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On Modelling the Nonlinear Relationship Between Random Fields by Means of Higher-Order Spectra

by Ahsan Kareem, Univ of Houston, United States,
Yousun Li, Univ of Houston, United States,



Document Type: Proceeding Paper

Part of: Probabilistic Methods in Civil Engineering

Abstract:

This paper addresses the input-output relationship of nonlinear systems that may be expressed in terms of a hierarchy of linear, quadratic and higher-order transfer functions or corresponding impulse response functions. Digitally implemented bispectral analysis permits modeling of the quadratic terms expressed in terms of cross bispectra or bicoherence functions. The bispectrum provides a measure of the multiplicative nonlinear interactions of frequency components and offers physical insight into the nature and characteristics of nonlinear fluctuations. The paper illustrates modelling of the nonlinear relationship of random fields by bispectral technique. The relationship between the far-field turbulence and the fluctuating pressure field around a bluff body is discussed in the light of simultaneous measurements of the approach flow turbulence and the pressure fields in a boundary layer wind tunnel. Other applications of the quadratic transfer functions, e.g., the evaluation of the slowly drifting response analysis of tension leg platforms and other floating marine systems are briefly discussed.

Subject Headings: Wind tunnel | Offshore structures | Turbulent flow | Turbulence | Offshore platforms | Nonlinear response | Nonlinear analysis

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