order 99.90-99.99% to be achievable under realistic experimental conditions.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Estimating the gravitational-wave content of initial-data sets for numerical relativity using the Beetle--Burko scalar

NASA Astrophysics Data System (ADS)

Burko, Lior M.

2006-04-01

The Beetle--Burko radiation scalar is a gauge independent, tetrad independent, and background independent quantity that depends only on the radiative degrees of freedom where the notion of radiation is incontrovertible, and can be computed from spatial data as is typical in numerical relativity simulations even for strongly dynamical spacetimes. We show that the Beetle--Burko radiation scalar can be used for estimating the graviational-wave content of initial-data sets in numerical relativity, and can thus be useful for the construction of physically meaningful ones, and the identification of ``junk'' data on the intial value surface. We apply this method for the case of a momentarily stationary black hole binary, and demonstrate how the Beetle-- Burko scalar distinguishes between Misner and Brill--Lindquist initial data. The method, however, is robust, and is applicable to generic initial data sets. In addition to initial data sets, the Beetle--Burko radiation scalar is equally applicable also for evolution data.

The Mixed Finite Element Multigrid Method for Stokes Equations

PubMed Central

Muzhinji, K.; Shateyi, S.; Motsa, S. S.

2015-01-01

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

General framework for dynamic large deformation contact problems based on phantom-node X-FEM

NASA Astrophysics Data System (ADS)

Broumand, P.; Khoei, A. R.

2018-04-01

This paper presents a general framework for modeling dynamic large deformation contact-impact problems based on the phantom-node extended finite element method. The large sliding penalty contact formulation is presented based on a master-slave approach which is implemented within the phantom-node X-FEM and an explicit central difference scheme is used to model the inertial effects. The method is compared with conventional contact X-FEM; advantages, limitations and implementational aspects are also addressed. Several numerical examples are presented to show the robustness and accuracy of the proposed method.

GO2OGS 1.0: a versatile workflow to integrate complex geological information with fault data into numerical simulation models

NASA Astrophysics Data System (ADS)

Fischer, T.; Naumov, D.; Sattler, S.; Kolditz, O.; Walther, M.

2015-11-01

We offer a versatile workflow to convert geological models built with the ParadigmTM GOCAD© (Geological Object Computer Aided Design) software into the open-source VTU (Visualization Toolkit unstructured grid) format for usage in numerical simulation models. Tackling relevant scientific questions or engineering tasks often involves multidisciplinary approaches. Conversion workflows are needed as a way of communication between the diverse tools of the various disciplines. Our approach offers an open-source, platform-independent, robust, and comprehensible method that is potentially useful for a multitude of environmental studies. With two application examples in the Thuringian Syncline, we show how a heterogeneous geological GOCAD model including multiple layers and faults can be used for numerical groundwater flow modeling, in our case employing the OpenGeoSys open-source numerical toolbox for groundwater flow simulations. The presented workflow offers the chance to incorporate increasingly detailed data, utilizing the growing availability of computational power to simulate numerical models.

Does Regular Online Testing Enhance Student Learning in the Numerical Sciences? Robust Evidence from a Large Data Set

ERIC Educational Resources Information Center

Angus, Simon D.; Watson, Judith

2009-01-01

While a number of studies have been conducted on the impact of online assessment and teaching methods on student learning, the field does not seem settled around the promised benefits of such approaches. It is argued that the reason for this state of affairs is that few studies have been able to control for a number of confounding factors in…

Two-photon absorption spectroscopy using intense phase-chirped entangled beams

NASA Astrophysics Data System (ADS)

Svozilík, Jiří; Peřina, Jan; León-Montiel, Roberto de J.

2018-06-01

We numerically analyze the use of intense entangled twin beams for ultra-sensitive spectroscopic measurements in chemical and biological systems. The examined scheme makes use of intense frequency-modulated (chirped) entangled beams to successfully extract information about the intermediate material states that contribute to the two-photon excitation of an absorbing medium. Robustness of the presented method is examined with respect to the applied intervals of the frequency chirp.

Robust and real-time rotor control with magnetic bearings

NASA Technical Reports Server (NTRS)

Sinha, A.; Wang, K. W.; Mease, K. L.

1991-01-01

This paper deals with the sliding mode control of a rigid rotor via radial magnetic bearings. The digital control algorithm and the results from numerical simulations are presented for an experimental rig. The experimental system which has been set up to digitally implement and validate the sliding mode control algorithm is described. Two methods for the development of control softwares are presented. Experimental results for individual rotor axis are discussed.

A robust component mode synthesis method for stochastic damped vibroacoustics

NASA Astrophysics Data System (ADS)

Tran, Quang Hung; Ouisse, Morvan; Bouhaddi, Noureddine

2010-01-01

In order to reduce vibrations or sound levels in industrial vibroacoustic problems, the low-cost and efficient way consists in introducing visco- and poro-elastic materials either on the structure or on cavity walls. Depending on the frequency range of interest, several numerical approaches can be used to estimate the behavior of the coupled problem. In the context of low frequency applications related to acoustic cavities with surrounding vibrating structures, the finite elements method (FEM) is one of the most efficient techniques. Nevertheless, industrial problems lead to large FE models which are time-consuming in updating or optimization processes. A classical way to reduce calculation time is the component mode synthesis (CMS) method, whose classical formulation is not always efficient to predict dynamical behavior of structures including visco-elastic and/or poro-elastic patches. Then, to ensure an efficient prediction, the fluid and structural bases used for the model reduction need to be updated as a result of changes in a parametric optimization procedure. For complex models, this leads to prohibitive numerical costs in the optimization phase or for management and propagation of uncertainties in the stochastic vibroacoustic problem. In this paper, the formulation of an alternative CMS method is proposed and compared to classical ( u, p) CMS method: the Ritz basis is completed with static residuals associated to visco-elastic and poro-elastic behaviors. This basis is also enriched by the static response of residual forces due to structural modifications, resulting in a so-called robust basis, also adapted to Monte Carlo simulations for uncertainties propagation using reduced models.

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation

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

Zhou, Ping; Lv, Youbin; Wang, Hong

Optimal operation of a practical blast furnace (BF) ironmaking process depends largely on a good measurement of molten iron quality (MIQ) indices. However, measuring the MIQ online is not feasible using the available techniques. In this paper, a novel data-driven robust modeling is proposed for online estimation of MIQ using improved random vector functional-link networks (RVFLNs). Since the output weights of traditional RVFLNs are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with outliers. This affects the modeling accuracy of RVFLNs. To solve this problem, a Cauchy distribution weighted M-estimation basedmore » robust RFVLNs is proposed. Since the weights of different outlier data are properly determined by the Cauchy distribution, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Moreover, given that the BF is a complex nonlinear system with numerous coupling variables, the data-driven canonical correlation analysis is employed to identify the most influential components from multitudinous factors that affect the MIQ indices to reduce the model dimension. Finally, experiments using industrial data and comparative studies have demonstrated that the obtained model produces a better modeling and estimating accuracy and stronger robustness than other modeling methods.« less

Robust Decision-making Applied to Model Selection

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

Hemez, Francois M.

2012-08-06

The scientific and engineering communities are relying more and more on numerical models to simulate ever-increasingly complex phenomena. Selecting a model, from among a family of models that meets the simulation requirements, presents a challenge to modern-day analysts. To address this concern, a framework is adopted anchored in info-gap decision theory. The framework proposes to select models by examining the trade-offs between prediction accuracy and sensitivity to epistemic uncertainty. The framework is demonstrated on two structural engineering applications by asking the following question: Which model, of several numerical models, approximates the behavior of a structure when parameters that define eachmore » of those models are unknown? One observation is that models that are nominally more accurate are not necessarily more robust, and their accuracy can deteriorate greatly depending upon the assumptions made. It is posited that, as reliance on numerical models increases, establishing robustness will become as important as demonstrating accuracy.« less

Robust optimisation-based microgrid scheduling with islanding constraints

DOE PAGES

Liu, Guodong; Starke, Michael; Xiao, Bailu; ...

2017-02-17

This paper proposes a robust optimization based optimal scheduling model for microgrid operation considering constraints of islanding capability. Our objective is to minimize the total operation cost, including generation cost and spinning reserve cost of local resources as well as purchasing cost of energy from the main grid. In order to ensure the resiliency of a microgrid and improve the reliability of the local electricity supply, the microgrid is required to maintain enough spinning reserve (both up and down) to meet local demand and accommodate local renewable generation when the supply of power from the main grid is interrupted suddenly,more » i.e., microgrid transitions from grid-connected into islanded mode. Prevailing operational uncertainties in renewable energy resources and load are considered and captured using a robust optimization method. With proper robust level, the solution of the proposed scheduling model ensures successful islanding of the microgrid with minimum load curtailment and guarantees robustness against all possible realizations of the modeled operational uncertainties. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator and a battery demonstrate the effectiveness of the proposed scheduling model.« less

A comparison of solute-transport solution techniques based on inverse modelling results

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2000-01-01

Five common numerical techniques (finite difference, predictor-corrector, total-variation-diminishing, method-of-characteristics, and modified-method-of-characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using randomly distributed homogeneous blocks of five sand types. This experimental model provides an outstanding opportunity to compare the solution techniques because of the heterogeneous hydraulic conductivity distribution of known structure, and the availability of detailed measurements with which to compare simulated concentrations. The present work uses this opportunity to investigate how three common types of results-simulated breakthrough curves, sensitivity analysis, and calibrated parameter values-change in this heterogeneous situation, given the different methods of simulating solute transport. The results show that simulated peak concentrations, even at very fine grid spacings, varied because of different amounts of numerical dispersion. Sensitivity analysis results were robust in that they were independent of the solution technique. They revealed extreme correlation between hydraulic conductivity and porosity, and that the breakthrough curve data did not provide enough information about the dispersivities to estimate individual values for the five sands. However, estimated hydraulic conductivity values are significantly influenced by both the large possible variations in model dispersion and the amount of numerical dispersion present in the solution technique.Five common numerical techniques (finite difference, predictor-corrector, total-variation-diminishing, method-of-characteristics, and modified-method-of-characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using randomly distributed homogeneous blocks of five sand types. This experimental model provides an outstanding opportunity to compare the solution techniques because of the heterogeneous hydraulic conductivity distribution of known structure, and the availability of detailed measurements with which to compare simulated concentrations. The present work uses this opportunity to investigate how three common types of results - simulated breakthrough curves, sensitivity analysis, and calibrated parameter values - change in this heterogeneous situation, given the different methods of simulating solute transport. The results show that simulated peak concentrations, even at very fine grid spacings, varied because of different amounts of numerical dispersion. Sensitivity analysis results were robust in that they were independent of the solution technique. They revealed extreme correlation between hydraulic conductivity and porosity, and that the breakthrough curve data did not provide enough information about the dispersivities to estimate individual values for the five sands. However, estimated hydraulic conductivity values are significantly influenced by both the large possible variations in model dispersion and the amount of numerical dispersion present in the solution technique.

Synthesis and Control of Flexible Systems with Component-Level Uncertainties

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Lim, Kyong B.

2009-01-01

An efficient and computationally robust method for synthesis of component dynamics is developed. The method defines the interface forces/moments as feasible vectors in transformed coordinates to ensure that connectivity requirements of the combined structure are met. The synthesized system is then defined in a transformed set of feasible coordinates. The simplicity of form is exploited to effectively deal with modeling parametric and non-parametric uncertainties at the substructure level. Uncertainty models of reasonable size and complexity are synthesized for the combined structure from those in the substructure models. In particular, we address frequency and damping uncertainties at the component level. The approach first considers the robustness of synthesized flexible systems. It is then extended to deal with non-synthesized dynamic models with component-level uncertainties by projecting uncertainties to the system level. A numerical example is given to demonstrate the feasibility of the proposed approach.

Composite SAR imaging using sequential joint sparsity

NASA Astrophysics Data System (ADS)

Sanders, Toby; Gelb, Anne; Platte, Rodrigo B.

2017-06-01

This paper investigates accurate and efficient ℓ1 regularization methods for generating synthetic aperture radar (SAR) images. Although ℓ1 regularization algorithms are already employed in SAR imaging, practical and efficient implementation in terms of real time imaging remain a challenge. Here we demonstrate that fast numerical operators can be used to robustly implement ℓ1 regularization methods that are as or more efficient than traditional approaches such as back projection, while providing superior image quality. In particular, we develop a sequential joint sparsity model for composite SAR imaging which naturally combines the joint sparsity methodology with composite SAR. Our technique, which can be implemented using standard, fractional, or higher order total variation regularization, is able to reduce the effects of speckle and other noisy artifacts with little additional computational cost. Finally we show that generalizing total variation regularization to non-integer and higher orders provides improved flexibility and robustness for SAR imaging.

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay.

PubMed

Sowmiya, C; Raja, R; Cao, Jinde; Rajchakit, G; Alsaedi, Ahmed

2017-01-01

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Suppressing spectral diffusion of emitted photons with optical pulses

DOE PAGES

Fotso, H. F.; Feiguin, A. E.; Awschalom, D. D.; ...

2016-01-22

In many quantum architectures the solid-state qubits, such as quantum dots or color centers, are interfaced via emitted photons. However, the frequency of photons emitted by solid-state systems exhibits slow uncontrollable fluctuations over time (spectral diffusion), creating a serious problem for implementation of the photon-mediated protocols. Here we show that a sequence of optical pulses applied to the solid-state emitter can stabilize the emission line at the desired frequency. We demonstrate efficiency, robustness, and feasibility of the method analytically and numerically. Taking nitrogen-vacancy center in diamond as an example, we show that only several pulses, with the width of 1more » ns, separated by few ns (which is not difficult to achieve) can suppress spectral diffusion. As a result, our method provides a simple and robust way to greatly improve the efficiency of photon-mediated entanglement and/or coupling to photonic cavities for solid-state qubits.« less

LEA Detection and Tracking Method for Color-Independent Visual-MIMO

PubMed Central

Kim, Jai-Eun; Kim, Ji-Won; Kim, Ki-Doo

2016-01-01

Communication performance in the color-independent visual-multiple input multiple output (visual-MIMO) technique is deteriorated by light emitting array (LEA) detection and tracking errors in the received image because the image sensor included in the camera must be used as the receiver in the visual-MIMO system. In this paper, in order to improve detection reliability, we first set up the color-space-based region of interest (ROI) in which an LEA is likely to be placed, and then use the Harris corner detection method. Next, we use Kalman filtering for robust tracking by predicting the most probable location of the LEA when the relative position between the camera and the LEA varies. In the last step of our proposed method, the perspective projection is used to correct the distorted image, which can improve the symbol decision accuracy. Finally, through numerical simulation, we show the possibility of robust detection and tracking of the LEA, which results in a symbol error rate (SER) performance improvement. PMID:27384563

LEA Detection and Tracking Method for Color-Independent Visual-MIMO.

PubMed

Kim, Jai-Eun; Kim, Ji-Won; Kim, Ki-Doo

2016-07-02

Communication performance in the color-independent visual-multiple input multiple output (visual-MIMO) technique is deteriorated by light emitting array (LEA) detection and tracking errors in the received image because the image sensor included in the camera must be used as the receiver in the visual-MIMO system. In this paper, in order to improve detection reliability, we first set up the color-space-based region of interest (ROI) in which an LEA is likely to be placed, and then use the Harris corner detection method. Next, we use Kalman filtering for robust tracking by predicting the most probable location of the LEA when the relative position between the camera and the LEA varies. In the last step of our proposed method, the perspective projection is used to correct the distorted image, which can improve the symbol decision accuracy. Finally, through numerical simulation, we show the possibility of robust detection and tracking of the LEA, which results in a symbol error rate (SER) performance improvement.

A robust interpolation method for constructing digital elevation models from remote sensing data

NASA Astrophysics Data System (ADS)

Chen, Chuanfa; Liu, Fengying; Li, Yanyan; Yan, Changqing; Liu, Guolin

2016-09-01

A digital elevation model (DEM) derived from remote sensing data often suffers from outliers due to various reasons such as the physical limitation of sensors and low contrast of terrain textures. In order to reduce the effect of outliers on DEM construction, a robust algorithm of multiquadric (MQ) methodology based on M-estimators (MQ-M) was proposed. MQ-M adopts an adaptive weight function with three-parts. The weight function is null for large errors, one for small errors and quadric for others. A mathematical surface was employed to comparatively analyze the robustness of MQ-M, and its performance was compared with those of the classical MQ and a recently developed robust MQ method based on least absolute deviation (MQ-L). Numerical tests show that MQ-M is comparative to the classical MQ and superior to MQ-L when sample points follow normal and Laplace distributions, and under the presence of outliers the former is more accurate than the latter. A real-world example of DEM construction using stereo images indicates that compared with the classical interpolation methods, such as natural neighbor (NN), ordinary kriging (OK), ANUDEM, MQ-L and MQ, MQ-M has a better ability of preserving subtle terrain features. MQ-M replaces thin plate spline for reference DEM construction to assess the contribution to our recently developed multiresolution hierarchical classification method (MHC). Classifying the 15 groups of benchmark datasets provided by the ISPRS Commission demonstrates that MQ-M-based MHC is more accurate than MQ-L-based and TPS-based MHCs. MQ-M has high potential for DEM construction.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

Some recent developments of the immersed interface method for flow simulation

NASA Astrophysics Data System (ADS)

Xu, Sheng

2017-11-01

The immersed interface method is a general methodology for solving PDEs subject to interfaces. In this talk, I will give an overview of some recent developments of the method toward the enhancement of its robustness for flow simulation. In particular, I will present with numerical results how to capture boundary conditions on immersed rigid objects, how to adopt interface triangulation in the method, and how to parallelize the method for flow with moving objects. With these developments, the immersed interface method can achieve accurate and efficient simulation of a flow involving multiple moving complex objects. Thanks to NSF for the support of this work under Grant NSF DMS 1320317.

Upwind differencing and LU factorization for chemical non-equilibrium Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun

1992-01-01

By means of either the Roe or the Van Leer flux-splittings for inviscid terms, in conjunction with central differencing for viscous terms in the explicit operator and the Steger-Warming splitting and lower-upper approximate factorization for the implicit operator, the present, robust upwind method for solving the chemical nonequilibrium Navier-Stokes equations yields formulas for finite-volume discretization in general coordinates. Numerical tests in the illustrative cases of a hypersonic blunt body, a ramped duct, divergent nozzle flows, and shock wave/boundary layer interactions, establish the method's efficiency.

Robust optimal design of diffusion-weighted magnetic resonance experiments for skin microcirculation

NASA Astrophysics Data System (ADS)

Choi, J.; Raguin, L. G.

2010-10-01

Skin microcirculation plays an important role in several diseases including chronic venous insufficiency and diabetes. Magnetic resonance (MR) has the potential to provide quantitative information and a better penetration depth compared with other non-invasive methods such as laser Doppler flowmetry or optical coherence tomography. The continuous progress in hardware resulting in higher sensitivity must be coupled with advances in data acquisition schemes. In this article, we first introduce a physical model for quantifying skin microcirculation using diffusion-weighted MR (DWMR) based on an effective dispersion model for skin leading to a q-space model of the DWMR complex signal, and then design the corresponding robust optimal experiments. The resulting robust optimal DWMR protocols improve the worst-case quality of parameter estimates using nonlinear least squares optimization by exploiting available a priori knowledge of model parameters. Hence, our approach optimizes the gradient strengths and directions used in DWMR experiments to robustly minimize the size of the parameter estimation error with respect to model parameter uncertainty. Numerical evaluations are presented to demonstrate the effectiveness of our approach as compared to conventional DWMR protocols.

Real-time PCR Machine System Modeling and a Systematic Approach for the Robust Design of a Real-time PCR-on-a-Chip System

PubMed Central

Lee, Da-Sheng

2010-01-01

Chip-based DNA quantification systems are widespread, and used in many point-of-care applications. However, instruments for such applications may not be maintained or calibrated regularly. Since machine reliability is a key issue for normal operation, this study presents a system model of the real-time Polymerase Chain Reaction (PCR) machine to analyze the instrument design through numerical experiments. Based on model analysis, a systematic approach was developed to lower the variation of DNA quantification and achieve a robust design for a real-time PCR-on-a-chip system. Accelerated lift testing was adopted to evaluate the reliability of the chip prototype. According to the life test plan, this proposed real-time PCR-on-a-chip system was simulated to work continuously for over three years with similar reproducibility in DNA quantification. This not only shows the robustness of the lab-on-a-chip system, but also verifies the effectiveness of our systematic method for achieving a robust design. PMID:22315563

Optimal reorientation of asymmetric underactuated spacecraft using differential flatness and receding horizon control

NASA Astrophysics Data System (ADS)

Cai, Wei-wei; Yang, Le-ping; Zhu, Yan-wei

2015-01-01

This paper presents a novel method integrating nominal trajectory optimization and tracking for the reorientation control of an underactuated spacecraft with only two available control torque inputs. By employing a pseudo input along the uncontrolled axis, the flatness property of a general underactuated spacecraft is extended explicitly, by which the reorientation trajectory optimization problem is formulated into the flat output space with all the differential constraints eliminated. Ultimately, the flat output optimization problem is transformed into a nonlinear programming problem via the Chebyshev pseudospectral method, which is improved by the conformal map and barycentric rational interpolation techniques to overcome the side effects of the differential matrix's ill-conditions on numerical accuracy. Treating the trajectory tracking control as a state regulation problem, we develop a robust closed-loop tracking control law using the receding-horizon control method, and compute the feedback control at each control cycle rapidly via the differential transformation method. Numerical simulation results show that the proposed control scheme is feasible and effective for the reorientation maneuver.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

Improved methods for simulating nearly extremal binary black holes

NASA Astrophysics Data System (ADS)

Scheel, Mark A.; Giesler, Matthew; Hemberger, Daniel A.; Lovelace, Geoffrey; Kuper, Kevin; Boyle, Michael; Szilágyi, Béla; Kidder, Lawrence E.

2015-05-01

Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen-York limit of S/{{m}2}=0.93. We present improved methods that enable us to simulate merging, nearly extremal black holes (i.e., black holes with S/{{m}2}\\gt 0.93) more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole (BBH) coalescence, where the larger black hole has S/{{m}2}=0.99. We also use these methods to simulate a non-precessing BBH coalescence, where both black holes have S/{{m}2}=0.994, nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called ‘orbital hangup’ effect).

Well-conditioning global-local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felicio Bruzzi

2016-11-01

Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.

Stretchable Materials for Robust Soft Actuators towards Assistive Wearable Devices

NASA Astrophysics Data System (ADS)

Agarwal, Gunjan; Besuchet, Nicolas; Audergon, Basile; Paik, Jamie

2016-09-01

Soft actuators made from elastomeric active materials can find widespread potential implementation in a variety of applications ranging from assistive wearable technologies targeted at biomedical rehabilitation or assistance with activities of daily living, bioinspired and biomimetic systems, to gripping and manipulating fragile objects, and adaptable locomotion. In this manuscript, we propose a novel two-component soft actuator design and design tool that produces actuators targeted towards these applications with enhanced mechanical performance and manufacturability. Our numerical models developed using the finite element method can predict the actuator behavior at large mechanical strains to allow efficient design iterations for system optimization. Based on two distinctive actuator prototypes’ (linear and bending actuators) experimental results that include free displacement and blocked-forces, we have validated the efficacy of the numerical models. The presented extensive investigation of mechanical performance for soft actuators with varying geometric parameters demonstrates the practical application of the design tool, and the robustness of the actuator hardware design, towards diverse soft robotic systems for a wide set of assistive wearable technologies, including replicating the motion of several parts of the human body.

Stretchable Materials for Robust Soft Actuators towards Assistive Wearable Devices

PubMed Central

Agarwal, Gunjan; Besuchet, Nicolas; Audergon, Basile; Paik, Jamie

2016-01-01

Soft actuators made from elastomeric active materials can find widespread potential implementation in a variety of applications ranging from assistive wearable technologies targeted at biomedical rehabilitation or assistance with activities of daily living, bioinspired and biomimetic systems, to gripping and manipulating fragile objects, and adaptable locomotion. In this manuscript, we propose a novel two-component soft actuator design and design tool that produces actuators targeted towards these applications with enhanced mechanical performance and manufacturability. Our numerical models developed using the finite element method can predict the actuator behavior at large mechanical strains to allow efficient design iterations for system optimization. Based on two distinctive actuator prototypes’ (linear and bending actuators) experimental results that include free displacement and blocked-forces, we have validated the efficacy of the numerical models. The presented extensive investigation of mechanical performance for soft actuators with varying geometric parameters demonstrates the practical application of the design tool, and the robustness of the actuator hardware design, towards diverse soft robotic systems for a wide set of assistive wearable technologies, including replicating the motion of several parts of the human body. PMID:27670953

Stretchable Materials for Robust Soft Actuators towards Assistive Wearable Devices.

PubMed

Agarwal, Gunjan; Besuchet, Nicolas; Audergon, Basile; Paik, Jamie

2016-09-27

Soft actuators made from elastomeric active materials can find widespread potential implementation in a variety of applications ranging from assistive wearable technologies targeted at biomedical rehabilitation or assistance with activities of daily living, bioinspired and biomimetic systems, to gripping and manipulating fragile objects, and adaptable locomotion. In this manuscript, we propose a novel two-component soft actuator design and design tool that produces actuators targeted towards these applications with enhanced mechanical performance and manufacturability. Our numerical models developed using the finite element method can predict the actuator behavior at large mechanical strains to allow efficient design iterations for system optimization. Based on two distinctive actuator prototypes' (linear and bending actuators) experimental results that include free displacement and blocked-forces, we have validated the efficacy of the numerical models. The presented extensive investigation of mechanical performance for soft actuators with varying geometric parameters demonstrates the practical application of the design tool, and the robustness of the actuator hardware design, towards diverse soft robotic systems for a wide set of assistive wearable technologies, including replicating the motion of several parts of the human body.

A two-dimensional composite grid numerical model based on the reduced system for oceanography

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

Xie, Y.F.; Browning, G.L.; Chesshire, G.

The proper mathematical limit of a hyperbolic system with multiple time scales, the reduced system, is a system that contains no high-frequency motions and is well posed if suitable boundary conditions are chosen for the initial-boundary value problem. The composite grid method, a robust and efficient grid-generation technique that smoothly and accurately treats general irregular boundaries, is used to approximate the two-dimensional version of the reduced system for oceanography on irregular ocean basins. A change-of-variable technique that substantially increases the accuracy of the model and a method for efficiently solving the elliptic equation for the geopotential are discussed. Numerical resultsmore » are presented for circular and kidney-shaped basins by using a set of analytic solutions constructed in this paper.« less

Chiral thiazoline and thiazole building blocks for the synthesis of peptide-derived natural products.

PubMed

Just-Baringo, Xavier; Albericio, Fernando; Alvarez, Mercedes

2014-01-01

Thiazoline and thiazole heterocycles are privileged motifs found in numerous peptide-derived natural products of biological interest. During the last decades, the synthesis of optically pure building blocks has been addressed by numerous groups, which have developed a plethora of strategies to that end. Efficient and reliable methodologies that are compatible with the intricate and capricious architectures of natural products are a must to further develop their science. Structure confirmation, structure-activity relationship studies and industrial production are fields of paramount importance that require these robust methodologies in order to successfully bring natural products into the clinic. Today's chemist toolbox is assorted with many powerful methods for chiral thiazoline and thiazole synthesis. Ranging from biomimetic approaches to stereoselective alkylations, one is likely to find a suitable method for their needs.

Robust rankings of socioeconomic health inequality using a categorical variable.

PubMed

Makdissi, Paul; Yazbeck, Myra

2017-09-01

When assessing socioeconomic health inequalities, researchers often draw upon measures of income inequality that were developed for ratio scale variables. As a result, the use of categorical data (such as self-reported health status) produces rankings that may be arbitrary and contingent to the numerical scale adopted. In this paper, we develop a method that overcomes this issue by providing conditions for which these rankings are invariant to the numerical scale chosen by the researcher. In doing so, we draw on the insight provided by Allison and Foster (2004) and extend their method to the dimension of socioeconomic inequality by exploiting the properties of rank-dependent indices such as Wagstaff (2002) achievement and extended concentration indices. We also provide an empirical illustration using the National Institute of Health Survey 2012. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

PubMed

Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

2012-07-02

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

Development on electromagnetic impedance function modeling and its estimation

NASA Astrophysics Data System (ADS)

Sutarno, D.

2015-09-01

Today the Electromagnetic methods such as magnetotellurics (MT) and controlled sources audio MT (CSAMT) is used in a broad variety of applications. Its usefulness in poor seismic areas and its negligible environmental impact are integral parts of effective exploration at minimum cost. As exploration was forced into more difficult areas, the importance of MT and CSAMT, in conjunction with other techniques, has tended to grow continuously. However, there are obviously important and difficult problems remaining to be solved concerning our ability to collect process and interpret MT as well as CSAMT in complex 3D structural environments. This talk aim at reviewing and discussing the recent development on MT as well as CSAMT impedance functions modeling, and also some improvements on estimation procedures for the corresponding impedance functions. In MT impedance modeling, research efforts focus on developing numerical method for computing the impedance functions of three dimensionally (3-D) earth resistivity models. On that reason, 3-D finite elements numerical modeling for the impedances is developed based on edge element method. Whereas, in the CSAMT case, the efforts were focused to accomplish the non-plane wave problem in the corresponding impedance functions. Concerning estimation of MT and CSAMT impedance functions, researches were focused on improving quality of the estimates. On that objective, non-linear regression approach based on the robust M-estimators and the Hilbert transform operating on the causal transfer functions, were used to dealing with outliers (abnormal data) which are frequently superimposed on a normal ambient MT as well as CSAMT noise fields. As validated, the proposed MT impedance modeling method gives acceptable results for standard three dimensional resistivity models. Whilst, the full solution based modeling that accommodate the non-plane wave effect for CSAMT impedances is applied for all measurement zones, including near-, transition-as well as the far-field zones, and consequently the plane wave correction is no longer needed for the impedances. In the resulting robust impedance estimates, outlier contamination is removed and the self consistency between the real and imaginary parts of the impedance estimates is guaranteed. Using synthetic and real MT data, it is shown that the proposed robust estimation methods always yield impedance estimates which are better than the conventional least square (LS) estimation, even under condition of severe noise contamination. A recent development on the constrained robust CSAMT impedance estimation is also discussed. By using synthetic CSAMT data it is demonstrated that the proposed methods can produce usable CSAMT transfer functions for all measurement zones.

Development on electromagnetic impedance function modeling and its estimation

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

Sutarno, D., E-mail: Sutarno@fi.itb.ac.id

2015-09-30

Today the Electromagnetic methods such as magnetotellurics (MT) and controlled sources audio MT (CSAMT) is used in a broad variety of applications. Its usefulness in poor seismic areas and its negligible environmental impact are integral parts of effective exploration at minimum cost. As exploration was forced into more difficult areas, the importance of MT and CSAMT, in conjunction with other techniques, has tended to grow continuously. However, there are obviously important and difficult problems remaining to be solved concerning our ability to collect process and interpret MT as well as CSAMT in complex 3D structural environments. This talk aim atmore » reviewing and discussing the recent development on MT as well as CSAMT impedance functions modeling, and also some improvements on estimation procedures for the corresponding impedance functions. In MT impedance modeling, research efforts focus on developing numerical method for computing the impedance functions of three dimensionally (3-D) earth resistivity models. On that reason, 3-D finite elements numerical modeling for the impedances is developed based on edge element method. Whereas, in the CSAMT case, the efforts were focused to accomplish the non-plane wave problem in the corresponding impedance functions. Concerning estimation of MT and CSAMT impedance functions, researches were focused on improving quality of the estimates. On that objective, non-linear regression approach based on the robust M-estimators and the Hilbert transform operating on the causal transfer functions, were used to dealing with outliers (abnormal data) which are frequently superimposed on a normal ambient MT as well as CSAMT noise fields. As validated, the proposed MT impedance modeling method gives acceptable results for standard three dimensional resistivity models. Whilst, the full solution based modeling that accommodate the non-plane wave effect for CSAMT impedances is applied for all measurement zones, including near-, transition-as well as the far-field zones, and consequently the plane wave correction is no longer needed for the impedances. In the resulting robust impedance estimates, outlier contamination is removed and the self consistency between the real and imaginary parts of the impedance estimates is guaranteed. Using synthetic and real MT data, it is shown that the proposed robust estimation methods always yield impedance estimates which are better than the conventional least square (LS) estimation, even under condition of severe noise contamination. A recent development on the constrained robust CSAMT impedance estimation is also discussed. By using synthetic CSAMT data it is demonstrated that the proposed methods can produce usable CSAMT transfer functions for all measurement zones.« less

A no-gold-standard technique for objective assessment of quantitative nuclear-medicine imaging methods

PubMed Central

Jha, Abhinav K; Caffo, Brian; Frey, Eric C

2016-01-01

The objective optimization and evaluation of nuclear-medicine quantitative imaging methods using patient data is highly desirable but often hindered by the lack of a gold standard. Previously, a regression-without-truth (RWT) approach has been proposed for evaluating quantitative imaging methods in the absence of a gold standard, but this approach implicitly assumes that bounds on the distribution of true values are known. Several quantitative imaging methods in nuclear-medicine imaging measure parameters where these bounds are not known, such as the activity concentration in an organ or the volume of a tumor. We extended upon the RWT approach to develop a no-gold-standard (NGS) technique for objectively evaluating such quantitative nuclear-medicine imaging methods with patient data in the absence of any ground truth. Using the parameters estimated with the NGS technique, a figure of merit, the noise-to-slope ratio (NSR), can be computed, which can rank the methods on the basis of precision. An issue with NGS evaluation techniques is the requirement of a large number of patient studies. To reduce this requirement, the proposed method explored the use of multiple quantitative measurements from the same patient, such as the activity concentration values from different organs in the same patient. The proposed technique was evaluated using rigorous numerical experiments and using data from realistic simulation studies. The numerical experiments demonstrated that the NSR was estimated accurately using the proposed NGS technique when the bounds on the distribution of true values were not precisely known, thus serving as a very reliable metric for ranking the methods on the basis of precision. In the realistic simulation study, the NGS technique was used to rank reconstruction methods for quantitative single-photon emission computed tomography (SPECT) based on their performance on the task of estimating the mean activity concentration within a known volume of interest. Results showed that the proposed technique provided accurate ranking of the reconstruction methods for 97.5% of the 50 noise realizations. Further, the technique was robust to the choice of evaluated reconstruction methods. The simulation study pointed to possible violations of the assumptions made in the NGS technique under clinical scenarios. However, numerical experiments indicated that the NGS technique was robust in ranking methods even when there was some degree of such violation. PMID:26982626

A no-gold-standard technique for objective assessment of quantitative nuclear-medicine imaging methods.

PubMed

Jha, Abhinav K; Caffo, Brian; Frey, Eric C

2016-04-07

The objective optimization and evaluation of nuclear-medicine quantitative imaging methods using patient data is highly desirable but often hindered by the lack of a gold standard. Previously, a regression-without-truth (RWT) approach has been proposed for evaluating quantitative imaging methods in the absence of a gold standard, but this approach implicitly assumes that bounds on the distribution of true values are known. Several quantitative imaging methods in nuclear-medicine imaging measure parameters where these bounds are not known, such as the activity concentration in an organ or the volume of a tumor. We extended upon the RWT approach to develop a no-gold-standard (NGS) technique for objectively evaluating such quantitative nuclear-medicine imaging methods with patient data in the absence of any ground truth. Using the parameters estimated with the NGS technique, a figure of merit, the noise-to-slope ratio (NSR), can be computed, which can rank the methods on the basis of precision. An issue with NGS evaluation techniques is the requirement of a large number of patient studies. To reduce this requirement, the proposed method explored the use of multiple quantitative measurements from the same patient, such as the activity concentration values from different organs in the same patient. The proposed technique was evaluated using rigorous numerical experiments and using data from realistic simulation studies. The numerical experiments demonstrated that the NSR was estimated accurately using the proposed NGS technique when the bounds on the distribution of true values were not precisely known, thus serving as a very reliable metric for ranking the methods on the basis of precision. In the realistic simulation study, the NGS technique was used to rank reconstruction methods for quantitative single-photon emission computed tomography (SPECT) based on their performance on the task of estimating the mean activity concentration within a known volume of interest. Results showed that the proposed technique provided accurate ranking of the reconstruction methods for 97.5% of the 50 noise realizations. Further, the technique was robust to the choice of evaluated reconstruction methods. The simulation study pointed to possible violations of the assumptions made in the NGS technique under clinical scenarios. However, numerical experiments indicated that the NGS technique was robust in ranking methods even when there was some degree of such violation.

A novel single thruster control strategy for spacecraft attitude stabilization

NASA Astrophysics Data System (ADS)

Godard; Kumar, Krishna Dev; Zou, An-Min

2013-05-01

Feasibility of achieving three axis attitude stabilization using a single thruster is explored in this paper. Torques are generated using a thruster orientation mechanism with which the thrust vector can be tilted on a two axis gimbal. A robust nonlinear control scheme is developed based on the nonlinear kinematic and dynamic equations of motion of a rigid body spacecraft in the presence of gravity gradient torque and external disturbances. The spacecraft, controlled using the proposed concept, constitutes an underactuated system (a system with fewer independent control inputs than degrees of freedom) with nonlinear dynamics. Moreover, using thruster gimbal angles as control inputs make the system non-affine (control terms appear nonlinearly in the state equation). This necessitates the control algorithms to be developed based on nonlinear control theory since linear control methods are not directly applicable. The stability conditions for the spacecraft attitude motion for robustness against uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.

COMPARISON OF NUMERICAL SCHEMES FOR SOLVING A SPHERICAL PARTICLE DIFFUSION EQUATION

EPA Science Inventory

A new robust iterative numerical scheme was developed for a nonlinear diffusive model that described sorption dynamics in spherical particle suspensions. he numerical scheme had been applied to finite difference and finite element models that showed rapid convergence and stabilit...

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

PubMed

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well and are fairly easy to program. In slices with no continuous symmetries, spectral integral-iteration algorithms and elliptic-PDE algorithms are fast and accurate, but require good initial guesses to converge. In many cases, Schnetter's "pretracking" algorithm can greatly improve an elliptic-PDE algorithm's robustness. Flow algorithms are generally quite slow but can be very robust in their convergence. Minimization methods are slow and relatively inaccurate in the context of a finite differencing simulation, but in a spectral code they can be relatively faster and more robust.

Reliable numerical computation in an optimal output-feedback design

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

PubMed

Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PubMed Central

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

Experiments study on attitude coupling control method for flexible spacecraft

NASA Astrophysics Data System (ADS)

Wang, Jie; Li, Dongxu

2018-06-01

High pointing accuracy and stabilization are significant for spacecrafts to carry out Earth observing, laser communication and space exploration missions. However, when a spacecraft undergoes large angle maneuver, the excited elastic oscillation of flexible appendages, for instance, solar wing and onboard antenna, would downgrade the performance of the spacecraft platform. This paper proposes a coupling control method, which synthesizes the adaptive sliding mode controller and the positive position feedback (PPF) controller, to control the attitude and suppress the elastic vibration simultaneously. Because of its prominent performance for attitude tracking and stabilization, the proposed method is capable of slewing the flexible spacecraft with a large angle. Also, the method is robust to parametric uncertainties of the spacecraft model. Numerical simulations are carried out with a hub-plate system which undergoes a single-axis attitude maneuver. An attitude control testbed for the flexible spacecraft is established and experiments are conducted to validate the coupling control method. Both numerical and experimental results demonstrate that the method discussed above can effectively decrease the stabilization time and improve the attitude accuracy of the flexible spacecraft.

A variational approach to multi-phase motion of gas, liquid and solid based on the level set method

NASA Astrophysics Data System (ADS)

Yokoi, Kensuke

2009-07-01

We propose a simple and robust numerical algorithm to deal with multi-phase motion of gas, liquid and solid based on the level set method [S. Osher, J.A. Sethian, Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79 (1988) 12; M. Sussman, P. Smereka, S. Osher, A level set approach for capturing solution to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146; J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999; S. Osher, R. Fedkiw, Level Set Methods and Dynamics Implicit Surface, Applied Mathematical Sciences, vol. 153, Springer, 2003]. In Eulerian framework, to simulate interaction between a moving solid object and an interfacial flow, we need to define at least two functions (level set functions) to distinguish three materials. In such simulations, in general two functions overlap and/or disagree due to numerical errors such as numerical diffusion. In this paper, we resolved the problem using the idea of the active contour model [M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision 1 (1988) 321; V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, International Journal of Computer Vision 22 (1997) 61; G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001; R. Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications, Springer-Verlag, 2003] introduced in the field of image processing.

Fast generating Greenberger-Horne-Zeilinger state via iterative interaction pictures

NASA Astrophysics Data System (ADS)

Huang, Bi-Hua; Chen, Ye-Hong; Wu, Qi-Cheng; Song, Jie; Xia, Yan

2016-10-01

We delve a little deeper into the construction of shortcuts to adiabatic passage for three-level systems by iterative interaction picture (multiple Schrödinger dynamics). As an application example, we use the deduced iterative based shortcuts to rapidly generate the Greenberger-Horne-Zeilinger (GHZ) state in a three-atom system with the help of quantum Zeno dynamics. Numerical simulation shows the dynamics designed by the iterative picture method is physically feasible and the shortcut scheme performs much better than that using the conventional adiabatic passage techniques. Also, the influences of various decoherence processes are discussed by numerical simulation and the results prove that the scheme is fast and robust against decoherence and operational imperfection.

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, J.-S.; Chen, K.-H.; Choi, Y.

1992-01-01

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Disentangling niche competition from grazing mortality in phytoplankton dilution experiments

PubMed Central

Weitz, Joshua S.

2017-01-01

The dilution method is the principal tool used to infer in situ microzooplankton grazing rates. However, grazing is the only mortality process considered in the theoretical model underlying the interpretation of dilution method experiments. Here we evaluate the robustness of mortality estimates inferred from dilution experiments when there is concurrent niche competition amongst phytoplankton. Using a combination of mathematical analysis and numerical simulations, we find that grazing rates may be overestimated—the degree of overestimation is related to the importance of niche competition relative to microzooplankton grazing. In response, we propose a conceptual method to disentangle the effects of niche competition and grazing by diluting out microzooplankton, but not phytoplankton. Our theoretical results suggest this revised “Z-dilution” method can robustly infer grazing mortality, regardless of the dominant phytoplankton mortality driver in our system. Further, we show it is possible to independently estimate both grazing mortality and niche competition if the classical and Z-dilution methods can be used in tandem. We discuss the significance of these results for quantifying phytoplankton mortality rates; and the feasibility of implementing the Z-dilution method in practice, whether in model systems or in complex communities with overlap in the size distributions of phytoplankton and microzooplankton. PMID:28505212

Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods.

PubMed

Maximov, Ivan I; Vinding, Mads S; Tse, Desmond H Y; Nielsen, Niels Chr; Shah, N Jon

2015-05-01

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community. Copyright © 2015 Elsevier Inc. All rights reserved.

Filter method without boundary-value condition for simultaneous calculation of eigenfunction and eigenvalue of a stationary Schrödinger equation on a grid.

PubMed

Nurhuda, M; Rouf, A

2017-09-01

The paper presents a method for simultaneous computation of eigenfunction and eigenvalue of the stationary Schrödinger equation on a grid, without imposing boundary-value condition. The method is based on the filter operator, which selects the eigenfunction from wave packet at the rate comparable to δ function. The efficacy and reliability of the method are demonstrated by comparing the simulation results with analytical or numerical solutions obtained by using other methods for various boundary-value conditions. It is found that the method is robust, accurate, and reliable. Further prospect of filter method for simulation of the Schrödinger equation in higher-dimensional space will also be highlighted.

Robust fault-tolerant tracking control design for spacecraft under control input saturation.

PubMed

Bustan, Danyal; Pariz, Naser; Sani, Seyyed Kamal Hosseini

2014-07-01

In this paper, a continuous globally stable tracking control algorithm is proposed for a spacecraft in the presence of unknown actuator failure, control input saturation, uncertainty in inertial matrix and external disturbances. The design method is based on variable structure control and has the following properties: (1) fast and accurate response in the presence of bounded disturbances; (2) robust to the partial loss of actuator effectiveness; (3) explicit consideration of control input saturation; and (4) robust to uncertainty in inertial matrix. In contrast to traditional fault-tolerant control methods, the proposed controller does not require knowledge of the actuator faults and is implemented without explicit fault detection and isolation processes. In the proposed controller a single parameter is adjusted dynamically in such a way that it is possible to prove that both attitude and angular velocity errors will tend to zero asymptotically. The stability proof is based on a Lyapunov analysis and the properties of the singularity free quaternion representation of spacecraft dynamics. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of external disturbances, actuator failures, and control input saturation. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Meshless Method for Simulation of Compressible Flow

NASA Astrophysics Data System (ADS)

Nabizadeh Shahrebabak, Ebrahim

In the present age, rapid development in computing technology and high speed supercomputers has made numerical analysis and computational simulation more practical than ever before for large and complex cases. Numerical simulations have also become an essential means for analyzing the engineering problems and the cases that experimental analysis is not practical. There are so many sophisticated and accurate numerical schemes, which do these simulations. The finite difference method (FDM) has been used to solve differential equation systems for decades. Additional numerical methods based on finite volume and finite element techniques are widely used in solving problems with complex geometry. All of these methods are mesh-based techniques. Mesh generation is an essential preprocessing part to discretize the computation domain for these conventional methods. However, when dealing with mesh-based complex geometries these conventional mesh-based techniques can become troublesome, difficult to implement, and prone to inaccuracies. In this study, a more robust, yet simple numerical approach is used to simulate problems in an easier manner for even complex problem. The meshless, or meshfree, method is one such development that is becoming the focus of much research in the recent years. The biggest advantage of meshfree methods is to circumvent mesh generation. Many algorithms have now been developed to help make this method more popular and understandable for everyone. These algorithms have been employed over a wide range of problems in computational analysis with various levels of success. Since there is no connectivity between the nodes in this method, the challenge was considerable. The most fundamental issue is lack of conservation, which can be a source of unpredictable errors in the solution process. This problem is particularly evident in the presence of steep gradient regions and discontinuities, such as shocks that frequently occur in high speed compressible flow problems. To solve this discontinuity problem, this research study deals with the implementation of a conservative meshless method and its applications in computational fluid dynamics (CFD). One of the most common types of collocating meshless method the RBF-DQ, is used to approximate the spatial derivatives. The issue with meshless methods when dealing with highly convective cases is that they cannot distinguish the influence of fluid flow from upstream or downstream and some methodology is needed to make the scheme stable. Therefore, an upwinding scheme similar to one used in the finite volume method is added to capture steep gradient or shocks. This scheme creates a flexible algorithm within which a wide range of numerical flux schemes, such as those commonly used in the finite volume method, can be employed. In addition, a blended RBF is used to decrease the dissipation ensuing from the use of a low shape parameter. All of these steps are formulated for the Euler equation and a series of test problems used to confirm convergence of the algorithm. The present scheme was first employed on several incompressible benchmarks to validate the framework. The application of this algorithm is illustrated by solving a set of incompressible Navier-Stokes problems. Results from the compressible problem are compared with the exact solution for the flow over a ramp and compared with solutions of finite volume discretization and the discontinuous Galerkin method, both requiring a mesh. The applicability of the algorithm and its robustness are shown to be applied to complex problems.

Numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis - Stanford Univ., Mar. 1989

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1990-01-01

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort.

GWAR: robust analysis and meta-analysis of genome-wide association studies.

PubMed

Dimou, Niki L; Tsirigos, Konstantinos D; Elofsson, Arne; Bagos, Pantelis G

2017-05-15

In the context of genome-wide association studies (GWAS), there is a variety of statistical techniques in order to conduct the analysis, but, in most cases, the underlying genetic model is usually unknown. Under these circumstances, the classical Cochran-Armitage trend test (CATT) is suboptimal. Robust procedures that maximize the power and preserve the nominal type I error rate are preferable. Moreover, performing a meta-analysis using robust procedures is of great interest and has never been addressed in the past. The primary goal of this work is to implement several robust methods for analysis and meta-analysis in the statistical package Stata and subsequently to make the software available to the scientific community. The CATT under a recessive, additive and dominant model of inheritance as well as robust methods based on the Maximum Efficiency Robust Test statistic, the MAX statistic and the MIN2 were implemented in Stata. Concerning MAX and MIN2, we calculated their asymptotic null distributions relying on numerical integration resulting in a great gain in computational time without losing accuracy. All the aforementioned approaches were employed in a fixed or a random effects meta-analysis setting using summary data with weights equal to the reciprocal of the combined cases and controls. Overall, this is the first complete effort to implement procedures for analysis and meta-analysis in GWAS using Stata. A Stata program and a web-server are freely available for academic users at http://www.compgen.org/tools/GWAR. pbagos@compgen.org. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Vector Observation-Aided/Attitude-Rate Estimation Using Global Positioning System Signals

NASA Technical Reports Server (NTRS)

Oshman, Yaakov; Markley, F. Landis

1997-01-01

A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.

A Numerical Investigation of Two-Different Drosophila Forward Flight Modes

NASA Astrophysics Data System (ADS)

Sahin, Mehmet; Dilek, Ezgi; Erzincanli, Belkis

2016-11-01

The parallel large-scale unstructured finite volume method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation has been applied in order to investigate the near wake structure of Drosophila in forward flight. DISTENE MeshGems-Hexa algorithm based on the octree method is used to generate the all hexahedral mesh for the wing-body combination. The mesh deformation algorithm is based on the indirect radial basis function (RBF) method at each time level while avoiding remeshing in order to enhance numerical robustness. The large-scale numerical simulations are carried out for a flapping Drosophila in forward flight. In the first case, the wing tip-path plane is tilted forward to generate forward force. In the second case, paddling wing motion is used to generate the forward fore. The λ2-criterion proposed by Jeong and Hussain (1995) is used for investigating the time variation of the Eulerian coherent structures in the near wake. The present simulations reveal highly detailed near wake topology for a hovering Drosophila. This is very useful in terms of understanding physics in biological flights which can provide a very useful tool for designing bio-inspired MAVs.

Numerical analysis of behaviour of cross laminated timber (CLT) in blast loading

NASA Astrophysics Data System (ADS)

Šliseris, J.; Gaile, L.; Pakrastiņš, L.

2017-10-01

A non-linear computation model for CLT wall element that includes explicit dynamics and composite damage constitutive model was developed. The numerical model was compared with classical beam theory and it turned out that shear wood layer has significant shear deformations that must be taken into account when designing CLT. It turned out that impulse duration time has a major effect on the strength of CLT. Special attention must be payed when designing CLT wall, window and door architectural system in order to guarantee the robustness of structure. The proposed numerical modelling framework can be used when designing CLT buildings that can be affected by blast loading, whilst structural robustness must be guaranteed.

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

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

Mu, Lin; Wang, Junping; Ye, Xiu

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of themore » method with respect to the plate thickness.« less

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-10-04

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of themore » method with respect to the plate thickness.« less

Stable and low diffusive hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1992-01-01

We introduce in this paper a new concept for upwinding: the Hybrid Upwind Splitting (HUS). This original strategy for upwinding is achieved by combining the two previous existing approaches, the Flux Vector (FVS) and Flux Difference Splittings (FDS), while retaining their own interesting features. Indeed, our approach yields upwind methods that share the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the capture of linear waves. We describe here some examples of such HUS methods obtained by hybridizing the Osher approach with FVS schemes. Numerical illustrations are displayed and will prove in particular the relevance of the HUS methods we propose for viscous calculations.

The development of a revised version of multi-center molecular Ornstein-Zernike equation

NASA Astrophysics Data System (ADS)

Kido, Kentaro; Yokogawa, Daisuke; Sato, Hirofumi

2012-04-01

Ornstein-Zernike (OZ)-type theory is a powerful tool to obtain 3-dimensional solvent distribution around solute molecule. Recently, we proposed multi-center molecular OZ method, which is suitable for parallel computing of 3D solvation structure. The distribution function in this method consists of two components, namely reference and residue parts. Several types of the function were examined as the reference part to investigate the numerical robustness of the method. As the benchmark, the method is applied to water, benzene in aqueous solution and single-walled carbon nanotube in chloroform solution. The results indicate that fully-parallelization is achieved by utilizing the newly proposed reference functions.

Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

NASA Astrophysics Data System (ADS)

Carraro, F.; Valiani, A.; Caleffi, V.

2018-03-01

Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

Robust cubature Kalman filter for GNSS/INS with missing observations and colored measurement noise.

PubMed

Cui, Bingbo; Chen, Xiyuan; Tang, Xihua; Huang, Haoqian; Liu, Xiao

2018-01-01

In order to improve the accuracy of GNSS/INS working in GNSS-denied environment, a robust cubature Kalman filter (RCKF) is developed by considering colored measurement noise and missing observations. First, an improved cubature Kalman filter (CKF) is derived by considering colored measurement noise, where the time-differencing approach is applied to yield new observations. Then, after analyzing the disadvantages of existing methods, the measurement augment in processing colored noise is translated into processing the uncertainties of CKF, and new sigma point update framework is utilized to account for the bounded model uncertainties. By reusing the diffused sigma points and approximation residual in the prediction stage of CKF, the RCKF is developed and its error performance is analyzed theoretically. Results of numerical experiment and field test reveal that RCKF is more robust than CKF and extended Kalman filter (EKF), and compared with EKF, the heading error of land vehicle is reduced by about 72.4%. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Stable dissipative optical vortex clusters by inhomogeneous effective diffusion.

PubMed

Li, Huishan; Lai, Shiquan; Qui, Yunli; Zhu, Xing; Xie, Jianing; Mihalache, Dumitru; He, Yingji

2017-10-30

We numerically show the generation of robust vortex clusters embedded in a two-dimensional beam propagating in a dissipative medium described by the generic cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion term, which is asymmetrical in the two transverse directions and periodically modulated in the longitudinal direction. We show the generation of stable optical vortex clusters for different values of the winding number (topological charge) of the input optical beam. We have found that the number of individual vortex solitons that form the robust vortex cluster is equal to the winding number of the input beam. We have obtained the relationships between the amplitudes and oscillation periods of the inhomogeneous effective diffusion and the cubic gain and diffusion (viscosity) parameters, which depict the regions of existence and stability of vortex clusters. The obtained results offer a method to form robust vortex clusters embedded in two-dimensional optical beams, and we envisage potential applications in the area of structured light.

Hierarchical extraction of urban objects from mobile laser scanning data

NASA Astrophysics Data System (ADS)

Yang, Bisheng; Dong, Zhen; Zhao, Gang; Dai, Wenxia

2015-01-01

Point clouds collected in urban scenes contain a huge number of points (e.g., billions), numerous objects with significant size variability, complex and incomplete structures, and variable point densities, raising great challenges for the automated extraction of urban objects in the field of photogrammetry, computer vision, and robotics. This paper addresses these challenges by proposing an automated method to extract urban objects robustly and efficiently. The proposed method generates multi-scale supervoxels from 3D point clouds using the point attributes (e.g., colors, intensities) and spatial distances between points, and then segments the supervoxels rather than individual points by combining graph based segmentation with multiple cues (e.g., principal direction, colors) of the supervoxels. The proposed method defines a set of rules for merging segments into meaningful units according to types of urban objects and forms the semantic knowledge of urban objects for the classification of objects. Finally, the proposed method extracts and classifies urban objects in a hierarchical order ranked by the saliency of the segments. Experiments show that the proposed method is efficient and robust for extracting buildings, streetlamps, trees, telegraph poles, traffic signs, cars, and enclosures from mobile laser scanning (MLS) point clouds, with an overall accuracy of 92.3%.

CT Image Sequence Restoration Based on Sparse and Low-Rank Decomposition

PubMed Central

Gou, Shuiping; Wang, Yueyue; Wang, Zhilong; Peng, Yong; Zhang, Xiaopeng; Jiao, Licheng; Wu, Jianshe

2013-01-01

Blurry organ boundaries and soft tissue structures present a major challenge in biomedical image restoration. In this paper, we propose a low-rank decomposition-based method for computed tomography (CT) image sequence restoration, where the CT image sequence is decomposed into a sparse component and a low-rank component. A new point spread function of Weiner filter is employed to efficiently remove blur in the sparse component; a wiener filtering with the Gaussian PSF is used to recover the average image of the low-rank component. And then we get the recovered CT image sequence by combining the recovery low-rank image with all recovery sparse image sequence. Our method achieves restoration results with higher contrast, sharper organ boundaries and richer soft tissue structure information, compared with existing CT image restoration methods. The robustness of our method was assessed with numerical experiments using three different low-rank models: Robust Principle Component Analysis (RPCA), Linearized Alternating Direction Method with Adaptive Penalty (LADMAP) and Go Decomposition (GoDec). Experimental results demonstrated that the RPCA model was the most suitable for the small noise CT images whereas the GoDec model was the best for the large noisy CT images. PMID:24023764

Optimization of controllability and robustness of complex networks by edge directionality

NASA Astrophysics Data System (ADS)

Liang, Man; Jin, Suoqin; Wang, Dingjie; Zou, Xiufen

2016-09-01

Recently, controllability of complex networks has attracted enormous attention in various fields of science and engineering. How to optimize structural controllability has also become a significant issue. Previous studies have shown that an appropriate directional assignment can improve structural controllability; however, the evolution of the structural controllability of complex networks under attacks and cascading has always been ignored. To address this problem, this study proposes a new edge orientation method (NEOM) based on residual degree that changes the link direction while conserving topology and directionality. By comparing the results with those of previous methods in two random graph models and several realistic networks, our proposed approach is demonstrated to be an effective and competitive method for improving the structural controllability of complex networks. Moreover, numerical simulations show that our method is near-optimal in optimizing structural controllability. Strikingly, compared to the original network, our method maintains the structural controllability of the network under attacks and cascading, indicating that the NEOM can also enhance the robustness of controllability of networks. These results alter the view of the nature of controllability in complex networks, change the understanding of structural controllability and affect the design of network models to control such networks.

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

NASA Astrophysics Data System (ADS)

Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric

2016-12-01

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily code various numerical algorithms. Two robust and optimized numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are used to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.

Direction of Coupling from Phases of Interacting Oscillators: A Permutation Information Approach

NASA Astrophysics Data System (ADS)

Bahraminasab, A.; Ghasemi, F.; Stefanovska, A.; McClintock, P. V. E.; Kantz, H.

2008-02-01

We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust.

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

NASA Astrophysics Data System (ADS)

Beretta, Elena; Micheletti, Stefano; Perotto, Simona; Santacesaria, Matteo

2018-01-01

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

NASA Astrophysics Data System (ADS)

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-05-01

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach's feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Numerical Modeling of Three-Dimensional Fluid Flow with Phase Change

NASA Technical Reports Server (NTRS)

Esmaeeli, Asghar; Arpaci, Vedat

1999-01-01

We present a numerical method to compute phase change dynamics of three-dimensional deformable bubbles. The full Navier-Stokes and energy equations are solved for both phases by a front tracking/finite difference technique. The fluid boundary is explicitly tracked by discrete points that are connected by triangular elements to form a front that is used to keep the stratification of material properties sharp and to calculate the interfacial source terms. Two simulations are presented to show robustness of the method in handling complex phase boundaries. In the first case, growth of a vapor bubble in zero gravity is studied where large volume increase of the bubble is managed by adaptively increasing the front resolution. In the second case, growth of a bubble under high gravity is studied where indentation at the rear of the bubble results in a region of large curvature which challenges the front tracking in three dimensions.

Meshfree and efficient modeling of swimming cells

NASA Astrophysics Data System (ADS)

Gallagher, Meurig T.; Smith, David J.

2018-05-01

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab® or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

Continuum topology optimization considering uncertainties in load locations based on the cloud model

NASA Astrophysics Data System (ADS)

Liu, Jie; Wen, Guilin

2018-06-01

Few researchers have paid attention to designing structures in consideration of uncertainties in the loading locations, which may significantly influence the structural performance. In this work, cloud models are employed to depict the uncertainties in the loading locations. A robust algorithm is developed in the context of minimizing the expectation of the structural compliance, while conforming to a material volume constraint. To guarantee optimal solutions, sufficient cloud drops are used, which in turn leads to low efficiency. An innovative strategy is then implemented to enormously improve the computational efficiency. A modified soft-kill bi-directional evolutionary structural optimization method using derived sensitivity numbers is used to output the robust novel configurations. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed algorithm.

Optimal Control for Fast and Robust Generation of Entangled States in Anisotropic Heisenberg Chains

NASA Astrophysics Data System (ADS)

Zhang, Xiong-Peng; Shao, Bin; Zou, Jian

2017-05-01

Motivated by some recent results of the optimal control (OC) theory, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on a single spin, with the aim of exploring how maximally entangled state can be prepared. To achieve the goal, we use a numerical optimization algorithm (e.g., the Krotov algorithm, which was shown to be capable of reaching the quantum speed limit) to search an optimal set of control parameters, and then obtain OC pulses corresponding to the target fidelity. We find that the minimum time for implementing our target state depending on the anisotropy parameter Δ of the model. Finally, we analyze the robustness of the obtained results for the optimal fidelities and the effectiveness of the Krotov method under some realistic conditions.

Robust optimal control of material flows in demand-driven supply networks

NASA Astrophysics Data System (ADS)

Laumanns, Marco; Lefeber, Erjen

2006-04-01

We develop a model based on stochastic discrete-time controlled dynamical systems in order to derive optimal policies for controlling the material flow in supply networks. Each node in the network is described as a transducer such that the dynamics of the material and information flows within the entire network can be expressed by a system of first-order difference equations, where some inputs to the system act as external disturbances. We apply methods from constrained robust optimal control to compute the explicit control law as a function of the current state. For the numerical examples considered, these control laws correspond to certain classes of optimal ordering policies from inventory management while avoiding, however, any a priori assumptions about the general form of the policy.

Fast and robust estimation of ophthalmic wavefront aberrations

NASA Astrophysics Data System (ADS)

Dillon, Keith

2016-12-01

Rapidly rising levels of myopia, particularly in the developing world, have led to an increased need for inexpensive and automated approaches to optometry. A simple and robust technique is provided for estimating major ophthalmic aberrations using a gradient-based wavefront sensor. The approach is based on the use of numerical calculations to produce diverse combinations of phase components, followed by Fourier transforms to calculate the coefficients. The approach does not utilize phase unwrapping nor iterative solution of inverse problems. This makes the method very fast and tolerant to image artifacts, which do not need to be detected and masked or interpolated as is needed in other techniques. These features make it a promising algorithm on which to base low-cost devices for applications that may have limited access to expert maintenance and operation.

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

PubMed

Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

2012-09-01

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

Conventional laboratory methods for cyanotoxins.

PubMed

Lawton, Linda A; Edwards, C

2008-01-01

It is clear from the literature that numerous methods are available for most cyanotoxins, although many publications on monitoring data indicate that the favored approach is the use proven, robust methods for individual toxins. The most effective approach is the utilization of a robust rapid screen, where positive samples are followed up by qualitative and quantitative analysis to provide the essential decision making data needed for successful management strategies (Fig. 2). Currently, rapid screens are available for microcystins, saxitoxins and anatoxin-a(s), whilst optimisation and validation is needed, many publications report good correlation with the mouse bioassay and HPLC. There is an urgent need for rapid, simple, and inexpensive assays for cylindrospermopsins, anatoxin-a and BMAA. Although methods exist for analysis of BMAA, the fact that a recent study showed 95% of cyanobacteria producing this, some at levels > 6,000 microg g(-1) dry wt, is of concern and rapid screening followed by robust analysis needed. An ideal approach would be a single method capable of extracting and detecting all cyanotoxins. Several publications describe such approaches using LC-MS, but as expected from a group of compounds with diverse chemistry, there are obvious limitations in recoveries during sample processing, chromatographic performance and sensitivity (Dahlmann et al. 2003, Dell'Aversano et al. 2004, Pietsch et al. 2001). Selection of methods must be based on the application requirements, equipment available and cost. For many organisations it may be more cost effective to out-source the occasional analysis. However, as the incidence of blooms appears to be increasing, the need for more rigorous monitoring is needed, sensible investment is needed to meet recommended guidelines. Most of the methods discussed in this paper are suitable for achieving this goal, although clean-up and concentration is usually necessary for physicochemical methods.

ACOSS Six (Active Control of Space Structures)

DTIC Science & Technology

1981-10-01

modes, specially useful simpler conditions for ensuring closed-loop asymptotic stability are also derived. In addition, conditions for robustness of...in this initial study of FOCL stability and robustness . Such a condition is strong but not unreasonable nor unrealistic. Many useful simple in- sights...smallest possible feedback gains) and many interesting numerical results on closed-loop stability and robustness of the modal-dashpot designs. The

An Analysis of the Optimal Control Modification Method Applied to Flutter Suppression

NASA Technical Reports Server (NTRS)

Drew, Michael; Nguyen, Nhan T.; Hashemi, Kelley E.; Ting, Eric; Chaparro, Daniel

2017-01-01

Unlike basic Model Reference Adaptive Control (MRAC)l, Optimal Control Modification (OCM) has been shown to be a promising MRAC modification with robustness and analytical properties not present in other adaptive control methods. This paper presents an analysis of the OCM method, and how the asymptotic property of OCM is useful for analyzing and tuning the controller. We begin with a Lyapunov stability proof of an OCM controller having two adaptive gain terms, then the less conservative and easily analyzed OCM asymptotic property is presented. Two numerical examples are used to show how this property can accurately predict steady state stability and quantitative robustness in the presence of time delay, and relative to linear plant perturbations, and nominal Loop Transfer Recovery (LTR) tuning. The asymptotic property of the OCM controller is then used as an aid in tuning the controller applied to a large scale aeroservoelastic longitudinal aircraft model for flutter suppression. Control with OCM adaptive augmentation is shown to improve performance over that of the nominal non-adaptive controller when significant disparities exist between the controller/observer model and the true plant model.

multiUQ: An intrusive uncertainty quantification tool for gas-liquid multiphase flows

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2017-11-01

Uncertainty quantification (UQ) can improve our understanding of the sensitivity of gas-liquid multiphase flows to variability about inflow conditions and fluid properties, creating a valuable tool for engineers. While non-intrusive UQ methods (e.g., Monte Carlo) are simple and robust, the cost associated with these techniques can render them unrealistic. In contrast, intrusive UQ techniques modify the governing equations by replacing deterministic variables with stochastic variables, adding complexity, but making UQ cost effective. Our numerical framework, called multiUQ, introduces an intrusive UQ approach for gas-liquid flows, leveraging a polynomial chaos expansion of the stochastic variables: density, momentum, pressure, viscosity, and surface tension. The gas-liquid interface is captured using a conservative level set approach, including a modified reinitialization equation which is robust and quadrature free. A least-squares method is leveraged to compute the stochastic interface normal and curvature needed in the continuum surface force method for surface tension. The solver is tested by applying uncertainty to one or two variables and verifying results against the Monte Carlo approach. NSF Grant #1511325.

Improved motion correction in PROPELLER by using grouped blades as reference.

PubMed

Liu, Zhe; Zhang, Zhe; Ying, Kui; Yuan, Chun; Guo, Hua

2014-03-01

To develop a robust reference generation method for improving PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) reconstruction. A new reference generation method, grouped-blade reference (GBR), is proposed for calculating rotation angle and translation shift in PROPELLER. Instead of using a single-blade reference (SBR) or combined-blade reference (CBR), our method classifies blades by their relative correlations and groups similar blades together as the reference to prevent inconsistent data from interfering the correction process. Numerical simulations and in vivo experiments were used to evaluate the performance of GBR for PROPELLER, which was further compared with SBR and CBR in terms of error level and computation cost. Both simulation and in vivo experiments demonstrate that GBR-based PROPELLER provides better correction for random motion or bipolar motion comparing with SBR or CBR. It not only produces images with lower error level but also needs less iteration steps to converge. A grouped-blade for reference selection was investigated for PROPELLER MRI. It helps to improve the accuracy and robustness of motion correction for various motion patterns. Copyright © 2013 Wiley Periodicals, Inc.

Robust volcano plot: identification of differential metabolites in the presence of outliers.

PubMed

Kumar, Nishith; Hoque, Md Aminul; Sugimoto, Masahiro

2018-04-11

The identification of differential metabolites in metabolomics is still a big challenge and plays a prominent role in metabolomics data analyses. Metabolomics datasets often contain outliers because of analytical, experimental, and biological ambiguity, but the currently available differential metabolite identification techniques are sensitive to outliers. We propose a kernel weight based outlier-robust volcano plot for identifying differential metabolites from noisy metabolomics datasets. Two numerical experiments are used to evaluate the performance of the proposed technique against nine existing techniques, including the t-test and the Kruskal-Wallis test. Artificially generated data with outliers reveal that the proposed method results in a lower misclassification error rate and a greater area under the receiver operating characteristic curve compared with existing methods. An experimentally measured breast cancer dataset to which outliers were artificially added reveals that our proposed method produces only two non-overlapping differential metabolites whereas the other nine methods produced between seven and 57 non-overlapping differential metabolites. Our data analyses show that the performance of the proposed differential metabolite identification technique is better than that of existing methods. Thus, the proposed method can contribute to analysis of metabolomics data with outliers. The R package and user manual of the proposed method are available at https://github.com/nishithkumarpaul/Rvolcano .

The robustness of multiplex networks under layer node-based attack

PubMed Central

Zhao, Da-wei; Wang, Lian-hai; Zhi, Yong-feng; Zhang, Jun; Wang, Zhen

2016-01-01

From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers. Network robustness, as one of the most successful application areas of complex networks, has attracted great interest in a myriad of research realms. In this regard, how multiplex networks respond to potential attack is still an open issue. Here we study the robustness of multiplex networks under layer node-based random or targeted attack, which means that nodes just suffer attacks in a given layer yet no additional influence to their connections beyond this layer. A theoretical analysis framework is proposed to calculate the critical threshold and the size of giant component of multiplex networks when nodes are removed randomly or intentionally. Via numerous simulations, it is unveiled that the theoretical method can accurately predict the threshold and the size of giant component, irrespective of attack strategies. Moreover, we also compare the robustness of multiplex networks under multiplex node-based attack and layer node-based attack, and find that layer node-based attack makes multiplex networks more vulnerable, regardless of average degree and underlying topology. PMID:27075870

The robustness of multiplex networks under layer node-based attack.

PubMed

Zhao, Da-wei; Wang, Lian-hai; Zhi, Yong-feng; Zhang, Jun; Wang, Zhen

2016-04-14

From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers. Network robustness, as one of the most successful application areas of complex networks, has attracted great interest in a myriad of research realms. In this regard, how multiplex networks respond to potential attack is still an open issue. Here we study the robustness of multiplex networks under layer node-based random or targeted attack, which means that nodes just suffer attacks in a given layer yet no additional influence to their connections beyond this layer. A theoretical analysis framework is proposed to calculate the critical threshold and the size of giant component of multiplex networks when nodes are removed randomly or intentionally. Via numerous simulations, it is unveiled that the theoretical method can accurately predict the threshold and the size of giant component, irrespective of attack strategies. Moreover, we also compare the robustness of multiplex networks under multiplex node-based attack and layer node-based attack, and find that layer node-based attack makes multiplex networks more vulnerable, regardless of average degree and underlying topology.

On decentralized adaptive full-order sliding mode control of multiple UAVs.

PubMed

Xiang, Xianbo; Liu, Chao; Su, Housheng; Zhang, Qin

2017-11-01

In this study, a novel decentralized adaptive full-order sliding mode control framework is proposed for the robust synchronized formation motion of multiple unmanned aerial vehicles (UAVs) subject to system uncertainty. First, a full-order sliding mode surface in a decentralized manner is designed to incorporate both the individual position tracking error and the synchronized formation error while the UAV group is engaged in building a certain desired geometric pattern in three dimensional space. Second, a decentralized virtual plant controller is constructed which allows the embedded low-pass filter to attain the chattering free property of the sliding mode controller. In addition, robust adaptive technique is integrated in the decentralized chattering free sliding control design in order to handle unknown bounded uncertainties, without requirements for assuming a priori knowledge of bounds on the system uncertainties as stated in conventional chattering free control methods. Subsequently, system robustness as well as stability of the decentralized full-order sliding mode control of multiple UAVs is synthesized. Numerical simulation results illustrate the effectiveness of the proposed control framework to achieve robust 3D formation flight of the multi-UAV system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Gradient descent for robust kernel-based regression

NASA Astrophysics Data System (ADS)

Guo, Zheng-Chu; Hu, Ting; Shi, Lei

2018-06-01

In this paper, we study the gradient descent algorithm generated by a robust loss function over a reproducing kernel Hilbert space (RKHS). The loss function is defined by a windowing function G and a scale parameter σ, which can include a wide range of commonly used robust losses for regression. There is still a gap between theoretical analysis and optimization process of empirical risk minimization based on loss: the estimator needs to be global optimal in the theoretical analysis while the optimization method can not ensure the global optimality of its solutions. In this paper, we aim to fill this gap by developing a novel theoretical analysis on the performance of estimators generated by the gradient descent algorithm. We demonstrate that with an appropriately chosen scale parameter σ, the gradient update with early stopping rules can approximate the regression function. Our elegant error analysis can lead to convergence in the standard L 2 norm and the strong RKHS norm, both of which are optimal in the mini-max sense. We show that the scale parameter σ plays an important role in providing robustness as well as fast convergence. The numerical experiments implemented on synthetic examples and real data set also support our theoretical results.

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-09-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi–Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier–Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier–Stokes equations.« less

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-01-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.« less

Robust stochastic optimization for reservoir operation

NASA Astrophysics Data System (ADS)

Pan, Limeng; Housh, Mashor; Liu, Pan; Cai, Ximing; Chen, Xin

2015-01-01

Optimal reservoir operation under uncertainty is a challenging engineering problem. Application of classic stochastic optimization methods to large-scale problems is limited due to computational difficulty. Moreover, classic stochastic methods assume that the estimated distribution function or the sample inflow data accurately represents the true probability distribution, which may be invalid and the performance of the algorithms may be undermined. In this study, we introduce a robust optimization (RO) approach, Iterative Linear Decision Rule (ILDR), so as to provide a tractable approximation for a multiperiod hydropower generation problem. The proposed approach extends the existing LDR method by accommodating nonlinear objective functions. It also provides users with the flexibility of choosing the accuracy of ILDR approximations by assigning a desired number of piecewise linear segments to each uncertainty. The performance of the ILDR is compared with benchmark policies including the sampling stochastic dynamic programming (SSDP) policy derived from historical data. The ILDR solves both the single and multireservoir systems efficiently. The single reservoir case study results show that the RO method is as good as SSDP when implemented on the original historical inflows and it outperforms SSDP policy when tested on generated inflows with the same mean and covariance matrix as those in history. For the multireservoir case study, which considers water supply in addition to power generation, numerical results show that the proposed approach performs as well as in the single reservoir case study in terms of optimal value and distributional robustness.

Optimization of design parameters of low-energy buildings

NASA Astrophysics Data System (ADS)

Vala, Jiří; Jarošová, Petra

2017-07-01

Evaluation of temperature development and related consumption of energy required for heating, air-conditioning, etc. in low-energy buildings requires the proper physical analysis, covering heat conduction, convection and radiation, including beam and diffusive components of solar radiation, on all building parts and interfaces. The system approach and the Fourier multiplicative decomposition together with the finite element technique offers the possibility of inexpensive and robust numerical and computational analysis of corresponding direct problems, as well as of the optimization ones with several design variables, using the Nelder-Mead simplex method. The practical example demonstrates the correlation between such numerical simulations and the time series of measurements of energy consumption on a small family house in Ostrov u Macochy (35 km northern from Brno).

Uncertainty Modeling for Robustness Analysis of Control Upset Prevention and Recovery Systems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.; Khong, Thuan H.; Shin, Jong-Yeob; Kwatny, Harry; Chang, Bor-Chin; Balas, Gary J.

2005-01-01

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. Such systems (developed for failure detection, identification, and reconfiguration, as well as upset recovery) need to be evaluated over broad regions of the flight envelope and under extreme flight conditions, and should include various sources of uncertainty. However, formulation of linear fractional transformation (LFT) models for representing system uncertainty can be very difficult for complex parameter-dependent systems. This paper describes a preliminary LFT modeling software tool which uses a matrix-based computational approach that can be directly applied to parametric uncertainty problems involving multivariate matrix polynomial dependencies. Several examples are presented (including an F-16 at an extreme flight condition, a missile model, and a generic example with numerous crossproduct terms), and comparisons are given with other LFT modeling tools that are currently available. The LFT modeling method and preliminary software tool presented in this paper are shown to compare favorably with these methods.

RootGraph: a graphic optimization tool for automated image analysis of plant roots

PubMed Central

Cai, Jinhai; Zeng, Zhanghui; Connor, Jason N.; Huang, Chun Yuan; Melino, Vanessa; Kumar, Pankaj; Miklavcic, Stanley J.

2015-01-01

This paper outlines a numerical scheme for accurate, detailed, and high-throughput image analysis of plant roots. In contrast to existing root image analysis tools that focus on root system-average traits, a novel, fully automated and robust approach for the detailed characterization of root traits, based on a graph optimization process is presented. The scheme, firstly, distinguishes primary roots from lateral roots and, secondly, quantifies a broad spectrum of root traits for each identified primary and lateral root. Thirdly, it associates lateral roots and their properties with the specific primary root from which the laterals emerge. The performance of this approach was evaluated through comparisons with other automated and semi-automated software solutions as well as against results based on manual measurements. The comparisons and subsequent application of the algorithm to an array of experimental data demonstrate that this method outperforms existing methods in terms of accuracy, robustness, and the ability to process root images under high-throughput conditions. PMID:26224880

Dynamic modelling and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances

NASA Astrophysics Data System (ADS)

Yang, Xinxin; Ge, Shuzhi Sam; He, Wei

2018-04-01

In this paper, both the closed-form dynamics and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances are developed. The dynamic model of the system is described with assumed modes approach and Lagrangian method. The flexible manipulators are represented as Euler-Bernoulli beams. Based on singular perturbation technique, the displacements/joint angles and flexible modes are modelled as slow and fast variables, respectively. A sliding mode control is designed for trajectories tracking of the slow subsystem under unknown but bounded disturbances, and an adaptive sliding mode control is derived for slow subsystem under unknown slowly time-varying disturbances. An optimal linear quadratic regulator method is proposed for the fast subsystem to damp out the vibrations of the flexible manipulators. Theoretical analysis validates the stability of the proposed composite controller. Numerical simulation results demonstrate the performance of the closed-loop flexible space robot system.

Robust preview control for a class of uncertain discrete-time systems with time-varying delay.

PubMed

Li, Li; Liao, Fucheng

2018-02-01

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Quantitative neuroanatomy for connectomics in Drosophila

PubMed Central

Schneider-Mizell, Casey M; Gerhard, Stephan; Longair, Mark; Kazimiers, Tom; Li, Feng; Zwart, Maarten F; Champion, Andrew; Midgley, Frank M; Fetter, Richard D; Saalfeld, Stephan; Cardona, Albert

2016-01-01

Neuronal circuit mapping using electron microscopy demands laborious proofreading or reconciliation of multiple independent reconstructions. Here, we describe new methods to apply quantitative arbor and network context to iteratively proofread and reconstruct circuits and create anatomically enriched wiring diagrams. We measured the morphological underpinnings of connectivity in new and existing reconstructions of Drosophila sensorimotor (larva) and visual (adult) systems. Synaptic inputs were preferentially located on numerous small, microtubule-free 'twigs' which branch off a single microtubule-containing 'backbone'. Omission of individual twigs accounted for 96% of errors. However, the synapses of highly connected neurons were distributed across multiple twigs. Thus, the robustness of a strong connection to detailed twig anatomy was associated with robustness to reconstruction error. By comparing iterative reconstruction to the consensus of multiple reconstructions, we show that our method overcomes the need for redundant effort through the discovery and application of relationships between cellular neuroanatomy and synaptic connectivity. DOI: http://dx.doi.org/10.7554/eLife.12059.001 PMID:26990779

Numerical analysis of the performance of rock weirs: Effects of structure configuration on local hydraulics

USGS Publications Warehouse

Holmquist-Johnson, C. L.

2009-01-01

River spanning rock structures are being constructed for water delivery as well as to enable fish passage at barriers and provide or improve the aquatic habitat for endangered fish species. Current design methods are based upon anecdotal information applicable to a narrow range of channel conditions. The complex flow patterns and performance of rock weirs is not well understood. Without accurate understanding of their hydraulics, designers cannot address the failure mechanisms of these structures. Flow characteristics such as jets, near bed velocities, recirculation, eddies, and plunging flow govern scour pool development. These detailed flow patterns can be replicated using a 3D numerical model. Numerical studies inexpensively simulate a large number of cases resulting in an increased range of applicability in order to develop design tools and predictive capability for analysis and design. The analysis and results of the numerical modeling, laboratory modeling, and field data provide a process-based method for understanding how structure geometry affects flow characteristics, scour development, fish passage, water delivery, and overall structure stability. Results of the numerical modeling allow designers to utilize results of the analysis to determine the appropriate geometry for generating desirable flow parameters. The end product of this research will develop tools and guidelines for more robust structure design or retrofits based upon predictable engineering and hydraulic performance criteria. ?? 2009 ASCE.

Non-robust numerical simulations of analogue extension experiments

NASA Astrophysics Data System (ADS)

Naliboff, John; Buiter, Susanne

2016-04-01

Numerical and analogue models of lithospheric deformation provide significant insight into the tectonic processes that lead to specific structural and geophysical observations. As these two types of models contain distinct assumptions and tradeoffs, investigations drawing conclusions from both can reveal robust links between first-order processes and observations. Recent studies have focused on detailed comparisons between numerical and analogue experiments in both compressional and extensional tectonics, sometimes involving multiple lithospheric deformation codes and analogue setups. While such comparisons often show good agreement on first-order deformation styles, results frequently diverge on second-order structures, such as shear zone dip angles or spacing, and in certain cases even on first-order structures. Here, we present finite-element experiments that are designed to directly reproduce analogue "sandbox" extension experiments at the cm-scale. We use material properties and boundary conditions that are directly taken from analogue experiments and use a Drucker-Prager failure model to simulate shear zone formation in sand. We find that our numerical experiments are highly sensitive to numerous numerical parameters. For example, changes to the numerical resolution, velocity convergence parameters and elemental viscosity averaging commonly produce significant changes in first- and second-order structures accommodating deformation. The sensitivity of the numerical simulations to small parameter changes likely reflects a number of factors, including, but not limited to, high angles of internal friction assigned to sand, complex, unknown interactions between the brittle sand (used as an upper crust equivalent) and viscous silicone (lower crust), highly non-linear strain weakening processes and poor constraints on the cohesion of sand. Our numerical-analogue comparison is hampered by (a) an incomplete knowledge of the fine details of sand failure and sand properties, and (b) likely limitations to the use of a continuum Drucker-Prager model for representing shear zone formation in sand. In some cases our numerical experiments provide reasonable fits to first-order structures observed in the analogue experiments, but the numerical sensitivity to small parameter variations leads us to conclude that the numerical experiments are not robust.

Advanced rotorcraft control using parameter optimization

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

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

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Comparative study of MacCormack and TVD MacCormack schemes for three-dimensional separation at wing/body junctions in supersonic flows

NASA Technical Reports Server (NTRS)

Lakshmanan, Balakrishnan; Tiwari, Surendra N.

1992-01-01

A robust, discontinuity-resolving TVD MacCormack scheme containing no dependent parameters requiring adjustment is presently used to investigate the 3D separation of wing/body junction flows at supersonic speeds. Many production codes employing MacCormack schemes can be adapted to use this method. A numerical simulation of laminar supersonic junction flow is found to yield improved separation location predictions, as well as the axial velocity profiles in the separated flow region.

Soil hydraulic properties estimate based on numerical analysis of disc infiltrometer three-dimensional infiltration curve

NASA Astrophysics Data System (ADS)

Latorre, Borja; Peña-Sancho, Carolina; Angulo-Jaramillo, Rafaël; Moret-Fernández, David

2015-04-01

Measurement of soil hydraulic properties is of paramount importance in fields such as agronomy, hydrology or soil science. Fundamented on the analysis of the Haverkamp et al. (1994) model, the aim of this paper is to explain a technique to estimate the soil hydraulic properties (sorptivity, S, and hydraulic conductivity, K) from the full-time cumulative infiltration curves. The method (NSH) was validated by means of 12 synthetic infiltration curves generated with HYDRUS-3D from known soil hydraulic properties. The K values used to simulate the synthetic curves were compared to those estimated with the proposed method. A procedure to identify and remove the effect of the contact sand layer on the cumulative infiltration curve was also developed. A sensitivity analysis was performed using the water level measurement as uncertainty source. Finally, the procedure was evaluated using different infiltration times and data noise. Since a good correlation between the K used in HYDRUS-3D to model the infiltration curves and those estimated by the NSH method was obtained, (R2 =0.98), it can be concluded that this technique is robust enough to estimate the soil hydraulic conductivity from complete infiltration curves. The numerical procedure to detect and remove the influence of the contact sand layer on the K and S estimates seemed to be robust and efficient. An effect of the curve infiltration noise on the K estimate was observed, which uncertainty increased with increasing noise. Finally, the results showed that infiltration time was an important factor to estimate K. Lower values of K or smaller uncertainty needed longer infiltration times.

Robustness of assembly supply chain networks by considering risk propagation and cascading failure

NASA Astrophysics Data System (ADS)

Tang, Liang; Jing, Ke; He, Jie; Stanley, H. Eugene

2016-10-01

An assembly supply chain network (ASCN) is composed of manufacturers located in different geographical regions. To analyze the robustness of this ASCN when it suffers from catastrophe disruption events, we construct a cascading failure model of risk propagation. In our model, different disruption scenarios s are considered and the probability equation of all disruption scenarios is developed. Using production capability loss as the robustness index (RI) of an ASCN, we conduct a numerical simulation to assess its robustness. Through simulation, we compare the network robustness at different values of linking intensity and node threshold and find that weak linking intensity or high node threshold increases the robustness of the ASCN. We also compare network robustness levels under different disruption scenarios.

An Assessment of Artificial Compressibility and Pressure Projection Methods for Incompressible Flow Simulations

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kiris, C.; Smith, Charles A. (Technical Monitor)

1998-01-01

Performance of the two commonly used numerical procedures, one based on artificial compressibility method and the other pressure projection method, are compared. These formulations are selected primarily because they are designed for three-dimensional applications. The computational procedures are compared by obtaining steady state solutions of a wake vortex and unsteady solutions of a curved duct flow. For steady computations, artificial compressibility was very efficient in terms of computing time and robustness. For an unsteady flow which requires small physical time step, pressure projection method was found to be computationally more efficient than an artificial compressibility method. This comparison is intended to give some basis for selecting a method or a flow solution code for large three-dimensional applications where computing resources become a critical issue.

A novel speckle pattern—Adaptive digital image correlation approach with robust strain calculation

NASA Astrophysics Data System (ADS)

Cofaru, Corneliu; Philips, Wilfried; Van Paepegem, Wim

2012-02-01

Digital image correlation (DIC) has seen widespread acceptance and usage as a non-contact method for the determination of full-field displacements and strains in experimental mechanics. The advances of imaging hardware in the last decades led to high resolution and speed cameras being more affordable than in the past making large amounts of data image available for typical DIC experimental scenarios. The work presented in this paper is aimed at maximizing both the accuracy and speed of DIC methods when employed with such images. A low-level framework for speckle image partitioning which replaces regularly shaped blocks with image-adaptive cells in the displacement calculation is introduced. The Newton-Raphson DIC method is modified to use the image pixels of the cells and to perform adaptive regularization to increase the spatial consistency of the displacements. Furthermore, a novel robust framework for strain calculation based also on the Newton-Raphson algorithm is introduced. The proposed methods are evaluated in five experimental scenarios, out of which four use numerically deformed images and one uses real experimental data. Results indicate that, as the desired strain density increases, significant computational gains can be obtained while maintaining or improving accuracy and rigid-body rotation sensitivity.

Attitude/attitude-rate estimation from GPS differential phase measurements using integrated-rate parameters

NASA Technical Reports Server (NTRS)

Oshman, Yaakov; Markley, Landis

1998-01-01

A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.

Measuring chromatic aberrations in imaging systems using plasmonic nanoparticles.

PubMed

Gennaro, Sylvain D; Roschuk, Tyler R; Maier, Stefan A; Oulton, Rupert F

2016-04-01

We demonstrate a method to measure chromatic aberrations of microscope objectives with metallic nanoparticles using white light. Extinction spectra are recorded while scanning a single nanoparticle through a lens's focal plane. We show a direct correlation between the focal wavelength and the longitudinal chromatic focal shift through our analysis of the variations between the scanned extinction spectra at each scan position and the peak extinction over the entire scan. The method has been tested on achromat and apochromat objectives using aluminum disks varying in size from 260-520 nm. Our method is straightforward, robust, low cost, and broadband with a sensitivity suitable for assessing longitudinal chromatic aberrations in high-numerical-aperture apochromatic corrected lenses.

Enabling multiplexed testing of pooled donor cells through whole-genome sequencing.

PubMed

Chan, Yingleong; Chan, Ying Kai; Goodman, Daniel B; Guo, Xiaoge; Chavez, Alejandro; Lim, Elaine T; Church, George M

2018-04-19

We describe a method that enables the multiplex screening of a pool of many different donor cell lines. Our method accurately predicts each donor proportion from the pool without requiring the use of unique DNA barcodes as markers of donor identity. Instead, we take advantage of common single nucleotide polymorphisms, whole-genome sequencing, and an algorithm to calculate the proportions from the sequencing data. By testing using simulated and real data, we showed that our method robustly predicts the individual proportions from a mixed-pool of numerous donors, thus enabling the multiplexed testing of diverse donor cells en masse.More information is available at https://pgpresearch.med.harvard.edu/poolseq/.

Characterization of Meta-Materials Using Computational Electromagnetic Methods

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Shin, Joon

2005-01-01

An efficient and powerful computational method is presented to synthesize a meta-material to specified electromagnetic properties. Using the periodicity of meta-materials, the Finite Element Methodology (FEM) is developed to estimate the reflection and transmission through the meta-material structure for a normal plane wave incidence. For efficient computations of the reflection and transmission over a wide band frequency range through a meta-material a Finite Difference Time Domain (FDTD) approach is also developed. Using the Nicholson-Ross method and the Genetic Algorithms, a robust procedure to extract electromagnetic properties of meta-material from the knowledge of its reflection and transmission coefficients is described. Few numerical examples are also presented to validate the present approach.

On the convergence of a linesearch based proximal-gradient method for nonconvex optimization

NASA Astrophysics Data System (ADS)

Bonettini, S.; Loris, I.; Porta, F.; Prato, M.; Rebegoldi, S.

2017-05-01

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Łojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications.

Direct SQP-methods for solving optimal control problems with delays

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

Goellmann, L.; Bueskens, C.; Maurer, H.

The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method formore » retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.« less

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented in an elementary fashion and includes the relationship with traditional point-vortex studies, the convergence to smooth solutions of the Euler equations, and the essential differences between two- and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. The overlap with the excellent review articles available is kept to a minimum and more emphasis is placed on the area of expertise, namely two-dimensional flows around bluff bodies. When solid walls are present, complete mathematical models are not available and a more heuristic attitude must be adopted. The imposition of inviscid and viscous boundary conditions without conformal mappings or image vortices and the creation of vorticity along solid walls are examined in detail. Methods for boundary-layer treatment and the question of the Kutta condition are discussed. Practical aspects and tips helpful in creating a method that really works are explained. The topics include the robustness of the method and the assessment of accuracy, vortex-core profiles, timemarching schemes, numerical dissipation, and efficient programming. Calculations of flows past streamlined or bluff bodies are used as examples when appropriate.

Constant pressure and temperature discrete-time Langevin molecular dynamics

NASA Astrophysics Data System (ADS)

Grønbech-Jensen, Niels; Farago, Oded

2014-11-01

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

Robust multivariate nonparametric tests for detection of two-sample location shift in clinical trials

PubMed Central

Jiang, Xuejun; Guo, Xu; Zhang, Ning; Wang, Bo

2018-01-01

This article presents and investigates performance of a series of robust multivariate nonparametric tests for detection of location shift between two multivariate samples in randomized controlled trials. The tests are built upon robust estimators of distribution locations (medians, Hodges-Lehmann estimators, and an extended U statistic) with both unscaled and scaled versions. The nonparametric tests are robust to outliers and do not assume that the two samples are drawn from multivariate normal distributions. Bootstrap and permutation approaches are introduced for determining the p-values of the proposed test statistics. Simulation studies are conducted and numerical results are reported to examine performance of the proposed statistical tests. The numerical results demonstrate that the robust multivariate nonparametric tests constructed from the Hodges-Lehmann estimators are more efficient than those based on medians and the extended U statistic. The permutation approach can provide a more stringent control of Type I error and is generally more powerful than the bootstrap procedure. The proposed robust nonparametric tests are applied to detect multivariate distributional difference between the intervention and control groups in the Thai Healthy Choices study and examine the intervention effect of a four-session motivational interviewing-based intervention developed in the study to reduce risk behaviors among youth living with HIV. PMID:29672555

Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

NASA Technical Reports Server (NTRS)

Ellison, Donald; Conway, Bruce; Englander, Jacob

2015-01-01

A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

Numerical modeling of suspended sediment tansfers at the catchment scale with TELEMAC

NASA Astrophysics Data System (ADS)

Taccone, Florent; Antoine, Germain; Delestre, Olivier; Goutal, Nicole

2017-04-01

In the mountainous regions, the filling of reservoirs is an important issue in terms of efficiency and environmental acceptability for producing hydro-electricity. Thus, the modelling of the sediment transfers on highly erodible watershed is a key challenge from both economic and scientific points of view. The sediment transfers at the watershed scale involve different local flow regimes due to the complex topography of the field and the time and space variability of the meteorological conditions, as well as several physical processes, because of the heterogeneity of the soil composition and cover. A physically-based modelling approach, associated with a fine discretization of the domain, provides an explicit representation of the hydraulic and sedimentary variables, and gives the opportunity to river managers to simulate the global effects of local solutions for decreasing erosion. On the other hand, this approach is time consuming, and needs both detailed data set for validation and robust numerical schemes for simulating various hydraulic and sediment transport conditions. The erosion processes being heavily reliant on the flow characteristics, this paper focus on a robust and accurate numerical resolution of the Shallow Water equations using TELEMAC 2D (www.opentelemac.org). One of the main difficulties is to have a numerical scheme able to represent correctly the hydraulic transfers, preserving the positivity of the water depths, dealing with the wet/dry interface and being well-balanced. Few schemes verifying these properties exist, and their accuracy still needs to be evaluated in the case of rain induced runoff on steep slopes. First, a straight channel test case with a variable slope (Kirstetter et al., 2015) is used to qualify the properties of several Finite Volume numerical schemes. For this test case, a steady rain applied on a dry domain has been performed experimentally in laboratory, and this configuration gives an analytical solution of the Shallow Water equations. The numerical scheme developed by Chen and Noelle (2015) appears to be the best compromise between robustness and accuracy. The sediment transport module SISYPHE of TELEMAC-MASCARET is also used for simulating suspended sediment transport and erosion in this configuration. Then, an application to a real, well-documented watershed is performed. With a total area of 86.4 ha, the Laval watershed is located in the Southern French Alps. It takes part of the Draix-Bleone Observatory, on which 30 years of collected data are available. On this site, several rainfall events have been simulated using high performance clusters and parallelized computation methods. The results show a good robustness and accuracy of the chosen numerical schemes for hydraulic and sediment transport. Furthermore, a good agreement with measured data is obtain if an infiltration model is added to the Shallow Water equations. This study gives promising perspectives for simulating sediment transfers at the catchment scale with a physically based approach. G. Chen et S. Noelle: A new hydrostatic reconstruction scheme motivated by the wet-dry front. 2015. G. Kirstetter et al: Modeling rain-driven overland fow: empirical versus analytical friction terms in the shallow water approximation. Journal of Hydrology, 2015.

Hybrid High-Order methods for finite deformations of hyperelastic materials

NASA Astrophysics Data System (ADS)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

Dynamic one-dimensional modeling of secondary settling tanks and design impacts of sizing decisions.

PubMed

Li, Ben; Stenstrom, Michael K

2014-03-01

As one of the most significant components in the activated sludge process (ASP), secondary settling tanks (SSTs) can be investigated with mathematical models to optimize design and operation. This paper takes a new look at the one-dimensional (1-D) SST model by analyzing and considering the impacts of numerical problems, especially the process robustness. An improved SST model with Yee-Roe-Davis technique as the PDE solver is proposed and compared with the widely used Takács model to show its improvement in numerical solution quality. The improved and Takács models are coupled with a bioreactor model to reevaluate ASP design basis and several popular control strategies for economic plausibility, contaminant removal efficiency and system robustness. The time-to-failure due to rising sludge blanket during overloading, as a key robustness indicator, is analyzed to demonstrate the differences caused by numerical issues in SST models. The calculated results indicate that the Takács model significantly underestimates time to failure, thus leading to a conservative design. Copyright © 2013 Elsevier Ltd. All rights reserved.

Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

NASA Astrophysics Data System (ADS)

Coco, Armando; Russo, Giovanni

2018-05-01

In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

A new way to improve the robustness of complex communication networks by allocating redundancy links

NASA Astrophysics Data System (ADS)

Shi, Chunhui; Peng, Yunfeng; Zhuo, Yue; Tang, Jieying; Long, Keping

2012-03-01

We investigate the robustness of complex communication networks on allocating redundancy links. The protecting key nodes (PKN) strategy is proposed to improve the robustness of complex communication networks against intentional attack. Our numerical simulations show that allocating a few redundant links among key nodes using the PKN strategy will significantly increase the robustness of scale-free complex networks. We have also theoretically proved and demonstrated the effectiveness of the PKN strategy. We expect that our work will help achieve a better understanding of communication networks.

A control method for bilateral teleoperating systems

NASA Astrophysics Data System (ADS)

Strassberg, Yesayahu

1992-01-01

The thesis focuses on control of bilateral master-slave teleoperators. The bilateral control issue of teleoperators is studied and a new scheme that overcomes basic unsolved problems is proposed. A performance measure, based on the multiport modeling method, is introduced in order to evaluate and understand the limitations of earlier published bilateral control laws. Based on the study evaluating the different methods, the objective of the thesis is stated. The proposed control law is then introduced, its ideal performance is demonstrated, and conditions for stability and robustness are derived. It is shown that stability, desired performance, and robustness can be obtained under the assumption that the deviation of the model from the actual system satisfies certain norm inequalities and the measurement uncertainties are bounded. The proposed scheme is validated by numerical simulation. The simulated system is based on the configuration of the RAL (Robotics and Automation Laboratory) telerobot. From the simulation results it is shown that good tracking performance can be obtained. In order to verify the performance of the proposed scheme when applied to a real hardware system, an experimental setup of a three degree of freedom master-slave teleoperator (i.e. three degree of freedom master and three degree of freedom slave robot) was built. Three basic experiments were conducted to verify the performance of the proposed control scheme. The first experiment verified the master control law and its contribution to the robustness and performance of the entire system. The second experiment demonstrated the actual performance of the system while performing a free motion teleoperating task. From the experimental results, it is shown that the control law has good performance and is robust to uncertainties in the models of the master and slave.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate.

PubMed

Kargar, Soudabeh; Borisch, Eric A; Froemming, Adam T; Kawashima, Akira; Mynderse, Lance A; Stinson, Eric G; Trzasko, Joshua D; Riederer, Stephen J

2018-05-01

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method. Copyright © 2017 Elsevier Inc. All rights reserved.

Minimal spanning trees at the percolation threshold: A numerical calculation

NASA Astrophysics Data System (ADS)

Sweeney, Sean M.; Middleton, A. Alan

2013-09-01

The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions d up to d=5. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method suitable for analyzing a wide array of randomly generated fractal structures. The trees analyzed using these techniques are built using a combination of Prim's and Kruskal's algorithms for finding minimal spanning trees. This combination reduces memory usage and allows for simulation of larger systems than would otherwise be possible. The path length fractal dimension ds of MSTs on critical percolation clusters is found to be compatible with the predictions of the perturbation expansion developed by T. S. Jackson and N. Read [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.81.021131 81, 021131 (2010)].

A Control Law Design Method Facilitating Control Power, Robustness, Agility, and Flying Qualities Tradeoffs: CRAFT

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Davidson, John B.

1998-01-01

A multi-input, multi-output control law design methodology, named "CRAFT", is presented. CRAFT stands for the design objectives addressed, namely, Control power, Robustness, Agility, and Flying Qualities Tradeoffs. The methodology makes use of control law design metrics from each of the four design objective areas. It combines eigenspace assignment, which allows for direct specification of eigenvalues and eigenvectors, with a graphical approach for representing the metrics that captures numerous design goals in one composite illustration. Sensitivity of the metrics to eigenspace choice is clearly displayed, enabling the designer to assess the cost of design tradeoffs. This approach enhances the designer's ability to make informed design tradeoffs and to reach effective final designs. An example of the CRAFT methodology applied to an advanced experimental fighter and discussion of associated design issues are provided.

LCC-Demons: a robust and accurate symmetric diffeomorphic registration algorithm.

PubMed

Lorenzi, M; Ayache, N; Frisoni, G B; Pennec, X

2013-11-01

Non-linear registration is a key instrument for computational anatomy to study the morphology of organs and tissues. However, in order to be an effective instrument for the clinical practice, registration algorithms must be computationally efficient, accurate and most importantly robust to the multiple biases affecting medical images. In this work we propose a fast and robust registration framework based on the log-Demons diffeomorphic registration algorithm. The transformation is parameterized by stationary velocity fields (SVFs), and the similarity metric implements a symmetric local correlation coefficient (LCC). Moreover, we show how the SVF setting provides a stable and consistent numerical scheme for the computation of the Jacobian determinant and the flux of the deformation across the boundaries of a given region. Thus, it provides a robust evaluation of spatial changes. We tested the LCC-Demons in the inter-subject registration setting, by comparing with state-of-the-art registration algorithms on public available datasets, and in the intra-subject longitudinal registration problem, for the statistically powered measurements of the longitudinal atrophy in Alzheimer's disease. Experimental results show that LCC-Demons is a generic, flexible, efficient and robust algorithm for the accurate non-linear registration of images, which can find several applications in the field of medical imaging. Without any additional optimization, it solves equally well intra & inter-subject registration problems, and compares favorably to state-of-the-art methods. Copyright © 2013 Elsevier Inc. All rights reserved.

Research in robust control for hypersonic aircraft

NASA Technical Reports Server (NTRS)

Calise, A. J.

1994-01-01

The research during the third reporting period focused on fixed order robust control design for hypersonic vehicles. A new technique was developed to synthesize fixed order H(sub infinity) controllers. A controller canonical form is imposed on the compensator structure and a homotopy algorithm is employed to perform the controller design. Various reduced order controllers are designed for a simplified version of the hypersonic vehicle model used in our previous studies to demonstrate the capabilities of the code. However, further work is needed to investigate the issue of numerical ill-conditioning for large order systems and to make the numerical approach more reliable.

Decomposing Multifractal Crossovers

PubMed Central

Nagy, Zoltan; Mukli, Peter; Herman, Peter; Eke, Andras

2017-01-01

Physiological processes—such as, the brain's resting-state electrical activity or hemodynamic fluctuations—exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. Here, we present two methods to identify breakpoints or crossovers in multimodal multifractal scaling functions. These methods incorporate the robust iterative fitting approach of the focus-based multifractal formalism (FMF). The first approach (moment-wise scaling range adaptivity) allows for a breakpoint-based adaptive treatment that analyzes segregated scale-invariant ranges. The second method (scaling function decomposition method, SFD) is a crossover-based design aimed at decomposing signal constituents from multimodal scaling functions resulting from signal addition or co-sampling, such as, contamination by uncorrelated fractals. We demonstrated that these methods could handle multimodal, mono- or multifractal, and exact or empirical signals alike. Their precision was numerically characterized on ideal signals, and a robust performance was demonstrated on exemplary empirical signals capturing resting-state brain dynamics by near infrared spectroscopy (NIRS), electroencephalography (EEG), and blood oxygen level-dependent functional magnetic resonance imaging (fMRI-BOLD). The NIRS and fMRI-BOLD low-frequency fluctuations were dominated by a multifractal component over an underlying biologically relevant random noise, thus forming a bimodal signal. The crossover between the EEG signal components was found at the boundary between the δ and θ bands, suggesting an independent generator for the multifractal δ rhythm. The robust implementation of the SFD method should be regarded as essential in the seamless processing of large volumes of bimodal fMRI-BOLD imaging data for the topology of multifractal metrics free of the masking effect of the underlying random noise. PMID:28798694

Minimum constitutive relation error based static identification of beams using force method

NASA Astrophysics Data System (ADS)

Guo, Jia; Takewaki, Izuru

2017-05-01

A new static identification approach based on the minimum constitutive relation error (CRE) principle for beam structures is introduced. The exact stiffness and the exact bending moment are shown to make the CRE minimal for given displacements to beam damages. A two-step substitution algorithm—a force-method step for the bending moment and a constitutive-relation step for the stiffness—is developed and its convergence is rigorously derived. Identifiability is further discussed and the stiffness in the undeformed region is found to be unidentifiable. An extra set of static measurements is complemented to remedy the drawback. Convergence and robustness are finally verified through numerical examples.

DOA Finding with Support Vector Regression Based Forward-Backward Linear Prediction.

PubMed

Pan, Jingjing; Wang, Yide; Le Bastard, Cédric; Wang, Tianzhen

2017-05-27

Direction-of-arrival (DOA) estimation has drawn considerable attention in array signal processing, particularly with coherent signals and a limited number of snapshots. Forward-backward linear prediction (FBLP) is able to directly deal with coherent signals. Support vector regression (SVR) is robust with small samples. This paper proposes the combination of the advantages of FBLP and SVR in the estimation of DOAs of coherent incoming signals with low snapshots. The performance of the proposed method is validated with numerical simulations in coherent scenarios, in terms of different angle separations, numbers of snapshots, and signal-to-noise ratios (SNRs). Simulation results show the effectiveness of the proposed method.

Robust optimization of the laser induced damage threshold of dielectric mirrors for high power lasers.

PubMed

Chorel, Marine; Lanternier, Thomas; Lavastre, Éric; Bonod, Nicolas; Bousquet, Bruno; Néauport, Jérôme

2018-04-30

We report on a numerical optimization of the laser induced damage threshold of multi-dielectric high reflection mirrors in the sub-picosecond regime. We highlight the interplay between the electric field distribution, refractive index and intrinsic laser induced damage threshold of the materials on the overall laser induced damage threshold (LIDT) of the multilayer. We describe an optimization method of the multilayer that minimizes the field enhancement in high refractive index materials while preserving a near perfect reflectivity. This method yields a significant improvement of the damage resistance since a maximum increase of 40% can be achieved on the overall LIDT of the multilayer.

Automated smoother for the numerical decoupling of dynamics models.

PubMed

Vilela, Marco; Borges, Carlos C H; Vinga, Susana; Vasconcelos, Ana Tereza R; Santos, Helena; Voit, Eberhard O; Almeida, Jonas S

2007-08-21

Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure. In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations. The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

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

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Towards robust and repeatable sampling methods in eDNA based studies.

PubMed

Dickie, Ian A; Boyer, Stephane; Buckley, Hannah; Duncan, Richard P; Gardner, Paul; Hogg, Ian D; Holdaway, Robert J; Lear, Gavin; Makiola, Andreas; Morales, Sergio E; Powell, Jeff R; Weaver, Louise

2018-05-26

DNA based techniques are increasingly used for measuring the biodiversity (species presence, identity, abundance and community composition) of terrestrial and aquatic ecosystems. While there are numerous reviews of molecular methods and bioinformatic steps, there has been little consideration of the methods used to collect samples upon which these later steps are based. This represents a critical knowledge gap, as methodologically sound field sampling is the foundation for subsequent analyses. We reviewed field sampling methods used for metabarcoding studies of both terrestrial and freshwater ecosystem biodiversity over a nearly three-year period (n = 75). We found that 95% (n = 71) of these studies used subjective sampling methods, inappropriate field methods, and/or failed to provide critical methodological information. It would be possible for researchers to replicate only 5% of the metabarcoding studies in our sample, a poorer level of reproducibility than for ecological studies in general. Our findings suggest greater attention to field sampling methods and reporting is necessary in eDNA-based studies of biodiversity to ensure robust outcomes and future reproducibility. Methods must be fully and accurately reported, and protocols developed that minimise subjectivity. Standardisation of sampling protocols would be one way to help to improve reproducibility, and have additional benefits in allowing compilation and comparison of data from across studies. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Adaptive estimation of state of charge and capacity with online identified battery model for vanadium redox flow battery

NASA Astrophysics Data System (ADS)

Wei, Zhongbao; Tseng, King Jet; Wai, Nyunt; Lim, Tuti Mariana; Skyllas-Kazacos, Maria

2016-11-01

Reliable state estimate depends largely on an accurate battery model. However, the parameters of battery model are time varying with operating condition variation and battery aging. The existing co-estimation methods address the model uncertainty by integrating the online model identification with state estimate and have shown improved accuracy. However, the cross interference may arise from the integrated framework to compromise numerical stability and accuracy. Thus this paper proposes the decoupling of model identification and state estimate to eliminate the possibility of cross interference. The model parameters are online adapted with the recursive least squares (RLS) method, based on which a novel joint estimator based on extended Kalman Filter (EKF) is formulated to estimate the state of charge (SOC) and capacity concurrently. The proposed joint estimator effectively compresses the filter order which leads to substantial improvement in the computational efficiency and numerical stability. Lab scale experiment on vanadium redox flow battery shows that the proposed method is highly authentic with good robustness to varying operating conditions and battery aging. The proposed method is further compared with some existing methods and shown to be superior in terms of accuracy, convergence speed, and computational cost.

A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A new weak Galerkin finite element method for elliptic interface problems

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

Mu, Lin; Wang, Junping; Ye, Xiu

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

Aerodynamic shape optimization using control theory

NASA Technical Reports Server (NTRS)

Reuther, James

1996-01-01

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter

2018-01-01

This paper presents a high order hybrid discontinuous Galerkin/finite volume scheme for solving the equations of the magnetohydrodynamics (MHD) and of the relativistic hydrodynamics (SRHD) on quadrilateral meshes. In this approach, for the spatial discretization, an arbitrary high order discontinuous Galerkin spectral element (DG) method is combined with a finite volume (FV) scheme in order to simulate complex flow problems involving strong shocks. Regarding the time discretization, a fourth order strong stability preserving Runge-Kutta method is used. In the proposed hybrid scheme, a shock indicator is computed at the beginning of each Runge-Kutta stage in order to flag those elements containing shock waves or discontinuities. Subsequently, the DG solution in these troubled elements and in the current time step is projected onto a subdomain composed of finite volume subcells. Right after, the DG operator is applied to those unflagged elements, which, in principle, are oscillation-free, meanwhile the troubled elements are evolved with a robust second/third order FV operator. With this approach we are able to numerically simulate very challenging problems in the context of MHD and SRHD in one, and two space dimensions and with very high order polynomials. We make convergence tests and show a comprehensive one- and two dimensional testbench for both equation systems, focusing in problems with strong shocks. The presented hybrid approach shows that numerical schemes of very high order of accuracy are able to simulate these complex flow problems in an efficient and robust manner.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

PubMed Central

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-01-01

Abstract. Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method. PMID:28464120

Holistic Assessment and Ethical Disputation on a New Trend in Solid Biofuels.

PubMed

Hašková, Simona

2017-04-01

A new trend in the production technology of solid biof uels has appeared. There is a wide consensus that most solid biofuels will be produced according to the new production methods within a few years. Numerous samples were manufactured from agro-residues according to conventional methods as well as new methods. Robust analyses that reviewed the hygienic, environmental, financial and ethical aspects were performed. The hygienic and environmental aspect was assessed by robust chemical and technical analyses. The financial aspect was assessed by energy cost breakdown. The ethical point of view was built on the above stated findings, the survey questionnaire and critical discussion with the literature. It is concluded that the new production methods are significantly favourable from both the hygienic and environmental points of view. Financial indicators do not allow the expressing of any preference. Regarding the ethical aspect, it is concluded that the new methods are beneficial in terms of environmental responsibility. However, it showed that most of the customers that took part in the survey are price oriented and therefore they tend to prefer the cheaper-conventional alternative. In the long term it can be assumed that expansion of the new technology and competition among manufacturers will reduce the costs.

Modern Perspectives on Numerical Modeling of Cardiac Pacemaker Cell

PubMed Central

Maltsev, Victor A.; Yaniv, Yael; Maltsev, Anna V.; Stern, Michael D.; Lakatta, Edward G.

2015-01-01

Cardiac pacemaking is a complex phenomenon that is still not completely understood. Together with experimental studies, numerical modeling has been traditionally used to acquire mechanistic insights in this research area. This review summarizes the present state of numerical modeling of the cardiac pacemaker, including approaches to resolve present paradoxes and controversies. Specifically we discuss the requirement for realistic modeling to consider symmetrical importance of both intracellular and cell membrane processes (within a recent “coupled-clock” theory). Promising future developments of the complex pacemaker system models include the introduction of local calcium control, mitochondria function, and biochemical regulation of protein phosphorylation and cAMP production. Modern numerical and theoretical methods such as multi-parameter sensitivity analyses within extended populations of models and bifurcation analyses are also important for the definition of the most realistic parameters that describe a robust, yet simultaneously flexible operation of the coupled-clock pacemaker cell system. The systems approach to exploring cardiac pacemaker function will guide development of new therapies, such as biological pacemakers for treating insufficient cardiac pacemaker function that becomes especially prevalent with advancing age. PMID:24748434

Stochastic Integration H∞ Filter for Rapid Transfer Alignment of INS.

PubMed

Zhou, Dapeng; Guo, Lei

2017-11-18

The performance of an inertial navigation system (INS) operated on a moving base greatly depends on the accuracy of rapid transfer alignment (RTA). However, in practice, the coexistence of large initial attitude errors and uncertain observation noise statistics poses a great challenge for the estimation accuracy of misalignment angles. This study aims to develop a novel robust nonlinear filter, namely the stochastic integration H ∞ filter (SIH ∞ F) for improving both the accuracy and robustness of RTA. In this new nonlinear H ∞ filter, the stochastic spherical-radial integration rule is incorporated with the framework of the derivative-free H ∞ filter for the first time, and the resulting SIH ∞ F simultaneously attenuates the negative effect in estimations caused by significant nonlinearity and large uncertainty. Comparisons between the SIH ∞ F and previously well-known methodologies are carried out by means of numerical simulation and a van test. The results demonstrate that the newly-proposed method outperforms the cubature H ∞ filter. Moreover, the SIH ∞ F inherits the benefit of the traditional stochastic integration filter, but with more robustness in the presence of uncertainty.

Fuzzy logic-based flight control system design

NASA Astrophysics Data System (ADS)

Nho, Kyungmoon

The application of fuzzy logic to aircraft motion control is studied in this dissertation. The self-tuning fuzzy techniques are developed by changing input scaling factors to obtain a robust fuzzy controller over a wide range of operating conditions and nonlinearities for a nonlinear aircraft model. It is demonstrated that the properly adjusted input scaling factors can meet the required performance and robustness in a fuzzy controller. For a simple demonstration of the easy design and control capability of a fuzzy controller, a proportional-derivative (PD) fuzzy control system is compared to the conventional controller for a simple dynamical system. This thesis also describes the design principles and stability analysis of fuzzy control systems by considering the key features of a fuzzy control system including the fuzzification, rule-base and defuzzification. The wing-rock motion of slender delta wings, a linear aircraft model and the six degree of freedom nonlinear aircraft dynamics are considered to illustrate several self-tuning methods employing change in input scaling factors. Finally, this dissertation is concluded with numerical simulation of glide-slope capture in windshear demonstrating the robustness of the fuzzy logic based flight control system.

On Multifunctional Collaborative Methods in Engineering Science

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2001-01-01

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

Investigation of progressive failure robustness and alternate load paths for damage tolerant structures

NASA Astrophysics Data System (ADS)

Marhadi, Kun Saptohartyadi

Structural optimization for damage tolerance under various unforeseen damage scenarios is computationally challenging. It couples non-linear progressive failure analysis with sampling-based stochastic analysis of random damage. The goal of this research was to understand the relationship between alternate load paths available in a structure and its damage tolerance, and to use this information to develop computationally efficient methods for designing damage tolerant structures. Progressive failure of a redundant truss structure subjected to small random variability was investigated to identify features that correlate with robustness and predictability of the structure's progressive failure. The identified features were used to develop numerical surrogate measures that permit computationally efficient deterministic optimization to achieve robustness and predictability of progressive failure. Analysis of damage tolerance on designs with robust progressive failure indicated that robustness and predictability of progressive failure do not guarantee damage tolerance. Damage tolerance requires a structure to redistribute its load to alternate load paths. In order to investigate the load distribution characteristics that lead to damage tolerance in structures, designs with varying degrees of damage tolerance were generated using brute force stochastic optimization. A method based on principal component analysis was used to describe load distributions (alternate load paths) in the structures. Results indicate that a structure that can develop alternate paths is not necessarily damage tolerant. The alternate load paths must have a required minimum load capability. Robustness analysis of damage tolerant optimum designs indicates that designs are tailored to specified damage. A design Optimized under one damage specification can be sensitive to other damages not considered. Effectiveness of existing load path definitions and characterizations were investigated for continuum structures. A load path definition using a relative compliance change measure (U* field) was demonstrated to be the most useful measure of load path. This measure provides quantitative information on load path trajectories and qualitative information on the effectiveness of the load path. The use of the U* description of load paths in optimizing structures for effective load paths was investigated.

Robust numerical electromagnetic eigenfunction expansion algorithms

NASA Astrophysics Data System (ADS)

Sainath, Kamalesh

This thesis summarizes developments in rigorous, full-wave, numerical spectral-domain (integral plane wave eigenfunction expansion [PWE]) evaluation algorithms concerning time-harmonic electromagnetic (EM) fields radiated by generally-oriented and positioned sources within planar and tilted-planar layered media exhibiting general anisotropy, thickness, layer number, and loss characteristics. The work is motivated by the need to accurately and rapidly model EM fields radiated by subsurface geophysical exploration sensors probing layered, conductive media, where complex geophysical and man-made processes can lead to micro-laminate and micro-fractured geophysical formations exhibiting, at the lower (sub-2MHz) frequencies typically employed for deep EM wave penetration through conductive geophysical media, bulk-scale anisotropic (i.e., directional) electrical conductivity characteristics. When the planar-layered approximation (layers of piecewise-constant material variation and transversely-infinite spatial extent) is locally, near the sensor region, considered valid, numerical spectral-domain algorithms are suitable due to their strong low-frequency stability characteristic, and ability to numerically predict time-harmonic EM field propagation in media with response characterized by arbitrarily lossy and (diagonalizable) dense, anisotropic tensors. If certain practical limitations are addressed, PWE can robustly model sensors with general position and orientation that probe generally numerous, anisotropic, lossy, and thick layers. The main thesis contributions, leading to a sensor and geophysical environment-robust numerical modeling algorithm, are as follows: (1) Simple, rapid estimator of the region (within the complex plane) containing poles, branch points, and branch cuts (critical points) (Chapter 2), (2) Sensor and material-adaptive azimuthal coordinate rotation, integration contour deformation, integration domain sub-region partition and sub-region-dependent integration order (Chapter 3), (3) Integration partition-extrapolation-based (Chapter 3) and Gauss-Laguerre Quadrature (GLQ)-based (Chapter 4) evaluations of the deformed, semi-infinite-length integration contour tails, (4) Robust in-situ-based (i.e., at the spectral-domain integrand level) direct/homogeneous-medium field contribution subtraction and analytical curbing of the source current spatial spectrum function's ill behavior (Chapter 5), and (5) Analytical re-casting of the direct-field expressions when the source is embedded within a NBAM, short for non-birefringent anisotropic medium (Chapter 6). The benefits of these contributions are, respectively, (1) Avoiding computationally intensive critical-point location and tracking (computation time savings), (2) Sensor and material-robust curbing of the integrand's oscillatory and slow decay behavior, as well as preventing undesirable critical-point migration within the complex plane (computation speed, precision, and instability-avoidance benefits), (3) sensor and material-robust reduction (or, for GLQ, elimination) of integral truncation error, (4) robustly stable modeling of scattered fields and/or fields radiated from current sources modeled as spatially distributed (10 to 1000-fold compute-speed acceleration also realized for distributed-source computations), and (5) numerically stable modeling of fields radiated from sources within NBAM layers. Having addressed these limitations, are PWE algorithms applicable to modeling EM waves in tilted planar-layered geometries too? This question is explored in Chapter 7 using a Transformation Optics-based approach, allowing one to model wave propagation through layered media that (in the sensor's vicinity) possess tilted planar interfaces. The technique leads to spurious wave scattering however, whose induced computation accuracy degradation requires analysis. Mathematical exhibition, and exhaustive simulation-based study and analysis of the limitations of, this novel tilted-layer modeling formulation is Chapter 7's main contribution.

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

NASA Technical Reports Server (NTRS)

Sandham, N. D.; Yee, H. C.; Kwak, Dochan (Technical Monitor)

2000-01-01

A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

An efficient numerical model for multicomponent compressible flow in fractured porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2014-12-01

An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant-Freidricks-Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20-130 times in 2D. In 3D, one may expect even a higher computational efficiency.

Unbiased and robust quantification of synchronization between spikes and local field potential.

PubMed

Li, Zhaohui; Cui, Dong; Li, Xiaoli

2016-08-30

In neuroscience, relating the spiking activity of individual neurons to the local field potential (LFP) of neural ensembles is an increasingly useful approach for studying rhythmic neuronal synchronization. Many methods have been proposed to measure the strength of the association between spikes and rhythms in the LFP recordings, and most existing measures are dependent upon the total number of spikes. In the present work, we introduce a robust approach for quantifying spike-LFP synchronization which performs reliably for limited samples of data. The measure is termed as spike-triggered correlation matrix synchronization (SCMS), which takes LFP segments centered on each spike as multi-channel signals and calculates the index of spike-LFP synchronization by constructing a correlation matrix. The simulation based on artificial data shows that the SCMS output almost does not change with the sample size. This property is of crucial importance when making comparisons between different experimental conditions. When applied to actual neuronal data recorded from the monkey primary visual cortex, it is found that the spike-LFP synchronization strength shows orientation selectivity to drifting gratings. In comparison to another unbiased method, pairwise phase consistency (PPC), the proposed SCMS behaves better for noisy spike trains by means of numerical simulations. This study demonstrates the basic idea and calculating process of the SCMS method. Considering its unbiasedness and robustness, the measure is of great advantage to characterize the synchronization between spike trains and rhythms present in LFP. Copyright © 2016 Elsevier B.V. All rights reserved.

Possibility-based robust design optimization for the structural-acoustic system with fuzzy parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2018-03-01

The conventional engineering optimization problems considering uncertainties are based on the probabilistic model. However, the probabilistic model may be unavailable because of the lack of sufficient objective information to construct the precise probability distribution of uncertainties. This paper proposes a possibility-based robust design optimization (PBRDO) framework for the uncertain structural-acoustic system based on the fuzzy set model, which can be constructed by expert opinions. The objective of robust design is to optimize the expectation and variability of system performance with respect to uncertainties simultaneously. In the proposed PBRDO, the entropy of the fuzzy system response is used as the variability index; the weighted sum of the entropy and expectation of the fuzzy response is used as the objective function, and the constraints are established in the possibility context. The computations for the constraints and objective function of PBRDO are a triple-loop and a double-loop nested problem, respectively, whose computational costs are considerable. To improve the computational efficiency, the target performance approach is introduced to transform the calculation of the constraints into a double-loop nested problem. To further improve the computational efficiency, a Chebyshev fuzzy method (CFM) based on the Chebyshev polynomials is proposed to estimate the objective function, and the Chebyshev interval method (CIM) is introduced to estimate the constraints, thereby the optimization problem is transformed into a single-loop one. Numerical results on a shell structural-acoustic system verify the effectiveness and feasibility of the proposed methods.

Multiple-correction hybrid k-exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids

NASA Astrophysics Data System (ADS)

Pont, Grégoire; Brenner, Pierre; Cinnella, Paola; Maugars, Bruno; Robinet, Jean-Christophe

2017-12-01

A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.

A fictitious domain approach for the simulation of dense suspensions

NASA Astrophysics Data System (ADS)

Gallier, Stany; Lemaire, Elisabeth; Lobry, Laurent; Peters, François

2014-01-01

Low Reynolds number concentrated suspensions do exhibit an intricate physics which can be partly unraveled by the use of numerical simulation. To this end, a Lagrange multiplier-free fictitious domain approach is described in this work. Unlike some methods recently proposed, the present approach is fully Eulerian and therefore does not need any transfer between the Eulerian background grid and some Lagrangian nodes attached to particles. Lubrication forces between particles play an important role in the suspension rheology and have been properly accounted for in the model. A robust and effective lubrication scheme is outlined which consists in transposing the classical approach used in Stokesian Dynamics to our present direct numerical simulation. This lubrication model has also been adapted to account for solid boundaries such as walls. Contact forces between particles are modeled using a classical Discrete Element Method (DEM), a widely used method in granular matter physics. Comprehensive validations are presented on various one-particle, two-particle or three-particle configurations in a linear shear flow as well as some O(103) and O(104) particle simulations.

Viscoacoustic anisotropic full waveform inversion

NASA Astrophysics Data System (ADS)

Qu, Yingming; Li, Zhenchun; Huang, Jianping; Li, Jinli

2017-01-01

A viscoacoustic vertical transverse isotropic (VTI) quasi-differential wave equation, which takes account for both the viscosity and anisotropy of media, is proposed for wavefield simulation in this study. The finite difference method is used to solve the equations, for which the attenuation terms are solved in the wavenumber domain, and all remaining terms in the time-space domain. To stabilize the adjoint wavefield, robust regularization operators are applied to the wave equation to eliminate the high-frequency component of the numerical noise produced during the backward propagation of the viscoacoustic wavefield. Based on these strategies, we derive the corresponding gradient formula and implement a viscoacoustic VTI full waveform inversion (FWI). Numerical tests verify that our proposed viscoacoustic VTI FWI can produce accurate and stable inversion results for viscoacoustic VTI data sets. In addition, we test our method's sensitivity to velocity, Q, and anisotropic parameters. Our results show that the sensitivity to velocity is much higher than that to Q and anisotropic parameters. As such, our proposed method can produce acceptable inversion results as long as the Q and anisotropic parameters are within predefined thresholds.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

NASA Astrophysics Data System (ADS)

Gjennestad, Magnus Aa.; Gruber, Andrea; Lervåg, Karl Yngve; Johansen, Øyvind; Ervik, Åsmund; Hammer, Morten; Munkejord, Svend Tollak

2017-11-01

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose thermodynamic properties are calculated using the Span-Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge-Kutta method. We demonstrate close to fifth-order convergence for advection-diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.

Assessment of WENO-extended two-fluid modelling in compressible multiphase flows

NASA Astrophysics Data System (ADS)

Kitamura, Keiichi; Nonomura, Taku

2017-03-01

The two-fluid modelling based on an advection-upwind-splitting-method (AUSM)-family numerical flux function, AUSM+-up, following the work by Chang and Liou [Journal of Computational Physics 2007;225: 840-873], has been successfully extended to the fifth order by weighted-essentially-non-oscillatory (WENO) schemes. Then its performance is surveyed in several numerical tests. The results showed a desired performance in one-dimensional benchmark test problems: Without relying upon an anti-diffusion device, the higher-order two-fluid method captures the phase interface within a fewer grid points than the conventional second-order method, as well as a rarefaction wave and a very weak shock. At a high pressure ratio (e.g. 1,000), the interpolated variables appeared to affect the performance: the conservative-variable-based characteristic-wise WENO interpolation showed less sharper but more robust representations of the shocks and expansions than the primitive-variable-based counterpart did. In two-dimensional shock/droplet test case, however, only the primitive-variable-based WENO with a huge void fraction realised a stable computation.

A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method

NASA Astrophysics Data System (ADS)

Shams, Mosayeb; Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko

2018-03-01

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier-Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier-Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas.

A deterministic Lagrangian particle separation-based method for advective-diffusion problems

NASA Astrophysics Data System (ADS)

Wong, Ken T. M.; Lee, Joseph H. W.; Choi, K. W.

2008-12-01

A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.

Efficient Computation of Info-Gap Robustness for Finite Element Models

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

Stull, Christopher J.; Hemez, Francois M.; Williams, Brian J.

2012-07-05

A recent research effort at LANL proposed info-gap decision theory as a framework by which to measure the predictive maturity of numerical models. Info-gap theory explores the trade-offs between accuracy, that is, the extent to which predictions reproduce the physical measurements, and robustness, that is, the extent to which predictions are insensitive to modeling assumptions. Both accuracy and robustness are necessary to demonstrate predictive maturity. However, conducting an info-gap analysis can present a formidable challenge, from the standpoint of the required computational resources. This is because a robustness function requires the resolution of multiple optimization problems. This report offers anmore » alternative, adjoint methodology to assess the info-gap robustness of Ax = b-like numerical models solved for a solution x. Two situations that can arise in structural analysis and design are briefly described and contextualized within the info-gap decision theory framework. The treatments of the info-gap problems, using the adjoint methodology are outlined in detail, and the latter problem is solved for four separate finite element models. As compared to statistical sampling, the proposed methodology offers highly accurate approximations of info-gap robustness functions for the finite element models considered in the report, at a small fraction of the computational cost. It is noted that this report considers only linear systems; a natural follow-on study would extend the methodologies described herein to include nonlinear systems.« less

A comparative analysis of spectral exponent estimation techniques for 1/fβ processes with applications to the analysis of stride interval time series

PubMed Central

Schaefer, Alexander; Brach, Jennifer S.; Perera, Subashan; Sejdić, Ervin

2013-01-01

Background The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f) = 1/fβ. The scaling exponent β is thus often interpreted as a “biomarker” of relative health and decline. New Method This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. Results The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Comparison with Existing Methods: Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. Conclusions The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series. PMID:24200509

Model reference tracking control of an aircraft: a robust adaptive approach

NASA Astrophysics Data System (ADS)

Tanyer, Ilker; Tatlicioglu, Enver; Zergeroglu, Erkan

2017-05-01

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.

Damage Identification in Beam Structure using Spatial Continuous Wavelet Transform

NASA Astrophysics Data System (ADS)

Janeliukstis, R.; Rucevskis, S.; Wesolowski, M.; Kovalovs, A.; Chate, A.

2015-11-01

In this paper the applicability of spatial continuous wavelet transform (CWT) technique for damage identification in the beam structure is analyzed by application of different types of wavelet functions and scaling factors. The proposed method uses exclusively mode shape data from the damaged structure. To examine limitations of the method and to ascertain its sensitivity to noisy experimental data, several sets of simulated data are analyzed. Simulated test cases include numerical mode shapes corrupted by different levels of random noise as well as mode shapes with different number of measurement points used for wavelet transform. A broad comparison of ability of different wavelet functions to detect and locate damage in beam structure is given. Effectiveness and robustness of the proposed algorithms are demonstrated experimentally on two aluminum beams containing single mill-cut damage. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer with PZT actuator as vibration excitation source for the experimental study.

A discrete geometric approach for simulating the dynamics of thin viscous threads

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

Audoly, B., E-mail: audoly@lmm.jussieu.fr; Clauvelin, N.; Brun, P.-T.

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistencymore » of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.« less

Long-time stability effects of quadrature and artificial viscosity on nodal discontinuous Galerkin methods for gas dynamics

NASA Astrophysics Data System (ADS)

Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan

2017-11-01

Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.

Design Considerations of ISTAR Hydrocarbon Fueled Combustor Operating in Air Augmented Rocket, Ramjet and Scramjet Modes

NASA Technical Reports Server (NTRS)

Andreadis, Dean; Drake, Alan; Garrett, Joseph L.; Gettinger, Christopher D.; Hoxie, Stephen S.

2003-01-01

The development and ground test of a rocket-based combined cycle (RBCC) propulsion system is being conducted as part of the NASA Marshall Space Flight Center (MSFC) Integrated System Test of an Airbreathing Rocket (ISTAR) program. The eventual flight vehicle (X-43B) is designed to support an air-launched self-powered Mach 0.7 to 7.0 demonstration of an RBCC engine through all of its airbreathing propulsion modes - air augmented rocket (AAR), ramjet (RJ), and scramjet (SJ). Through the use of analytical tools, numerical simulations, and experimental tests the ISTAR program is developing and validating a hydrocarbon-fueled RBCC combustor design methodology. This methodology will then be used to design an integrated RBCC propulsion system that produces robust ignition and combustion stability characteristics while maximizing combustion efficiency and minimizing drag losses. First order analytical and numerical methods used to design hydrocarbon-fueled combustors are discussed with emphasis on the methods and determination of requirements necessary to establish engine operability and performance characteristics.

Design Considerations of Istar Hydrocarbon Fueled Combustor Operating in Air Augmented Rocket, Ramjet and Scramjet Modes

NASA Technical Reports Server (NTRS)

Andreadis, Dean; Drake, Alan; Garrett, Joseph L.; Gettinger, Christopher D.; Hoxie, Stephen S.

2002-01-01

The development and ground test of a rocket-based combined cycle (RBCC) propulsion system is being conducted as part of the NASA Marshall Space Flight Center (MSFC) Integrated System Test of an Airbreathing Rocket (ISTAR) program. The eventual flight vehicle (X-43B) is designed to support an air-launched self-powered Mach 0.7 to 7.0 demonstration of an RBCC engine through all of its airbreathing propulsion modes - air augmented rocket (AAR), ramjet (RJ), and scramjet (SJ). Through the use of analytical tools, numerical simulations, and experimental tests the ISTAR program is developing and validating a hydrocarbon-fueled RBCC combustor design methodology. This methodology will then be used to design an integrated RBCC propulsion system thai: produces robust ignition and combustion stability characteristics while maximizing combustion efficiency and minimizing drag losses. First order analytical and numerical methods used to design hydrocarbon-fueled combustors are discussed with emphasis on the methods and determination of requirements necessary to establish engine operability and performance characteristics.

A consistent modelling methodology for secondary settling tanks: a reliable numerical method.

PubMed

Bürger, Raimund; Diehl, Stefan; Farås, Sebastian; Nopens, Ingmar; Torfs, Elena

2013-01-01

The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection-diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2015-11-01

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

Optical information encryption based on incoherent superposition with the help of the QR code

NASA Astrophysics Data System (ADS)

Qin, Yi; Gong, Qiong

2014-01-01

In this paper, a novel optical information encryption approach is proposed with the help of QR code. This method is based on the concept of incoherent superposition which we introduce for the first time. The information to be encrypted is first transformed into the corresponding QR code, and thereafter the QR code is further encrypted into two phase only masks analytically by use of the intensity superposition of two diffraction wave fields. The proposed method has several advantages over the previous interference-based method, such as a higher security level, a better robustness against noise attack, a more relaxed work condition, and so on. Numerical simulation results and actual smartphone collected results are shown to validate our proposal.

A speciation solver for cement paste modeling and the semismooth Newton method

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

Georget, Fabien, E-mail: fabieng@princeton.edu; Prévost, Jean H., E-mail: prevost@princeton.edu; Vanderbei, Robert J., E-mail: rvdb@princeton.edu

2015-02-15

The mineral assemblage of a cement paste may vary considerably with its environment. In addition, the water content of a cement paste is relatively low and the ionic strength of the interstitial solution is often high. These conditions are extreme conditions with respect to the common assumptions made in speciation problem. Furthermore the common trial and error algorithm to find the phase assemblage does not provide any guarantee of convergence. We propose a speciation solver based on a semismooth Newton method adapted to the thermodynamic modeling of cement paste. The strong theoretical properties associated with these methods offer practical advantages.more » Results of numerical experiments indicate that the algorithm is reliable, robust, and efficient.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Research on knowledge representation, machine learning, and knowledge acquisition

NASA Technical Reports Server (NTRS)

Buchanan, Bruce G.

1987-01-01

Research in knowledge representation, machine learning, and knowledge acquisition performed at Knowledge Systems Lab. is summarized. The major goal of the research was to develop flexible, effective methods for representing the qualitative knowledge necessary for solving large problems that require symbolic reasoning as well as numerical computation. The research focused on integrating different representation methods to describe different kinds of knowledge more effectively than any one method can alone. In particular, emphasis was placed on representing and using spatial information about three dimensional objects and constraints on the arrangement of these objects in space. Another major theme is the development of robust machine learning programs that can be integrated with a variety of intelligent systems. To achieve this goal, learning methods were designed, implemented and experimented within several different problem solving environments.

Robust entanglement between a movable mirror and atomic ensemble and entanglement transfer in coupled optomechanical system

PubMed Central

Bai, Cheng-Hua; Wang, Dong-Yang; Wang, Hong-Fu; Zhu, Ai-Dong; Zhang, Shou

2016-01-01

We propose a scheme for the creation of robust entanglement between a movable mirror and atomic ensemble at the macroscopic level in coupled optomechanical system. We numerically simulate the degree of entanglement of the bipartite macroscopic entanglement and show that it depends on the coupling strength between the cavities and is robust with respect to the certain environment temperature. Inspiringly and surprisingly, according to the reported relation between the mechanical damping rate and the mechanical frequency of the movable mirror, the numerical simulation result shows that such bipartite macroscopic entanglement persists for environment temperature up to 170 K, which breaks the liquid nitrogen cooling and liquid helium cooling and largely lowers down the experiment cost. We also investigate the entanglement transfer based on this coupled system. The scheme can be used for the realization of quantum memories for continuous variable quantum information processing and quantum-limited displacement measurements. PMID:27624534

Hierarchical mutual information for the comparison of hierarchical community structures in complex networks

NASA Astrophysics Data System (ADS)

Perotti, Juan Ignacio; Tessone, Claudio Juan; Caldarelli, Guido

2015-12-01

The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust, and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the hierarchical mutual information, which is a generalization of the traditional mutual information and makes it possible to compare hierarchical partitions and hierarchical community structures. The normalized version of the hierarchical mutual information should behave analogously to the traditional normalized mutual information. Here the correct behavior of the hierarchical mutual information is corroborated on an extensive battery of numerical experiments. The experiments are performed on artificial hierarchies and on the hierarchical community structure of artificial and empirical networks. Furthermore, the experiments illustrate some of the practical applications of the hierarchical mutual information, namely the comparison of different community detection methods and the study of the consistency, robustness, and temporal evolution of the hierarchical modular structure of networks.

Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

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

Lester, Brian; Scherzinger, William

2017-01-19

Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, andmore » compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.« less

Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

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

Lester, Brian T.; Scherzinger, William M.

2017-01-19

A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and comparedmore » to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.« less

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

Wiebenga, J. H.; Atzema, E. H.; Boogaard, A. H. van den

Robust design of forming processes using numerical simulations is gaining attention throughout the industry. In this work, it is demonstrated how robust optimization can assist in further stretching the limits of metal forming processes. A deterministic and a robust optimization study are performed, considering a stretch-drawing process of a hemispherical cup product. For the robust optimization study, both the effect of material and process scatter are taken into account. For quantifying the material scatter, samples of 41 coils of a drawing quality forming steel have been collected. The stochastic material behavior is obtained by a hybrid approach, combining mechanical testingmore » and texture analysis, and efficiently implemented in a metamodel based optimization strategy. The deterministic and robust optimization results are subsequently presented and compared, demonstrating an increased process robustness and decreased number of product rejects by application of the robust optimization approach.« less

Robust large-scale parallel nonlinear solvers for simulations.

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

Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson

2005-11-01

This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their usemore » in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.« less

Adaptive target binarization method based on a dual-camera system

NASA Astrophysics Data System (ADS)

Lei, Jing; Zhang, Ping; Xu, Jiangtao; Gao, Zhiyuan; Gao, Jing

2018-01-01

An adaptive target binarization method based on a dual-camera system that contains two dynamic vision sensors was proposed. First, a preprocessing procedure of denoising is introduced to remove the noise events generated by the sensors. Then, the complete edge of the target is retrieved and represented by events based on an event mosaicking method. Third, the region of the target is confirmed by an event-to-event method. Finally, a postprocessing procedure of image open and close operations of morphology methods is adopted to remove the artifacts caused by event-to-event mismatching. The proposed binarization method has been extensively tested on numerous degraded images with nonuniform illumination, low contrast, noise, or light spots and successfully compared with other well-known binarization methods. The experimental results, which are based on visual and misclassification error criteria, show that the proposed method performs well and has better robustness on the binarization of degraded images.

A semi-implicit finite element method for viscous lipid membranes

NASA Astrophysics Data System (ADS)

Rodrigues, Diego S.; Ausas, Roberto F.; Mut, Fernando; Buscaglia, Gustavo C.

2015-10-01

A finite element formulation to approximate the behavior of lipid membranes is proposed. The mathematical model incorporates tangential viscous stresses and bending elastic forces, together with the inextensibility constraint and the enclosed volume constraint. The membrane is discretized by a surface mesh made up of planar triangles, over which a mixed formulation (velocity-curvature) is built based on the viscous bilinear form (Boussinesq-Scriven operator) and the Laplace-Beltrami identity relating position and curvature. A semi-implicit approach is then used to discretize in time, with piecewise linear interpolants for all variables. Two stabilization terms are needed: The first one stabilizes the inextensibility constraint by a pressure-gradient-projection scheme (Codina and Blasco (1997) [33]), the second couples curvature and velocity to improve temporal stability, as proposed by Bänsch (2001) [36]. The volume constraint is handled by a Lagrange multiplier (which turns out to be the internal pressure), and an analogous strategy is used to filter out rigid-body motions. The nodal positions are updated in a Lagrangian manner according to the velocity solution at each time step. An automatic remeshing strategy maintains suitable refinement and mesh quality throughout the simulation. Numerical experiments show the convergent and robust behavior of the proposed method. Stability limits are obtained from numerous relaxation tests, and convergence with mesh refinement is confirmed both in the relaxation transient and in the final equilibrium shape. Virtual tweezing experiments are also reported, computing the dependence of the deformed membrane shape with the tweezing velocity (a purely dynamical effect). For sufficiently high velocities, a tether develops which shows good agreement, both in its final radius and in its transient behavior, with available analytical solutions. Finally, simulation results of a membrane subject to the simultaneous action of six tweezers illustrate the robustness of the method.

Space-time adaptive ADER-DG schemes for dissipative flows: Compressible Navier-Stokes and resistive MHD equations

NASA Astrophysics Data System (ADS)

Fambri, Francesco; Dumbser, Michael; Zanotti, Olindo

2017-11-01

This paper presents an arbitrary high-order accurate ADER Discontinuous Galerkin (DG) method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent partial differential equations for compressible dissipative flows : the compressible Navier-Stokes equations and the equations of viscous and resistive magnetohydrodynamics in two and three space-dimensions. The work continues a recent series of papers concerning the development and application of a proper a posteriori subcell finite volume limiting procedure suitable for discontinuous Galerkin methods (Dumbser et al., 2014, Zanotti et al., 2015 [40,41]). It is a well known fact that a major weakness of high order DG methods lies in the difficulty of limiting discontinuous solutions, which generate spurious oscillations, namely the so-called 'Gibbs phenomenon'. In the present work, a nonlinear stabilization of the scheme is sequentially and locally introduced only for troubled cells on the basis of a novel a posteriori detection criterion, i.e. the MOOD approach. The main benefits of the MOOD paradigm, i.e. the computational robustness even in the presence of strong shocks, are preserved and the numerical diffusion is considerably reduced also for the limited cells by resorting to a proper sub-grid. In practice the method first produces a so-called candidate solution by using a high order accurate unlimited DG scheme. Then, a set of numerical and physical detection criteria is applied to the candidate solution, namely: positivity of pressure and density, absence of floating point errors and satisfaction of a discrete maximum principle in the sense of polynomials. Furthermore, in those cells where at least one of these criteria is violated the computed candidate solution is detected as troubled and is locally rejected. Subsequently, a more reliable numerical solution is recomputed a posteriori by employing a more robust but still very accurate ADER-WENO finite volume scheme on the subgrid averages within that troubled cell. Finally, a high order DG polynomial is reconstructed back from the evolved subcell averages. We apply the whole approach for the first time to the equations of compressible gas dynamics and magnetohydrodynamics in the presence of viscosity, thermal conductivity and magnetic resistivity, therefore extending our family of adaptive ADER-DG schemes to cases for which the numerical fluxes also depend on the gradient of the state vector. The distinguished high-resolution properties of the presented numerical scheme standout against a wide number of non-trivial test cases both for the compressible Navier-Stokes and the viscous and resistive magnetohydrodynamics equations. The present results show clearly that the shock-capturing capability of the news schemes is significantly enhanced within a cell-by-cell Adaptive Mesh Refinement (AMR) implementation together with time accurate local time stepping (LTS).

Multigrid Computations of 3-D Incompressible Internal and External Viscous Rotating Flows

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Taylor, Lafayette K.; Chen, Jen-Ping; Jiang, Min-Yee; Whitfield, David L.

1996-01-01

This report presents multigrid methods for solving the 3-D incompressible viscous rotating flows in a NASA low-speed centrifugal compressor and a marine propeller 4119. Numerical formulations are given in both the rotating reference frame and the absolute frame. Comparisons are made for the accuracy, efficiency, and robustness between the steady-state scheme and the time-accurate scheme for simulating viscous rotating flows for complex internal and external flow applications. Prospects for further increase in efficiency and accuracy of unsteady time-accurate computations are discussed.

A Gas-Kinetic Scheme for Reactive Flows

NASA Technical Reports Server (NTRS)

Lian,Youg-Sheng; Xu, Kun

1998-01-01

In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.

Computer vision

NASA Technical Reports Server (NTRS)

Gennery, D.; Cunningham, R.; Saund, E.; High, J.; Ruoff, C.

1981-01-01

The field of computer vision is surveyed and assessed, key research issues are identified, and possibilities for a future vision system are discussed. The problems of descriptions of two and three dimensional worlds are discussed. The representation of such features as texture, edges, curves, and corners are detailed. Recognition methods are described in which cross correlation coefficients are maximized or numerical values for a set of features are measured. Object tracking is discussed in terms of the robust matching algorithms that must be devised. Stereo vision, camera control and calibration, and the hardware and systems architecture are discussed.

Generalized shrunken type-GM estimator and its application

NASA Astrophysics Data System (ADS)

Ma, C. Z.; Du, Y. L.

2014-03-01

The parameter estimation problem in linear model is considered when multicollinearity and outliers exist simultaneously. A class of new robust biased estimator, Generalized Shrunken Type-GM Estimation, with their calculated methods are established by combination of GM estimator and biased estimator include Ridge estimate, Principal components estimate and Liu estimate and so on. A numerical example shows that the most attractive advantage of these new estimators is that they can not only overcome the multicollinearity of coefficient matrix and outliers but also have the ability to control the influence of leverage points.

Recognition of blurred images by the method of moments.

PubMed

Flusser, J; Suk, T; Saic, S

1996-01-01

The article is devoted to the feature-based recognition of blurred images acquired by a linear shift-invariant imaging system against an image database. The proposed approach consists of describing images by features that are invariant with respect to blur and recognizing images in the feature space. The PSF identification and image restoration are not required. A set of symmetric blur invariants based on image moments is introduced. A numerical experiment is presented to illustrate the utilization of the invariants for blurred image recognition. Robustness of the features is also briefly discussed.

A New Domain Decomposition Approach for the Gust Response Problem

NASA Technical Reports Server (NTRS)

Scott, James R.; Atassi, Hafiz M.; Susan-Resiga, Romeo F.

2002-01-01

A domain decomposition method is developed for solving the aerodynamic/aeroacoustic problem of an airfoil in a vortical gust. The computational domain is divided into inner and outer regions wherein the governing equations are cast in different forms suitable for accurate computations in each region. Boundary conditions which ensure continuity of pressure and velocity are imposed along the interface separating the two regions. A numerical study is presented for reduced frequencies ranging from 0.1 to 3.0. It is seen that the domain decomposition approach in providing robust and grid independent solutions.

Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers.

PubMed

Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping

2014-11-01

In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Examining robustness of model selection with half-normal and LASSO plots for unreplicated factorial designs

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

Jang, Dae -Heung; Anderson-Cook, Christine Michaela

When there are constraints on resources, an unreplicated factorial or fractional factorial design can allow efficient exploration of numerous factor and interaction effects. A half-normal plot is a common graphical tool used to compare the relative magnitude of effects and to identify important effects from these experiments when no estimate of error from the experiment is available. An alternative is to use a least absolute shrinkage and selection operation plot to examine the pattern of model selection terms from an experiment. We examine how both the half-normal and least absolute shrinkage and selection operation plots are impacted by the absencemore » of individual observations or an outlier, and the robustness of conclusions obtained from these 2 techniques for identifying important effects from factorial experiments. As a result, the methods are illustrated with 2 examples from the literature.« less

Three-Component Soliton States in Spinor F =1 Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Bersano, T. M.; Gokhroo, V.; Khamehchi, M. A.; D'Ambroise, J.; Frantzeskakis, D. J.; Engels, P.; Kevrekidis, P. G.

2018-02-01

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F =1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

Three-Component Soliton States in Spinor F=1 Bose-Einstein Condensates.

PubMed

Bersano, T M; Gokhroo, V; Khamehchi, M A; D'Ambroise, J; Frantzeskakis, D J; Engels, P; Kevrekidis, P G

2018-02-09

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F=1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

Examining robustness of model selection with half-normal and LASSO plots for unreplicated factorial designs

DOE PAGES

Jang, Dae -Heung; Anderson-Cook, Christine Michaela

2017-04-12

When there are constraints on resources, an unreplicated factorial or fractional factorial design can allow efficient exploration of numerous factor and interaction effects. A half-normal plot is a common graphical tool used to compare the relative magnitude of effects and to identify important effects from these experiments when no estimate of error from the experiment is available. An alternative is to use a least absolute shrinkage and selection operation plot to examine the pattern of model selection terms from an experiment. We examine how both the half-normal and least absolute shrinkage and selection operation plots are impacted by the absencemore » of individual observations or an outlier, and the robustness of conclusions obtained from these 2 techniques for identifying important effects from factorial experiments. As a result, the methods are illustrated with 2 examples from the literature.« less

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

NASA Astrophysics Data System (ADS)

Wang, Gang; Chen, Changzheng; Yu, Shenbo

2017-07-01

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

Space-Time Conservation Element and Solution Element Method Being Developed

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Himansu, Ananda; Jorgenson, Philip C. E.; Loh, Ching-Yuen; Wang, Xiao-Yen; Yu, Sheng-Tao

1999-01-01

The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically reacting flows.

Robust digital image watermarking using distortion-compensated dither modulation

NASA Astrophysics Data System (ADS)

Li, Mianjie; Yuan, Xiaochen

2018-04-01

In this paper, we propose a robust feature extraction based digital image watermarking method using Distortion- Compensated Dither Modulation (DC-DM). Our proposed local watermarking method provides stronger robustness and better flexibility than traditional global watermarking methods. We improve robustness by introducing feature extraction and DC-DM method. To extract the robust feature points, we propose a DAISY-based Robust Feature Extraction (DRFE) method by employing the DAISY descriptor and applying the entropy calculation based filtering. The experimental results show that the proposed method achieves satisfactory robustness under the premise of ensuring watermark imperceptibility quality compared to other existing methods.

Global robust stability of bidirectional associative memory neural networks with multiple time delays.

PubMed

Senan, Sibel; Arik, Sabri

2007-10-01

This correspondence presents a sufficient condition for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point for bidirectional associative memory neural networks with discrete time delays. The results impose constraint conditions on the network parameters of the neural system independently of the delay parameter, and they are applicable to all bounded continuous nonmonotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.

Plane Smoothers for Multiblock Grids: Computational Aspects

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Diskin, Boris; Melson, N. Duane

1999-01-01

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Short stack modeling of degradation in solid oxide fuel cells. Part II. Sensitivity and interaction analysis

NASA Astrophysics Data System (ADS)

Gazzarri, J. I.; Kesler, O.

In the first part of this two-paper series, we presented a numerical model of the impedance behaviour of a solid oxide fuel cell (SOFC) aimed at simulating the change in the impedance spectrum induced by contact degradation at the interconnect-electrode, and at the electrode-electrolyte interfaces. The purpose of that investigation was to develop a non-invasive diagnostic technique to identify degradation modes in situ. In the present paper, we appraise the predictive capabilities of the proposed method in terms of its robustness to uncertainties in the input parameters, many of which are very difficult to measure independently. We applied this technique to the degradation modes simulated in Part I, in addition to anode sulfur poisoning. Electrode delamination showed the highest robustness to input parameter variations, followed by interconnect oxidation and interconnect detachment. The most sensitive degradation mode was sulfur poisoning, due to strong parameter interactions. In addition, we simulate several simultaneous two-degradation-mode scenarios, assessing the method's capabilities and limitations for the prediction of electrochemical behaviour of SOFC's undergoing multiple simultaneous degradation modes.

Development of a universal measure of quadrupedal forelimb-hindlimb coordination using digital motion capture and computerised analysis.

PubMed

Hamilton, Lindsay; Franklin, Robin J M; Jeffery, Nick D

2007-09-18

Clinical spinal cord injury in domestic dogs provides a model population in which to test the efficacy of putative therapeutic interventions for human spinal cord injury. To achieve this potential a robust method of functional analysis is required so that statistical comparison of numerical data derived from treated and control animals can be achieved. In this study we describe the use of digital motion capture equipment combined with mathematical analysis to derive a simple quantitative parameter - 'the mean diagonal coupling interval' - to describe coordination between forelimb and hindlimb movement. In normal dogs this parameter is independent of size, conformation, speed of walking or gait pattern. We show here that mean diagonal coupling interval is highly sensitive to alterations in forelimb-hindlimb coordination in dogs that have suffered spinal cord injury, and can be accurately quantified, but is unaffected by orthopaedic perturbations of gait. Mean diagonal coupling interval is an easily derived, highly robust measurement that provides an ideal method to compare the functional effect of therapeutic interventions after spinal cord injury in quadrupeds.

A scalable parallel black oil simulator on distributed memory parallel computers

NASA Astrophysics Data System (ADS)

Wang, Kun; Liu, Hui; Chen, Zhangxin

2015-11-01

This paper presents our work on developing a parallel black oil simulator for distributed memory computers based on our in-house parallel platform. The parallel simulator is designed to overcome the performance issues of common simulators that are implemented for personal computers and workstations. The finite difference method is applied to discretize the black oil model. In addition, some advanced techniques are employed to strengthen the robustness and parallel scalability of the simulator, including an inexact Newton method, matrix decoupling methods, and algebraic multigrid methods. A new multi-stage preconditioner is proposed to accelerate the solution of linear systems from the Newton methods. Numerical experiments show that our simulator is scalable and efficient, and is capable of simulating extremely large-scale black oil problems with tens of millions of grid blocks using thousands of MPI processes on parallel computers.

Three-dimensional local ALE-FEM method for fluid flow in domains containing moving boundaries/objects interfaces

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

Carrington, David Bradley; Monayem, A. K. M.; Mazumder, H.

2015-03-05

A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is amore » fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.« less

Implementation of the Jacobian-free Newton-Krylov method for solving the for solving the first-order ice sheet momentum balance

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

Salinger, Andy; Evans, Katherine J; Lemieux, Jean-Francois

2011-01-01

We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the rst-order ice sheet momentum equation in order to improve the numerical performance of the Community Ice Sheet Model (CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on signicant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.84-3.62 times more efficient than the standard Picard solver in CISM. Importantly, this computational gain of JFNK over themore » Picard solver increases when rening the grid. Global convergence of the JFNK solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.« less

Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method.

PubMed

Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong

2011-12-01

In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

Seismic data restoration with a fast L1 norm trust region method

NASA Astrophysics Data System (ADS)

Cao, Jingjie; Wang, Yanfei

2014-08-01

Seismic data restoration is a major strategy to provide reliable wavefield when field data dissatisfy the Shannon sampling theorem. Recovery by sparsity-promoting inversion often get sparse solutions of seismic data in a transformed domains, however, most methods for sparsity-promoting inversion are line-searching methods which are efficient but are inclined to obtain local solutions. Using trust region method which can provide globally convergent solutions is a good choice to overcome this shortcoming. A trust region method for sparse inversion has been proposed, however, the efficiency should be improved to suitable for large-scale computation. In this paper, a new L1 norm trust region model is proposed for seismic data restoration and a robust gradient projection method for solving the sub-problem is utilized. Numerical results of synthetic and field data demonstrate that the proposed trust region method can get excellent computation speed and is a viable alternative for large-scale computation.

An integrated approach to flood hazard assessment on alluvial fans using numerical modeling, field mapping, and remote sensing

USGS Publications Warehouse

Pelletier, J.D.; Mayer, L.; Pearthree, P.A.; House, P.K.; Demsey, K.A.; Klawon, J.K.; Vincent, K.R.

2005-01-01

Millions of people in the western United States live near the dynamic, distributary channel networks of alluvial fans where flood behavior is complex and poorly constrained. Here we test a new comprehensive approach to alluvial-fan flood hazard assessment that uses four complementary methods: two-dimensional raster-based hydraulic modeling, satellite-image change detection, fieldbased mapping of recent flood inundation, and surficial geologic mapping. Each of these methods provides spatial detail lacking in the standard method and each provides critical information for a comprehensive assessment. Our numerical model simultaneously solves the continuity equation and Manning's equation (Chow, 1959) using an implicit numerical method. It provides a robust numerical tool for predicting flood flows using the large, high-resolution Digital Elevation Models (DEMs) necessary to resolve the numerous small channels on the typical alluvial fan. Inundation extents and flow depths of historic floods can be reconstructed with the numerical model and validated against field- and satellite-based flood maps. A probabilistic flood hazard map can also be constructed by modeling multiple flood events with a range of specified discharges. This map can be used in conjunction with a surficial geologic map to further refine floodplain delineation on fans. To test the accuracy of the numerical model, we compared model predictions of flood inundation and flow depths against field- and satellite-based flood maps for two recent extreme events on the southern Tortolita and Harquahala piedmonts in Arizona. Model predictions match the field- and satellite-based maps closely. Probabilistic flood hazard maps based on the 10 yr, 100 yr, and maximum floods were also constructed for the study areas using stream gage records and paleoflood deposits. The resulting maps predict spatially complex flood hazards that strongly reflect small-scale topography and are consistent with surficial geology. In contrast, FEMA Flood Insurance Rate Maps (FIRMs) based on the FAN model predict uniformly high flood risk across the study areas without regard for small-scale topography and surficial geology. ?? 2005 Geological Society of America.

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

A Bootstrap Based Measure Robust to the Choice of Normalization Methods for Detecting Rhythmic Features in High Dimensional Data.

PubMed

Larriba, Yolanda; Rueda, Cristina; Fernández, Miguel A; Peddada, Shyamal D

2018-01-01

Motivation: Gene-expression data obtained from high throughput technologies are subject to various sources of noise and accordingly the raw data are pre-processed before formally analyzed. Normalization of the data is a key pre-processing step, since it removes systematic variations across arrays. There are numerous normalization methods available in the literature. Based on our experience, in the context of oscillatory systems, such as cell-cycle, circadian clock, etc., the choice of the normalization method may substantially impact the determination of a gene to be rhythmic. Thus rhythmicity of a gene can purely be an artifact of how the data were normalized. Since the determination of rhythmic genes is an important component of modern toxicological and pharmacological studies, it is important to determine truly rhythmic genes that are robust to the choice of a normalization method. Results: In this paper we introduce a rhythmicity measure and a bootstrap methodology to detect rhythmic genes in an oscillatory system. Although the proposed methodology can be used for any high-throughput gene expression data, in this paper we illustrate the proposed methodology using several publicly available circadian clock microarray gene-expression datasets. We demonstrate that the choice of normalization method has very little effect on the proposed methodology. Specifically, for any pair of normalization methods considered in this paper, the resulting values of the rhythmicity measure are highly correlated. Thus it suggests that the proposed measure is robust to the choice of a normalization method. Consequently, the rhythmicity of a gene is potentially not a mere artifact of the normalization method used. Lastly, as demonstrated in the paper, the proposed bootstrap methodology can also be used for simulating data for genes participating in an oscillatory system using a reference dataset. Availability: A user friendly code implemented in R language can be downloaded from http://www.eio.uva.es/~miguel/robustdetectionprocedure.html.

A Bootstrap Based Measure Robust to the Choice of Normalization Methods for Detecting Rhythmic Features in High Dimensional Data

PubMed Central

Larriba, Yolanda; Rueda, Cristina; Fernández, Miguel A.; Peddada, Shyamal D.

2018-01-01

Motivation: Gene-expression data obtained from high throughput technologies are subject to various sources of noise and accordingly the raw data are pre-processed before formally analyzed. Normalization of the data is a key pre-processing step, since it removes systematic variations across arrays. There are numerous normalization methods available in the literature. Based on our experience, in the context of oscillatory systems, such as cell-cycle, circadian clock, etc., the choice of the normalization method may substantially impact the determination of a gene to be rhythmic. Thus rhythmicity of a gene can purely be an artifact of how the data were normalized. Since the determination of rhythmic genes is an important component of modern toxicological and pharmacological studies, it is important to determine truly rhythmic genes that are robust to the choice of a normalization method. Results: In this paper we introduce a rhythmicity measure and a bootstrap methodology to detect rhythmic genes in an oscillatory system. Although the proposed methodology can be used for any high-throughput gene expression data, in this paper we illustrate the proposed methodology using several publicly available circadian clock microarray gene-expression datasets. We demonstrate that the choice of normalization method has very little effect on the proposed methodology. Specifically, for any pair of normalization methods considered in this paper, the resulting values of the rhythmicity measure are highly correlated. Thus it suggests that the proposed measure is robust to the choice of a normalization method. Consequently, the rhythmicity of a gene is potentially not a mere artifact of the normalization method used. Lastly, as demonstrated in the paper, the proposed bootstrap methodology can also be used for simulating data for genes participating in an oscillatory system using a reference dataset. Availability: A user friendly code implemented in R language can be downloaded from http://www.eio.uva.es/~miguel/robustdetectionprocedure.html PMID:29456555

The Robust Learning Model (RLM): A Comprehensive Approach to a New Online University

ERIC Educational Resources Information Center

Neumann, Yoram; Neumann, Edith F.

2010-01-01

This paper outlines the components of the Robust Learning Model (RLM) as a conceptual framework for creating a new online university offering numerous degree programs at all degree levels. The RLM is a multi-factorial model based on the basic belief that successful learning outcomes depend on multiple factors employed together in a holistic…

Light and Life in Baltimore—and Beyond

PubMed Central

Edidin, Michael

2015-01-01

Baltimore has been the home of numerous biophysical studies using light to probe cells. One such study, quantitative measurement of lateral diffusion of rhodopsin, set the standard for experiments in which recovery after photobleaching is used to measure lateral diffusion. Development of this method from specialized microscopes to commercial scanning confocal microscopes has led to widespread use of the technique to measure lateral diffusion of membrane proteins and lipids, and as well diffusion and binding interactions in cell organelles and cytoplasm. Perturbation of equilibrium distributions by photobleaching has also been developed into a robust method to image molecular proximity in terms of fluorescence resonance energy transfer between donor and acceptor fluorophores. PMID:25650914

Completely automated modal analysis procedure based on the combination of different OMA methods

NASA Astrophysics Data System (ADS)

Ripamonti, Francesco; Bussini, Alberto; Resta, Ferruccio

2018-03-01

In this work a completely automated output-only Modal Analysis procedure is presented and all its benefits are listed. Based on the merging of different Operational Modal Analysis methods and a statistical approach, the identification process has been improved becoming more robust and giving as results only the real natural frequencies, damping ratios and mode shapes of the system. The effect of the temperature can be taken into account as well, leading to the creation of a better tool for automated Structural Health Monitoring. The algorithm has been developed and tested on a numerical model of a scaled three-story steel building present in the laboratories of Politecnico di Milano.

Artificial Boundary Conditions Based on the Difference Potentials Method

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1996-01-01

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

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

Pelanti, Marica, E-mail: Marica.Pelanti@ens.f; Bouchut, Francois, E-mail: francois.bouchut@univ-mlv.f; Mangeney, Anne, E-mail: mangeney@ipgp.jussieu.f

2011-02-01

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resultingmore » relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.« less

Asynchronous machine rotor speed estimation using a tabulated numerical approach

NASA Astrophysics Data System (ADS)

Nguyen, Huu Phuc; De Miras, Jérôme; Charara, Ali; Eltabach, Mario; Bonnet, Stéphane

2017-12-01

This paper proposes a new method to estimate the rotor speed of the asynchronous machine by looking at the estimation problem as a nonlinear optimal control problem. The behavior of the nonlinear plant model is approximated off-line as a prediction map using a numerical one-step time discretization obtained from simulations. At each time-step, the speed of the induction machine is selected satisfying the dynamic fitting problem between the plant output and the predicted output, leading the system to adopt its dynamical behavior. Thanks to the limitation of the prediction horizon to a single time-step, the execution time of the algorithm can be completely bounded. It can thus easily be implemented and embedded into a real-time system to observe the speed of the real induction motor. Simulation results show the performance and robustness of the proposed estimator.

Fluctuating hydrodynamics of multispecies nonreactive mixtures

DOE PAGES

Balakrishnan, Kaushik; Garcia, Alejandro L.; Donev, Aleksandar; ...

2014-01-22

In this study we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of nonequilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well asmore » reverse diffusion in a ternary mixture. Finally, good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multispecies fluids.« less

Influence of intra-pigment vibrations on dynamics of photosynthetic exciton.

PubMed

Sato, Yoshihiro; Doolittle, Brian

2014-11-14

We have numerically investigated the effect of an underdamped intra-pigment vibrational mode on an exciton's quantum coherence and energy transfer efficiency. Our model describes a bacteriochlorophyll a pigment-protein dimer under the conditions at which photosynthetic energy transfer occurs. The dimer is modeled using a theoretical treatment of a vibronic exciton, and its dynamics are numerically analyzed using a non-Markovian and non-perturbative method. We examined the system's response to various values of the Huang-Rhys factor, site energy difference, reorganization energy, and reorganization energy difference. We found that the inclusion of the intra-pigment vibronic mode allows for long-lived oscillatory quantum coherences to occur. This excitonic coherence is robust against static site-energy disorder. The vibrational mode also promotes exciton transfer along the site-energy landscape thus improving the overall energy transfer efficiency.

Fast angular synchronization for phase retrieval via incomplete information

NASA Astrophysics Data System (ADS)

Viswanathan, Aditya; Iwen, Mark

2015-08-01

We consider the problem of recovering the phase of an unknown vector, x ∈ ℂd, given (normalized) phase difference measurements of the form xjxk*/|xjxk*|, j,k ∈ {1,...,d}, and where xj* denotes the complex conjugate of xj. This problem is sometimes referred to as the angular synchronization problem. This paper analyzes a linear-time-in-d eigenvector-based angular synchronization algorithm and studies its theoretical and numerical performance when applied to a particular class of highly incomplete and possibly noisy phase difference measurements. Theoretical results are provided for perfect (noiseless) measurements, while numerical simulations demonstrate the robustness of the method to measurement noise. Finally, we show that this angular synchronization problem and the specific form of incomplete phase difference measurements considered arise in the phase retrieval problem - where we recover an unknown complex vector from phaseless (or magnitude) measurements.

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

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

Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.

2014-06-01

The applicability of ADER finite volume methods to solve hyperbolic balance laws with stiff source terms in the context of well-balanced and non-conservative schemes is extended to solve a one-dimensional blood flow model for viscoelastic vessels, reformulated as a hyperbolic system, via a relaxation time. A criterion for selecting relaxation times is found and an empirical convergence rate assessment is carried out to support this result. The proposed methodology is validated by applying it to a network of viscoelastic vessels for which experimental and numerical results are available. The agreement between the results obtained in the present paper and thosemore » available in the literature is satisfactory. Key features of the present formulation and numerical methodologies, such as accuracy, efficiency and robustness, are fully discussed in the paper.« less

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

A robust optimization methodology for preliminary aircraft design

NASA Astrophysics Data System (ADS)

Prigent, S.; Maréchal, P.; Rondepierre, A.; Druot, T.; Belleville, M.

2016-05-01

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.

ℓ1-Regularized full-waveform inversion with prior model information based on orthant-wise limited memory quasi-Newton method

NASA Astrophysics Data System (ADS)

Dai, Meng-Xue; Chen, Jing-Bo; Cao, Jian

2017-07-01

Full-waveform inversion (FWI) is an ill-posed optimization problem which is sensitive to noise and initial model. To alleviate the ill-posedness of the problem, regularization techniques are usually adopted. The ℓ1-norm penalty is a robust regularization method that preserves contrasts and edges. The Orthant-Wise Limited-Memory Quasi-Newton (OWL-QN) method extends the widely-used limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to the ℓ1-regularized optimization problems and inherits the efficiency of L-BFGS. To take advantage of the ℓ1-regularized method and the prior model information obtained from sonic logs and geological information, we implement OWL-QN algorithm in ℓ1-regularized FWI with prior model information in this paper. Numerical experiments show that this method not only improve the inversion results but also has a strong anti-noise ability.

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

NASA Astrophysics Data System (ADS)

Zhong, Xiaolin

1998-08-01

Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that numerical methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference schemes which are stable and are less dissipative than a straightforward upwind scheme using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge-Kutta schemes for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new schemes are validated by numerical experiments of the linear wave equation and nonlinear Navier-Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.

Classifying the Sizes of Explosive Eruptions using Tephra Deposits: The Advantages of a Numerical Inversion Approach

NASA Astrophysics Data System (ADS)

Connor, C.; Connor, L.; White, J.

2015-12-01

Explosive volcanic eruptions are often classified by deposit mass and eruption column height. How well are these eruption parameters determined in older deposits, and how well can we reduce uncertainty using robust numerical and statistical methods? We describe an efficient and effective inversion and uncertainty quantification approach for estimating eruption parameters given a dataset of tephra deposit thickness and granulometry. The inversion and uncertainty quantification is implemented using the open-source PEST++ code. Inversion with PEST++ can be used with a variety of forward models and here is applied using Tephra2, a code that simulates advective and dispersive tephra transport and deposition. The Levenburg-Marquardt algorithm is combined with formal Tikhonov and subspace regularization to invert eruption parameters; a linear equation for conditional uncertainty propagation is used to estimate posterior parameter uncertainty. Both the inversion and uncertainty analysis support simultaneous analysis of the full eruption and wind-field parameterization. The combined inversion/uncertainty-quantification approach is applied to the 1992 eruption of Cerro Negro (Nicaragua), the 2011 Kirishima-Shinmoedake (Japan), and the 1913 Colima (Mexico) eruptions. These examples show that although eruption mass uncertainty is reduced by inversion against tephra isomass data, considerable uncertainty remains for many eruption and wind-field parameters, such as eruption column height. Supplementing the inversion dataset with tephra granulometry data is shown to further reduce the uncertainty of most eruption and wind-field parameters. We think the use of such robust models provides a better understanding of uncertainty in eruption parameters, and hence eruption classification, than is possible with more qualitative methods that are widely used.

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization

PubMed Central

Li, Zukui; Ding, Ran; Floudas, Christodoulos A.

2011-01-01

Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263

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

PubMed

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

2012-01-01

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

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

A new method for recognizing hand configurations of Brazilian gesture language.

PubMed

Costa Filho, C F F; Dos Santos, B L; de Souza, R S; Dos Santos, J R; Costa, M G F

2016-08-01

This paper describes a new method for recognizing hand configurations of the Brazilian Gesture Language - LIBRAS - using depth maps obtained with a Kinect® camera. The proposed method comprised three phases: hand segmentation, feature extraction, and classification. The segmentation phase is independent from the background and depends only on pixel depth information. Using geometric operations and numerical normalization, the feature extraction process was done independent from rotation and translation. The features are extracted employing two techniques: (2D)2LDA and (2D)2PCA. The classification is made with a novelty classifier. A robust database was constructed for classifier evaluation, with 12,200 images of LIBRAS and 200 gestures of each hand configuration. The best accuracy obtained was 95.41%, which was greater than previous values obtained in the literature.

A comparative analysis of spectral exponent estimation techniques for 1/f(β) processes with applications to the analysis of stride interval time series.

PubMed

Schaefer, Alexander; Brach, Jennifer S; Perera, Subashan; Sejdić, Ervin

2014-01-30

The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline. This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series. Copyright © 2013 Elsevier B.V. All rights reserved.

Equation-free analysis of agent-based models and systematic parameter determination

NASA Astrophysics Data System (ADS)

Thomas, Spencer A.; Lloyd, David J. B.; Skeldon, Anne C.

2016-12-01

Agent based models (ABM)s are increasingly used in social science, economics, mathematics, biology and computer science to describe time dependent systems in circumstances where a description in terms of equations is difficult. Yet few tools are currently available for the systematic analysis of ABM behaviour. Numerical continuation and bifurcation analysis is a well-established tool for the study of deterministic systems. Recently, equation-free (EF) methods have been developed to extend numerical continuation techniques to systems where the dynamics are described at a microscopic scale and continuation of a macroscopic property of the system is considered. To date, the practical use of EF methods has been limited by; (1) the over-head of application-specific implementation; (2) the laborious configuration of problem-specific parameters; and (3) large ensemble sizes (potentially) leading to computationally restrictive run-times. In this paper we address these issues with our tool for the EF continuation of stochastic systems, which includes algorithms to systematically configuration problem specific parameters and enhance robustness to noise. Our tool is generic and can be applied to any 'black-box' simulator and determines the essential EF parameters prior to EF analysis. Robustness is significantly improved using our convergence-constraint with a corrector-repeat (C3R) method. This algorithm automatically detects outliers based on the dynamics of the underlying system enabling both an order of magnitude reduction in ensemble size and continuation of systems at much higher levels of noise than classical approaches. We demonstrate our method with application to several ABM models, revealing parameter dependence, bifurcation and stability analysis of these complex systems giving a deep understanding of the dynamical behaviour of the models in a way that is not otherwise easily obtainable. In each case we demonstrate our systematic parameter determination stage for configuring the system specific EF parameters.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

NASA Astrophysics Data System (ADS)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Symmetry-plane model of 3D Euler flows: Mapping to regular systems and numerical solutions of blowup

NASA Astrophysics Data System (ADS)

Mulungye, Rachel M.; Lucas, Dan; Bustamante, Miguel D.

2014-11-01

We introduce a family of 2D models describing the dynamics on the so-called symmetry plane of the full 3D Euler fluid equations. These models depend on a free real parameter and can be solved analytically. For selected representative values of the free parameter, we apply the method introduced in [M.D. Bustamante, Physica D: Nonlinear Phenom. 240, 1092 (2011)] to map the fluid equations bijectively to globally regular systems. By comparing the analytical solutions with the results of numerical simulations, we establish that the numerical simulations of the mapped regular systems are far more accurate than the numerical simulations of the original systems, at the same spatial resolution and CPU time. In particular, the numerical integrations of the mapped regular systems produce robust estimates for the growth exponent and singularity time of the main blowup quantity (vorticity stretching rate), converging well to the analytically-predicted values even beyond the time at which the flow becomes under-resolved (i.e. the reliability time). In contrast, direct numerical integrations of the original systems develop unstable oscillations near the reliability time. We discuss the reasons for this improvement in accuracy, and explain how to extend the analysis to the full 3D case. Supported under the programme for Research in Third Level Institutions (PRTLI) Cycle 5 and co-funded by the European Regional Development Fund.

Robust portfolio selection based on asymmetric measures of variability of stock returns

NASA Astrophysics Data System (ADS)

Chen, Wei; Tan, Shaohua

2009-10-01

This paper addresses a new uncertainty set--interval random uncertainty set for robust optimization. The form of interval random uncertainty set makes it suitable for capturing the downside and upside deviations of real-world data. These deviation measures capture distributional asymmetry and lead to better optimization results. We also apply our interval random chance-constrained programming to robust mean-variance portfolio selection under interval random uncertainty sets in the elements of mean vector and covariance matrix. Numerical experiments with real market data indicate that our approach results in better portfolio performance.

Robust stability of fractional order polynomials with complicated uncertainty structure

PubMed Central

Şenol, Bilal; Pekař, Libor

2017-01-01

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. PMID:28662173

Robust functional regression model for marginal mean and subject-specific inferences.

PubMed

Cao, Chunzheng; Shi, Jian Qing; Lee, Youngjo

2017-01-01

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well as interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals (PIs) for conditional mean curves. Numerical studies show that the proposed model provides a robust approach against data contamination or distribution misspecification, and the proposed PIs maintain the nominal confidence levels. A real data application is presented as an illustrative example.

Robust DEA under discrete uncertain data: a case study of Iranian electricity distribution companies

NASA Astrophysics Data System (ADS)

Hafezalkotob, Ashkan; Haji-Sami, Elham; Omrani, Hashem

2015-06-01

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the real-world problems often deal with imprecise or ambiguous data. In this paper, we propose a novel robust data envelopment model (RDEA) to investigate the efficiencies of decision-making units (DMU) when there are discrete uncertain input and output data. The method is based upon the discrete robust optimization approaches proposed by Mulvey et al. (1995) that utilizes probable scenarios to capture the effect of ambiguous data in the case study. Our primary concern in this research is evaluating electricity distribution companies under uncertainty about input/output data. To illustrate the ability of proposed model, a numerical example of 38 Iranian electricity distribution companies is investigated. There are a large amount ambiguous data about these companies. Some electricity distribution companies may not report clear and real statistics to the government. Thus, it is needed to utilize a prominent approach to deal with this uncertainty. The results reveal that the RDEA model is suitable and reliable for target setting based on decision makers (DM's) preferences when there are uncertain input/output data.

Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

NASA Astrophysics Data System (ADS)

García-Senz, Domingo; Cabezón, Rubén M.; Escartín, José A.; Ebinger, Kevin

2014-10-01

Context. The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. Aims: We propose and check a method to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the sinc function). Methods: The proposed method was checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities, and the collapse of a Sun-like polytrope. Results: The analysis of the hydrodynamical simulations suggests that the scheme devised to equalize the accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Numerical techniques for high-throughput reflectance interference biosensing

NASA Astrophysics Data System (ADS)

Sevenler, Derin; Ünlü, M. Selim

2016-06-01

We have developed a robust and rapid computational method for processing the raw spectral data collected from thin film optical interference biosensors. We have applied this method to Interference Reflectance Imaging Sensor (IRIS) measurements and observed a 10,000 fold improvement in processing time, unlocking a variety of clinical and scientific applications. Interference biosensors have advantages over similar technologies in certain applications, for example highly multiplexed measurements of molecular kinetics. However, processing raw IRIS data into useful measurements has been prohibitively time consuming for high-throughput studies. Here we describe the implementation of a lookup table (LUT) technique that provides accurate results in far less time than naive methods. We also discuss an additional benefit that the LUT method can be used with a wider range of interference layer thickness and experimental configurations that are incompatible with methods that require fitting the spectral response.

Insights into the Streaming Instability in Protoplanetary Disks

NASA Astrophysics Data System (ADS)

Youdin, Andrew N.; Lin, Min-Kai; Li, Rixin

2017-10-01

The streaming instability is a leading mechanism to concentrate particles in protoplanetary disks, thereby triggering planetesimal formation. I will present recent analytical and numerical work on the origin of the streaming instability and its robustness. Our recent analytic work examines the origin of, and relationship between, a variety of drag-induced instabilities, including the streaming instability as well as secular gravitational instabilities, a drag instability driven by self-gravity. We show that drag instabilities are powered by a specific phase relationship between gas pressure and particle concentrations, which power the instability via pressure work. This mechanism is analogous to pulsating instabilities in stars. This mechanism differs qualitatively from other leading particle concentration mechanisms in pressure bumps and vortices. Our recent numerical work investigates the numerical robustness of non-linear particle clumping by the streaming instability, especially with regard to the location and boundary condition of vertical boundaries. We find that particle clumping is robust to these choices in boxes that are not too short. However, hydrodynamic activity away from the particle-dominated midplane is significantly affected by vertical boundary conditions. This activity affects the observationally significant lofting of small dust grains. We thus emphasize the need for larger scale simulations which connect disk surface layers, including outflowing winds, to the planet-forming midplane.

Robust double gain unscented Kalman filter for small satellite attitude estimation

NASA Astrophysics Data System (ADS)

Cao, Lu; Yang, Weiwei; Li, Hengnian; Zhang, Zhidong; Shi, Jianjun

2017-08-01

Limited by the low precision of small satellite sensors, the estimation theories with high performance remains the most popular research topic for the attitude estimation. The Kalman filter (KF) and its extensions have been widely applied in the satellite attitude estimation and achieved plenty of achievements. However, most of the existing methods just take use of the current time-step's priori measurement residuals to complete the measurement update and state estimation, which always ignores the extraction and utilization of the previous time-step's posteriori measurement residuals. In addition, the uncertainty model errors always exist in the attitude dynamic system, which also put forward the higher performance requirements for the classical KF in attitude estimation problem. Therefore, the novel robust double gain unscented Kalman filter (RDG-UKF) is presented in this paper to satisfy the above requirements for the small satellite attitude estimation with the low precision sensors. It is assumed that the system state estimation errors can be exhibited in the measurement residual; therefore, the new method is to derive the second Kalman gain Kk2 for making full use of the previous time-step's measurement residual to improve the utilization efficiency of the measurement data. Moreover, the sequence orthogonal principle and unscented transform (UT) strategy are introduced to robust and enhance the performance of the novel Kalman Filter in order to reduce the influence of existing uncertainty model errors. Numerical simulations show that the proposed RDG-UKF is more effective and robustness in dealing with the model errors and low precision sensors for the attitude estimation of small satellite by comparing with the classical unscented Kalman Filter (UKF).

Do the surface Fermi arcs in Weyl semimetals survive disorder?

NASA Astrophysics Data System (ADS)

Wilson, Justin H.; Pixley, J. H.; Huse, David A.; Refael, Gil; Das Sarma, S.

2018-06-01

We theoretically study the topological robustness of the surface physics induced by Weyl Fermi-arc surface states in the presence of short-ranged quenched disorder and surface-bulk hybridization. This is investigated with numerically exact calculations on a lattice model exhibiting Weyl Fermi arcs. We find that the Fermi-arc surface states, in addition to having a finite lifetime from disorder broadening, hybridize with nonperturbative bulk rare states making them no longer bound to the surface (i.e., they lose their purely surface spectral character). Thus, we provide strong numerical evidence that the Weyl Fermi arcs are not topologically protected from disorder. Nonetheless, the surface chiral velocity is robust and survives in the presence of strong disorder, persisting all the way to the Anderson-localized phase by forming localized current loops that live within the localization length of the surface. Thus, the Weyl semimetal is not topologically robust to the presence of disorder, but the surface chiral velocity is.

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2012-11-01

A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems onmore » arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.« less

Optimal and robust control of quantum state transfer by shaping the spectral phase of ultrafast laser pulses.

PubMed

Guo, Yu; Dong, Daoyi; Shu, Chuan-Cun

2018-04-04

Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.

Petroleum refinery operational planning using robust optimization

NASA Astrophysics Data System (ADS)

Leiras, A.; Hamacher, S.; Elkamel, A.

2010-12-01

In this article, the robust optimization methodology is applied to deal with uncertainties in the prices of saleable products, operating costs, product demand, and product yield in the context of refinery operational planning. A numerical study demonstrates the effectiveness of the proposed robust approach. The benefits of incorporating uncertainty in the different model parameters were evaluated in terms of the cost of ignoring uncertainty in the problem. The calculations suggest that this benefit is equivalent to 7.47% of the deterministic solution value, which indicates that the robust model may offer advantages to those involved with refinery operational planning. In addition, the probability bounds of constraint violation are calculated to help the decision-maker adopt a more appropriate parameter to control robustness and judge the tradeoff between conservatism and total profit.

Info-gap robust-satisficing model of foraging behavior: do foragers optimize or satisfice?

PubMed

Carmel, Yohay; Ben-Haim, Yakov

2005-11-01

In this note we compare two mathematical models of foraging that reflect two competing theories of animal behavior: optimizing and robust satisficing. The optimal-foraging model is based on the marginal value theorem (MVT). The robust-satisficing model developed here is an application of info-gap decision theory. The info-gap robust-satisficing model relates to the same circumstances described by the MVT. We show how these two alternatives translate into specific predictions that at some points are quite disparate. We test these alternative predictions against available data collected in numerous field studies with a large number of species from diverse taxonomic groups. We show that a large majority of studies appear to support the robust-satisficing model and reject the optimal-foraging model.

Passivity-based Robust Control of Aerospace Systems

NASA Technical Reports Server (NTRS)

Kelkar, Atul G.; Joshi, Suresh M. (Technical Monitor)

2000-01-01

This report provides a brief summary of the research work performed over the duration of the cooperative research agreement between NASA Langley Research Center and Kansas State University. The cooperative agreement which was originally for the duration the three years was extended by another year through no-cost extension in order to accomplish the goals of the project. The main objective of the research was to develop passivity-based robust control methodology for passive and non-passive aerospace systems. The focus of the first-year's research was limited to the investigation of passivity-based methods for the robust control of Linear Time-Invariant (LTI) single-input single-output (SISO), open-loop stable, minimum-phase non-passive systems. The second year's focus was mainly on extending the passivity-based methodology to a larger class of non-passive LTI systems which includes unstable and nonminimum phase SISO systems. For LTI non-passive systems, five different passification. methods were developed. The primary effort during the years three and four was on the development of passification methodology for MIMO systems, development of methods for checking robustness of passification, and developing synthesis techniques for passifying compensators. For passive LTI systems optimal synthesis procedure was also developed for the design of constant-gain positive real controllers. For nonlinear passive systems, numerical optimization-based technique was developed for the synthesis of constant as well as time-varying gain positive-real controllers. The passivity-based control design methodology developed during the duration of this project was demonstrated by its application to various benchmark examples. These example systems included longitudinal model of an F-18 High Alpha Research Vehicle (HARV) for pitch axis control, NASA's supersonic transport wind tunnel model, ACC benchmark model, 1-D acoustic duct model, piezo-actuated flexible link model, and NASA's Benchmark Active Controls Technology (BACT) Wing model. Some of the stability results for linear passive systems were also extended to nonlinear passive systems. Several publications and conference presentations resulted from this research.