Concepts for Frequency Sweeps and Efficient Repeated Analysis in the Context of Vibroacoustic Optimization and Uncertainty Quantification

This paper aims at passive noise control for vibroacoustic problems, which are analyzed by finite and boundary element techniques. The author distinguishes interior and exterior problems mainly because of the quantities used as the objective function to assess the acoustic quality. For interior problems, it is common to use local quantities such as the sound pressure at a field point or, in rare cases, energy density at a field point. The situation is different for exterior problems where the radiated sound power accounts for a suitable and global quantity to assess the emission from a vibrating structure. For most engineering purposes, the assessment requires frequency sweeps in which the problem needs to be solved at many discrete frequencies. In vibroacoustic optimization and in sampling based uncertainty quantification, it is very common that structural parameters are varied, while the acoustic field remains the same throughout the entire process. We will review concepts and recent developments of efficient frequency sweeps and repeated analysis with unmodified fluid domain. For many practical cases, the situation for interior problems is rather simple to survey. Either the authors have applied a modal analysis and used a modal superposition for the frequency sweep and repeated analysis, or the concept of unmodified acoustic transfer vectors is applied. Both concepts are quite successful as long as certain conditions are fulfilled. For exterior problems, a modal superposition is possible but, so far, only for a limited number of cases practically applicable as discussed herein. The concept of using acoustic transfer vectors becomes inefficient since the evaluation of the radiated sound power asanintegral over a closed enveloping surface would require an excessively high amount of storage capacity. Therefore, other concepts are being followed. For frequency sweeps, a number of methods are using a frequency interpolation based on a limited number of discrete sample frequencies. Often, these techniques are used together with Krylov–subspace model order reduction techniques. Further recently published approaches investigate low-rank approximations, greedy algorithms, and deflated Krylov subspace techniques. A completely different kind of approach is based on multi–fidelity models and Gaussian processes. The field of efficient repeated analysis shows some interesting developments, which can be easily applied to sampling based uncertainty quantification but do not seem to be easily and generally applied to optimization.