Multifidelity Uncertainty Quantification Using Non-Intrusive Polynomial Chaos and Stochastic Collocation

Leo Wai-Tsun Ng, Michael Eldred
2012 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference20th AIAA/ASME/AHS Adaptive Structures Conference14th AIAA   unpublished
This paper explores the extension of multifidelity modeling concepts to the field of uncertainty quantification. Motivated by local correction functions that enable the provable convergence of a multifidelity optimization approach to an optimal high-fidelity point solution, we extend these ideas to global discrepancy modeling within a stochastic domain and seek convergence of a multifidelity uncertainty quantification process to globally integrated high-fidelity statistics. For constructing
more » ... or constructing stochastic models of both the low fidelity model and the model discrepancy, we employ stochastic expansion methods (nonintrusive polynomial chaos and stochastic collocation) computed from sparse grids, where we seek to employ a coarsely resolved grid for the discrepancy in combination with a more finely resolved grid for the low fidelity model. The resolutions of these grids may be statically defined or determined through uniform and adaptive refinement processes. Adaptive refinement is particularly attractive, as it has the ability to preferentially target stochastic regions where the model discrepancy becomes more complex; i.e., where the predictive capabilities of the low-fidelity model start to break down and greater reliance on the high fidelity model (via the discrepancy) is necessary. These adaptive refinement processes can either be performed separately for the different sparse grids or within a unified multifidelity algorithm. In particular, we propose an adaptive greedy multifidelity approach in which we extend the generalized sparse grid concept to consider candidate index set refinements drawn from multiple sparse grids. We demonstrate that the multifidelity UQ process converges more rapidly than a single-fidelity UQ in cases where the variance of the discrepancy is reduced relative to the variance of the high fidelity model (resulting in reductions in initial stochastic error) and/or where the spectrum of the expansion coefficients of the model discrepancy decays more rapidly than that of the high-fidelity model (resulting in accelerated convergence rates).
doi:10.2514/6.2012-1852 fatcat:5ch2focigbhfpnl5g6xmupftqi