Towards a more realistic modelling of the uncertainty on identified mode shapes due to measurement noise

Many damage identification methods use the information from mode shapes. In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the mode shapes in the form of independent noise at each measured location. In doing so, the potential spatial correlation in the mode shapes uncertainty is not taken into account. A better approach consists in adding uncorrelated noise on the time domain responses at each sensor before doing the identification. The spatial correlation resulting from the identification can then be evaluated using the covariance matrices of the identified mode shapes. In this study, we apply this approach to the numerical example of a simply supported beam. Modal identification is performed using stochastic subspace based algorithms developed in the toolbox MACEC. The covariance matrices of the mode shapes shows that there is a strong spatial correlation in the mode shapes uncertainty. This result shows that adding independent noise directly on the mode shapes is not a very realistic approach to assess the impact of noise on damage identification methods. The approach used to characterize noise uncertainty on modeshapes identification is totally general and can be applied to any mode, structure or sensing technology.