A new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body

This paper presents a system identification scheme to determine the geometric shape of an inclusion in a finite body. The proposed algorithm is based on the minimization of the least-squared errors between the measured displacement field and calculated displacement field by the finite element model. The domain parameterization technique is adopted to manipulate the shape variation of an inclusion. To stabilize the optimization process, a new regularization function defined by the length of the boundary curve of an inclusion is added to the error function. A variable regularization factor scheme is proposed for a consistent regularization effect. The modified Newton method with the active set method is adopted for optimization.