一类改进最大熵方法的可调参数分析

Adjustable parameter analysis of an improved maximum entropy method

在结构可靠性分析中,引入含可调参数的转换函数能对传统的最大熵方法进行改进,获得更高的失效概率预测精度。但是,此可调参数的最佳取值很难确定。针对这一问题,引入概率守恒方程,从功能函数转换前后所得概率密度函数出发,建立其最大熵值的变化关系,给出转换前后最大熵值之差的理论形式。通过对三种典型单调非线性转换函数开展算例研究,发现功能函数转换前后的最大熵值之差与转换函数的最佳可调参数值有关。改变可调参数值驱使最大熵值之差变化的同时,改进最大熵方法能遍历到更好的失效概率估计值。

In structural reliability analysis,the classical maximum entropy method can be improved to estimate the failure probability more accurately by introducing the transformation function with an adjustable parameter.But it is still difficult to determine the best value of the adjustable parameter.To solve this problem,in this paper the relationship between the maximum information entropies before and after the transformation is established from the probability density functions of the original and transformed performance functions by introducing the probability conservation equation.The theoretical form of the difference between the maximum entropy values before and after the transformation is also obtained.Three typical monotone nonlinear transformation functions are studied in numerical examples.It is found that the difference between maximum entropy values before and after transformation is related to the selection of the optimal adjustable parameters.When the difference between the corresponding maximum entropy values is modulated according to the changing of the adjustable parameter,a better estimation of the failure probability can be obtained by using the improved maximum entropy method with the transformation function.