Bending waves focusing in arbitrary shaped plate-like structures: Study of temperature effects, development of a digital twin and of an associated neural-network based compensation procedure

Abstract

Advanced automotive audio applications are more and more demanding with respect to the visual impact of loudspeakers while still requiring more and more channels for high quality spatial audio rendering. Removing classical heavy and large electrodynamic loudspeakers and using car interior plate-like structures driven by state of the art spatial sound algorithms appear as a promising solution to tackle both issues. However, to meet spatial audio rendering constraints, the bending waves generated within car interior plate-like structures must be focused at a given position and to a certain extent within the host structure. Theoretically, this means being able to invert in a robust manner the spatio-temporal wave propagation operator for the generated bending waves to fit a given target shape. The propagation operator inversion method considered here is the spatio-temporal inverse filtering (STIF) method based on the knowledge of the propagation operator on a regular spatial grid over the structure at a given temperature. However, in a car interior a high temperature variations exist and can adversely impact the performances of the STIF method, mainly because dynamical properties of the host structure (built up with polypropylene in most cases) largely vary within this temperature range. Even if the STIF method has already been adapted and assessed in the context of automotive audio reproduction, no study dealing with the effects of temperature on the STIF method and providing potential mitigation procedures avoiding experimental measurements at each temperature has been reported. To address that issue, the influence of temperature on the behavior of a polypropylene plate is first experimentally quantified. A model updating method is used to build a finite-element model of the plate taking into account temperature effects. This digital twin of the host-structure is then used to assess the influence of the temperature on the STIF method. A neural network based controller is finally trained and validated on the digital twin in order to compensate for the effects of temperature on STIF filters. Obtained results demonstrate that this procedure successfully allows to compensate for temperature effects on the STIF method applied to polypropylene plate with very limited experimental needs, thus paving the way through an industrial development of such approaches.