Enhancing accuracy and robustness in FBS decoupling through Tikhonov regularization and unit balancing

Frequency-based Substructuring (FBS) enables the prediction of transfer functions for an assembled system based on those of a single-unit system. Conversely, FBS decoupling derives the frequency response function (FRF) of a single-unit system from the assembled system. This approach is valuable when obtaining the transfer functions of a system is challenging due to boundary conditions and deformation conditions. FBS decoupling can enhance accuracy by using additional indicator sensors. However, this often results in significant noise due to the ill-posed FRF matrix inversion. In this paper, Tikhonov regularization is employed to reduce noise-induced errors. Furthermore, this paper addresses the issue of inadequate Tikhonov regularization caused by the inherent scaling differences between the rotational and translational components within the FRF matrix. To rectify this challenge, a unit balancing method is proposed to mitigate the influence of scaling differences. This method enhances the accuracy and reliability of FRF matrix inversion processes, contributing to enhanced noise reduction and robustness in practical applications.