Physically motivated rank constraint on direct throughput of state-space models

Paper in proceeding, 2018

In frequency range vibration testing a few outside band eigenmodes are often included in the system identification to compensate for residual mass and stiffness influences. It has been observed that, in particular, energy conjugate input-output pair transfer functions with strong outside band modes tend to render models with poor fit even after inclusion of mass and stiffness residuals. For such problems the inclusion of another complementary residual term has been found to improve the fit to data. In this paper, modal models identified from acceleration data with a subspace state-space method are considered. The residual mass influence is modelled with a state-space direct throughput while the stiffness and complementary residuals are modelled with extra states. Furthermore, for state-space models on accelerance form it is shown that the direct throughput matrix can be partitioned into a flexible and rigid motion partition. For systems with more inputs and outputs than rigid body modes it is shown that the rigid body motion partition has a bounded rank. The upper bound is equal to the number of rigid body modes. Therefore, for identified models on accelerance form this constraint must be enforced for physical consistency. The proposed method is applied on simulated finite element test data from an automotive component.