Information uncertainty evaluated by parameter estimation and its effect on reliability-based multiobjective optimization

Abstract

Reliability-based multiobjective optimization (RBMO) is a method that integrates multiobjective optimization with a reliability analysis. The method is useful for a large or complicated design problem such as aerospace structure design. Reliability analysis generally requires the probabilistic distribution parameters of random variables such as the mean and standard deviation. However, for an actual design problem, the probabilistic parameters are sometimes estimated with insufficient accuracy because of a limited number of experiments. In that case, the uncertainty in the distribution parameter is not negligible. This study proposes the evaluation method to estimate the effect of the information uncertainty at first, where the uncertainty is evaluated by using the confidence interval. Some numerical examples illustrates the effectiveness of the proposed method in comparison with a conventional method, Gibbs sampling. Then, the effect of the parameter uncertainty on the RBMO is illustrated through numerical examples. The RBMO problem is formulated by using the satisficing trade-off method (STOM), where the multiobjective optimization problem is transformed into the equivalent single-objective optimization method. For the reliability-based design optimization, a modified SLSV (single-loop-single-vector) method is adopted for the computational efficiency. The effects of the parameter uncertainty on the selected Pareto solutions according to the aspiration level are investigated by using the confidence intervals of the Pareto solutions.