复杂工程结构非概率可靠度分析的高斯过程动态响应面法

Gaussian Process Based Dynamic Response Surface Method of Non-probabilistic Reliability Analysis for Complicated Engineering Structure

复杂工程结构非概率可靠度分析中,由于功能函数是隐式的,采用解析方法难以求解,针对这一问题提出基于粒子群优化的高斯过程动态响应面方法.该方法通过有限元生成少量训练样本,然后采用高斯过程回归模型重构隐式功能函数的响应面,实现小样本下隐式函数的显示表达,进而利用粒子群优化算法搜索设计点,并构造合理的迭代方式,利用各迭代步的设计点信息动态提升响应面对结构功能函数的重构精度.算例结果表明,该方法是可行的,与基于二次多项式的传统响应面法相比较,该方法的计算效率与计算精度均较高,易于与已有的有限元软件相结合,适用于具有隐式功能函数且计算代价较高的复杂工程结构非概率可靠度分析.

In order to overcome the difficulty in the analytic method based non-probabilistic reliability analysis of complex engineering structure with implicit performance function,a new Gaussian Process Regression（ GPR） dynamic response surface was presented for reliability analysis based on the Particle Swarm Optimization（ PSO） algorithm. A small number of training samples are created first by using the Finite Element Method（ FEM）,and then the highly nonlinear and implicit performance function is approximated by the GPR with the created samples.Meanwhile,the design point is searched quickly using the PSO without any extra FEM analysis,and an iterative algorithm is presented to improve the precision of the response surface by adding the updated information of the design point. The examples results showed that computation efficiency and precision of the proposed method was superior to the traditional response surface method based on quadratic polynomial. The proposed method is feasible for reliability analysis of complex engineering structure with implicit performance function and timeconsuming computation by combining with the existing FEM software.