考虑状态模糊性时广义失效概率计算的鞍点逼近方法  

Saddlepoint Approximation for General Failure Probability with Fuzzy Failure and Fuzzy Safety State

作　　者：李贵杰[1] 吕震宙[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《力学季刊》2010年第1期76-82,共7页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(10572117,50875213);新世纪优秀人才支持计划(NCET-05-0868);航空基础基金(2007ZA53012)和863计划课题(2007AA04Z401)

摘　　要：针对状态具有模糊性的广义可靠性分析问题,提出了一种广义失效概率计算的鞍点逼近方法。所提方法首先将广义失效概率的积分区域依据功能函数的取值离散化,在离散的积分区域中,功能函数对模糊失效域的隶属函数近似保持为常数,从而将模糊可靠性问题转化为随机可靠性问题,进而利用近似的鞍点逼近方法求得广义失效概率。该文给出了所提方法的实现步骤和原理,并用算例验证了所提方法的合理性和可行性。由于基于鞍点逼近的考虑状态模糊性时广义失效概率的计算方法具有较高的效率和精度,因而所提方法具有一定的工程意义。For general reliability analysis with fuzzy failure state and fuzzy safety state, the saddlepoint approximation was proposed to calculate general failure probability. In the integral operation of general failure probability, the integral region was scattered according to the value of performance function. In the scattered integral region, the membership function of the performance function to the fuzzy failure region keeps approximately constant, on which the calculation of the general failure probability was transformed into that of the random failure probability. After the transformation from the general failure probability to the random failure probability was completed, the saddlepoint approximation was employed to ob- tain the general failure probability directly. The concept and the implementation of proposed method were described step by step, and the results of the examples show the rationality and the feasibility of the presented method. Due to the efficiency and precision of saddlepoint approximation for general failure probability with fuzzy failure and fuzzy safety state, the presented method is valuable for engineering.

关 键 词：模糊性 广义失效概率 离散积分区域 隶属函数 鞍点逼近 

分 类 号：TB114.3[理学—概率论与数理统计]