  To tackle the curse of dimensionality and multicollinearity problems of
polynomial chaos expansion for analyzing global sensitivity and reliability of
models with high stochastic dimensions, this paper proposes a novel
non-intrusive algorithm called second order hierarchical partial least squares
regression-polynomial chaos expansion. The first step of the innovative
algorithm is to divide the polynomials into several groups according to their
interaction degrees and nonlinearity degrees, which avoids large data sets and
reflects the relationship between polynomial chaos expansion and high
dimensional model representation. Then a hierarchical regression algorithm
based on partial least squares regression is devised for extracting latent
variables from each group at different variable levels. The optimal interaction
degree and the corresponding nonlinearity degrees are automatically estimated
with an improved cross validation scheme. Based on the relationship between
variables at two adjacent levels, Sobol' sensitivity indices can be obtained by
a simple post-processing of expansion coefficients. Thus, the expansion is
greatly simplified through retaining the important inputs, leading to accurate
reliability analysis without requirements of additional model evaluations.
Finally, finite element models with three different types of structures
verified that the proposed method can greatly improve the computational
efficiency compared with the ordinary least squares regression-based method.
