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Stability and identification for rational approximation of frequency response function of unbounded soil

机译：无界土频率响应函数的合理逼近稳定性与辨识

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摘要

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.
机译：无边界土壤的精确表示包含物理空间或变换空间中力与位移之间的单个输出-单个输入关系。这种关系是时域中的全局卷积积分。在频域中对其频率响应函数（频域卷积核）进行合理逼近，然后将其作为集总参数模型或递归公式实现到时域中，是获得无边界土壤的时域局部表示的有效方法。研究了有理逼近的稳定性和辨识。基于线性系统的稳定性理论，给出了一个充要条件。通过使用混合遗传-单纯形优化算法直接解决非线性最小二乘拟合问题，进一步开发了一种参数识别方法，其中通过罚函数方法强制提出了作为约束条件的所提出的稳定性条件。因此，事先保证了稳定性。还讨论了稳定系统中不常见的不良共振现象。通过几个动态土-结构-相互作用实例验证了所提出的稳定性条件和识别方法。

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