An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis

• Published in: Probabilistic engineering mechanics Vol. 25; no. 2; pp. 183 - 197
• Main Authors: Blatman, Géraud, Sudret, Bruno
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.2010; Elsevier
• Subjects: Adaptive stochastic finite elements; Algorithms; Applied sciences; Building structure; Buildings. Public works; Chaos theory; Computational efficiency; Construction (buildings and works); Exact sciences and technology; Experimental design; Finite element method; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Mathematics; Personal computers; Physics; Probability and statistics; Probability theory and stochastic processes; Regression; Response surfaces; Sciences and techniques of general use; Sequential experimental design; Solid mechanics; Sparse polynomial chaos expansion; Statistics; Stochastic processes; Stochasticity; Structural and continuum mechanics; Structural reliability; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Regression; Structural reliability; Adaptive stochastic finite elements; Sparse polynomial chaos expansion; Sequential experimental design; Response surfaces; Chaos; Adaptive algorithm; Cross validation; Random vector; Stochastic process; Modeling; Adaptive method; Finite element method; Sparse matrix; Probability learning; Random variable; Statistical analysis; Probabilistic approach; Sequential design; Frame construction; Well posed problem; Orthogonal polynomial; Program verification; Stochastic analysis; Truss structure; Experimental design; Deterministic model; Galerkin method

Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which make...