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Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

NETWORKS & SPATIAL ECONOMICS 2019年第3期19卷 869-902页

作者： Han, Ke Eve, Gabriel Friesz, Terry L. Imperial Coll London Dept Civil & Environm Engn London SW7 2BU England Penn State Univ Dept Ind & Mfg Engn State Coll PA 16803 USA

Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment (DTA), in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational theory of DUE, which is numerically implemented in a MATLAB package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the Lighthill-Whitham-Richards fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixed-point algorithm is employed to solve the DUE problems with simultaneous route and departure time choices on several large-scale networks. We make openly available the MATLAB package, which can be used to solve DUE problems on user-defined networks, aiming to not only facilitate benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. The MATLAB package and computational examples are available at https://***/DrKeHan/DTA.

关键词： Dynamic traffic assignment Dynamic user equilibrium Dynamic network loading Traffic flow model fixed-point algorithm Software

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Time-accurate multi-scale anisotropic mesh adaptation for unsteady flows in CFD

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JOURNAL OF COMPUTATIONAL PHYSICS 2018年 373卷 28-63页

作者： Alauzet, F. Loseille, A. Olivier, G. INRIA Saclay Ile France Projet Gamma3 1 Rue Honore dEstienne dOrves F-91126 Palaiseau France

This paper deals with anisotropic mesh adaptation applied to unsteady inviscid CFD simulations. Anisotropic metric-based mesh adaptation is an efficient strategy to reduce the extensive CPU time currently required by time-dependent simulations in an industrial context. In this work, we detail the time-accurate extension of multi-scale anisotropic mesh adaptation for steady flows [35] (a control of the interpolation error in L(P )norm to capture all the scales of the solution contrary to the L-infinity norm that only focuses on the larger scales) to unsteady flows when time advancing discretizations are considered. This is based on a space-time error analysis and an enhanced version of the fixed-point algorithm [3]. We also show that each stage - remeshing, metric field computation, solution transfer, and flow solution - is important to design an efficient time-accurate anisotropic mesh adaptation process. The parallelization of the whole mesh adaptation platform is also discussed. The efficiency of the approach is emphasized on three-dimensional problems with convergence rate and CPU time analysis. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Anisotropic mesh adaptation Time-accurate Multi-scale Metric fixed-point algorithm Unsteady flows

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Linear and Nonlinear Regression-Based Maximum Correntropy Extended Kalman Filtering

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第5期51卷 3093-3102页

作者： Liu, Xi Ren, Zhigang Lyu, Hongqiang Jiang, Zhihong Ren, Pengju Chen, Badong Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Beijing Inst Technol Sch Mechatron Engn Beijing 100081 Peoples R China

The extended Kalman filter (EKF) is a method extensively applied in many areas, particularly, in nonlinear target tracking. The optimization criterion commonly used in EKF is the celebrated minimum mean square error (MMSE) criterion, which exhibits excellent performance under Gaussian noise assumption. However, its performance may degrade dramatically when the noises are heavy tailed. To cope with this problem, this paper proposes two new nonlinear filters, namely the linear regression maximum correntropy EKF (LRMCEKF) and nonlinear regression maximum correntropy EKF (NRMCEKF), by applying the maximum correntropy criterion (MCC) rather than the MMSE criterion to EKF. In both filters, a regression model is formulated, and a fixed-point iterative algorithm is utilized to obtain the posterior estimates. The effectiveness and robustness of the proposed algorithms in target tracking are confirmed by an illustrative example.

关键词： Kalman filters Covariance matrices Kernel Linear regression Noise measurement Iterative methods Mathematical model Extended Kalman filter (EKF) fixed-point algorithm maximum correntropy criterion (MCC)

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A novel FastICA algorithm based on improved secant method for Intelligent drive

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第1期40卷 165-178页

作者： Liu, Hongzhe Zhang, Qikun Xu, Cheng Ye, Zhao Beijing Union Univ Beijing Key Lab Informat Serv Engn Beijing Peoples R China Beijing Union Univ Coll Robot Beijing Peoples R China

Blind Source Separation(BSS) is one of the research hotspots in the field of signal processing. In order to improve the accuracy of speech recognition in driving environment, the driver's speech signal must be enhanced to improve its signal to noise ratio(SNR). Independent component analysis (ICA) algorithm is the most classical and efficient blind statistical signal processing technique. Compared with other improved ICA algorithms, fixed-point algorithm (FastICA) is well known for its fast convergence speed and good robustness. However, the convergence of FastICA algorithm is comparatively susceptible to the initial value selection of the original demixing matrix and the calculation of the iterative process is relatively large. In this paper, the gradient descent method is used to reduce the effect of initial value. What's more, the improved secant method is proposed to speed up the convergence rate and reduce the amount of computation. As the results of mixed speech separation experiment turn out, the improved algorithm is of better performance relative to the standard FastICA algorithm. Experimental results show that the proposed algorithm improves the speech quality of the target driver. It is suitable for speech separation in driving environment with low SNR.

关键词： Blind source separation fixed-point algorithm gradient descent improved secant method speech separation

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Simultaneous kinetic spectrometric determination of three flavonoid antioxidants in fruit with the aid of chemometrics

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SPECTROCHIMICA ACTA PART A-MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2014年 122卷 529-535页

作者： Sun, Ruiling Wang, Yong Ni, Yongnian Kokot, Serge Nanchang Univ State Key Lab Food Sci & Technol Nanchang 330047 Peoples R China Nanchang Univ Dept Chem Nanchang 330031 Peoples R China Queensland Univ Technol Sch Chem Phys & Mech Engn Brisbane Qld 4001 Australia

A simple, inexpensive and sensitive kinetic spectrophotometric method was developed for the simultaneous determination of three anti-carcinogenic flavonoids: catechin, quercetin and naringenin, in fruit samples. A yellow chelate product was produced in the presence neocuproine and Cu(I) - a reduction product of the reaction between the flavonoids with Cu(II), and this enabled the quantitative measurements with UV-vis spectrophotometry. The overlapping spectra obtained, were resolved with chemometrics calibration models, and the best performing method was the fast independent component analysis (fast-ICA/PCR (Principal component regression));the limits of detection were 0.075, 0.057 and 0.063 mg L-1 for catechin, quercetin and naringenin, respectively. The novel method was found to outperform significantly the common HPLC procedure. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Flavonoids Kinetic spectroscopy Fruit fixed-point algorithm Chemometrics

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A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier-Stokes and Euler Equations on Unstructured Meshes

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JOURNAL OF SCIENTIFIC COMPUTING 2017年第3期71卷 1375-1411页

作者： Costa, Ricardo Clain, Stephane Machado, Gaspar J. Loubere, Raphael Univ Paul Sabatier Inst Math Toulouse F-31062 Toulouse France Univ Minho Ctr Matemat Campus Azurem P-4800058 Guimaraes Portugal

We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order convergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme.

关键词： Finite volume method High-order scheme Polynomial reconstruction Navier-Stokes equations Euler equations fixed-point algorithm

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Stochastic H_∞ control problem with state-dependent noise for weakly coupled large-scale systems

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2007年第6期2卷 571-578页

作者： Sagara, Muneomi Mukaidani, Hiroaki Yamamoto, Toru Hiroshima Univ Grad Sch Educ Higashihiroshima 7398524 Japan

In this paper, stochastic H-infinity state feedback control with state-dependent noise for weakly coupled large-scale systems is discussed. After establishing the asymptotic structure of the stochastic algebraic Riccati equation (SARE), a new iterative algorithm that combines the Newton's method with the fixed-point algorithm is derived for the first time. As a result, both the quadratic convergence and the reduced-order computation in the same dimension of the subsystems are attained. (c) 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

关键词： stochastic H-infinity control state-dependent noise weakly coupled large-scale systems stochastic algebraic Riccati equation (SARE) Newton's method fixed-point algorithm

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Rotational linear discriminant analysis technique for dimensionality reduction

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2008年第10期20卷 1336-1347页

作者： Sharma, Alok Paliwal, Kuldip K. Griffith Univ Signal Proc Lab Nathan Qld 4111 Australia Univ S Pacific Sch Phys & Engn Suva Fiji

The linear discriminant analysis (LDA) technique is very popular in pattern recognition for dimensionality reduction. It is a supervised learning technique that finds a linear transformation such that the overlap between the classes is minimum for the projected feature vectors in the reduced feature space. This overlap, if present, adversely affects the classification performance. In this paper, we introduce prior to dimensionality-reduction transformation an additional rotational transform that rotates the feature vectors in the original feature space around their respective class centroids in such a way that the overlap between the classes in the reduced feature space is further minimized. As a result, the classification performance significantly improves, which is demonstrated using several data corpuses.

关键词： rotational linear discriminant analysis dimensionality reduction classification error fixed-point algorithm probability of error

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A FFT solver for variational phase-field modeling of brittle fracture

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019年 349卷 167-190页

作者： Chen, Yang Vasiukov, Dmytro Gelebart, Lionel Park, Chung Hae Inst Mines Telecom Polymers & Composites Technol & Mech Engn Dept IMT Lille Douai Paris France Univ Lille Lille France Univ Paris Saclay DEN Serv Rech Met Appl CEA Paris France

The variational phase-field method is an attractive non-local approach of modeling fracture in heterogeneous materials. However, these materials usually require a fine mesh to resolve the fracture process zone. Consequently, the standard finite element solver becomes cumbersome due to the large number of elements in applications with highly heterogeneous materials. Motivated by this limitation, an algorithm based on FFT methods has been introduced in this paper to solve the phase-field model of brittle fracture. Relying on a staggered update scheme, the proposed algorithm solves the fracture problem and mechanical problem separately, both using the FFT technique. It inherits the advantages of classical FFT methods in terms of simplicity of mesh generation and parallel implementation. Introduced within a FFT-based code "AMITEX", it takes the advantage of massively parallel capabilities associated with a distributed memory implementation. The characteristics of the proposed method are analyzed in a single edge notched specimen benchmark. Representative numerical examples demonstrate that the proposed FFT solver is capable of predicting different crack modes and complex crack configuration, such as crack interaction, branching and coalescence. Finally, a model of an idealized continuous fiber composite with void involving over 32 million voxels is solved, illustrating the potential of the FFT solver in large-scale problems. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Phase-field model FFT method Brittle fracture fixed-point algorithm

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Nonnegative matrix factorization with constrained second-order optimization

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SIGNAL PROCESSING 2007年第8期87卷 1904-1916页

作者： Zdunek, Rafal Cichocki, Andrzej RIKEN Brain Sci Inst Lab Adv Brain Signal Proc Wako Saitama 3510198 Japan Wroclaw Univ Technol Inst Telecommun Teleinformat & Acoust Wroclaw Poland Warsaw Univ Technol Warsaw Poland

Nonnegative matrix factorization (NMF) solves the following problem: find notinegative matrices A epsilon R-+(MxR) and X epsilon R-+(RxT) such that Y congruent to AX, given only Y epsilon R-MxT and the assigned index R. This method has found a wide spectrum of applications in signal and image processing, such as blind source separation (BSS), spectra recovering, pattern recognition, segmentation or clustering. Such a factorization is usually performed with an alternating gradient descent technique that is applied to the squared Euclidean distance or Kullback-Leibler divergence. This approach has been used in the widely known Lee-Seung NMF algorithms that belong to a class of multiplicative iterative algorithms. It is well known that these algorithms, in spite of their low complexity, are slowly convergent, give only a strictly positive solution, and can easily fall into local minima of a nonconvex cost function. In this paper, we propose to take advantage of the second-order terms of a cost function to overcome the disadvantages of gradient (multiplicative) algorithms. First, a projected quasi-Newton method is presented, where a regularized Hessian with the Levenberg-Marquardt approach is inverted with the Q-less QR decomposition. Since the matrices A and/or X are usually sparse, a more sophisticated hybrid approach based on the gradient projection conjugate gradient (GPCG) algorithm, which was invented by More and Toraldo, is adapted for NMF. The gradient projection (GP) method is exploited to find zero-value components (active), and then the Newton steps are taken only to compute positive components (inactive) with the conjugate gradient (CG) method. As a cost function, we used the a-divergence that unifies many well-known cost functions. We applied our new NMF method to a BSS problem with mixed signals and images. The results demonstrate the high robustness of our method. (C) 2007 Elsevier B.V. All rights reserved.

关键词： nonnegative matrix factorization blind source separation quasi-Newton method GPCG second-order optimization fixed-point algorithm

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