Partial least squares-based polynomial chaos Kriging for high-dimensional reliability analysis

To alleviate the computational overhead of high-dimensional reliability analysis, a cost-effective surrogate model called PPCK is proposed by combining partial least squares (PLS) and polynomial chaos Kriging (PCK) in a non-intrusive way. Three major contributions are made in PPCK. First, when calibrating a PCK in PLS-based reduced space, the multivariate polynomial basis orthonormal with respect to those reduced variables is built by a data-driven approach. Second, to identify the optimal number of reduced variables, rational identification criteria are defined for three different performance metrics. Third, a parallel procedure coupled with adaptive adjustment is devised to replace the traditional progressive addition of reduced variables, so as to accelerate the workflow of PPCK. The performances of both the proposed PPCK and the associated reliability algorithm are illustrated on one benchmark analytical function and two practical engineering problems. The results show that, different from PCK whose training time rises dramatically during adaptive enrichment process, PPCK provides sufficient predictive accuracy, but maintains relatively low training time consistently. Then, PPCK-based reliability algorithm achieves favorable savings in terms of both the number of computational model evaluations and total computational time.