An analytical model was developed to justify the results obtained from the numerical simulations; in this case, a train wagon transiting over a railway bridge was modelled as a concentrated mass passing over an Euler-Bernoulli beam; whereas the damage to the beam was modelled as a rotational spring the stiffness of which could be changed for simulating different magnitudes of damage. On the other hand, a numerical model considering the characteristics of the experimental test-rig utilised in this study was developed by using commercial software based on the finite element method. Different types of damage to the bridge were simulated and a code was written to perform transient analyses by incorporating a load which moved along the beam nodes at constant speed. Both the displacement and the acceleration vertical responses were collected in the time domain for all the nodes and for the complete duration of the load crossing the beam.

Likewise, a MATLAB® code was written to post-process the data obtained from the simulations. Continuous wavelet transform (CWT) diagrams showed that if a convenient mother wavelet is selected, damage can be detected and localised using any or both vibration responses (displacements or accelerations), even with significant percentages of noise.

Nevertheless, the method was improved by filtering the noisy signals, removing the border effects from the CWT diagrams, selecting an adequate range of scales, and calculating the wavelet energy from the coefficients along the selected range of scales for many different points along the beam. Thus, a significant peak of wavelet energy accumulation indicated the presence of a malfunction, whereas its location and intensity were also estimated according with the position and magnitude of the maximum peak of wavelet energy, respectively. The reliability and precision in detecting and localizing damage was increased if the average of a few wavelet energies corresponding to different measuring points was considered.

Finally, experiments were conducted to validate this work using a test-rig composed by an aluminium bridge with flexible supports. The vertical responses were acquired with accelerometers attached along the bridge while a crossing load passed over the bridge. Damage was represented by attaching a mass over the bridge. The same damage detection and localization method above described was applied and a good agreement among analytical, numerical, and experimental results was obtained; the percentage of error between the position of the maximum energy for damaged cases and the damage location was very small.

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