Stability and Identification for Continuous-Time Rational Approximation of Foundation Frequency Response

Abstract eng:
Continuous-time rational approximation (CRA) of foundation frequency response is the first step of a systematic procedure for constructing various high-order lumped-parameter models (LPMs) in foundation vibration analysis. The stability and accuracy of CRA determine those of its LPMs as realizations. In this paper, the stability and identification of CRA are studied. The necessary and sufficient stability conditions are presented based on the linear-system stability theory and the input-output case of LPMs. A parameter identification method is further proposed by directly solving a nonlinear least-squares fitting problem using the hybrid genetic-simplex optimization algorithm, where the proposed stability conditions are considered by the penalty function method. A stable and accurate CRA is obtained by this method and is then realized as Wu-Lee’s and Wolf’s LPMs. The proposed stability theory and identification method is verified by analyzing several typical foundation vibration problems and comparing with Wu-Lee’ and Wolf’s results.

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