Efficient low rank model order reduction of vibroacoustic problems under stochastic loads

TL;DR

This paper introduces a combined low-rank SVD and Krylov subspace-based model order reduction method to efficiently propagate stochastic uncertainties in vibroacoustic models, significantly reducing computational costs.

Contribution

It presents a novel approach integrating SVD-based low-rank approximation with Krylov subspace MOR for efficient uncertainty propagation in vibroacoustic problems.

Findings

Reduces evaluation cost of large-scale vibroacoustic models

Efficiently approximates output uncertainties with fewer samples

Potential for significant computational savings in stochastic simulations

Abstract

This contribution combines a low-rank matrix approximation through Singular Value Decomposition (SVD) with second-order Krylov subspace-based Model Order Reduction (MOR), in order to efficiently propagate input uncertainties through a given vibroacoustic model. The vibroacoustic model consists of a plate coupled to a fluid into which the plate radiates sound due to a turbulent boundary layer excitation. This excitation is subject to uncertainties due to the stochastic nature of the turbulence and the computational cost of simulating the coupled problem with stochastic forcing is very high. The proposed method approximates the output uncertainties in an efficient way, by reducing the evaluation cost of the model in terms of DOFs and samples by using the factors of the SVD low-rank approximation directly as input for the MOR algorithm. Here, the covariance matrix of the vector of unknowns can efficiently be approximated with only a fraction of the original number of evaluations. Therefore, the approach is a promising step to further reducing the computational effort of large-scale vibroacoustic evaluations.