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.

由于工程问题中存在非线性和不确定性，因此预测工程模型响应的概率分布非常重要。由于高的计算成本，常常没有足够的精度来构造概率分布。本文提出了一种概率分布构造的最可能点（MPP）方法。首先，基于高斯混合分布（GMD）和逆一阶可靠性方法，建立了MPP组件的预测模型。然后使用一阶和二阶可靠性方法的混合来计算累积分布函数（CDF）的离散点。最后，响应的CDF由GMD构建。