| Inverse problems are the most common problems in almost every scientific and engineering field. It is, therefore, necessary to have a unified and systematic approach for inverse problems, especially for time-dependent inverse problems. In this study, a unified FE-FD (Finite Element - Finite Difference) approach with a data filtering algorithm is established. By integrating the finite element method, finite difference method, and extended data filtering method, this approach is able to handle complicated structure geometry and is suitable for both linear and non-linear time-dependent problems. It provides an effective and accurate method to identify material properties based on structural thermoelasticity or dynamics parameters and measurements. It has a capability to automatically filter out errors contained in the experimental data that is an unavoidable problem in data collection. Because of this capability, this approach can provide a stable solution for various time-dependent inverse problems.; For thermoelastic problems, this approach can identify material properties very well when random errors in displacement measurements are less than ±30%, and random errors in temperature measurements are less than ±15%. The weight matrix W can be used to reduce the effect of large measurement errors.; For structural dynamic problems, this approach provides appropriate formulas for the dynamic stiffness matrix (DSM), consistent mass matrix (CMM) and lump mass matrix (LMM). Simulation results indicate the best solution is from DSM for the identification of material properties.; This approach is also extended, with a nine-point operator introduced in this study. It provides an effective and reliable method for treating data measured from any complicated spatial surface. The extended matrix filter developed in this study can successfully filter the data at non-rectangular mesh points on the planes and surfaces. The correction of the data is very fast and can be conducted in real time. |
