Tikhonov regularization for operational transfer path analysis

To overcome the shortcomings of the traditional operational transfer path analysis (OTPA), this paper proposes a novel OTPA model for inverse problems based on Tikhonov regularization through theoretical and experimental analysis. First, we analyzed the theoretical advantages of Tikhonov regularization and provided the basic criteria for determining Tikhonov regularization parameters. We obtained operational data according to changing rotational speeds of the motors and studied the vibration transfer paths of the shell structure by singular value decomposition. Furthermore, we analyzed the errors of total contributions and path contributions for traditional OTPA. Next, we proposed a novel OTPA method based on Tikhonov regularization with Picard conditions and analyzd the effects of regularization parameters. Finally, the comparative study results showed that the proposed method reduced the errors of total contributions, path contributions, and path misjudgment. This study thus provides theoretical references for the monitoring, reduction and control of vibration and noise.