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Matrix algorithms for modeling acoustic waves in piezoelectric multilayers

IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2007年第10期54卷 2016-2023页

作者： Tan, Eng Leong Nanyang Technol Univ Singapore 639798 Singapore

Matrix algorithms for modeling acoustic waves in piezoelectric multilayers are presented. All the algorithms considered are capable of resolving the numerical instability of transfer matrix at high frequency-thickness product. The formulation of basic matrices for the algorithm building blocks, and the development of recursive algorithms for the stack matrices, are systematically presented for both the conventional scattering and impedance matrices as well as the more recent hybrid matrix. Many variants of the algorithms are discussed, along with their respective usefulness and deficiency. Comparisons are made in their computational efficiency and numerical stability. For unconditional stability throughout large and small thicknesses, both scattering and hybrid matrix algorithms are applicable. For most efficiency, the algorithms that synergize both scattering and hybrid or impedance submatrices are superior, using surface matrix approach. Other aspects of algorithms such as formula conciseness, physical insight, versatility in incorporating boundary conditions, etc., are also noted.

关键词： S-matrix theory acoustic waves impedance matrix multilayers numerical stability piezoelectric materials computational efficiency hybrid matrix algorithms impedance matrices piezoelectric multilayers recursive algorithms scattering matrix algorithms surfa Scattering recursive algorithms multilayers Numerical stability algorithms matrices Acoustic Wave Computational efficiency S-matrix theory impedance matrix Piezoelectric materials

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recursive NONLINEAR ESTIMATION - A GEOMETRIC APPROACH

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AUTOMATICA 1990年第3期26卷 545-555页

作者： KULHAVY, R Institute of Information Theory and Automation Czechoslovak Academy of Sciences 182 08 Prague Pod vodarenskou vezi 4 Czech Republic

The paper deals with approximation of nonlinear estimation within the Bayesian framework. The underlying idea is to project the true posterior density orthogonally onto a prespecified approximation family. The problem to be coped with is that the true posterior density is not typically at disposal when estimation is implemented recursively . It is shown that there exists a Bayes-closed description of the posterior density which is recursively computable without complete knowledge of the true posterior. We study a mutual relationship between the equivalence class, composed of densities matching the current description, and a prespecified parametric family. It is proved that if the approximation family is of the mixture type, the equivalence classes can be made orthogonal to this family. Then the approximating density done by the orthogonal projection of the true posterior density minimizes the Kullback-Leibler distance between both densities. On the contrary, if the approximation family is of the exponential type, the analogous result holds at most locally. To be able to give a sensible definition of the orthogonal projection, we have been forced to introduce a Riemannian geometry on the family of probability distributions. Being aware that the differential-geometric concepts and tools do not belong to common knowledge of control engineers, we include necessary preliminary information.

关键词： approximation theory Bayes statistics differential geometry Parameter estimation recursive algorithms sampled data systems

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Efficient Algorithm for Evaluating the Required Volume of Resource in Wireless Communication Systems under Joint Servicing of Heterogeneous Traffic for the Internet of Things

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AUTOMATION AND REMOTE CONTROL 2019年第11期80卷 2017-2032页

作者： Stepanov, S. N. Stepanov, M. S. Moscow Tech Univ Coinmunicat & Comp Sci Moscow Russia

We construct and study a mathematical model of the distribution of the resource for transmitting information for an isolated cell of an LTE standard mobile network with the joint servicing of heterogeneous traffic from Internet of Things devices. The model considers an arbitrary number of streams of multimedia traffic, which differ in the intensity of the arrival of communication sessions, the size of the resource used to service one session, the time of resource occupation, and the probability of a session being allowed to transmit the information stream. We determine quality of service characteristics for incoming sessions and construct an effective algorithm for estimating the amount of resource required to service given traffic flows with required quality. Efficiency of the algorithm is achieved as a result of the implementation of recursion with respect to the available resource and the use of normalized probabilities of model states during calculations. The algorithm is computationally stable and allows to solve the resource estimation problem many times faster than traditional approaches based on calculating the probabilities of all states for each resource value and their subsequent normalization. We give numerical examples illustrating the implementation features of developed computational procedures.

关键词： Internet of Things multiservice traffic Markov models system of equilibrium equations recursive algorithms transmission resource planning

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Commuting charges of the quantum Korteweg-DeVries and Boussinesq theories from the reduction of W_∞ and W_1+∞ algebras

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MODERN PHYSICS LETTERS A 1998年第7期13卷 541-552页

作者： Bordner, AJ Kyoto Univ Yukawa Inst Theoret Phys Kyoto 606 Japan

Integrability of the quantum Boussinesq equation for c = -2 is demonstrated by giving a recursive algorithm for generating explicit expressions for the infinite number of commuting charges based on a reduction of the W-infinity-algebra. These charges exist for all spins s greater than or equal to 2. Likewise, reductions of the W-infinity/2- and W(1+infinity/2)-algebras yield the commuting quantum charges for the quantum KdV equation at c = -2 and c = 1/2, respectively.

关键词： Toda field-theories Kac-moody algebras Hamiltonian-structure Virasoro symmetries Conformal systems Construction Equations Liouville field theory (physics) Commuting recursive algorithms Greater than or equal to quanta Algebra

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ADAPTIVE AND recursive TIME RELAXED MONTE CARLO METHODS FOR RAREFIED GAS DYNAMICS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2009年第2期31卷 1379-1398页

作者： Trazzi, Stefano Pareschi, Lorenzo Wennberg, Bernt Univ Ferrara Dept Math I-44100 Ferrara Italy Chalmers Univ Technol Dept Math SE-41296 Gothenburg Sweden

Recently a new class of Monte Carlo methods, called time relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes has been introduced [L. Pareschi and G. Russo, SIAM J. Sci. Comput., 23 (2001), pp. 1253-1273]. A generalized Wild sum expansion of the solution is the basis of the simulation schemes. After a splitting of the equation, the time discretization of the collision step is obtained from the Wild sum expansion of the solution by replacing high order terms in the expansion with the equilibrium Maxwellian distribution;in this way speed-up of the methods close to fluid regimes is obtained by efficiently thermalizing particles close to the equilibrium state. In this work we present an improvement of such methods which allows us to obtain an effective uniform accuracy in time without any restriction on the time step and subsequent increase of the computational cost. The main ingredient of the new algorithms is recursivity [L. Pareschi and B. Wennberg, Monte Carlo Methods Appl., 7 (2001), pp. 349-358]. Several techniques can be used to truncate the recursive trees generated by the schemes without degrading the accuracy of the numerical solution. Techniques based on adaptive strategies are presented. Numerical results emphasize the gain of efficiency of the present simulation schemes with respect to standard DSMC (direct simulation Monte Carlo) methods.

关键词： Boltzmann equation Monte Carlo methods time relaxed schemes fluid dynamic limit stiff systems recursive algorithms

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STOCHASTIC-APPROXIMATION AND LARGE DEVIATIONS - UPPER-BOUNDS AND W.P.1 CONVERGENCE

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1989年第5期27卷 1108-1135页

作者： DUPUIS, P KUSHNER, HJ BROWN UNIV LEFSCHENCE CTR DYNAM SYSTDIV APPL MATHPROVIDENCERI 02912

With probability one convergence results are obtained for stochastic recursive approximation algorithms under very general conditions. The gain sequence $\{ a_n \} $ can go to zero very slowly and state-dependent noise, discontinuous dynamical equations, and the projected or constrained algorithm are all treated. The basic technique is the theory of large deviations. Prior results obtained via this theory are extended in many directions. Let $\dot x = \bar b(x)$ denote the “mean” equation for the algorithm, let $\delta > 0$ be given, and let $G(\theta )$ be a neighborhood of a stable point $\theta $ of that ordinary differential equation. Then, asymptotic upper bounds to $a_N \log P\{ X_n \notin G(\theta ),n \geqq N\mid | {X_N - \theta } | \leqq \delta \} $, are obtained. These are often more informative than the usual classical rate of convergence results (that use a “local linearization”) and, furthermore, are obtained for the constrained and nonsmooth cases, for which there are no “rate of convergence” results. The methods are also used to extend currently available upper bounds for algorithms with constant gains, with simpler proofs.

关键词： 60F10 62L20 93E10 93E12 stochastic approximation large deviations recursive algorithms errors for tracking systems

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recursive dual-linear-programming approach for parameter-uncertainty-interval estimation

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 2003年第3期150卷 303-310页

作者： Sun, XF Zhang, HY Fan, YZ Beijing Univ Aeronaut & Astronaut Sch Automat Sci & Elect Engn Beijing 100083 Peoples R China

The parameter-uncertainty-interval-estimation (PIE) problem is transferred into several dual-linear-programming (DLP) problems, and a recursive DLP algorithm is proposed and applied in PIE. This recursive algorithm is based on a modified dual-simplex method that is specifically developed for solving the DLP problems derived from the PIE problem. Because the scale of the DLP problems is considerably smaller than that of the primal linear-programming problems for solving the PIE problem, the recursive DLP algorithm is computationally efficient and suitable for online-engineering applications. Simulations show the effectiveness of the proposed recursive algorithm.

关键词： recursive algorithms project independence evaluation system Simplex method

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CONVERGENCE RATE DETERMINATION FOR GRADIENT-BASED ADAPTIVE ESTIMATORS

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AUTOMATICA 1986年第2期22卷 185-191页

作者： BITMEAD, RR ANDERSON, BDO NG, TS UNIV WOLLONGONG DEPT ELECT ENGNWOLLONGONGNSW 2500AUSTRALIA

A convergence rate estimate is derived for the homogeneous gradient-based adaptive linear estimator algorithm. This estimate involves the eigenvalues of the regression vector covariance matrix, yielding a useful measure for the choice of input signals for adaptive parameter estimation. The connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas.

关键词： Adaptive systems averaging theory convergence parameter estimation recursive algorithms stochastic systems

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Online Updating Belief-Rule-Base Using the RIMER Approach

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 2011年第6期41卷 1225-1243页

作者： Zhou, Zhi-Jie Hu, Chang-Hua Yang, Jian-Bo Xu, Dong-Ling Zhou, Dong-Hua High Tech Inst Xian Xian 710025 Peoples R China Tsinghua Univ TNList Dept Automat Beijing 100084 Peoples R China Univ Manchester Manchester Business Sch Manchester M15 6PB Lancs England

In order to determine the parameters of belief-rule-base (BRB) accurately, several optimization methods have been proposed for training BRB, on the basis of a generic rule-base inference methodology using the evidential reasoning (RIMER) approach. These optimization methods are implemented offline, and such are not suitable for training BRB in a dynamic fashion. In this paper, two recursive algorithms are proposed to update BRB online that can simulate dynamic systems. The main feature of the proposed algorithms is that only partial input and output information is required, which can be incomplete or vague, numerical or judgmental, or mixed. If the internal structure of a BRB is initially decided using expert judgments, domain-specific knowledge and/or commonsense rules, the proposed algorithms can be used to fine-tune the initial BRB online, once input and output datasets become available. Using the proposed algorithms, there is no need to collect a complete set of data before a BRB can be trained, which is necessary if the BRB is used to simulate a dynamic system. A numerical example and a case study are reported to demonstrate the potential of the algorithms for online fault diagnosis.

关键词： Belief-rule-base (BRB) evidential reasoning (ER) inference recursive algorithms uncertainty

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SELF-TUNING CONTROL

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1979年第6期126卷 633-640页

作者： CLARKE, DW GAWTHROP, PJ Department of Engineering Science University of Oxford Oxford UK

Self tuning is an important new branch of control which is attracting increasing theoretical and practical interest. The objective of self tuning is to control systems with unknown constant or slowly varying parameters, so theoretical interest is concerned with the stability, performance and convergence of the recursive algorithms involved, while practical interest derives from its potential as a simple controller commissioning tool, both as a method for controlling time-varying or nonlinear plant over a range of operating points, and for dealing with batch problems where the plant or materials vary over successive batches. This paper summarises and expands previous work on the design of self-tuning controllers. It discusses the closed-loop properties of various classes of self tuner, convergence concepts and results, and some of the technical problems involved with implementing self tuners on small computers or microprocessors.

关键词： controller commissioning tool controllers microprocessor implemented systems Nonlinear control systems Control system analysis and synthesis methods performance recursive algorithms convergence computerised control control system synthesis self tuning control Controllers Control engineering computing nonlinear control systems

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