A Reduced Order Model for Damage Detection of Dynamic Problems

Structure health monitoring (SHM) is essential for monitoring damage in dynamic systems. It helps in the early detection of damage which, prevent any economic and life loss ensuring the safety of the system. In this work, we are interested in damage detection for dynamic problems having noisy data. The noisy data may be collected from sensors. It is always difficult to deal with noisy data when there is damage in a dynamic system as it is a high-dimensional problem. For that reason, the proper orthogonal decomposition (POD) has been used to reduce dimensionality. As a result, it was possible to represent a dynamic problem by a very low number of POD modes. Furthermore, the governing differential equations were represented using the state space model, and the Bayesian filtering approach was used to predict the responses and parameters. The developed model was first fitted by the noisy data on the reduced space, and the model parameters were found. Thereafter, Bayesian filtering was used for the prediction of responses and system parameters (i.e. stiffness) for a dynamic problem. Often, for a dynamic problem, the data is updated continuously. To take into account the case, the main idea of the developed model was to predict the stiffness in an online manner, such that it can predict the real-time behaviour of the stiffness, and the damage can be measured in the online mode as well. The developed model was applied to a muti-degrees of freedom dynamical system with synthetic data for validation. It was found that the developed approach can predict the evolution of the response and stiffness quite accurately and efficiently.