Reference-based combined deterministic-stochastic subspace identification for experimental and operational modal analysis

In this paper, the use of the combined deterministic-stochastic subspace identification algorithm for the experimental modal analysis of mechanical structures is discussed. The algorithm requires artificial forces to be applied to the structure, so it can be used for experimental modal analysis (EMA). The algorithm can also be used for operational modal analysis (OMA), since the excitation level of the artificial force(s) can be low compared to the excitation level of the ambient forces. Both the modes that are artificially excited and those that are excited by the ambient forces are identified. This type of operational modal analysis is called an OMAX analysis (Operational Modal Analysis with eXogenous inputs) [

1

]. The main advantages of OMAX over OMA are that the modes that are excited by the artificial forces can be scaled to unity modal mass and that a higher number of modes can be identified.

An original contribution of the paper is that the time-domain combined deterministic-stochastic subspace (CSI) algorithm of [

2

] is extended to a reference-based version (CSI/ref), which makes use of a Kalman filter that is constructed with reference outputs only. Advantages of CSI/ref over CSI are a faster performance because of the data reduction and the possibility to lower the influence of noisy channels without loosing their useful information.

The capabilities of both algorithms for the determination of the eigenfrequencies, mode shapes, modal damping factors and modal scaling factors of mechanical structures in both experimental and operational conditions are illustrated by simulated tests. With these simulations, it is demonstrated that both the CSI and the CSI/ref identification methods provide accurate estimates for the modal parameters of a structure, even if the measurement errors are relatively high compared to the amplitude of the signals. It is even possible to combine output channels in which only ambient excitation is present with output channels in which only artificial excitation is present, while still obtaining accurate modal parameters. It is also shown that, if the channels with the highest SNR are chosen to be the reference channels, the CSI/ref method gives the most accurate estimates for the modal parameters, because with these reference channels, the CSI/ref method gets rid of the noise faster than the CSI method and so it does not need high model orders to produce a clear stabilization diagram.