Modal Mass Estimation from State-Space Models and Frequency Response Functions

In operational modal analysis with exogenous inputs, the modal parameters are estimated based on partly measured inputs and outputs. Different algorithms can be used, like combined deterministic stochastic subspace identification (CSI) algorithms or the poly-reference Least Squares Complex Frequency (pLSCF) algorithm. Common for both types of algorithms are the computation of modal mass to normalize the estimated mode shapes according to the inputs. In this work, the modal mass computation for CSI and the pLSCF-algorithm is revisited, where a particular focus is put on the assumption on the intersample behavior that is required for the relation between estimates obtained from the discrete-time system (where the data comes from) and the corresponding continuous-time system (where the modal mass is computed). The discretization methods: zero-order hold, first-order hold, and the impulse invariant discretization are studied and discussed. It is shown that the modal mass estimates are heavily dependent on the discretization approach used. The results are illustrated in the context of Monte Carlo simulation of a six-degrees-of-freedom chain system.