Rapid inverse parameter estimation using reduced-basis approximation with asymptotic error estimation

This paper presents a rapid and reliable approach to solve inverse problems of parameter estimation for structural systems using reduced-basis method (RBM). A reduced-basis model is first developed with asymptotic error estimation and is used for fast computation of solving forward mechanics problems of solids and structures. A genetic algorithm (GA) is then used in the inverse search procedure for parameter estimation. The approach is applied to a typical inverse problem of estimating the crack location, length and orientation inside a cantilever beam. The displacements measured at five points on the lower surface of the beam which can also be evaluated by our fast RBM solver are used as inputs for constructing objective functions of error. The genetic algorithm is used to search these parameters of the crack inside cantilever beam that minimize the objective function. An example has been presented. It is found that the estimated results are very accurate and reliable due to the use of RBM forward model with an effective and robust error estimation and detailed sensitivity analysis. The present procedure is 460 times faster than the full FEM model used inverse procedure.