Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Generalização de um modelo linear de impedância eletroquímica

Em geral, a função de um modelo de impedância para processos de eletrodo simples é deduzida de um modelo elétrico equivalente, denominado circuito de Randles. Neste trabalho estudou-se a generalização dessa função, mediante a introdução de um parâmetro não-elétrico, relacionado com a flexibilidade do ângulo de fase e da magnitude. A função foi ajustada às medidas experimentais de impedância obtidas de um sistema constituído de uma liga Ti-10%Al (m/m) em solução de cloreto de sódio 0,9%, variando-se a amplitude de perturbação. Verificou-se que a função generalizada foi adequada para descrever a impedância do sistema analisado, reduzindo as distorções entre a curva experimental e a curva teórica. Além disso, os melhores resultados foram obtidos para sinais de perturbação do sistema com amplitude igual a 10 mV.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Introdução à identificação de sistemas utilizando o System Identification Toolbox do MATLAB em conjunto com o Arduino para o laboratório de controle linear

The education designed and planned in a clear and objective manner is of paramount importance for universities to prepare competent professionals for the labor market, and above all can serve the population with an efficient work. Specifically, in relation to engineering, conducting classes in the laboratories it is very important for the application of theory and development of the practical part of the student. The planning and preparation of laboratories, as well as laboratory equipment and activities should be developed in a succinct and clear way, showing to students how to apply in practice what has been learned in theory and often shows them why and where it can be used when they become engineers. This work uses the MATLAB together with the System Identification Toolbox and Arduino for the identification of linear systems in Linear Control Lab. MATLAB is a widely used program in the engineering area for numerical computation, signal processing, graphing, system identification, among other functions. Thus the introduction to MATLAB and consequently the identification of systems using the System Identification Toolbox becomes relevant in the formation of students to thereafter when necessary to identify a system the base and the concept has been seen. For this procedure the open source platform Arduino was used as a data acquisition board being the same also introduced to the student, offering them a range of software and hardware for learning, giving you every day more luggage to their training

Introdução à identificação de sistemas utilizando o System Identification Toolbox do MATLAB em conjunto com o Arduino para o laboratório de controle linear

The education designed and planned in a clear and objective manner is of paramount importance for universities to prepare competent professionals for the labor market, and above all can serve the population with an efficient work. Specifically, in relation to engineering, conducting classes in the laboratories it is very important for the application of theory and development of the practical part of the student. The planning and preparation of laboratories, as well as laboratory equipment and activities should be developed in a succinct and clear way, showing to students how to apply in practice what has been learned in theory and often shows them why and where it can be used when they become engineers. This work uses the MATLAB together with the System Identification Toolbox and Arduino for the identification of linear systems in Linear Control Lab. MATLAB is a widely used program in the engineering area for numerical computation, signal processing, graphing, system identification, among other functions. Thus the introduction to MATLAB and consequently the identification of systems using the System Identification Toolbox becomes relevant in the formation of students to thereafter when necessary to identify a system the base and the concept has been seen. For this procedure the open source platform Arduino was used as a data acquisition board being the same also introduced to the student, offering them a range of software and hardware for learning, giving you every day more luggage to their training

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Heterogeneous multicore systems for signal processing

This thesis explores the capabilities of heterogeneous multi-core systems, based on multiple Graphics Processing Units (GPUs) in a standard desktop framework. Multi-GPU accelerated desk side computers are an appealing alternative to other high performance computing (HPC) systems: being composed of commodity hardware components fabricated in large quantities, their price-performance ratio is unparalleled in the world of high performance computing. Essentially bringing “supercomputing to the masses”, this opens up new possibilities for application fields where investing in HPC resources had been considered unfeasible before. One of these is the field of bioelectrical imaging, a class of medical imaging technologies that occupy a low-cost niche next to million-dollar systems like functional Magnetic Resonance Imaging (fMRI). In the scope of this work, several computational challenges encountered in bioelectrical imaging are tackled with this new kind of computing resource, striving to help these methods approach their true potential. Specifically, the following main contributions were made: Firstly, a novel dual-GPU implementation of parallel triangular matrix inversion (TMI) is presented, addressing an crucial kernel in computation of multi-mesh head models of encephalographic (EEG) source localization. This includes not only a highly efficient implementation of the routine itself achieving excellent speedups versus an optimized CPU implementation, but also a novel GPU-friendly compressed storage scheme for triangular matrices. Secondly, a scalable multi-GPU solver for non-hermitian linear systems was implemented. It is integrated into a simulation environment for electrical impedance tomography (EIT) that requires frequent solution of complex systems with millions of unknowns, a task that this solution can perform within seconds. In terms of computational throughput, it outperforms not only an highly optimized multi-CPU reference, but related GPU-based work as well. Finally, a GPU-accelerated graphical EEG real-time source localization software was implemented. Thanks to acceleration, it can meet real-time requirements in unpreceeded anatomical detail running more complex localization algorithms. Additionally, a novel implementation to extract anatomical priors from static Magnetic Resonance (MR) scansions has been included.

Spectral estimates and preconditioning for saddle point systems arising from optimization problems

In this thesis, we consider the problem of solving large and sparse linear systems of saddle point type stemming from optimization problems. The focus of the thesis is on iterative methods, and new preconditioning srategies are proposed, along with novel spectral estimtates for the matrices involved.

X-parameters based analytical design of non-linear microwave circuits Application to oscillator design

Resumen El diseño clásico de circuitos de microondas se basa fundamentalmente en el uso de los parámetros s, debido a su capacidad para caracterizar de forma exitosa el comportamiento de cualquier circuito lineal. La relación existente entre los parámetros s con los sistemas de medida actuales y con las herramientas de simulación lineal han facilitado su éxito y su uso extensivo tanto en el diseño como en la caracterización de circuitos y subsistemas de microondas. Sin embargo, a pesar de la gran aceptación de los parámetros s en la comunidad de microondas, el principal inconveniente de esta formulación reside en su limitación para predecir el comportamiento de sistemas no lineales reales. En la actualidad, uno de los principales retos de los diseñadores de microondas es el desarrollo de un contexto análogo que permita integrar tanto el modelado no lineal, como los sistemas de medidas de gran señal y los entornos de simulación no lineal, con el objetivo de extender las capacidades de los parámetros s a regímenes de operación en gran señal y por tanto, obtener una infraestructura que permita tanto la caracterización como el diseño de circuitos no lineales de forma fiable y eficiente. De acuerdo a esta filosofía, en los últimos años se han desarrollado diferentes propuestas como los parámetros X, de Agilent Technologies, o el modelo de Cardiff que tratan de proporcionar esta plataforma común en el ámbito de gran señal. Dentro de este contexto, uno de los objetivos de la presente Tesis es el análisis de la viabilidad del uso de los parámetros X en el diseño y simulación de osciladores para transceptores de microondas. Otro aspecto relevante en el análisis y diseño de circuitos lineales de microondas es la disposición de métodos analíticos sencillos, basados en los parámetros s del transistor, que permitan la obtención directa y rápida de las impedancias de carga y fuente necesarias para cumplir las especificaciones de diseño requeridas en cuanto a ganancia, potencia de salida, eficiencia o adaptación de entrada y salida, así como la determinación analítica de parámetros de diseño clave como el factor de estabilidad o los contornos de ganancia de potencia. Por lo tanto, el desarrollo de una formulación de diseño analítico, basada en los parámetros X y similar a la existente en pequeña señal, permitiría su uso en aplicaciones no lineales y supone un nuevo reto que se va a afrontar en este trabajo. Por tanto, el principal objetivo de la presente Tesis consistiría en la elaboración de una metodología analítica basada en el uso de los parámetros X para el diseño de circuitos no lineales que jugaría un papel similar al que juegan los parámetros s en el diseño de circuitos lineales de microondas. Dichos métodos de diseño analíticos permitirían una mejora significativa en los actuales procedimientos de diseño disponibles en gran señal, así como una reducción considerable en el tiempo de diseño, lo que permitiría la obtención de técnicas mucho más eficientes. Abstract In linear world, classical microwave circuit design relies on the s-parameters due to its capability to successfully characterize the behavior of any linear circuit. Thus the direct use of s-parameters in measurement systems and in linear simulation analysis tools, has facilitated its extensive use and success in the design and characterization of microwave circuits and subsystems. Nevertheless, despite the great success of s-parameters in the microwave community, the main drawback of this formulation is its limitation in the behavior prediction of real non-linear systems. Nowadays, the challenge of microwave designers is the development of an analogue framework that allows to integrate non-linear modeling, large-signal measurement hardware and non-linear simulation environment in order to extend s-parameters capabilities to non-linear regimen and thus, provide the infrastructure for non-linear design and test in a reliable and efficient way. Recently, different attempts with the aim to provide this common platform have been introduced, as the Cardiff approach and the Agilent X-parameters. Hence, this Thesis aims to demonstrate the X-parameter capability to provide this non-linear design and test framework in CAD-based oscillator context. Furthermore, the classical analysis and design of linear microwave transistorbased circuits is based on the development of simple analytical approaches, involving the transistor s-parameters, that are able to quickly provide an analytical solution for the input/output transistor loading conditions as well as analytically determine fundamental parameters as the stability factor, the power gain contours or the input/ output match. Hence, the development of similar analytical design tools that are able to extend s-parameters capabilities in small-signal design to non-linear ap- v plications means a new challenge that is going to be faced in the present work. Therefore, the development of an analytical design framework, based on loadindependent X-parameters, constitutes the core of this Thesis. These analytical nonlinear design approaches would enable to significantly improve current large-signal design processes as well as dramatically decrease the required design time and thus, obtain more efficient approaches.

Linear instability of orthogonal compressible leading-edge boundary layer flow

Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.

Linear system solvers for parallel computers /

Includes bibliographical references.