Feasible Probabilistic Learning Method for Model-Form Uncertainty Quantification in Vibration Analysis

Abstract

Recently, a novel probabilistic method for modeling and quantifying model-form uncertainties in a deterministic high-dimensional computational model was proposed and demonstrated for numerous applications in linear vibrations and nonlinear structural dynamics. The method relies on a stochastic projection-based reduced-order model (SPROM) grounded in a randomized reduced-order basis to accelerate the stochastic computations it incurs, and it accounts for all modeling uncertainties introduced by model reduction. It builds the probability model of the SPROM using a small number of hyperparameters, and it determines them so that the mean value and statistical fluctuations of quantities of interest predicted using the SPROM match target values obtained from available data. Hence, it can be interpreted as a probabilistic model learning or updating method. Unfortunately, even though it is performed using a reduced-order model, the hyperparameter identification process can be cost prohibitive. For this reason, the method is reformulated in this paper around the concept of hyper-reduction. Specifically, a reduced version of the mesh underlying the high-dimensional model is constructed and used to hyper-reduce the SPROM. The feasibility of the resulting approach is demonstrated for the model-form uncertainty quantification of generalized eigencomputations performed during what-if scenarios associated with shape changes of a jet engine nozzle.