A Kalman-filter based time-domain analysis for structural damage diagnosis with noisy signals

In this paper, a procedure is presented for the time-domain analysis of noise-contaminated vibration signals for global structural damage diagnosis. It extends from a previously established acceleration response-only time-domain Auto-Regressive- with-eXogenous input (ARX) model, where the “process” is defined such that the acceleration response at a given degree of freedom (dof) is regarded as the “input”, while the accelerations at other dofs are the “state” with which the “measurements” are associated. The novel idea in the present procedure is to retrieve the intrinsic input–output set from noisy signals by using the Kalman filter, so that the underlying physical system is best presented to the subsequent diagnosis operation. The theoretical basis of representing the system by pairing the raw measured input and the filtered response through the Kalman filter is discussed. When such raw input and filtered response signals are fed into the reference ARX model, the error feature becomes indicative of the change of the physical system. By analyzing the residual error, the damage status of the structure can be diagnosed. Applications to numerical and experimental examples demonstrate that the approach is effective in tackling the noises, and both the occurrence and relative extent of damage can be assessed with an appropriate damage feature.