Sparse identification of blocked forces using a global-residual interface representation

Choosing an appropriate interface representation is a crucial step when identifying forces by inverse methods. A preferred interface representation should be interpretable, but also well conditioned and able to recover forces with low error. Currently, the most widely adopted representation is that of the Virtual Point (VP), a local projection of measured degrees of freedom (DoFs) onto a set of co-located rigid-interface modes. Though easily interpretable, poor conditioning/large errors are often obtained at low frequencies when the source dynamics are dominated by global rigid body motions; a result of over-parametrising the interface model. In this paper we explore a reformulation of the VP representation by separating the global and residual components of the interface dynamics; global dynamics are filtered out of the local interface motions and projected onto their own global VP, the remaining residual interface motions are projected onto a set of local VPs. The result is an interpretable interface representation that provides a clear separation of the local and global source dynamics. Its application is demonstrated on a heavy weight stamping press under rigid and resilient boundary conditions. Results suggest that the proposed Global Residual Virtual Point (GR-VP) performs on par with the standard VP, with notable improvements in the low and high frequency range. We further investigate the application of the GR-VP in conjunction with best subset DoF selection. It is shown that compared to the standard VP, the GR-VP can provide a more robust interface representation when comparing blocked forces obtained from rigid and resilient installations.