# Damage Identification in Warren Truss Bridges by Two Different Time-Frequency Algorithms
###### Abstract  
Recently, a number of authors have been focusing on drive-by monitoring methods, exploiting sensors mounted on the vehicle rather than on the bridge to be monitored, with clear advantages in terms of cost and flexibility. This work aims at further exploring the feasibility and effectiveness of novel tools for indirect health monitoring of railway structures, by introducing a higher level of accuracy in damage modelling, achieve more close-to-reality results. A numerical study is carried out by means of a FE 3D model of a short span Warren truss bridge, simulating the dynamic interaction of the bridge/track/train structure. Two kinds of defects are simulated, the first one affecting the connection between the lower chord and the side diagonal member, the second one involving the joint between the cross-girder and the lower chord. Accelerations gathered from the train bogie in different working conditions and for different intensities of the damage level are analyzed through two time-frequency algorithms, namely Continuous Wavelet and Huang-Hilbert transforms, to evaluate their robustness to disturbing factors. Compared to previous studies, a complete 3D model of the rail vehicle, together with a 3D structural scheme of the bridge in place of the 2D equivalent scheme widely adopted in the literature, allow a more detailed and realistic representation of the effects of the bridge damage on the vehicle dynamics. Good numerical results are obtained from both the two algorithms in the case of the time-invariant track profile, whereas the Continuous Wavelet Transform is found to be more robust when a deterioration of track irregularity is simulated. a 2021 11 10605 11 11 10605 11 11 10605 11 11 10605 11 11 10605 11 11 110605 11 110605 11 110605 11 110605 110605 110605 110605 110605 110605 110605 1  
personnel and on the possibility to interrupt the vehicle service on the infrastructure. To improve the effectiveness of the inspections, additional means are desirable, like additional diagnostic systems. The general way to reveal the presence of a local failure in a structure requires the comparison of some measurable indexes calculated from raw data in the current condition and in a reference healthy condition. The follow-up of such evolution enables, in principle, to distinguish a damaged condition from a healthy one. Basically, there can be two ways to monitor the status of a bridge: the most straightforward is to place dedicated instrumentation [5] on the structure. This solution, that can be called a _direct method_, can be worthwhile in the case of the main bridges of high-speed lines, but it is not a feasible prospective for regional or national networks, due the large number of bridges and the high related costs [6]. On-site measurements require several sensors to be mounted on the structure, leading to a significant cost of installation and maintenance of the entire set-up. In order to overcome the issues concerning direct methods, in the last two decades a significant number of researchers have investigated new methods relying on sensors mounted onboard the vehicle [7], rather than on the structure to be monitored. The idea of using an indirect approach for structural health monitoring (commonly named Drive-by Methods [1] for SHM) derived from [8] in which the authors proposed the extraction of bridge frequencies from the dynamic response of a passing vehicle. The fundamental concept behind these approaches is that structural damage causes a change in the mechanical properties of the bridge, and consequently a change in the dynamic behavior of the vehicle interacting with the structure. The bridge health status can then be extracted from the dynamic response measured on-board train, e.g., on the axle box, on the bogie frame and on the carbody. For the time being, drive-by methods have been mainly developed for highway bridges (both numerically and experimentally), but in fewer cases they have been applied to railways too (only numerical studies).