Second order hierarchical partial least squares regression-polynomial chaos expansion for global sensitivity and reliability analyses of high-dimensional models

TL;DR

This paper introduces a novel hierarchical partial least squares regression-polynomial chaos expansion method to efficiently perform global sensitivity and reliability analyses on high-dimensional models, overcoming the curse of dimensionality and multicollinearity.

Contribution

It proposes a new non-intrusive algorithm that groups polynomials by interaction and nonlinearity degrees, automatically estimates optimal degrees, and simplifies Sobol' sensitivity analysis for high-dimensional models.

Findings

Significantly improves computational efficiency over traditional methods.

Accurately estimates Sobol' sensitivity indices from expansion coefficients.

Validated on finite element models with different structures.

Abstract

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.