A new method to optimize the truncated PCE order of collocation-based SRSM in reliability analysis and its application to geotechnical problems

Purpose The collocation-based stochastic response surface method (CSRSM) is widely used in geotechnical reliability analyses due to its efficiency and accuracy. Determining the optimal truncated order of the associated polynomial chaos expansion (PCE) is important, as it may strongly affect the practical applicability of CSRSM. Design/methodology/approach This study investigates the performance of different optimal order selection strategies used in the CSRSM and proposes a new cross-order validation method. First, several methods commonly used for optimal order selection are briefly reviewed, and their merits and limitations for reliability analyses are discussed. Then, an improved optimal order selection method that achieves a better trade-off between efficiency and accuracy is proposed. Findings In total, ten simple mathematical examples from the literature are employed to perform a preliminary test on the proposed method, and a comparative study is conducted to demonstrate its advantages with respect to some other existing methods. Practical implications A total of three typical geotechnical problems are employed to demonstrate the performance of the proposed method in geotechnical practice. Originality/value An improved optimal order selection method that achieves a better trade-off between efficiency and accuracy is proposed. The threshold value of the deterministic coefficient used for the proposed method is discussed.