# Deterministic and stochastic damage detection via dynamic response analysis

## TL;DR

This paper introduces a method for damage detection in elastic materials using dynamic response analysis, combining deterministic and Bayesian stochastic calibration of wave parameters to identify damage.

## Contribution

It presents a novel approach that integrates deterministic and Bayesian stochastic methods for calibrating acoustic wave parameters in damage detection.

## Key findings

- Successful calibration of wave speed and damping coefficient
- Bayesian posterior distributions enable damage testing
- Experimental validation supports method effectiveness

## Abstract

The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. A case study is presented consisting of experimental measurements and their mathematical analysis. The decisive parameters (wave speed and damping coefficient) of a mathematical model of the acoustic wave are calibrated by comparing the measurement data with the numerically evaluated exact solution predicted by the mathematical model. The calibration is done both deterministically by minimizing the square error over time and stochastically by a Bayesian approach, implemented through the Metropolis-Hastings algorithm. The resulting posterior distribution of the parameters can be used to construct a Bayesian test for damage.