Response Surface Method Using Sequential Sampling for Reliability-Based Design Optimization

Abstract

Traditional RBDO requires the sensitivity for both the most probable point (MPP) search in inverse reliability analysis and design optimization. However, the sensitivity is often unavailable or difficult to compute in complex multi-physics or multidisciplinary engineering applications. Hence, the response surface method (RSM) is often used to calculate both function evaluations and sensitivity effectively. Researchers have been developing the RSM for decades, and yet are still searching for an approach with an efficient sampling method for fast convergence while meeting the accuracy criteria. This paper proposes a new adaptive sequential sampling method to be integrated with the Kriging method for RBDO. By using the bandwidth of the prediction interval from the Kriging method, a new sampling strategy and a new local response surface accuracy criteria are proposed. In this sequential sampling method, the response surface is initiated using very few samples. An additional sampling point will then be determined by finding the point that has the largest absolute ratio between the bandwidth of the prediction interval and the predicted response within a neighboring area of current point of interest. The insertion of additional sampling will continue until the accuracy criterion of the response surface in the neighborhood of the current point of interest is achieved. Case studies show this proposed adaptive sequential sampling technique yields better result in terms of convergence speed compared with other sampling methods, such as the Latin hypercube sampling and the grid sampling, when the same sample size is used. Both a highly nonlinear mathematical example and a vehicle durability engineering example show that the proposed RSM yields accurate RBDO results that are comparable to the sensitivity-based RBDO results, as well as significant savings in computational time for function evaluation and sensitivity computation.