Bayesian updating and model class selection with Subset Simulation
Bayesian updating and model class selection with Subset Simulation
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DOI：
10.1016/j.cma.2017.01.006
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发表时间：
2015-10
影响因子：
7.2
通讯作者：
F. DiazDelaO;A. Garbuno-Iñigo;S. Au;Ikumasa Yoshida
中科院分区：
文献类型：
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作者：
F. DiazDelaO;A. Garbuno-Iñigo;S. Au;Ikumasa Yoshida
基于实测数据的模型参数识别和模型评价是现代科学和工程中最重要和最具挑战性的课题之一，在结构系统识别、模型更新和高保真度模型开发中具有巨大的应用潜力。这些问题原则上可以使用贝叶斯概率方法来解决，其中待识别的参数被视为不确定的，并且它们的推断信息根据它们的后验概率分布给出。对于应用中遇到的复杂模型，需要对问题中的不确定参数的数量具有鲁棒性的高效计算工具来计算后验统计，后验统计通常可以被公式化为不确定参数空间上的多维积分。子集模拟是解决复杂系统可靠性问题的一种新方法，它对不确定参数的数目具有鲁棒性。最近已经建立了一个类比之间的贝叶斯更新问题和可靠性问题，这开辟了有效的解决方案的子集模拟的可能性。该公式被称为BUS（贝叶斯更新与结构可靠性方法），是基于标准拒绝原则。它的理论正确性和效率要求谨慎选择乘数，这仍然是一个悬而未决的问题。本文提出了一个基本的研究乘数，并探讨其偏差效应时，它是不正确的选择。提出了一种改进的BUS公式，从根本上解决了在不知道乘子先验的情况下实现子集模拟的问题。还提供了自动停止条件。最后通过实例说明了该方法的理论和应用。
Identifying the parameters of a model and rating competitive models based on measured data has been among the most important and challenging topics in modern science and engineering, with great potential of application in structural system identification, updating and development of high fidelity models. These problems in principle can be tackled using a Bayesian probabilistic approach, where the parameters to be identified are treated as uncertain and their inference information are given in terms of their posterior probability distribution. For complex models encountered in applications, efficient computational tools robust to the number of uncertain parameters in the problem are required for computing the posterior statistics, which can generally be formulated as a multi-dimensional integral over the space of the uncertain parameters. Subset Simulation has been developed for solving reliability problems involving complex systems and it is found to be robust to the number of uncertain parameters. An analogy has been recently established between a Bayesian updating problem and a reliability problem, which opens up the possibility of efficient solution by Subset Simulation. The formulation, called BUS (Bayesian Updating with Structural reliability methods), is based on the standard rejection principle. Its theoretical correctness and efficiency require the prudent choice of a multiplier, which has remained an open question. This paper presents a fundamental study of the multiplier and investigates its bias effect when it is not properly chosen. A revised formulation of BUS is proposed, which fundamentally resolves the problem such that Subset Simulation can be implemented without knowing the multiplier a priori. An automatic stopping condition is also provided. Examples are presented to illustrate the theory and applications.