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

TL;DR

This paper tackles efficient uncertainty propagation in vibroacoustic models with stochastic turbulent boundary layer excitation. It introduces a combined approach that merges a low-rank covariance representation of the stochastic input with intrusive second-order Krylov model order reduction, yielding a ROM capable of accurately estimating both the mean response and the covariance across frequency. By feeding the low-rank input factors directly into the MOR framework, the method achieves a single projection basis that approximates both mean and covariance, significantly reducing the computational burden. The results on a plate-cavity benchmark demonstrate accurate predictions and substantial online speedups, enabling feasible frequency sweeps and uncertainty quantification for vibroacoustic analyses with stochastic loads.

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.

Figures (7)

• Figure 1: Schematic of the examined model with an extruded view of the physical domain. $\Gamma$ denotes the fluid structure interface relevant for the strong coupling.
• Figure 2: Size of singular values of the covariance of the excitation. For simplicity, only the first $50$ singular values are shown here.
• Figure 3: Plate (gray) and cavity (blue) model. The plate is excited by a TBL and radiates sound into the cavity.
• Figure 4: Left: Starting point of this contribution. Right: After low-rank and MOR, significant reductions of dimensions and equations can be obtained.
• Figure 5: Comparison between a displacement DOF of the FOM (red) and ROM (green). The expansion points are marked in blue.