Estimating the modal parameters from multiple measurement setups using a joint state space model

• The global mode shapes are estimated from multiple measurement setups.
• A new state space model is presented to solve the problem.
• The state space model is estimated using the Expectation Maximization algorithm.
• The proposed method is fully automatic and does not require further treatment.
• The proposed method does not need reference sensors, only needs overlapped sensors among setups.

Computing the modal parameters of structural systems often requires processing data from multiple non-simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors, which are fixed for all measurements, while the other sensors change their position from one setup to the next. One possibility is to process the setups separately resulting in different modal parameter estimates for each setup. Then, the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global mode shapes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a new state space model that processes all setups at once. The result is that the global mode shapes are obtained automatically, and only a value for the natural frequency and damping ratio of each mode is estimated. We also investigate the estimation of this model using maximum likelihood and the Expectation Maximization algorithm, and apply this technique to simulated and measured data corresponding to different structures.