Different Displacement Reduction Spaces for the Use in Admittance-Based TPA Methods

When determining critical paths for transmission of sound and vibration in assembled products, transfer path analysis (TPA) is a reliable and effective tool. TPA represents a source with a set of forces that replicate the operational responses. The indirect determination of the forces at the interface is commonly performed using an inverse procedure; however, admittance-based TPA methods are often strongly influenced by imperfect measurements. Given that the condition number of the transfer path admittance is high, this can lead to severe error amplification in the equivalent (also known as blocked) forces. In order to overcome this problem, regularization techniques such as singular value truncation or Tikhonov regularization are usually suggested. These techniques generally improve the accuracy of the determined interface forces but provide little insight into what is the actual source of errors. In this chapter, we investigate the benefits of projecting measured displacements into various representative subspaces in the scope of admittance-based TPA methods. In particular, a comparative investigation of three established reduction bases using singular, physical, and interface deflection modes is conducted. The definition of the reduced subspace using different sets of modes assures only dynamic information, which is relevant and dominant for the measured configuration, is retained after the reduction. Hence, badly observed dynamic, commonly dominated by measurement errors, is effectively filtered out. The main point of interest of this study is the effect of projecting measured displacements to the reduced domain on the transferability of the equivalent forces. The feasibility of all approaches is supported by an experimental case study, which can guide the reader in selecting a suitable approach for their specific needs.