SPARSE PARTIAL LEAST SQUARES REGRESSION-POLYNOMIAL CHAOS EXPANSION METAMODELING METHOD

To circumvent the curse of dimensionality and multicollinearity problems of traditional polynomial chaos expansion approach when analyzing global sensitivity and structural reliability of high-dimensional models, this paper proposes a sparse partial least squares regression-polynomial chaos expansion metamodeling method. Firstly, an initial estimation of polynomial chaos expansion coefficients is obtained with the partial least squares regression. Secondly, according to the principle of maximum sparsity under the allowance of regression error threshold, polynomials which have strong correlation with the structural response are adaptively retained with the penalized matrix decomposition scheme. Next, an updated estimation of the polynomial chaos expansion coefficients is obtained with the partial least squares regression. Sobol sensitivity indices are obtained with a simple post-processing of the expansion coefficients. Finally, the metamodel is greatly simplified by regressing with important inputs, leading to accurate estimations of the failure probability without additional computational cost. The results show that with acceptable accuracies, the new method overperforms the traditional counterpart in terms of computational efficiency when solving high-dimensional global sensitivity and structural reliability analysis problems.