Surface shape reconstruction from phaseless scattered acoustic data using a random forest algorithm

Recent studies have demonstrated that acoustic waves can be used to reconstruct the roughness profile of a rigid scattering surface. In particular, the use of multiple microphones placed above a rough surface as well as an analytical model based on the linearised Kirchhoff integral equations provides a sufficient base for the inversion algorithm to estimate surface geometrical properties. Prone to fail in the presence of high noise and measurement uncertainties, the analytical approach may not always be suitable in analysing measured scattered acoustic pressure. With the aim to improve the robustness of the surface reconstruction algorithms, here it is proposed to use a data-driven approach through the application of a random forest regression algorithm to reconstruct specific parameters of one-dimensional sinusoidal surfaces from airborne acoustic phase-removed pressure data. The data for the training set are synthetically generated through the application of the Kirchhoff integral in predicting scattered sound, and they are further verified with data produced from laboratory measurements. The surface parameters from the measurement sample were found to be recovered accurately for various receiver combinations and with a wide range of noise levels ranging from 0.1% to 30% of the average scattered acoustical pressure amplitude.