Application of Bayesian Approach for Damage Characterization in Beams Utilizing Guided Waves

A Bayesian approach for characterizing the damage in beams utilizing guided waves is presented. The proposed methodology treats the damage location, length, depth and the Young's modulus of the material as unknown model parameters. A two-stage optimization approach is applied for damage characterization using simulated annealing algorithm to first guarantee that the solution is close to the global optimum, followed by a standard simplex search method that maximizes the probability density function of a damage scenario conditional on the measurement data. One advantage of the proposed method is that instead of only pinpointing the damage location and extent, the uncertainty associated with the damage characterization results is also quantified. A series of comprehensive numerical case studies utilizing the spectral finite element method to model the wave propagation and scattering at the step damage are used to examine the accuracy and robustness of the proposed methodology. The studies include investigations of the influence of practical situations such as the effects of measurement noise, uncertainty of Young's modulus due to the temperature change, and interference of boundary reflections and scattered waves on the damage characterization results.