Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation

Abstract

Since variances in the input variables of the engineering system cause subsequent variances in the product output performance, reliability-based design optimization (RBDO) is getting much attention recently. However, RBDO requires expensive computational time. Therefore, the response surface method is often used for computational efficiency in solving RBDO problems. A method to estimate the effect of the response surface error on the RBDO result is developed in this paper. The effect of the error is expressed in terms of the prediction interval, which is utilized as the error metric for the response surface used for RBDO. The prediction interval provides upper and lower bounds for the confidence level that the design engineer specified. Using the prediction interval of the response surface, the upper and lower limits of the reliability are computed. The lower limit of reliability is compared with the target reliability to obtain a conservative optimum design and thus safeguard against the inaccuracy of the response surface. On the other hand, in order to avoid obtaining a design that is too conservative, the developed method also constrains the upper limit of the reliability in the design optimization process. The proposed procedure is combined with an adaptive sampling strategy to refine the response surface. Numerical examples show the usefulness and the efficiency of the proposed method.