A most probable point method for probability distribution construction

Abstract

With nonlinearity and uncertainty existing in engineering problems, it is important to predict the probability distribution of a response of an engineering model. The probability distribution is often constructed without sufficient accuracy due to a high computational cost. In this paper, a most probable point (MPP) method for the probability distribution construction is proposed. First, predictive models of the MPP components are established based on the Gaussian mixture distribution (GMD) and the inverse first-order reliability method. A mixture of first- and second-order reliability methods is then used to calculate discrete points of the cumulative distribution function (CDF). Finally, the CDF of the response is constructed by the GMD. A mathematical example and three engineering examples are used to verify the effectiveness of the proposed method.