In most cases, engineering problems are expressed in terms of mathematical models. The sought primary variables are usually calculated under consideration of certain boundary conditions. However, it is very costly and challenging to determine the boundary conditions for vibroacoustic systems experimentally. Perturbations are introduced into a model, if the boundary conditions are not determined correctly or approximated due to simplified assumptions. It is preferred to measure the primary variable, i.e. the sound pressure at specific locations in the system, instead of measuring the boundary conditions. The information about the sound pressure can be used to solve the model inversely – i.e. to infer boundary conditions or system parameters from the observations of the primary variable. A direct solution of the inverse problem is often formulated in terms of an optimization problem. However, direct solution approaches often suffer from ill-posedness. Direct solutions hence frequently yield instable solutions for the inferred parameters. A statistical approach for the primary variable as well as for the sought system parameters offers advantages to avoid the ill-posedness.
An open-source tool is developed at the Chair of Vibroacoustics of Vehicles and Machines in order to determine the most likelihood values of system parameters for a given set of sound pressure measurement data. The tool is based on statistical inference (Bayes method). Research at the institute focuses on the implementation of the tool as well as on model reduction approaches to speed up the solution of inverse problems. Furthermore, the applicability of the tool to other current research areas in vibroacoustics is a main research topic. The quantification of surface impedances of large areas composed of different materials, such as in a car cabin, is one major application area under investigation. The iterative model updating process allows for an optimization of damping properties in a system. The localization of sound sources on large structural surfaces is another main purpose of the inverse tool. By this, sound radiation contributions from the structure to the interior of for example an aircraft cabin can be analyzed efficiently. The determination of material parameters for surrogate models of porous media or acoustic metamaterials is another scope of the vibroacoustic inverse framework.