基于高斯过程回归的工程结构失效概率快速估计方法

Fast estimation of failure probability for engineering structure using Gaussian Process Regression

高斯过程机器学习是基于严格的统计学习理论而新发展的方法,该方法在求解小样本、高维数的非线性问题上具有一定的适应性.针对采用直接蒙特卡洛方法进行功能函数计算代价较高的结构可靠度分析时计算效率过低的瓶颈问题,提出了一种基于高斯过程回归模型的直接蒙特卡洛模拟方法.该方法利用有限元等数值方法构造少量的学习样本,通过学习后的高斯过程回归模型重构隐式功能函数,直接建立随机变量与功能函数值的映射关系,进而结合直接蒙特卡洛方法推求结构的失效概率与可靠指标.算例研究表明,该方法简单易行,与传统蒙特卡洛模拟法相比较,计算效率明显较高,且易于与各种工程结构分析程序或商业计算软件相结合.

Gaussian Process （GP） is a newly developed machine learning method based on the strict statisti- cal learning theory. GP is capable of solving the highly nonlinear problem with small samples and high dimensions. Aiming to the bottleneck problem of the direct Monte Carlo method, which has the very low computational efficiency for structural reliability analysis with high calculation cost of performance function, a new method named Gaussian Process Regression based on Monte Carlo Simulation （GPR-based MCS） method was proposed. The small amount of learning samples were built by numerical methods such as finite element analysis in the method. The implicit performance function was approximated and recon- structed by GP regression model, which the mapping of random variables and function values was directly established. Then, Monte Carlo method was applied to get the failure probability and reliability index of the structure. Compared to Monte Carlo method, the proposed method has high efficiency and can directly combine with existing engineering structural software without modification.