基于信息熵理论中的含模糊参数的响应面法

利用信息熵理论中的概率熵与模糊熵之间的关系式，建立两类不同性质变量之间的转换关系，然后利用这种关系建立一种新型的含有模糊随机变量的响应面法，或根据不确定的信息量，用最大熵法直接建立近似的概率密度函数表达式，算例显示本文方法的可行性和有效性，最后指出，如果结合并行算法，可以从根本上解决响应面法计算效率不高的缺点，使响应面法可用于大型结构的可靠性分析。

RESPONSE SURFACE METHOD IN FUZZY PARAMETERS UNDER THE ENTROPY

Firstly, to estimate the reliability of uncertain structural systems by considering both the randomness in some of design parameters and the fuzzy imprecision in some other parameters representing the conditions of the systems, two kinds of methods are presented. In the first method, a fuzzy parameter is transformed into a random parameter using the entropy concept. In the second method, a fuzzy parameter is replaced by a similar random parameter, which probability density function is a polynomial expression using the maximum entropy. In this way the fuzz-random reliability of the engineering structures is estimated using well-established theories of probability. According to the methods a new fuzz-random structural reliability analysis method-Response surface method (RSM) is presented in this paper. Examples show the accuracy and efficiency of the RSM with the contest of highly nonlinear and structurally complex fuzzy-random reliability problems. Finally, after on the basis of analyzing the RSM process, it is pointed that the RSM can be easily combined with the parallel algorithm and the computing quantity of the RSM solution can be reduced greatly. From this point of view, the proposed RSM can be totally applied in the fuzzy reliability analysis of the large complex structural systems.