Noise-enhanced effect in moving dynamic force identification

It is well-known that the response matrix in moving force identification (MFI) is ill-posed, so the identified force is apt to be affected by measurement noise. The effect of noise could be mitigated to some extent by traditional regularization methods, which do not distinguish between white noise and colored noise. However, this paper addresses that adding certain types of white noise can be helpful in suppressing the influence of colored noise because stochastic resonance (SR) can occur due to the interaction between the white noise and the nonlinear process of the MFI. With these understandings, this paper proposes a new MFI method that has two levels of regularization. In the first level, the response matrix is transformed to the time-frequency domain by wavelets with high time-frequency resolution. Thus, the new response matrix is more robust because the major frequency components are more prominent. In the second level, the element-wise Bayesian regularization is adopted to apply regularization on each force element. As regularization weights are determined by the measurement with noise, optimal weights can be obtained by adding certain white noise. This noise enhancement effect is demonstrated by several numerical simulations. Then, the performance of the proposed method is further validated in experimental studies.