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结合贝叶斯公式、最大熵法和条件概率马尔科夫链法,发展了一种高效求解功能函数的累积分布函数(CDF)的方法。该方法首先由贝叶斯公式将功能函数CDF转换为后验分布和全局失效概率的数学表达式,接着由条件概率马尔科夫链法求得全局失效概率,由最大熵法求得后验分布,进而求得功能函数的CDF。与传统方法相比,该方法在先验分布均值附近区域求解精度高,计算代价与概率水平无关,在求解小失效概率附近极限状态的CDF时具有极高的求解效率。
Combining the Bayesian formula, the maximum entropy method and the conditional probability Markov chain method, an efficient method for solving the cumulative distribution function (CDF) of functional functions is developed. In this method, the functional function CDF is first transformed into the mathematical expression of posterior distribution and global failure probability by the Bayesian formula, then the global failure probability is obtained by the conditional probability Markov chain method, and the posterior distribution is obtained by the maximum entropy method , And then find the function of the CDF. Compared with the traditional method, this method has high solution accuracy in the vicinity of the a priori distribution mean, and the computational cost has nothing to do with the probability level. It has a very high solution efficiency when solving the CDF in the limit state near the small failure probability.