## 3 Application of Drive-by Methodologies on the Bridge Subsystem
### Bridge Damage Identification
#### 3.2.2 Feature Extraction
A train-bridge dynamic interaction model was used to show the influence of velocity and span/pier stiffness changes on the train response signals. Changes in the flexural stiffness of a span had a modest effect, while changes in the stiffness of a pier had a more significant effect when the instrumented vehicle was in the adjacent spans. It was found that instrumented trains could be successfully used for an ongoing monitoring of condition and, by implication, for identification of the need for repair or rehabilitation. A novel method to determine apparent profile (AP) of the track and detect railway bridge condition using sensors on in-service trains was proposed by [PERSON] et al. [75]. An optimization algorithm was used to find vehicle dynamic properties and speed, and the apparent profile was used to calculate the moving reference deflection influence line. The results show that the moving reference influence line can be found accurately and that constitutes an effective indicator of the condition of a bridge. The fleet monitoring concept combines the Inverse Newmark-\(\beta\) method with Cross-Entropy (CE) optimization to calculate the APs of track and vehicle properties accurately using batches of trains. A two-axle half-car and track beam model was tested with different bridge damage levels, and the results show that the moving reference influence line is a good indicator of the bridge damage level. The concept has the potential to monitor bridges by combining drive-by data from several in-service trains. Further work is needed to extend this to a 3D train model and allow for non-linearity in the vehicle, and field testing is needed to validate the concept. [PERSON] et al. [76] proposed a methodology in which the feasibility of applying cepstrum analysis components to the indirect damage detection in high-speed railway (HSR) bridges by onboard sensors is evaluated numerically. A finite element (FEM) 2D VTBI model that incorporates the train, ballasted track, and bridge subsystems was presented, whose formulation includes track irregularities and a damaged condition (stiffness reduction) induced in a specified structure region. Dynamic analyses were performed through a code implemented in MATLAB, where different damage scenarios and external excitations, such as measurement noises and different levels of track irregularities, were simulated. The Mel-frequency cepstrum coefficients (MFCC) were taken by a signal processing technique that involves taking the short-time Fourier transform (STFT) of the train acceleration signal, taking the logarithm of the resulting spectrum magnitude, and then taking the inverse Fourier transform of the logarithm. The resulting cepstrum was then used to extract features--Damage Index (DI)--sensitive to signal changes, such as damage in a structure. The results indicated that although MFCC-based DI values provide reliable information on the location and severity of the damage, the amplitude of the MFCC feature correlates with vehicle speed and track irregularities as it is more sensitive to track irregularities than damage locations.