## 3 Application of Drive-by Methodologies on the Bridge Subsystem
### Bridge Modal Identification
#### 3.1.1 Natural Frequency Extraction
In this study, environmental effects such as temperature variation which may cause extra difficulties in real applications were not considered. Aiming to enhance the capabilities of the drive-by to detect frequencies from higher order modes, [PERSON] and [PERSON] [45] proposed the application of the Empirical Mode Decomposition (EMD) signal processing technique to obtain Empirical Mode Functions (IMFs). The bridge frequencies were then identified from the frequency content of each IMF derived from its Fourier transform. The authors validated their methodology by numerically modeling the bridge as a simply supported beam and the vehicle as a sprung mass, and experimentally by a test vehicle identical to the one used in [36]. The results obtained, both numerical and experimental, indicated that the application of the EMD provides much better precision in identifying higher-order modes. However, a common issue that affects the accuracy of this technique is the mode mixing problem associated with the EMD algorithm when the bridge frequencies are contained in two or more elements of the decomposed signal. To address this issue, [PERSON] and [PERSON] [46] proposed an enhancement of the formulation by applying the Ensemble Empirical Mode Decomposition (EEMD) [47] algorithm which is an improved version of the EMD that presents a better performance under noise conditions and can deal with the mode mixing problem. The authors conducted an extensive numerical study comparing the performance of both formulations under simulated measurement noise and different velocities and obtained errors of approximately 2% with EEMD compared to 10% when the EMD algorithm was applied. Figure 5: Acceleration spectra considering Class 4 irregularities (\(\omega_{v}\) vehicle natural frequency and \(\omega_{b}\) bridge frequency): (**a**) without TSM and (**b**) with TSM [24]. A field study conducted by [PERSON] et al. [26] applied the Hilbert Huang Transform (HHT) algorithm in the identification of the natural frequencies of each one of the 12 individual spans of the Malahide viaduct in Ireland. HHT is a two-step process where the signal is first decomposed by the EEMD algorithm and the Hilbert Transform (HT) is applied to the IMFs to access the instantaneous frequencies. The authors instrumented the front bogie of the leading carriage of a five-carriage train shown in Figure 6a with a set of accelerometers at the positions indicated in Figure 6b. Vertical acceleration was recorded for 5 weeks, totalizing 41 viaduct crossings. To serve as a reference for evaluating the drive-by results, the natural frequency of each span was also measured by forced and free vibration tests using instrumentation installed directly on the viaduct. Accurate results were obtained for the middle spans; however, for the pair of initial and final spans that are shorter, the method presented some difficulties in the precise identification of the natural frequencies. The authors investigated the causes and concluded that the information regarding the natural frequencies of these spans was somewhat scattered in more than one IMF. This reveals that the EEMD was not so efficient in avoiding the mode mixing problem for the information gathered in these spans. To develop an automatic methodology to bridge natural frequency identification, [PERSON] et al. [27] proposed a deep learning approach, more specifically a six fully connected layers neural network (NN), to identify the bridge's natural frequency from the acceleration response of high-speed trains. A dataset of acceleration frequency spectra was developed based on 3131 simulated train passages and 52 passages measured with accelerometers installed on the wheelsets of an ICE 4 passenger train (see Figure 7a). This dataset contains passages at different speeds and, in the case of the simulated one, different  
Figure 6: Drive-by natural frequency identification of the Malahide viaduct: (**a**) overview of the train and (**b**) experimental setup [26]. bridges.