Quantitative solution of 2-D inverse elastodynamics problems using hybrid FDM-FEM and PSO

It is clear that, having a exact knowledge about the geometry and properties of the materials and the domain that engineering problems are involved are very important specially in structural health monitoring, geotechnical earthquake engineering and other related field in civil engineering; in many cases, it might be useful if a suitable inverse solution is applied in order to detect the characteristics of the problems domain.
The main purpose of this paper is to development of the hybrid finite element- finite difference method for solving inverse elastodynamic and elastostatic scattering problems and combining that with particle swarm optimization algorithm as a quantitative approach fo solving these types of the problems. This hybrid method has been used in order to preparing the forward solution of the problems and by defining a suitable cost function and minimizing that using PSO algorithm, various kind of inverse problems are solved.
In general, an inverse scattering problem can be solved using qualitative or quantitative approaches. In some branches of quantitative techniques, usually, a forward solution is required and then using heuristic algorithm, the goal will be achieved. In this study, a hybrid FE-FD method is used as forward solver (which has the flexibility of finite element method and low computational cost of finite difference method); so, the domain inside and outside of the inclusion will be dicretized using finite difference method and the boundaries near the inclusion will be discretized by finite element method, and in this condition, the solution will be more flexible near the scatterer. In each solution step, first the finite element will be solved and the results will be transferred to the finite difference code and when the result is prepared in it, again, the response of the problem will go to finite element region.
In this research, at first, a geometry and related location will be assumes, randomly and then regarding that, using an OpenSees program code, the boundaries of the inclusion will be discretized and using the MATLAB program the related to finite difference region is discretized, then the results from these two codes will go and back until the response goes converge. Then, the PSO code which is developed in MATLAB will qualify the results and evaluate the cost function (e.g., the cost function is defined by minimizing the the error between the displacement that is from the main model and the predicted model), and if the cost function is large, the PSO algorithm will propose the new location and/or geometry of the inclusion and again, the loop will be repeated until the cost function be near the zero and the solution procedure will be terminated.
In order to evaluate, the efficiency and accuracy of the proposed approach, several problems are solved, where this algorithm could find the location and geometry of the inclusions (e.g., regular and irregular inclusion), the non-homogeneity of the inclusion and also detecting the soil layers by both static and dynamic loading.; the results show a very good accuracy as well as efficiency of the proposed approach for solving inverse problems in bounded and smi-infinite domains.