结构可靠度分析的响应面法及其Matlab实现

对功能函数不能明确表达的问题进行可靠度分析，常采用响应面法。其中以求得验算点为目的迭代的二次多项式序列响应面法应用较为广泛，本文给出了该方法的Mattab源程序。提出了基于Mattab的插值响应面法和BP神经网络响应面法，介绍了其在Mattab环境下的实现方法，并进行了三种方法的对比分析。Mattab语言基本元素是矩阵，提供了各种矩阵的运算和操作，其中包含结构可靠度计算中常用的各种数值计算方法工具箱。采用Mattab语言构造响应面函数，进行结构可靠度计算，可充分发挥其矩阵运算功能及各种工具箱的作用，使编程效率大大提高，且语法简便，易于掌握。Mattab语言在可靠度计算中的应用，会对结构可靠性理论的推广使用起到积极推进作用。

Response surface method for structural reliability analysis and its realization with Matlab

The response surface method for structural reliability analysis can be used when performance function is unknown, in which the iterative sequence response surface method of quadratic polynomial is often used. This paper introduces how to realize the programs of the response surface method of interpolation and BP artificial neural network(ANN) in Matlab. The contrast analysis is made among the three methods. The basic element of Matlab is matrix which provides many kinds of operation and calculation of matrix including some toolboxes in common use for the numerical computation of reliability. The advantages of matrix operation and various toolboxes can be fully used if the response surface function is adopted and programmed in Matlab. It is very efficient and convenient to program in Matlab for the reliability calculation. Because of the above advantages of Matlab, its extensive use in the structural reliability analysis will push forward the theory and application of structural reliability.