基于通用生成函数的可靠性分析方法  

Reliability analysis method based on universal generating function

作　　者：张小玲[1] 黄洪钟[1] 肖宁聪[1] 汪忠来[1] 何俐萍[1] 

机构地区：[1]电子科技大学机械电子工程学院,四川成都611731

出　　处：《机械设计》2011年第11期93-96,共4页Journal of Machine Design

摘　　要：提出了基于通用生成函数的可靠性分析方法。首先把连续随机变量离散化,并用离散变量的概率质量函数予以表示;其次根据通用生成函数运算法则计算极限状态函数的概率质量函数,再对极限状态函数的概率质量函数求各阶导数,得到极限状态函数的各阶矩;最后利用极大熵原理建立设计优化问题的数学模型,求解极限状态函数的概率密度函数和累积分布函数。文中所提出的方法避免了对极限状态函数进行灵敏度分析,也不需要求解设计验算点(MostProbable Point,MPP),适于求解混合离散变量和高度非线性问题。实例分析和与蒙特卡洛仿真对比结果验证了所提方法的有效性。Uncertainty is inevitable in practical engineering problems. Probabilistic reliability method is one of the uncertainty analysis methods. Integral calculation is needed in the probabilistic reliability method. However, it is very difficult or even impossible to obtain an analytical solution to the probabilistic reliability method based on sensitivity when involving high dimensionality and nonlinear integration. Therefore, a reliability analysis method based on the universal generating function is proposed. Firstly, the continuous random variables are diseretized, and the probability mass function （PMF） is used to describe the discrete variables. Secondly, the operation algorithm by the universal generating function is used to calculate the PMF of the limit state function. Thirdly, the mo- ments of the limit state function is analyzed by successively differentiating the PMF of the limit state function. Finally, an optimization design problem is formulated based on maximal entropy principle for estimating the probability density function and the cumulative distribution function of the limit state function. The sensitivity analysis and the calenlation for solving the most probable failure points （MPP） are avoided in the proposed method, therefore, this method is proper for mixed-discrete and highly nonlinear problems. Comparison of the results from the proposed method and the Monte Carlo simulation method are presented to demonstrate the efficiency of the proposed method.

关 键 词：可靠性 通用生成函数 离散变量 概率质量函数 极限状态函数 

分 类 号：TB1[一般工业技术]