NONLINEAR SYSTEM TECHNIQUES AND APPLICA-

TIONS, Julius S. Bendat, John Wiley & Sons, Inc.,Wiley-Interscience Publication, 1998, 474 pages,ISBN 0-471-16576-X.

1. INTRODUCTION

Nonlinear System ¹echniques and Applications byJulius S. Bendat is the author's second book cover-ing ongoing developments focusing on frequencydomain spectral and correlation techniques fornonlinear systems. The "rst book entitled Nonlin-ear System Analysis and Identi,cation from Ran-dom Data [1] focused on theoretical foundationsand described several applications. Due to the suc-cessful completion of ocean engineering and bi-omedical research in the eight years following his"rst book on nonlinear systems, the present bookdevotes over one-half of its pages to applications.This book presents a logical extension of

Dr. Bendat's many contributions to the "eld ofrandom data analysis of linear dynamic systems. Itprovides a distinct focus on the frequency domainviewpoint, which is his primary area of concentra-tion. Earlier contributions by this author, overa roughly 50-year period to the "eld of linearsystem analysis have had a profound in#uenceon engineering practice in both theoretical andexperimental arenas. The present book o!ersa convincing case for the application of provenfrequency domain techniques to the study of non-linear systems.

2. MAIN BODY

Nonlinear System ¹echniques and Applicationsopens, in Chapter 1, with a review of random dataanalysis theory which is thoroughly developed inprevious books by Bendat and Piersol [2, 3]. Thesecond chapter provides an extensive discussion ofthe e!ect of zero-memory nonlinearity on prob-ability density functions. Chapters 3 and 4 intro-duce the adaptation of multi-input, single-outputspectral analysis procedures to direct and reversenonlinear system models. In Chapter 4, a series ofelementary applications are discussed. An exten-sive discussion of ocean engineering applicationsand results are the subject of Chapters 5}7. Chap-ters 8 and 9 complete the book, with a discussionof higher order spectral analysis of bilinear andtrilinear systems.

An essential part of the process of identifyingnonlinear systems from measured time historydata involves recognition of both the presence andtype of nonlinear behavior. Dr. Bendat's theoret-ical discussion of the characteristics of output (re-sponse) probability density for nonlinear systemssubjected to Gaussian inputs (Chapter 2), providesa clear approach to the task of identifying thegeneral extent and type of nonlinearity. Examplesof piecewise nonlinear systems, dead-zone andclipped systems, square- and cubic-law systems,square-law with sign systems, hardening, softeningand hardening-softening spring systems constitutea representative set of common zero-memory non-linear physical phenomena. Results for these typesof nonlinear systems convincingly exhibit the util-ity of probability density as a diagnostic tool forpreliminary nonlinear system identi"cation. InChapter 4, an additional method for the prelimi-nary identi"cation of nonlinear behavior, consist-ing of &x}y' graphing of signal pairs, is brie#ydiscussed.Nonlinear System ¹echniques and Applications fo-

cuses on the estimation of frequency domain char-acteristics as a means of system identi"cation. Twogeneral spectral analysis approaches are presented,namely, (1) the conventional multiple input/singleoutput (MI/SO) procedure [2, 3], and (2) a Volterraseries based method. The conventional MI/SO pro-cedure, adapted for nonlinear systems, is quitestraightforward and can be applied for a wide var-iety of situations. It is applied to MI/SO systemscast in either direct (forward) or reverse dynamicforms. In both of these forms, the nonlinear termsare expressed as zero-memory functions of mea-sured responses. The key to properly identifyinga particular nonlinear system involves the employ-ment of nonlinear functions appropriately describ-ing its physical behaviour. Frequency dependentfunctions of both linear and zero-memory nonlinearvariables are identi"ed by MI/SO spectral analysis.Both the signi"cance and appropriateness of thenonlinear terms are evaluated from the cumulativecoherence function, which is computed by the con-ventional MI/SO procedure. The Volterra seriesbased method employs higher order spectral func-tions, which are di$cult to compute. Moreover,bilinear and trilinear models, covered in Chapters8 and 9, describe a limited subset of possibilities fornonlinear behaviour. Dr. Bendat correctly recog-nizes the advantage of the conventional MI/SOprocedure, adapted for nonlinear systems, over Vol-terra series methodology and provides results fora variety of simulated and actual test situations inChapters 4}7.

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Copyright � 2001 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2001; 11:789}796

3. CONCLUSIONS

Nonlinear System ¹echniques and Applications is ofextreme value to scientists and engineers engagedin nonlinear system identi"cation projects. Thematerial presented in the book is suitable for anaudience of graduate-level background. Familiar-ity with random data analysis theory [1, 2] is anessential pre-requisite. The author very appro-priately devotes a large portion of the book to casestudy applications, since the success of the nonlin-ear system identi"cation process depends heavilyon the proper recognition and selection of nonlin-ear functions and the interpretation of MI/SOresults. In particular, Dr. Bendat's thorough pre-sentation of two basin studies on frigate and bargedynamics is instructive to both novices andexperienced professionals. Nonlinear System ¹ech-niques and Applications represents a valuable

contribution to the emerging "eld of nonlinearsystem identi"cation, due to its clear treatment ofmathematical theory and engineering applications.

ROBERT N. COPPOLINO, PhD9832 Aura Avenue

Northridge, CA 91324U.S.A.

REFERENCES

1. Bendat JS. Nonlinear System Identi,cation from Ran-dom Data. Wiley-Interscience: New York, 1990.

2. Bendat JS, Piersol AG. Random Data Analysis andMeasurement Procedures. (3rd edn.) Wiley-Intersci-ence: New York, 2000.

3. Bendat JS, Piersol AG. Engineering Applications ofCorrelation and Spectral Analysis. (2nd edn.) Wiley-Interscience: New York, 1993.

796 BOOK REVIEWS

Copyright � 2001 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2001; 11:789}796