Construction of probability box model based on maximum entropy principle and corresponding hybrid reliability analysis approach

In this paper, a new method for constructing the probability box (p-box) model is developed based on maximum entropy principle. The distribution characteristics of probability box variable can be described by the nature of moments. The moment conditions are used to ensure the consistency of the cumulative distribution function (CDF), and the shape conditions are adopted to guarantee the validity of the cumulative distribution function. To ensure the uniqueness of the cumulative distribution function, simultaneously, the cumulative distribution function of the probability box variable is reconstructed based on maximum entropy principle. Then, considering that both aleatory and epistemic uncertainty exist in many engineering problems, a reliability analysis approach based on probability and probability box hybrid model is also developed for uncertain structures. Finally, four numerical examples and two engineering examples are investigated to demonstrate the effectiveness of the present method.