## 3 Application of Drive-by Methodologies on the Bridge Subsystem
### Bridge Damage Identification
#### 3.2.2 Feature Extraction  
Regarding drive-by railway bridge inspection, [PERSON] et al. [21] proposed a damage detection method using the analysis of vehicle accelerations resulting from a numerical  
Figure 11: Bridge damage identification approaches. train-track-bridge interaction in which the damage was simulated in the bridge structure by reducing the stiffness of affected bridge elements. Using a wavelet transform-based technique, this method could detect and locate the damage in terms of the change in pseudo frequency. However, the method is not as efficient in the presence of noise. [PERSON] et al. [67] proposed a method for detecting damage in railway bridges by analyzing the dynamic response of passing trains in conjunction with an optimization technique to identify railway track stiffness variation. The method involves comparing the \"apparent profiles\" of the bridge, which are virtual profiles that generate a similar response in passing trains, before and after damage occurs. The Cross-Entropy optimization method is used to determine these profiles. The study used a 3D train-bridge interaction model to generate input signals and introduced damage by simulating a sudden impact from a vehicle strike. The algorithm was tested for resilience to sensor noise and effectiveness in the presence of track irregularities. While the accuracy of their approach has shown to be high, it presented the drawback of being computationally demanding and has not been validated by experimental data. [PERSON] et al. [68] proposed the use of the response of the contact point of the moving vehicle with the bridge rather than that acquired from the carbody since the former is free of the vehicle frequency, which is an inconvenience when scanning bridge characteristics using a moving test vehicle. In this research, the contact-point response was processed to produce the instantaneous amplitude squared (IAS) via the Hilbert transform, which was shown to be an extremely useful parameter for the damage detection of bridges. In this concept, the damage feature is derived from the square operation involved in the IAS definition and the second derivative necessary for calculating the contact-point reaction. According to the authors, the second derivative of the vehicle acceleration has the effect of magnifying any discontinuity of the beam while having little or no impact on continuous signals, which may aid in identifying the damage location in the contact-point response time history. Figure 12 shows the IAS results obtained through numerical simulations performed for a test vehicle moving over a damaged beam that has supported ends and a crack located at the mid-span, which is simulated by a hinge with a rotational spring. The results confirmed the IASs' capability for damage detection when calculated from the contact-point response since they efficiently intensify the discontinuity signal at the damage location. Additionally, even if there is no visible discontinuity point in the time domain, the IAS is still capable of detecting the site of the damage and is typically insensitive to ambient noise, vehicle damping, and bridge damping. Figure 12: IAS results from numerical simulations of a test vehicle passing over a damaged beam: (**a**) FFT spectrum of the contact-point acceleration and (**b**) IAS amplitude [68]. [PERSON] et al. [69] proposed a drive-by method for numerically detecting scour based on modeled accelerations recorded on a train bogie and processed using the Continuous Wavelet Transform (CWT). Using the Complex Morlet, the CWT wavelet is applied to the bogie accelerations obtained during multiple train passages over a bridge, and then the moduli of the wavelet coefficients are interpolated to vehicle location on the bridge (instead of time). It has been shown that a scour indicator, defined as the difference in average CWT coefficients between healthy and scoured batches of railway crossings, is useful not only in identifying the existence of scour, but also in locating it.