Inverse Problem Solving for a Porous Acoustical Multilayered System Based on the Transfer Matrix Approach

The acoustical modelling of multilayered systems is crucial for researchers and engineers aiming to evaluate and control the behaviour of complex media and to determine their internal properties. In this work, we first develop a forward model describing the propagation of acoustic waves through various types of materials, including fluids, solids, and poroelastic media. The model relies on the classical theoretical frameworks of Thomson and Haskell for non-porous layers, while Biot’s theory is employed to describe wave propagation in poroelastic materials. The propagation is mathematically treated using the transfer matrix method, which links the acoustic displacement and stress at the extremities of each layer. Appropriate boundary conditions are applied at each interface to assemble all local matrices into a single global matrix representing the entire multilayer system. This forward model allows the calculation of theoretical transmission coefficients, which are then compared to experimental measurements to validate the approach proposed. Secondly, this modelling framework is used as the basis for solving inverse problems, where the goal is to retrieve unknown internal parameters, such as mechanical or acoustic properties, by minimizing the discrepancy between simulated and experimental transmission spectra. This inverse problem approach is essential in non-destructive evaluation applications, where direct measurements are often unfeasible.