Wave propagation in random media, parameter estimation and damage detection via stochastic Fourier integral operators

TL;DR

This paper introduces a stochastic Fourier integral operator approach for modeling wave propagation in random elastic media, enabling parameter estimation and damage detection even with uncertain material properties.

Contribution

It develops a novel stochastic FIO framework for wave modeling, parameter identification, and damage detection in random media, supported by theoretical and numerical validation.

Findings

Effective damage detection in random media demonstrated

Parameter estimation remains accurate despite material uncertainties

The method successfully distinguishes damaged from undamaged states

Abstract

This paper presents a new approach to modelling wave propagation in random, linearly elastic materials, namely by means of Fourier integral operators (FIOs). The FIO representation of the solution to the equations of motion can be used to identify the elastic parameters of the underlying media, as well as their statistical hyperparameters in the randomly perturbed case. A stochastic version of the FIO representation can be used for damage detection. Hypothesis tests are proposed and validated, which are capable of distinguishing between an undamaged and a damaged material, even in the presence of random material parameters. The paper presents both the theoretical fundamentals as well as a numerical experiment, in which the applicability of the proposed method is demonstrated.