A polynomial chaos method for arbitrary random inputs using B-splines

authored by: Christoph Eckert, Michael Beer, Pol D. Spanos
Abstract: Isogeometric analysis which extends the finite element method through the usage of B-splines has become well established in engineering analysis and design procedures. In this paper, this concept is considered in context with the methodology of polynomial chaos as applied to computational stochastic mechanics. In this regard it is noted that many random processes used in several applications can be approximated by the chaos representation by truncating the associated series expansion. Ordinarily, the basis of these series are orthogonal Hermite polynomials which are replaced by B-spline basis functions. Further, the convergence of the B-spline chaos is presented and substantiated by numerical results. Furthermore, it is pointed out, that the B-spline expansion is a generalization of the Legendre multi-element generalized polynomial chaos expansion, which is proven by solving several stochastic differential equations.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): University of Liverpool
Tongji University
Rice University
Type: Article
Journal: Probabilistic Engineering Mechanics
Volume: 60
ISSN: 0266-8920
Publication date: 04.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Civil and Structural Engineering, Nuclear Energy and Engineering, Condensed Matter Physics, Aerospace Engineering, Ocean Engineering, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.probengmech.2020.103051 (Access: Closed)