A perceptual evaluation of numerical errors in acoustic FEM simulation for sound quality applications

Abstract

Sound perception is a key aspect in many industrial applications where the acoustic comfort of the final user is relevant. In the case of automotive industry, an important effort is put into prediction of sound quality, which in turn necessitates detailed description of the acoustic problem. The complexity of boundaries and constraints in the typical engineering problems requires the use of numerical methods for this description, and the Finite Elements Method (FEM) is one of the most spread. Numerical methods in general and FEM in particular, can be rather accurate if the simulated model is fine enough. However, this usually means a high computational load, with an associate long computation time and (or) very high hardware requirements. These costs need to be diminished to make future design process faster and more efficient. Several ways to address this problem have been proposed and successfully used, usually based on the idea of making more efficient the mathematical formulation and solution of the simulation. Another option is to consider limits of human hearing system to reduce the accuracy requirements of FE meshes. The basic idea is that, since humans are not able to detect very small differences between sounds, a simulation can have a certain degree of numerical error without affecting the perception. Despite the concept being so simple, its development is rather complex since it requires two complicated fields (numerical analysis and sound perception) to merge into one unique solution. Outcome cannot be forecast in a simple manner, and introductory studies are required to form a solid base on which future research can be built. This paper analyses the sensitivities of human perception with respect to some numerical parameters typical of a FE model for exterior acoustic problems. The concept of adaptive mesh is taken into account and the Perfectly Matched Layer (PML) is used to ensure the Sommerfeld radiation condition, thus introducing a set of parameters to be analyzed. Several sounds are obtained by convolving a source signal with several simulated Transfer Functions (TF). These TFs represent the same acoustic path but are obtained through FE models with different parameters. Psychoacoustic metrics are used to check how the changes in FE models affect the sound properties. Lastly, jury tests are performed to assess how these differences modify human perception.