Multi-fidelity models based on Gaussian processes in acoustic applications

Abstract

Accurate predictions are generally accompanied with high costs and expenses. As a conesquence, system observations can only be generated for a few samples. The idea of multi-fidelity modeling aims to merge observations from different models of varying complexities and costs. This contribution introduces multi-fidelity models applied to acoustic problems. Therefore, we deploy models with different fidelity levels to treat the frequency-dependent Helmholtz equation. While the spatial solution is acquired with the boundary element method, Gaussian processes are used as surrogates to approximate the system’s response in the frequency dimension. This way, multi-fidelity models are adopted to efficiently approximate the solution of the Helmholtz equation for a certain frequency range. For validation purposes, the low frequency booming noise problem occurring in vehicle cabins is treated. Our findings demonstrate that multi-fidelity models yield an accurate approximation. In addition, the computational costs are reduced when compared with the high-fidelity solution at each frequency. In the sense of a Bayesian technique, multi-fidelity models based on Gaussian processes allow to consider uncertainties. Beyond fast and accurate predictions, the proposed method paves the way for accelerated decision-making processes in early design stages, where uncertainties due to limited information on the model or simplifying assumptions are omnipresent.