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Sensitivity and Hessian matrix analysis of structural reliability for uniformly modulated random seismic response

机译:均匀调制随机地震反应结构可靠度的敏感性和Hessian矩阵分析

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This paper presents a numerical method for calculation of the sensitivity and Hessian matrix of the time variant reliability of structures subjected to uniformly modulated evolutionary random seismic excitation. The first three spectral moments, their first and second derivatives are obtained using the auto PSD functions, their sensitivity and Hessian matrix information. The formulas of the first and second derivatives of reliability are derived by direct differentiation based on the reliability formula that assumes the threshold crossings to obey a two-state Markov process. The computational procedure is given in detail for the reliability, its first and second derivatives. Finally, the reliability, its sensitivity and Hessian matrix analysis of a planar frame subjected to the uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method. The accuracy and efficiency of the proposed method in this paper are discussed by comparison with the developed method. (C) 2014 Elsevier Ltd. All rights reserved.
机译:本文提出了一种数值方法,用于计算受均匀调制的演化随机地震激励作用的结构的时变可靠性的灵敏度和Hessian矩阵。前三个频谱矩,其一阶和二阶导数是使用自动PSD函数,其灵敏度和Hessian矩阵信息获得的。可靠性的一阶和二阶导数的公式是基于可靠性公式通过直接微分得出的,该可靠性公式假定阈值交叉以服从二态马尔可夫过程。详细给出了可靠性及其一阶和二阶导数的计算过程。最后,研究了平面框架在均匀调制的演化随机地震地震动作用下的可靠性,灵敏度和Hessian矩阵分析,以阐明该方法。通过与提出的方法比较,讨论了本文提出的方法的准确性和效率。 (C)2014 Elsevier Ltd.保留所有权利。

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