Generalized Multi-Parameter Tikhonov Regularization for Time-Domain Identification of Various Types of Forces

Force identification problem is highly ill-posed. Currently, single-parameter regularization method is widely adopted in force identification. Multi-parameter regularization provides more degrees of freedom for solving problems and has been proven to perform better in solving certain inverse problems. This study applies multi-parameter Tikhonov regularization to force identification and integrates it with adaptive Lq regularization for accurately identifying various types of forces, presenting a generalized multi-parameter Tikhonov regularization method. Regarding the selection of regularization parameters, this study, based on a Bayesian framework and the uniform penalty principle, proposes a method suitable for generalized multi-parameter Tikhonov regularization. The proposed method is validated through numerical simulations and experiments. The comparative results with existing methods indicate that the proposed method is suitable for identifying different types of forces and performs well even at relatively high noise levels.