A boundary displacement-based defect identification method inspired by topology optimization

Nondestructive testing is crucial for appropriate structural health monitoring. This paper proposes a density-based topology optimization method for defect identification. The proposed numerical method maintains the integrity of structures by utilizing only boundary displacement data. Due to the sensitivity to material distribution, Young’s modulus is used as the criterion for defect detection. Specifically, defect identification is transformed into an optimization problem targeting the distribution of Young’s modulus. The solid isotropic material with penalization method is employed to establish a nonlinear interpolation model for Young’s modulus. Moreover, a hyperbolic tangent projection strategy is applied to suppress the intermediate-state distributions of Young’s modulus. It significantly shrinks the transition zones between the intact material and the defect, improving the accuracy of the defect geometry reconstruction. An iterative four-stage defect identification framework that involves adjusting the projection slope is formulated, which enhances the model’s defect detection capability. The model identifies distributed defects and defects featuring complex geometries with mean relative errors below 2%, which verifies its accuracy. Numerical results demonstrate that the reconstruction results are only correlated with the boundary displacements. Furthermore, the model is unaffected by the initial conditions and excels in distinguishing adjacent defects.