Hybrid FE–IDQ–CG method for dynamic parameters estimation of multilayered half-space

As a first endeavor, a hybrid finite element (FE)–incremental differential quadrature (IDQ) method together with the discrepancy principle and the conjugate gradient method (CGM) is used to develop an inverse algorithm for the parameters estimation of the axisymmetric multilayered half-spaces. The approach is based on the measurement of the dynamic transverse displacement at some boundary points of the half-space to estimate the unknown parameters of its layers. Using the accuracy and unconditional stability of the hybrid FE–IDQ method, the direct problem is solved to get the dynamic transverse displacements. After adding some random errors to the obtained results, they are considered as the measured responses by sensors. Then, the conjugate gradient method as a general and robustness optimization technique is employed to minimize the error between the measured and calculated dynamic surface responses at sensor locations. The sensitivity analysis of the displacement field is performed using a semi-analytical method. The applicability and correctness of the proposed hybrid algorithm is demonstrated through different examples by considering the influence of the layers arrangement, the measurement errors and sensor numbers.