## Nonlinear System Techniques and ApplicationsNew practical techniques for nonlinear system research and evaluation Nonlinear Systems Techniques and Applications provides the most practical techniques currently available for analyzing and identifying nonlinear systems from random data measured at the input and output points of the nonlinear systems. These new techniques require only one-dimensional spectral functions that are much simpler to compute and apply than previous nonlinear procedures. The new results show when and how to replace a wide class of single-input/single-output nonlinear models with simpler equivalent multiple-input/single-output linear models. While other techniques are usually restricted to Gaussian data, the new techniques developed here apply to data with arbitrary probability, correlation, and spectral properties. Numerous examples used in the book are based on the analysis of real physical data passing through real nonlinear systems in the fields of oceanography, automotive engineering, and biomedical research. For practicing engineers and scientists involved in aerospace, automotive, biomedical, electrical, mechanical, oceanographic, and other activities concerned with nonlinear system analysis, Nonlinear Systems Techniques and Applications is the essential reference work in the field. |

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### Contents

Linear Systems Random Data | 1 |

ZeroMemory Nonlinear Systems | 21 |

Direct and Reverse MISO Techniques for Analysis | 77 |

Copyright | |

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### Common terms and phrases

Al(f autocorrelation function autospectral density function beam sea bilinear chapter computed constant-parameter correlated cross-correlation cubic system cumulative coherence function defined Direct MI/SO equation of motion estimates force input formulas Fourier transform FREQUENCY HZ frequency response function frequency-domain Gaussian input data head seas heave motion HZ Figure input x(t input/output linear and nonlinear linear frequency response linear model linear system mathematical input MI/SO ANALYSIS MI/SO nonlinear model of Figure motion output non-Gaussian nonlinear damping nonlinear differential equation nonlinear frequency response nonlinear term output PDF phase angle physical parameters pitch motion probability density function properties quartering seas response function associated reverse dynamic Reverse MI/SO Techniques roll motion SDOF second-order shown in Figure spectral density spectral density functions spring system square-law system stationary random data sway Sxx(f Sxy(f system frequency response Syy(f third-order trilinear systems undisturbed wave motion wave input weighting function zero mean value zero-memory nonlinear system