Statistical Structural Damage Detection of Functionally Graded Euler–Bernoulli Beams Based on Element Modal Strain Energy Sensitivity

In practical engineering, uncertainties inevitably exist in the models and measurement data used for structures. Therefore, a statistical strategy related to damage detection methods become crucial. In this paper, a probabilistic statistical damage detection method for FG Euler–Bernoulli beam structures is proposed, extending the approach originally developed for isotropic materials. Our approach determines the probability of damage occurrence for each element, which aids in evaluating whether beam structures have been damaged. This evaluation is based on integrating the sensitivity of modal strain energy for each element with the perturbation method. To demonstrate the effectiveness and accuracy of the proposed method, several numerical examples are investigated. These examples include a simply supported FG Euler–Bernoulli beam subjected to both single and multiple element damages. The influence of gradient index, damage severity, boundary condition, and noise level on the accuracy of detection are also considered. The studies demonstrate that the probability of damage for each element remains relatively stable despite variations in the gradient indices. For the damaged elements, these probabilities approach 1, indicating that the proposed method effectively identifies damage in FG beams even when the gradient index varies. Additionally, as the level of damage increases, the accuracy of damage detection tends to improve. However, varying boundary conditions can substantially affect the outcomes of damage identification, potentially leading to inconsistencies in results. Furthermore, our proposed method demonstrates excellent resistance against noise levels of up to 5%. We also found that different boundary conditions have a great impact on the damage detection.