近期,上海交通大学自然科学研究院及数学科学学院特别研究员李敬来课题组在国际学术期刊计算物理杂志 ( Journal of Computational Physics)上发表了题为“Gaussian process surrogates for failure detection: a Bayesian experimental design approach”的论文,报道了他们关于使用贝叶斯方法对工程系统中的故障模式进行识别的工作。

对复杂工程系统的故障模型进行预测与识别并对系统的可靠性进行评估是诸如结构工程,机械工程,航空航天等若干若干工程领域中的重要问题。长期以来在处理这样的问题中的一个困难是,现代工程系统的复杂性比较高因此对系统进行电脑仿真的计算量非常大,为了有效率的解决这个问题,本文借鉴了机器学习领域的若干方法,使用了贝叶斯统计的框架,将问题转化为寻找失效边界(failure boundary)的贝叶斯推断问题,并且给出了基于最优实验设计理论的选点策略,从而得到了一个既有效率又能够保证精度的故障模式识别方法。作者预期该方法能够在许多实际工程问题中得到应用。


参考文献:Hongqiao Wang, Guang Lin, Jinglai Li, “Gaussian process surrogates for failure detection: A Bayesian experimental design approach”, Journal of Computational Physics, Volume 313, 15 May 2016, Pages 247-259.

Abstract: An important task of uncertainty quantification is to identify the probability of undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian process surrogates for failure detection and failure probability estimation. In particular, we consider the situation that the underlying computer models are extremely expensive, and in this setting, determining the sampling points in the state space is of essential importance. We formulate the problem as an optimal experimental design for Bayesian inferences of the limit state (i.e., the failure boundary) and propose an efficient numerical scheme to solve the resulting optimization problem. In particular, the proposed limit-state inference method is capable of determining multiple sampling points at a time, and thus it is well suited for problems where multiple computer simulations can be performed in parallel. The accuracy and performance of the proposed method is demonstrated by both academic and practical examples.