Hybrid Polynomial Chaos Expansion and proper generalized decomposition approach for uncertainty quantification problems in the frame of elasticity

• Published in: Finite elements in analysis and design Vol. 212; p. 103838
• Main Authors: Wei, Y., Vazeille, F., Serra, Q., Florentin, E.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022; Elsevier
• Subjects: Engineering Sciences; Finite elements; Mechanics; Polynomial Chaos Expansion; Proper generalized decomposition; Uncertainty quantification; Uncertainty quantification; Finite elements; Proper generalized decomposition; Polynomial Chaos Expansion
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2022.103838

Polynomial Chaos Expansion (PCE) is a powerful and flexible metamodeling technique, but suffers from the fact that the number of required training samples grows exponentially with the dimensionality of the problem. Recently, proper generalized decomposition (PGD) has become a popular way to address this challenge since its complexity grows linearly with the dimension of the problem. In this work, we present a new technique called PGD–PCE, which combines the advantages of both methods. The algorithm is based on separate representations and constructed by orthonormal polynomial functions. We test the proposed approach on simple toy problems and engineering finite element problems. The results show that PGD–PCE performs well in terms of accuracy and computational efficiency when dealing with large problems. •We propagate uncertainties in mechanical problems.•We develop a simple to implement and non-intrusive method.•We show that accuracy is preserved while cost drastically decrease.•We illustrate the capabilities of the approach on various numerical tests.