Dual reciprocity BEM and dynamic programming filter for inverse   elastodynamic problems
  This paper presents the first coupling application of the dual reciprocity BEM (DRBEM) and dynamic programming filter to inverse elastodynamic problem. The DRBEM is the only BEM method, which does not require domain discretization for general linear and nonlinear dynamic problems. Since the size of numerical discretization system has a great effect on the computing effort of recursive or iterative calculations of inverse analysis, the intrinsic boundary-only merit of the DRBEM causes a considerable computational saving. On the other hand, the strengths of the dynamic programming filter lie in its mathematical simplicity, easy to program and great flexibility in the type, number and locations of measurements and unknown inputs. The combination of these two techniques is therefore very attractive for the solution of practical inverse problems. In this study, the spatial and temporal partial derivatives of the governing equation are respectively discretized first by the DRBEM and the precise integration method, and then, by using dynamic programming with regularization, dynamic load is estimated based on noisy measurements of velocity and displacement at very few locations. Numerical experiments involved with the periodic and Heaviside impact load are conducted to demonstrate the applicability, efficiency and simplicity of this strategy. The affect of noise level, regularization parameter, and measurement types on the estimation is also investigated. 
Masataka Tanaka, W Chen