Modeling and quantification of model-form uncertainties in eigenvalue computations using a stochastic reduced model

Abstract : A feasible, nonparametric, probabilistic approach for modeling and quantifying model-form uncertainties associated with a computational model designed for the solution of a generalized eigenvalue problem is presented. It is based on the construction of a Stochastic, Projection-based, Reduced-Order Model (SPROM) associated with a High-Dimensional Model (HDM) using three innovative ideas: the substitution of the deterministic Reduced-Order Basis (ROB) with a stochastic counterpart (SROB) featuring a reduced number of hyperparameters; the construction of this SROB on a subset of a compact Stiefel manifold in order to guarantee the linear independence of its column vectors and the satisfaction of any constraints of interest; and the formulation and solution of a reduced-order inverse statistical problem to determine the hyperparameters so that the mean value and statistical fluctuations of the eigenvalues predicted using the SPROM match target values obtained from available data. Consequently, the proposed approach for modeling model-form uncertainties can be interpreted as an effective approach for extracting from data fundamental information and/or knowledge that are not captured by a deterministic computational model, and incorporating them in this model. Its potential for quantifying model-form uncertainties in generalized eigencomputations is demonstrated for a natural vibration analysis of a small-scale replica of an X-56 type aircraft made of a composite material for which ground ground vibration test data are available.
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Charbel Farhat, Adrien Bos, Philip Avery, Christian Soize. Modeling and quantification of model-form uncertainties in eigenvalue computations using a stochastic reduced model. AIAA Journal, American Institute of Aeronautics and Astronautics, 2018, 56 (3), pp.1198-1210. ⟨10.2514/1.J056314⟩. ⟨hal-01625205⟩

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