An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis - Blatman, Géraud; Sudret, Bruno (Probabilistic engineering mechanics, 2010)
Keywords: 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