Conservative Surrogate Model Using Weighted Kriging Variance for Sampling-Based RBDO.

摘要

In sampling-based reliability-based design optimization (RBDO) of practical complex engineering applications, the Monte Carlo simulation (MCS) for stochastic sensitivity analysis and probability of failure calculation is based on the prediction from the surrogate model for the performance functions. When the number of samples used to construct the surrogate model is small, the prediction from the surrogate model becomes inaccurate and thus MCS becomes inaccurate as well. Therefore, to count in the prediction error from the surrogate model and assure the obtained optimum design from sampling-based RBDO satisfies the probabilistic constraints, a conservative surrogate model is needed. In this paper, a conservative surrogate model is constructed using the weighted Kriging variance where the weight is determined by the relative change in the corrected Akaike information Criterion (AICc) of the dynamic Kriging model. The proposed conservative surrogate model performs better than the traditional Kriging prediction interval approach because it does not generate unnecessary local optimum. It also performs better than the constant safety margin approach because it adaptively counts in the uncertainty of the surrogate model in the place that the samples are sparse. Numerical examples show that using the proposed conservative surrogate model for sampling-based RBDO is necessary to assure that the optimum design satisfies the probabilistic constraints when the number of samples is limited.