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Stability and identification for rational approximation of frequency response function of unbounded soil
Author(s) -
Du Xiuli,
Zhao Mi
Publication year - 2010
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.936
Subject(s) - frequency domain , mathematics , stability (learning theory) , rational function , nonlinear system , representation (politics) , convolution (computer science) , frequency response , domain (mathematical analysis) , time domain , function (biology) , mathematical analysis , mathematical optimization , control theory (sociology) , computer science , artificial neural network , engineering , physics , electrical engineering , control (management) , quantum mechanics , machine learning , artificial intelligence , politics , political science , law , computer vision , evolutionary biology , biology
Exact representation of unbounded soil contains the single output–single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency‐domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped‐parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least‐squares fitting problem using the hybrid genetic‐simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori . The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil–structure‐interaction examples. Copyright © 2009 John Wiley & Sons, Ltd.