A local adaptive sampling method for reliability-based design optimization using Kriging model

Significance statement

Unlike deterministic design optimization, reliability-based design optimization (RBDO) considers uncertainties of design variables stemming from various sources and can yield a reliable design. However, the practical application of RBDO is hindered by its huge computational cost during structure reliability evaluating process.To overcome this problem, meta-model method is used, among which the Kriging is the most promising one. However, the accuracy of Kriging model depends directly on how to select the sample points.

Sampling strategy is crucial in constructing the meta-model, which can be classified into one-stage sampling and sequential sampling. In one-stage sampling, the meta-model is built only once. The accuracy of meta-model will not be improved afterwards. Different from one-stage sampling, with the experiments progressing, new samples are added into the model and the meta-model gets updated. Therefore, the sequential sampling allows engineers to control the sampling process. Also, in most cases, it’s more efficient than one-stage sampling method. Adaptive sampling is one of the sequential sampling methods where the new sampling point is relevant to the previous meta-model.

The local adaptive sampling method (LAS) is such an adaptive sampling method which is proposed to improve the efficiency and accuracy of RBDO using Kriging model. As we all know, in the design optimization and reliability analysis process, the local region in the vicinity of the current design point is more important than other region which should be fitted accurately, and the limit state constraint boundaries within the local region are more critical than the non-boundary domain. Therefore, after initial sampling, the local adaptive sampling method will add new samples along the limit state constraint boundaries within the local region around the current design point, which can make the Kriging models for the probabilistic constraint functions more precise within the critical design region. Also the sampling process will be more effective. The size of local adaptive sampling region is adaptively defined according to the nonlinearity of the constraint function in the vicinity of the current design point. The constraint boundary sampling criterion and mean squared error criterion are adaptively used to locate sample points for the probabilistic constraints in RBDO. The simulation reliability method, Monte Carlo simulation (MCS), is selected to perform reliability analysis in this paper.

The accuracy and efficiency of the proposed method are demonstrated by several examples.

The sampling process of LHS, SS, CBS and LAS for example 1 are shown in the flowing figure.

Fig. 1 The sampling process of LHS, SS, CBS and LAS for example 1

A local adaptive sampling method for reliability-based design optimization using Kriging model

Journal Reference

Structural and Multidisciplinary Optimization, March 2014, Volume 49, Issue 3, pp 401-416.

Zhenzhong Chen, Haobo Qiu, Liang Gao, Xiaoke Li, Peigen Li.

The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074, Wuhan, People’s Republic of China.