A numerical study on detecting defects in a plane-stressed body by system identification Original Research Article

A parametric system identification algorithm is applied for detecting holes or cracks in an elastic plane-stressed body using measured static response at the boundaries. A linearly constrained nonlinear optimization problem is solved for optimal constitutive parameters by minimizing the error between the measured and computed displacements. Each finite element in the model is parameterized by decomposing its stiffness matrix into constitutive parameters and kernel matrices. Because locations and sizes of actual holes or cracks in a body are not the a priori knowledge, the finite element model for detecting such defects is simply set up for the defect-free state with the assumption of a linear elastic behavior. Defects in a plane-stressed body are predicted by the reduction in the constitutive parameters of each element from their baseline values without modifying the geometry and topology of the defined finite element model. The proposed defect-detection algorithm allows sparse measured data with respect to the number of degrees of freedom of the model and also provides statistical defect indices when considering noise in measurements. An adaptive parameter grouping scheme is applied to localize defects when limited measurements are provided. The proposed method is investigated through numerically simulated examples.