Identification of Linear Systems with Nonlinear Distortions

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Identification of Linear Systems with Nonlinear Distortions

Identification of Linear Systems with Nonlinear Distortions

Johan Schoukens¹, Rik Pintelon¹, Tadeusz Dobrowiecki², Yves Rolain¹•Institutions (2)

Vrije Universiteit Brussel¹, Budapest University of Technology and Economics²

27 Aug 2003-

TL;DR: A theoretical framework is proposed that extends the linear system description to include the impact of nonlinear distortions: the nonlinear system is replaced by a linear model plus a 'nonlinear noise source'.

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Abstract: This paper studies the impact of nonlinear distortions on linear system identification. It collects a number of previously published methods in a fully integrated approach to measure and model these systems from experimental data. First a theoretical framework is proposed that extends the linear system description to include the impact of nonlinear distortions: the nonlinear system is replaced by a linear model plus a 'nonlinear noise source'. The class of nonlinear systems covered by this approach is described and the properties of the extended linear representation are studied. These results are used to design the experiments; to detect the level of the nonlinear distortions; to measure efficiently the 'best' linear approximation; to reveal the even or odd nature of the nonlinearity; to identify a parametric linear model; and to improve the model selection procedures in the presence of nonlinear distortions.

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Citations

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Journal Article•DOI•

From experiment design to closed-loop control

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Håkan Hjalmarsson¹•Institutions (1)

Royal Institute of Technology¹

01 Mar 2005-Automatica

TL;DR: It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy.

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500 citations

Journal Article•DOI•

System Identification Methods for (Operational) Modal Analysis: Review and Comparison

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Edwin Reynders¹•Institutions (1)

Katholieke Universiteit Leuven¹

09 Feb 2012-Archives of Computational Methods in Engineering

TL;DR: In this article, the authors extensively review operational modal analysis approaches and related system identification methods and compare them in an extensive Monte Carlo simulation study, and then compare the results with the results obtained in an experimental setting.

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Abstract: Operational modal analysis deals with the estimation of modal parameters from vibration data obtained in operational rather than laboratory conditions. This paper extensively reviews operational modal analysis approaches and related system identification methods. First, the mathematical models employed in identification are related to the equations of motion, and their modal structure is revealed. Then, strategies that are common to the vast majority of identification algorithms are discussed before detailing some powerful algorithms. The extraction and validation of modal parameter estimates and their uncertainties from the identified system models is discussed as well. Finally, different modal analysis approaches and algorithms are compared in an extensive Monte Carlo simulation study.

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481 citations

Book Chapter•DOI•

Nonlinear System Identification

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Gail D. Baura

01 Jan 2002

TL;DR: This chapter contains sections titled: Historical Review Supervised Multilayer Networks unsupervised Neural Networks: Kohonen Network Unsupervised Networks: Adaptive Resonance Theory Network Model Validation and Recommended Exercises.

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Abstract: This chapter contains sections titled: Historical Review Supervised Multilayer Networks Unsupervised Neural Networks: Kohonen Network Unsupervised Networks: Adaptive Resonance Theory Network Model Validation Summary References Recommended Exercises

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452 citations

Journal Article•DOI•

Identification of nonlinear systems using Polynomial Nonlinear State Space models

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Johan Paduart¹, Lieve Lauwers¹, Jan Swevers², Kris Smolders², Johan Schoukens¹, Rik Pintelon¹ - Show less +2 more•Institutions (2)

Vrije Universiteit Brussel¹, Katholieke Universiteit Leuven²

01 Apr 2010-Automatica

TL;DR: A method to model nonlinear systems using polynomial nonlinear state space equations by identifying first the best linear approximation of the system under test is proposed.

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247 citations

Cites background from "Identification of Linear Systems wi..."

...Hence, a lower uncertainty is achieved for the BLA [64]....
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Journal Article•DOI•

Nonlinear System Analysis and Identification from Random Data

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A. V. Metcalfe¹, Julius S. Bendat•Institutions (1)

University of Newcastle¹

01 Mar 1993-The Statistician

TL;DR: This paper presents a meta-analysis of statistical errors in Nonlinear Estimates of Linear and Nonlinear Systems and their applications in Input/Output Relationships and Bilinear and Trilinear Systems.

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Abstract: Linear Systems, Random Data, Spectra Zero-Memory Nonlinear Systems Bilinear and Trilinear Systems Nonlinear System Input/Output Relationships Square-Law and Cubic Nonlinear Systems Statistical Errors in Nonlinear Estimates Parallel Linear and Nonlinear Systems.

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207 citations

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References

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Journal Article•DOI•

A new look at the statistical model identification

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Hirotugu Akaike

01 Dec 1974-IEEE Transactions on Automatic Control

TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.

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Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

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47,133 citations

"Identification of Linear Systems wi..." refers methods in this paper

...There exist a number of tools like the AIC and MDL criteria that are used to choose between different models (Akaike, 1974; Rissanen, 1978)....
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Book•

System Identification: Theory for the User

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Lennart Ljung

01 Jan 1987

TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.

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Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...

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20,436 citations

"Identification of Linear Systems wi..." refers background or methods in this paper

...…in agreement with the classical result, showing that the output of a nonlinear system can be split in two parts (Bendat, 1990 and 1998; Forsell and Ljung, 1999): a first part that is linearly related with the input (in our case leading to ), and a second part that is uncorrelated with the input…...
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...For such a well selected model order and under the classical identifiability assumptions (Ljung, 1999), the following result is obtained: Theorem 5: Consider a system belonging to the set , excited with an excitation ....
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...The first one is the classical prediction error approach (Söderström and Stoica, 1989; Ljung, 1999) where a parametric plant and noise model are simultaneously estimated....
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...For the standard identification methods this is done implicitly during the estimation of the noise variance starting from the residuals (Söderström and Stoica, 1989; Ljung, 1999)....
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...INTRODUCTION 1 Identification of linear systems became a mature scientific discipline over the last decades (Ljung, 1999; Söderström and Stoica, 1989; Pintelon and Schoukens, 2001)....
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Journal Article•DOI•

Paper: Modeling by shortest data description

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Jorma Rissanen¹•Institutions (1)

IBM¹

01 Sep 1978-Automatica

TL;DR: The number of digits it takes to write down an observed sequence x1,...,xN of a time series depends on the model with its parameters that one assumes to have generated the observed data.

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6,254 citations

"Identification of Linear Systems wi..." refers methods in this paper

...There exist a number of tools like the AIC and MDL criteria that are used to choose between different models (Akaike, 1974; Rissanen, 1978)....
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Book•

Engineering Applications of Correlation and Spectral Analysis

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Julius S. Bendat, Allan G. Piersol

13 May 1980

TL;DR: This chapter discusses single-Input/Single-Output Relationships, nonstationary data analysis techniques, and procedures to Solve Multiple- Input/Multiple-Output Problems.

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Abstract: Discusses engineering applications and recent developments based upon correlation and spectral analysis. Illustrations deal with applications to acoustics, mechanical vibrations, system identification, and fluid dynamics problems in aerospace, automotive, industrial noise control, civil engineering and oceanographic fields, as well as similar problems in other fields. Tackles problems and solutions, assuming reader has required hardware and software to compute estimates of correlation, spectra, coherence, and phase functions.

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2,447 citations

"Identification of Linear Systems wi..." refers background in this paper

...(9) Note that this is the classical result for FRF measurements of linear systems (Bendat and Piersol, 1980)....
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Journal Article•DOI•

Nonlinear black-box modeling in system identification: a unified overview

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Jonas Sjöberg¹, Qinghua Zhang², Lennart Ljung¹, Albert Benveniste², Bernard Delyon², Pierre-Yves Glorennec³, Håkan Hjalmarsson¹, Anatoli Juditsky² - Show less +4 more•Institutions (3)

Linköping University¹, French Institute for Research in Computer Science and Automation², Intelligence and National Security Alliance³

01 Dec 1995-Automatica

TL;DR: What are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques are described, from a user's perspective.

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2,031 citations

"Identification of Linear Systems wi..." refers methods in this paper

...A large number of proposed identification methods is based on this idea (Baumgartner and Rugh, 1975; Bendat, 1990; Bendat, 1998; Billings and Fakhouri, 1980; Billings and Fakhouri, 1982; Chen, 1995; Korenberh and Hunter, 1986; Korenberg, 1991; Sjöberg et al., 1995; Tan and Godfrey, 2002; Wysocki and Rugh, 1976; Wysocki and Wilson, 1979; Weiss et al., 1998)....
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...Also neural network and wavelet modelling can be fitted in this framework (Sjöberg et al., 1995; Juditsky et al., 1995; Nelles, 2001)....
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...…this idea (Baumgartner and Rugh, 1975; Bendat, 1990; Bendat, 1998; Billings and Fakhouri, 1980; Billings and Fakhouri, 1982; Chen, 1995; Korenberh and Hunter, 1986; Korenberg, 1991; Sjöberg et al., 1995; Tan and Godfrey, 2002; Wysocki and Rugh, 1976; Wysocki and Wilson, 1979; Weiss et al., 1998)....
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