Reliability-Based Design With the Mixture of Random and Interval Variables

In Reliability-Based Design (RBD), uncertainties usually imply for randomness. Nondeterministic variables are assumed to follow certain probability distributions. However, in real engineering applications, some of distributions may not be precisely known or uncertainties associated with some uncertain variables are not from randomness. These nondeterministic variables are only known within intervals. In this paper, a method of RBD with the mixture of random variables with distributions and uncertain variables with intervals is proposed. The reliability is considered under the condition of the worst combination of interval variables. In comparison with traditional RBD, the computational demand of RBD with the mixture of random and interval variables increases dramatically. To alleviate the computational burden, a sequential single-loop procedure is developed to replace the computationally expensive double-loop procedure when the worst case scenario is applied directly. With the proposed method, the RBD is conducted within a series of cycles of deterministic optimization and reliability analysis. The optimization model in each cycle is built based on the Most Probable Point (MPP) and the worst case combination obtained in the reliability analysis in previous cycle. Since the optimization is decoupled from the reliability analysis, the computational amount for MPP search is decreased to the minimum extent. The proposed method is demonstrated with a structural design example.