A neural network copula function approach for solving joint basic probability assignment in structural reliability analysis

Abstract

Applying evidence theory to structural reliability analysis under epistemic uncertainty, it is necessary to consider the correlation of evidence variables. Among them, solving the joint basic probability assignment (BPA) of the evidence variables is a crucial link. In this study, a solution method of joint BPA based on neural network copula function is proposed. This method is to automatically construct copula function through neural network, which avoids the process of selecting the optimal copula function. Firstly, the neural network copula function is constructed based on the sample set of evidence variables. Then, the expression for solving the joint BPA using the neural network copula function is derived through vectors. Furthermore, the expression is used to map the marginal BPA of evidence variables to joint BPA, thus realizing the solution of joint BPA. Finally, the effectiveness of this method is verified by three examples. The results show that the neural network copula function describes the data distribution better than the optimal copula function selected by the traditional method. In addition, there is actually an error in solving the reliability intervals using the traditional optimal copula function method, whereas the results of this paper's neural network copula function method are more accurate and better for decision making.