An improved state space method for force identification based on function interpolation in the presence of large noise

The conventional state space method for force identification has the disadvantage of large discretization error with a low sampling frequency. This paper presents an improved method based on the function interpolation of the external force in time domain. Two types of the interpolation functions are investigated, one is the linear interpolation, and the other type is the sigmoid curve interpolation. Gauss integration method is used for integration computation. Numerical studies show that both of the improved methods based on the two types of interpolation function are more accurate especially when the sampling is long and/or with a low sampling frequency. In addition, the proposed method is also extended for the case of high noise level. The key idea is to divide the time step of measured responses into several smaller time steps to form an overdetermined equation of the inverse force identification. Then, the least square algorithm is adopted, which helps to reduce the effect of the high random noise to improve the accuracy of identified solution.