STABILITY AND IDENTIFICATION FOR RATIONAL APPROXIMATION OF FOUNDATION FREQUENCY RESPONSE: CONTINUOUS-TIME LUMPED-PARAMETER MODELS
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摘要: 基础频率响应的连续时间有理近似是构建基础振动分析的高阶集中参数模型的起点，连续时间有理近似的稳定性和参数识别直接决定集中参数模型以及土-结系统的动力稳定性和精度。该文基于线性系统稳定性理论并结合集中参数模型的具体输入-输出情况，提出连续时间有理近似(也即集中参数模型)稳定的充分必要条件；进而基于罚函数法和遗传-单纯形法建立可以考虑稳定性约束的有理近似识别方法。将获得的稳定、精确的连续时间有理近似分别实现为Wu-Lee和Wolf的高阶集中参数模型，通过几个典型基础振动问题验证了提出的稳定性理论和参数识别方法。Abstract: a continuous-time rational approximation (CRA) for the foundation frequency response is a starting point for constructing various high-order lumped-parameter models (LPMs) in the foundation vibration analysis. The stability and identification of CRA determine directly the stability and accuracy of its resulting LPMs and a soil-structure interaction system. In this paper, the necessary and sufficient stability conditions for the CRA and its LPMs are proposed based on linear-system stability theory and the input-output case of the LPMs. A parameter identification method including the proposed stability constraints is further developed by using the penalty func-tion method and the hybrid genetic-simplex optimization algorithm. A stable and accurate CRA is thus obtained by this method and is then realized as Wu-Lee’s and Wolf’s LPMs. The proposed stability and identification methods are verified by analyzing several typical foundation vibration problems and the comparision with Wu-Lee’ and Wolf’s results.
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