A revised time domain force identification method based on Bayesian formulation

Summary Time domain force identification problems are generally ill‐posed. Regularization techniques are widely adopted to well‐condition the problem. Traditional regularization such as Tikhonov regularization is mathematically equivalent to assuming a zero‐mean prior distribution on the unknown force. This assumption could be unreasonable for problems where notable trend components exist in force histories, such as vehicle‐bridge moving force identification and cutting tool force identification. In this paper, a revised method is proposed to address this issue. The proposed method formulates the force identification problem within the Bayesian framework. The trend components are considered as low‐order polynomials and as the mean term in the prior distribution of the force history. The joint maximum a posterior estimate of unknown variables is derived. The solution algorithm is given based on conditional maximization. A mass‐spring system and a cutting tool under forces containing various types of trend components and vehicle‐bridge systems under moving interaction forces are simulated to validate the proposed method.