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Hammerstein system identification with quantised inputs and quantised output observations

IET CONTROL theory AND applications 2017年第4期11卷 593-599页

作者： Guo, Jin Liu, Haitao Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China

This study focuses on a discrete-time Hammerstein system to investigate the identification with quantised inputs and quantised output observations. After the discussion of the system identifiability and by parameterising the static non-linear function, a three-step algorithm is proposed to estimate the unknown parameters for the identifiable system. The strong convergence and the mean-square convergence rate of the algorithm are established. It is shown that the asymptotic efficiency can be achieved in terms of the Cramer-Rao lower bound by selecting a suitable transformation matrix. A numerical simulation is given to demonstrate the effectiveness of the algorithm.

关键词： discrete time systems nonlinear control systems convergence of numerical methods matrix algebra parameter estimation quantised inputs quantised output discrete-time Hammerstein system identification system identifiability static nonlinear function parameterisation three-step algorithm unknown parameter estimation identifiable system mean-square convergence rate asymptotic efficiency Cramer-Rao lower bound transformation matrix

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Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

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numerical linear algebra WITH applications 2018年第3期25卷

作者： Hessenthaler, A. Nordsletten, D. Roehrle, O. Schroder, J. B. Falgout, R. D. Univ Stuttgart Inst Appl Mech CE Pfaffenwaldring 7 D-70569 Stuttgart Germany Kings Coll London Div Imaging Sci & Biomed Engn St Thomas Hosp 4th FloorLambeth Wing London SE1 7EH England Lawrence Livermore Natl Lab Ctr Appl Sci Comp POB 808L-561 Livermore CA 94551 USA

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel-in-time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel-in-time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF-relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel-in-time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. The paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.

关键词： convergence estimate linear elasticity multigrid reduction in time (MGRIT) parallel-in-time

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Foundations and applications of Statistics 2

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丛书名： Pure and Applied Undergraduate Texts

2018年

作者： Randall Pruim

ISBN: (数字)9781470443542

ISBN: (纸本)9781470428488

Foundations and applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals. The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool. In this vein, the statistical computing environment $\mathsf{R}$ is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically. Foundations and applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations. In the second edition, the $\mathsf{R}$ code has been updated throughout to take advantage of new $\mathsf{R}$ packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinea

关键词：数学

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Fundamental Limits of Weak Recovery with applications to Phase Retrieval 31

Fundamental Limits of Weak Recovery with Applications to Pha...

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31st Annual conference on Learning theory, COLT 2018

作者： Mondelli, Marco Montanari, Andrea Department of Electrical Engineering Stanford University United States Department of Electrical Engineering Department of Statistics Stanford University United States

In phase retrieval we want to recover an unknown signal x ∈ Cd from n quadratic measurements of the form yi = |hai, xi|2 + wi where ai ∈ Cd are known sensing vectors and wi is measurement noise. We ask the following weak recovery question: what is the minimum number of measurements n needed to produce an estimator x^(y) that is positively correlated with the signal x? We consider the case of Gaussian vectors ai. We prove that – in the high-dimensional limit – a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For n ≤ d−o(d) no estimator can do significantly better than random and achieve a strictly positive correlation. For n ≥ d + o(d) a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theory arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper and lower bound generalize beyond phase retrieval to measurements yi produced according to a generalized linear model. As a byproduct of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm. © 2018 M. Mondelli & A. Montanari.

关键词： Recovery

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Large eddy simulation of turbulent flow using the parallel computational fluid dynamics code GASFLOW-MPI

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NUCLEAR ENGINEERING AND TECHNOLOGY 2017年第6期49卷 1310-1317页

作者： Zhang, Han Li, Yabing Xiao, Jianjun Jordan, Thomas Karlsruhe Inst Technol Inst Nucl & Energy Technol Hermann von Helmholtz Pl 1 D-76344 Eggenstein Leopoldshafen Germany

GASFLOW-MPI is a widely used scalable computational fluid dynamics numerical tool to simulate the fluid turbulence behavior, combustion dynamics, and other related thermalehydraulic phenomena in nuclear power plant containment. An efficient scalable linear solver for the large-scale pressure equation is one of the key issues to ensure the computational efficiency of GASFLOW-MPI. Several advanced Krylov subspace methods and scalable preconditioning methods are compared and analyzed to improve the computational performance. With the help of the powerful computational capability, the large eddy simulation turbulent model is used to resolve more detailed turbulent behaviors. A backward-facing step flow is performed to study the free shear layer, the recirculation region, and the boundary layer, which is widespread in many scientific and engineering applications. numerical results are compared with the experimental data in the literature and the direct numerical simulation results by GASFLOW-MPI. Both time-averaged velocity profile and turbulent intensity are well consistent with the experimental data and direct numerical simulation result. Furthermore, the frequency spectrum is presented and a e5/3 energy decay is observed for a wide range of frequencies, satisfying the turbulent energy spectrum theory. Parallel scaling tests are also implemented on the KIT/IKET cluster and a linear scaling is realized for GASFLOW-MPI. (C) 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license.

关键词： GASFLOW-MPI large eddy simulation M&C2017 scalable linear solver

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ARITHMETIC MATRICES FOR NUMBER FIELDS I

arXiv

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arXiv 2018年

作者： Hambleton, Samuel A. School of Mathematics and Physics University of Queensland St. LuciaQLD4072 Australia

We provide a simple way to add, multiply, invert, and take traces and norms of algebraic integers of a number field using integral matrices. With formulas for the integral bases of the ring of integers of at least a significant proportion of numbers fields, we obtain explicit formulas for these matrices and discuss their generalization. These results are useful in proving statements about the particular number fields they work in. We give a meaningful diagonalization that is helpful in this regard and can be used to define such matrices in general. The matrix identities provided suggest that consideration of numerical methods in linear algebra may have applications in algebraic number theory. Multiplication of several algebraic integers at once might be more efficiently implemented using methods of efficient matrix multiplication. If we are multiplying an algebraic integer in a field of degree n by each of n algebraic integers, then this can be done in O (nlog2(7))multiplications. The matrix identities given here generalize Brahmagupta’s identity upon taking determinants, which are multiplicative. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

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numerical approximation of GB-splines by a convolutional approach

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APPLIED numerical MATHEMATICS 2017年 116卷 273-285页

作者： Roman, Fabio Manni, Carla Speleers, Hendrik Univ Turin Dept Math Turin Italy Univ Roma Tor Vergata Dept Math Rome Italy

Generalized splines are smooth functions belonging piecewisely to spaces which are a natural generalization of algebraic polynomials. GB-splines are a B-spline-like basis for generalized splines, and they are usually defined by means of an integral recurrence relation which makes their evaluation quite cumbersome and computationally expensive. We present a simple strategy for approximating the values of a cardinal GB-spline of arbitrary degree p, with a particular focus on hyperbolic and trigonometric GB-splines due to their interest in applications. The proposed strategy is based on the Fourier properties of cardinal GB-splines. The approximant is expressed as a linear combination of scaled and dilated versions of (polynomial) cardinal B-splines of degree p, whose coefficients can be efficiently computed via discrete convolution. Sharp error estimates are provided and illustrated with some numerical examples. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： GB-splines Cardinal GB-splines Convolution Fourier transform

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algebraic multigrid for directed graph Laplacian linear systems (NS-LAMG)

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numerical linear algebra WITH applications 2018年第3期25卷

作者： Fox, Alyson Manteuffel, Thomas Lawrence Livermore Natl Lab Ctr Appl Sci Comp Livermore CA 94551 USA Univ Colorado Dept Appl Math Boulder CO 80303 USA

We propose nonsymmetric lean algebraic multigrid (NS-LAMG), a new algebraic multigrid algorithm for directed graph Laplacian systems that combines ideas from undirected graph Laplacian multigrid solvers and multigrid algorithms for Markov chain stationary distribution systems. Low-degree elimination, proposed in LAMG for undirected graphs, is generalized to directed graphs and is a key component of NS-LAMG. In the setup phase, we propose a simple stationary-aggregation multigrid algorithms for Markov chain stationary distribution systems solver enhanced by low-degree elimination to find the right null-space vector that is used for the intergrid transfer operators. numerical results show that low-degree elimination improves performance and that NS-LAMG outperforms generalized minimal residual method with restart and stable bi-conjugate gradient method for real-world, directed graph Laplacian linear systems.

关键词： algebraic multigrid directed graphs graph Laplacians

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Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces 12

Approximation of Periodic PDE Solutions with Anisotropic Tra...

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12th International conference on Sampling theory and applications (SAMPTA)

作者： Bergmann, Ronny Merkert, Dennis Univ Kaiserslautern Dept Math Kaiserslautern Germany

ISBN: (纸本)9781538615652

We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. We analyse the connection between the discrete solution spaces and demonstrate the numerical benefits. Finite element methods arise as a special case of periodised Box spline translates.

关键词： Estimation Field programmable gate arrays OFDM Modulation Filtration Clocks Signal processing algorithms

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Primal and dual first order methods for SVM: applications to driver monitoring

Primal and dual first order methods for SVM: applications to...

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International conference on System theory, Control, and Computing (ICSTCC)

作者： Daniela Lupu Ion Necoara Automatic Control and Systems Engineering Department University Politehnica Bucharest Bucharest Romania

Machine learning tools are become recently very popular for solving real applications from many areas. Most of the learning problems are formulated as optimization problems with simple objective function but large number of constraints of order the number of training data. When considering the dual formulation, usually the objective function is difficult to minimize but the constraints are simple. One relevant application that fits into this pattern is the support vector machine (SVM). A popular approach for solving the primal SVM problem is based on first order methods due to their superior empirical performance. When considering the dual SVM formulation, which has simple constraints, coordinate descent schemes are typically the method of choice in practice due to their cheap iteration. In this paper we present a comparative study of several first order methods for solving primal or dual SVM problems. numerical evidence on support vector machine classification for automatic detection of driver fatigue supports the effectiveness of such first order methods in real-world problems.

关键词： Support vector machines linear programming Optimization Fatigue Machine learning Convergence Machine learning algorithms

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