基于高斯过程分类与蒙特卡洛模拟的岩土工程结构可靠度分析方法

岩土工程结构可靠度分析中,功能函数一般呈隐式且需借助有限元等数值计算来构建,采用传统蒙特卡洛模拟法求解时常遇到计算耗时大和计算效率低的问题,进而导致该方法在实际工程应用中受到极大限制。将结构可靠度求解问题转化为二元分类问题,把分类性能优异的高斯过程分类模型与蒙特卡洛法相结合,提出了岩土工程结构可靠度分析的高斯过程分类——蒙特卡洛法。根据所建立的隐式功能函数,采用岩土工程结构分析程序构造少量的学习样本,利用学习后的高斯过程分类模型重构极限状态方程,实现随机样本的安全或失效状态的准确识别,进而采用蒙特卡洛抽样模拟获得结构的失效概率与可靠指标。算例研究表明,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,且易于与各种岩土工程结构分析程序或商业计算软件相结合。

Reliability Analysis Method for Geotechnical Engineering Structure Using Gaussian Process Classification Based Monte Carlo Simulation

The limit state function is always expressed in implicit function for geotechnical engineering structure, Typically, it needs to be evaluated implicitly through a numerical code such as a Finite Element method (FEM). Although reliability analysis can be carried out using Monte Carlo Simulation (MCS), a large number of FEM executions for structural analysis can make the computational burden of the process very high. It results in the limitation of application of MCS in practical engineering. The reliability problem can be transformed into the binary classification problem. A new method, that is, Gaussian process classification (GPC) based MCS is proposed to solve the reliability problem of geotechnical engineering structure. The small amount of learning samples was built by structure analysis code. The implicit limit state function was reconstructed by GPC model based on learning samples. Thus, it can achieve to identify the safe or failure state of any samples generated randomly. Then, Monte Carlo method is applied to get the structure of failure probability and reliability index. The study results show that the proposed method is feasible. It has advantages of high efficiency compared to Monte Carlo method. The present methods can directly take advantage of existing geotechnical engineering software without modification, and thus are convenient to be used for practitioner engineers.