Damage detection in time-varying systems by means of the PCA method

Natural frequencies of real structures are affected not only by the presence of damage but also by environmental conditions, such as temperature and humidity. As developed during the last years, the Principal Component Analysis (PCA) is used to remove the effects of the external factors and the Novelty Index is successively executed to detect the damage. This procedure has been always applied to Time-Invariant systems, but it can be also performed when analyzing a Time-Varying system, whose modal parameters change instantaneously. Referring to this case, one of the most studied systems showing these characteristics is the railway bridge crossed by a train. The mass and the velocity of the train can be considered as environmental conditions, because they modify the natural frequencies and moreover their values are unknown. This paper shows firstly a numerical study on the relationship between the natural frequencies and the load characteristics, and then a numerical example is presented in order to demonstrate the reliability of the method. The results show that this technique is able to well detect the presence of damage and also to properly distinguish among different levels of crack depths.