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.

中文翻译：

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通过动态响应分析进行确定性和随机损坏检测

本文提出了一种弹性材料损伤检测方法，该方法基于分析由声信号激发的材料的时间相关（动态）响应。案例研究由实验测量及其数学分析组成。声波数学模型的决定性参数（波速和阻尼系数）通过将测量数据与数学模型预测的数值评估精确解进行比较来校准。校准是通过最小化随时间的平方误差来确定性地完成的，也是通过贝叶斯方法随机地完成的，通过 Metropolis-Hastings 算法实现。所得参数的后验分布可用于构建贝叶斯损伤检验。