A novel method for force identification based on filter and FEM

Force identification plays a vital role in vibration control and structural health monitoring. Force identification is an inverse problem to determine the excitation load from the responses. In general, the inverse problem has strong ill-posedness and ill-condition, especially in the case of low signal-to-noise ratio. Singular value decomposition and Tikhonov regularization are widely used for the reconstruction of the input force. Nevertheless, the anti-noise performance and accuracy of the two methods are still unsatisfactory. In this paper, we present a novel method for force identification based on a filter and the finite element method (FEM). The filter is used to suppress the noise of the input signals. FEM is introduced to reduce the discretization error and the regularization parameters are optimized by the genetic algorithm. After the signal is filtered, the characteristics of the signal will be changed. Especially, the initial and the last segments of the input signal will be lost. These changes may make the identified force inaccurate, even more inaccurate than the force identified with no filtering. To deal with this problem, cubic spline interpolation and a nonlinear autoregressive neural network are introduced to repair the input signals. Finally, three numerical examples and experiments are used to verify the superiority of the method.