# Damage Identification in Warren Truss Bridges by Two Different Time-Frequency Algorithms
###### Abstract
A major concern about the practical validity of drive-by approach consists in the fact that the train response might be influenced not only by the bridge status, but also by other factors not related to the damage, like the level of track irregularities, a different dynamic response of the vehicle due to different passenger loads, or other uncertainties related the train speed variation and accuracy of its positioning with respect to the bridge. They can be divided in two main categories 1: _modal parameter-based_ and _non-modal parameter-based_ methods. The former, consisting in the identification of bridge properties like natural frequencies [9; 10; 11], damping values [12] and mode shapes [13; 14] based on the vehicle response, have been shown to be effective up to limited speeds (i.e., a maximum of 60 km/h), and in the first two cases not able to identify the exact location of a defect. The effectiveness of most of the _modal parameter-based_ techniques was only demonstrated through numerical simulations, and their outcomes can be affected by environmental conditions like temperature, especially in the case of damping and natural frequencies [15; 16; 17]. Conversely, _non-modal parameter-based_ methods do not explicitly seek the computation of bridge modal parameters, but rather focus on the bridge deflection under passing loads (e.g., apparent profile [18; 19] or change of curvature [20; 21]) or on the dynamic response of the vehicle crossing the bridge [22; 23; 24; 25; 26; 27], which is also the method investigated in this paper. Concerning bridge modelling, most of the mentioned papers adopt a simply supported beam representation considering mainly the vertical deflection. [PERSON] and [PERSON] showed good outcomes when considering single force and a half-car vehicle model crossing a simply supported beam [28]; [PERSON] et al. [26] investigated a ballasted bridge modelled as a simply supported beam without any track irregularity profile, where the train was modelled as a half-car vehicle (10 DOFs). [PERSON] et al. proposed a numerical study on the scour phenomenon [29], with a 2D vehicle model (10 DOFs) moving on simply supported beams, with several beams in series to represent a multiple-span bridge. In this latter work, the track irregularity profile is taken into account, by introducing a time-invariant profile which does not allow consideration of any degradation process in the track. The results demonstrated good performance in terms of damage detection for vehicle speeds up to 80 km/h. In all the mentioned works, the Continuous Wavelet Transform is adopted to analyze the motion of the vehicle: the wavelet coefficients are evaluated separately on the vehicle accelerations resulting from the simulations of the damaged and of the healthy bridges, assumed as a reference condition. The wavelet coefficients related to the damaged and healthy condition are subtracted from each other, so that any peak in the absolute value of this difference is used as an index to reveal the presence of a damage in the bridge structure. In most of the previously mentioned papers, the bridge defect is modelled through an equivalent representation of the damage, consisting of a reduction in the flexural stiffness of one of the finite elements of the beam schematization. The present paper, starting from the previously mentioned papers, investigates the feasibility of the drive-by method applied to the basic 3D example of a short span Warren truss bridge, which according to the authors' knowledge has not been done before. These bridges can be subjected to different degradation processes affecting the structure, such as corrosion, ageing, crack-growth and beam connection deterioration. Damage affecting a single member may represent a critical event, and it can lead to an increase in the load on the adjacent elements, and in some cases to sudden failures of the whole structure [30].