Drive-by Methodologies Applied to Railway Infrastructure Subsystems: A Literature Review—Part I: Bridges and Viaducts

Abstract

Bridges and viaducts are critical components of railway transport infrastructures, providing safe and efficient means for trains to cross over natural barriers such as rivers and valleys. Ensuring the continuous safe operation of these structures is therefore essential to avoid disastrous economic consequences and even human losses. Drive-by methodologies have emerged as a potential and cost-effective monitoring solution for accurately and prematurely detecting damage based on instrumented vehicles while minimizing disruptions to train operations. This paper presents a critical review of drive-by methodologies applied to bridges and viaducts. Firstly, the premises of the method are briefly reviewed, and the potential applications are discussed. In sequence, several works involving the use of drive-by methodologies for modal characteristic extraction are presented, encompassing the most important methodologies developed over time as well as recent advancements in the field. Finally, the problem of damage identification is discussed—both in relation to modal and non-modal parameter-based techniques considering the most promising features and the current advancements in the development of methodologies for damage detection based on machine learning algorithms. A comprehensive conclusion is presented at the end of the article, summarizing the achievements and providing perspectives for future developments. By critically assessing the application of drive-by methodologies to bridges and viaducts, this paper contributes to the advancement of knowledge in this crucial area, emphasizing the significance of continuous monitoring for ensuring the integrity and safety of these vital transport infrastructures.

1. Introduction

Railway infrastructure plays a vital role in the economic and sustainable development of societies worldwide. A well-maintained railway system is key to ensuring efficient transport of goods, people and services, contributing towards reducing carbon footprint [1]. Structural Health Monitoring (SHM) is an essential aspect when it comes to assessing the condition-based performance of various subsystems that make up the railway infrastructure network. It allows for early detection of faults or defects before they cause extensive damage or lead to unplanned shutdowns which could result in severe economic losses [2].

The railway industry heavily relies on various subsystems, and among them, bridges hold an extremely crucial position. It is of utmost importance to ensure that these structures are constantly monitored for their condition in order to guarantee the safety of passengers as well as avoid potential damage or delays caused by bridge failures. Over the past few decades, there has been a significant surge in the development of direct SHM approaches for railway bridges [3]. These approaches employ distinct sensor technologies to measure different parameters such as vibrations, deflection, deformation, temperature, and humidity, among others. The strategies used to acquire data from the sensors vary from traditional wired systems to more advanced wireless sensor networks and Internet of Things (IoT) platforms [4].

Currently, there is a growing trend toward the development of innovative drive-by methodologies for railway bridge subsystems within the domain of railway infrastructure management [5,6]. In contrast to direct approaches, drive-by techniques involve the use of sensors or cameras mounted on moving trains to collect data, and therefore the condition of the bridge can be assessed without requiring a dedicated monitoring system directly installed on the bridge. The dynamic interaction between the moving train, track and the bridge can provide valuable insight into the structural health of the infrastructure [7]. This approach has the potential to significantly reduce the cost and complexity associated with traditional structural health monitoring approaches, making it an attractive option for railway infrastructure managers.

Given the recent advancements in drive-by methodologies, several authors have focused their efforts on identifying research trends in this field and providing guidance through review articles. One of the first approaches aimed at it was carried out by Ward et al. [8] in 2011, presenting condition monitoring opportunities based on onboard instrumentation on railway vehicles. The article focused on works dedicated to identifying damage in the railway tracks, assessment of vehicles’ dynamic performance characteristics, and vehicle speed monitoring; however, the condition monitoring of bridges was not investigated. Later on, in 2015, Weston et al. [9] exposed perspectives on railway track geometry condition monitoring from onboard sensors. In addition, Zhu and Law [10] presented a comprehensive review addressing the identification of bridge damage through vehicle-induced excitation based on both bridge or vehicle responses. Malekjafarian et al. [11] presented the first review completely dedicated to drive-by methodologies applied to bridge condition assessment. Despite presenting some railway applications, both preceding works are mainly focused on road applications. Afterward, in 2018, Yang and Yang [12] presented a new review work on drive-by methodologies focused on highway bridge condition assessment which was later updated, in 2020, by Yang et al. [13] including a section dedicated to railway track condition assessment. When it comes to railway vehicle damage identification, Li et al. [14] presented a review focused on railway vehicle onboard health monitoring systems. More recently, Bernal et al. [15] presented a broad review of the state of the art in the industry involving onboard instrumentation techniques for detecting damage to railway vehicles. In 2022, Wang et al. [16] presented a recent review of drive-by methodologies for highway bridges and railway tracks updating the previous work conducted by Yang et al. [13]. In the same year, Malekjafarian et al. [17] presented an extensive review of drive-by methodologies for the condition assessment of bridges. The review covered theoretical, numerical, and experimental approaches, with most of the works reviewed relating to road applications. Nonetheless, a few works related to the railway transport system were also presented.

Table 1. Main topics addressed by the state-of-the-art review articles.

Reference		Bridge Subsystem		Railway Track Subsystem	Railway Vehicles Subsystem
		Highway	Railway
Ward et al. [8]		--	--	✓	✓
Weston et al. [9]		--	--	✓	--
Zhu and Law [10]		✓	--	--	--
Malekjafarian et al. [11]		✓	--	--	--
Li et al. [14]		--	--	✓	✓
Yang and Yang [12]		✓	--	--	--
Bernal et al. [15]		--	--	--	✓
Yang et al. [13]		✓	--	✓	--
Wang et al. [16]		✓	--	✓	--
Malekjafarian et al. [17]		✓	--	--	--
Present work	Part I	--	✓	--	--
	Part II	--	--	✓	✓

summarizes the available literature review articles highlighting the subjects discussed in comparison with those that are covered by this work. A clear gap exists in the literature when it comes to works dedicated to the application of drive-by methodologies in railway subsystems. This is especially true when it comes to bridges, where most of the reviews are focused on highway applications, and only a few studies related to the railway are cited. To the best of the authors’ knowledge, no review has been conducted to cover the application of drive-by techniques to all the three railway subsystems, namely vehicle, track, and bridge. Therefore, this work aims at filling this gap by presenting a critical state-of-the-art review of drive-by methodologies applied to the three railway subsystems.

Due to the extension of the subject addressed in this work, the authors present the discussion on the theme split into two articles: Part I is dedicated to bridge condition assessment while all the content regarding track and vehicle condition assessment is presented in Part II [18]. Combined, the two papers comprise applications of drive-by methodologies applied to all the main railway infrastructure subsystems which will contribute to this field of knowledge.

This paper analyzes the literature surrounding drive-by methodologies as applied to railway bridges, examining each technique in detail and evaluating their associated benefits and limitations. Additionally, it explores potential difficulties that could arise during practical implementation of these techniques within rail transportation systems, with a particular focus on environmental and operational factors. To provide readers with a comprehensive overview of this topic, recent advancements made by authors in this field are highlighted, along with promising areas for future research aimed at addressing the challenges discussed throughout the article review. Finally, through careful analysis of current knowledge on this subject matter, this work aims to make a valuable contribution towards facilitating more effective utilization of drive-by methodologies across railway infrastructure networks.

2. Overview of Drive-by Condition Assessment of Railway Bridges

Indirect monitoring of bridges based on their dynamic response recorded by sensors installed on a vehicle during its passage has attracted the interest of several researchers due to the advantages it offers over direct monitoring, which involves installing instruments on the bridge itself and assessing their recordings as they evolve. Through indirect observation, we account for the fact that both the vehicle and the bridge vibrate during the crossing and that their dynamic responses are coupled as long as their contact is maintained through the vehicle wheels. Hence, the vehicle has a dual mission, both as an exciter and receiver of the bridge’s vibrations when it travels over it. Making use of this dual purpose, several methods for detecting structural degradation have been developed, particularly for highway bridges. So far, however, little research has been published evaluating the feasibility of indirect monitoring approaches for railway bridges [19].

Recent technologies for monitoring the structural integrity of railway bridges include so-called drive-by damage detection [20,21]—the concept of employing the train passing over the bridge as an excitation source and the sensors placed on the vehicle as opposed to the bridge. A limited number of commercial trains equipped with a small number of sensors might monitor the condition of a large number of bridges using the train’s response to determine whether bridge damage exists. The detection methods rely primarily on comparing acceleration data obtained from instrumented trains with a reference condition corresponding to a healthy structure.

The primary idea behind these techniques is that structural damage modifies the mechanical properties of the bridge and, therefore, the dynamic behavior of the vehicle interacting with it [22]. Then, the condition of the bridge may be determined based on the dynamic responses detected on board the train, such as on the axle box, bogie frame, and carbody. According to Bernardini et al. [22], the primary concern regarding the practical applicability of the drive-by method is that the train’s response may be affected not only by the condition of the bridge but also by factors unrelated to the damage, such as the level of track irregularities, the vehicle’s dynamic response to different passenger loads, and other uncertainties related to the train’s speed variation and accurate positioning with respect to the bridge.

Drive-by methods may be divided into two primary groups: (a) modal parameter-based techniques and (b) non-modal parameter-based techniques. The former, consisting of the identification of bridge properties such as natural frequencies [23,24,25,26,27], damping values [28,29], and mode shapes [29,30,31] based on the vehicle response for most of the proposed methodologies has been demonstrated to be effective up to limited speeds (i.e., 60 km/h). These modal properties can be further used for damage assessment; however, in the first two cases, they are incapable of identifying accurately the damage location. The success of most modal parameter-based methodologies was only proved via numerical simulations, and their results are quite susceptible to external factors such as temperature variations, wind, the mass ratio between vehicle and bridge, and presence of other vehicles on the bridge, among others. In contrast, non-modal parameter-based methods do not explicitly seek the computation of bridge modal parameters, but instead focus on the bridge deflection under passing loads (e.g., apparent profile or change in curvature) or on the dynamic response of the vehicle crossing the bridge, which is also the method examined in this paper.

Numerous research groups have conducted both numerical and experimental investigations to explore various methodologies for assessing the condition of railway bridges using vehicle scanning (drive-by) techniques. These studies evaluated the potential of detecting diverse types of damage and devising strategies to address operational and environmental interferences associated with this assessment approach. Part I of this review article provides a detailed overview of several of these recent studies identified by the authors. The article’s layout is illustrated in Figure 1 through a comprehensive flowchart. To enhance clarity, the article was divided into subsections based on the two main categories into which the applications of drive-by methodologies in railway bridges are divided. Section 3.1 discusses the application of drive-by methodologies in railway bridges for the extraction of modal parameters. This involves, specifically, the use of sensors mounted on vehicles to estimate the bridge’s natural frequencies, mode shapes and damping ratios. Section 3.2 focuses on the aspects related to railway bridge damage identification through drive-by techniques, namely feature extraction and machine learning (ML) methodologies. This clear and concise categorization provides a structured approach to better understand the contents presented in the following sections of the article.

It is worth noting that although some of the studies presented in Section 3.1 do not specifically refer to the application of the drive-by methodology in the context of railway bridges, the importance of including these studies in this literature review lies in the fact that, due to their analytical or numerical nature, these works provide insight into the premises of the drive-by methodology and, to a large extent, can be generalized to the bridge infrastructure for railway transportation systems. Similarly, some of the works reviewed in Section 3.2.2 present feature extraction methodologies that can be applied to railway bridges, although they were not originally studied in this context.

3. Application of Drive-by Methodologies on the Bridge Subsystem

In this section, the application of drive-by methodologies involving bridges and viaducts is reviewed based on works dedicated to the identification of modal properties (Section 3.1) and to the identification of damage (Section 3.2).

3.1. Bridge Modal Identification

In this Section, the problem of assessing the bridge’s modal properties, namely natural frequencies, mode shapes, and damping ratios, is presented. It is also intended to provide an overview of the fundamentals behind drive-by methodologies, as well as some techniques developed over the years to deal with specific operational and environmental disturbances. Works by several authors addressing different methods involving analytical, numerical, and experimental aspects are presented, as well as critical analyzes of each technique with a view to its transposition into practical applications.

3.1.1. Natural Frequency Extraction

The feasibility of extracting the dynamic properties of a bridge based on vehicle responses was initially raised in the study conducted by Yang et al. [32]. For a simplified model (see Figure 2) with a sprung mass and a simply supported beam representing, respectively, the vehicle and the bridge, the authors derived a closed-form solution for the vertical displacement, velocity, and acceleration of the vehicle. In this solution, only the first mode of the bridge was considered, and the authors could demonstrate the presence of the bridge’s natural frequency in the vehicle’s response. The authors also addressed the influence of bridge damping and vehicle speed on the responses. It was shown that the increase in bridge damping is responsible for reducing the magnitude of the bridge’s contribution to the vehicle’s response. Regarding the vehicle’s speed, the authors noticed an increase in the response associated with higher vehicle speeds. This finding lead to the conclusion that higher speeds may help the identification of bridge frequencies; however, this preliminary study did not account for track irregularities which later studies have shown to cause difficulties for the identification when the vehicle is moving at high speeds.

Further investigating the problem, Yang and Lin [33] derived closed-form solutions for the dynamic responses of both the vehicle and bridge by the modal superposition method and convolution integrals which are equivalent to the ones obtained in [32] if only the first bridge mode is considered. By comparison with a more detailed formulation, the authors demonstrated that considering only the first mode provides sufficiently accurate results. Slight differences between the two formulations were attributed to (i) the non-updating of the interaction forces between the vehicle and track and (ii) the assumption that the mass of the vehicle is much lower than that of the bridge, used to derive the analytical solutions. Using the Fourier transform of the vehicle’s acceleration response, the authors demonstrated that it is governed by three main frequency components: (i) the driving frequency; (ii) the bridge’s first and second natural frequencies shifted by the driving frequency, and (iii) the vehicle’s natural frequency. The peaks corresponding to the contribution of each of these frequencies to the vehicle’s acceleration response are indicated in Figure 3, as well as their mathematical expression. Among all these components, it was shown that the one from the bridge’s first natural frequency dominates the vehicle’s acceleration response, which can be clearly seen in Figure 3 by the prominence of the peaks associated with this frequency. The influence of the suspension damping was also evaluated in this study, demonstrating that it significantly reduces the magnitude of the vehicle frequency on the vehicle acceleration response; however, the bridge frequencies are much less affected as can be seen in Figure 3. This behavior regarding the suspension damping was studied in greater detail by Yang and Lee [34] who demonstrated that higher suspension damping tends not only to reduce the vehicle frequency but also improve identification in situations of higher amplitude track irregularities. These findings are quite encouraging in the context of the application of drive-by techniques in railway structures since railway vehicles tend to have suspensions with high damping ratios [35].

To validate the findings regarding natural frequency identification presented in the previous studies, Lin and Yang [36] conducted an experimental campaign on a 30 m span bridge in Taiwan. An instrumented trailer was pulled by a truck over the bridge at different speeds registering its vertical dynamic response. From the acceleration frequency spectra, the bridge’s first natural frequency could be easily distinguished from other frequency components for low speeds of the testing vehicle. However, with the increase in the speed, high frequency components from structural components of the vehicle and track irregularities start to couple with the natural frequency of the bridge, making both completely indistinguishable for speeds of approximately 50 km/h. These influences had not been taken into account in the previous analytical and numerical studies [32,33]. Besides that, higher speeds results in shorter measurement times, and, consequently, a lower frequency resolution. All these issues impose extra difficulties for applications involving high-speed vehicles.

These preliminary studies [32,33,36] formed the basis for the development of drive-by methodologies for identifying the natural frequencies of bridges. The issues raised by these studies regarding contributions due to vehicle frequencies and track irregularities have been treated in several other studies. Yang et al. [37] introduced the concept of the residual spectrum, defined as the difference between the frequency spectra calculated from measurements taken in two consecutive vehicles. The authors demonstrated that this technique reduces the contribution of undesirable frequency components from the vehicle and track irregularities. On the other hand, Kong et al. [38] proposed the calculation of a residual response in the time domain by subtracting the responses of two identical consecutive vehicles corresponding to the instants of time in which both were in the same position on the bridge. Since in these time instants the vehicles are subject to the same excitations arising from the irregularities, this subtraction allows eliminating their effect. Taking a different approach, Yang et al. [39] proposed the use of bandpass filters, singular spectrum analysis, or a combination of both (which has proved to be the most effective) to remove undesirable frequency components. The combined use of these two techniques allowed the vehicle frequency to be removed without introducing spurious peaks in the signal. Yang et al. [40] introduced the idea of using the contact-point response to assess the bridges’ natural frequencies. Since the contact point is below the suspension components, it will not be affected by the vehicle frequency [41]. However, the application of this technique requires precise knowledge of the vehicle dynamics since the contact-point response is derived from the responses of other parts of the vehicle. In addition, this specific response is not easily measured from the practical point of view.

Yang et al. [42] derived analytical expressions for assessing both vehicle and contact-point responses considering a simplified single-DOF vehicle model, such as the one in Figure 2, running over a simply supported railway bridge. The track structure was modeled by a beam, representing the rail, attached to the bridge by a set of spring–dashpot assemblies representing the sleepers and ballast interfaces. The derived analytical expressions were successfully validated by comparison with a FEM-based simulation. The Fourier transform of the responses was performed and the one from the contact point has shown to be much more suitable for estimating the natural frequency of both bridge and track since it was not influenced by vehicle and driving frequencies. In a parametric study, the method showed to decrease in performance for high values of speed, track irregularities, and track damping. He and Yang [43] proposed the use of the residual spectrum calculated from the contact response of each one of the axles of a two-axle vehicle. The combined use of the residual spectrum and the contact response is an efficient way to take advantage of the aforementioned potentialities of both and which the authors showed to be essential for the correct distinction of bridge modes under conditions of track irregularities. The authors developed an analytical formulation of the bridge–vehicle interaction problem from which the contact-point response was derived. A parametric study was conducted testing the performance of the method under varying irregularity levels, vehicle design parameters and velocities, bridge damping ratio as well as support conditions, and the number of spans. Under all these conditions, the method provided reliable results for at least the first three natural frequencies of the bridge with data from only a single vehicle.

A different approach for dealing with the vehicle and driving frequency disturbance was adopted by Erduran et al. [23] which is schematically presented in Figure 4. Firstly, the vertical acceleration at the bogies from a few time steps before entering the bridge to a few moments after leaving it needs to be measured and its FFT computed. Then, some peaks of the Fourier amplitude spectrum are selected as candidate frequencies, and for each candidate frequency, the Continuous Wavelet Transform (CWT) coefficients are investigated over time. The frequencies which only presented significant energy levels during the bridge crossing are considered to be bridge natural frequencies. The validation of the technique was performed based on simulation data generated through detailed 3D models of the bridge, track, and vehicle. It was demonstrated that the first natural frequency of the bridge can be properly distinguished from contributions due to the vehicle and driving frequencies and track irregularities for speeds up to 90 km/h.

Aiming to reduce the negative influence of track irregularities, Zhan et al. [24] applied the time-domain subtraction method (TSM), proposed by [38], to the assessment of natural frequencies of a one-span simply supported railway bridge. The performance of the TSM was evaluated for the six classes of irregularities established by the American standards [44] in which 6 is the best grade. As stated in Figure 5a, Class 4 irregularities are enough to make bridge frequencies practically indistinguishable from background noise while applying the TSM (Figure 5b); the first natural frequency becomes very evident, and even the second natural frequency can be detected. The authors also conducted studies varying the design parameters of the vehicle and the bridge as well as the driving speed. The method performed well under different design parameters; however, the increase in vehicle speed seems to be an issue. For speeds around 20 m/s, errors of approximately 5% are associated with the estimative of the first natural frequency which can be a problem in applications involving high-speed trains.

In a recent study involving high-speed trains, Zhan et al. [25] proposed a very robust methodology for detecting the natural frequency of bridges based on the dynamic response of the vehicles. The authors minimized the influence of the irregularities of the rails and the frequency components of the vehicles calculating the residual response computed by the subtraction between the acceleration response of consecutive vehicles. Additionally, the robustness of the method was significantly improved by combining the residual responses from several pairs of consecutive wagons to calculate the residual spectrum, increasing the amount of temporal information available. The authors numerically demonstrated the accuracy of the method for different levels of irregularities, vehicle speeds, bridge stiffness, damping, and measurements of noise levels. The technique performed well in distinguishing the bridge’s first natural frequency; however, the second natural frequency already appeared with very little amplitude, and the others could not be identified. 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, Yang and Chang [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, Zhu and Malekjafarian [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.

A field study conducted by Malekjafarian 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, Lorenzen 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 bridges. Additionally, a set of accelerometers was installed at the bridge to derive reference values for the natural frequencies which were extracted by the Stochastic Subspace Identification (SSI) algorithm. Firstly, the NN was trained using only the simulated dataset and the weights of the layers stored; then, the concept of transfer learning was used and the previously trained NN had its last layer weights tuned during the training with experimental data. The results obtained with and without the transfer learning are presented in Figure 7b in the form of a scatter 2D plot in which the vertical axis represents the predicted natural frequency and the horizontal axis represents the “true natural frequency”. The variation presented in the “true” values is due to the nonlinear behavior of the bridge that presents lower frequency values associated with higher excitations provided by higher vehicle speeds. As can be seen in Figure 7b, the model trained with transfer learning can capture the true results very well; however, the same was not accomplished for the model trained with simulation data only. In turn, the authors argue that this is largely due to the extremely simple simulation model used which was unable to capture the torsion modes of the bridge, and better results are expected with the use of more sophisticated models.

3.1.2. Mode Shape Extraction

The application of the drive-by concept for the dynamic characterization of bridges is not limited to natural frequency assessment. Accurately extracting a bridge mode shape with sufficient spatial resolution usually requires a large number of sensors or multiple experimental setups. These issues make very attractive the idea of using the vehicle as a moving sensor to scan virtually every point along the bridge’s length. Zhang et al. [48] were pioneers in the development of a methodology for mode shape assessment from dynamic data of a moving vehicle. They proposed the use of a vehicle equipped with an exciter capable of applying a sinusoidal force. For this special vehicle moving over a bridge modeled as a plate, the authors analytically derived a solution for its vertical acceleration and proved that, under the assumption of a very stiff vehicle, the square of the modal ordinate amplitude is proportional to the amplitude of the acceleration spectra. The method was tested and demonstrated both numerically and experimentally in a reduced-scale experiment. However, the necessity to install a shaker on the vehicle imposed extra difficulties on practical applications.

Yang et al. [30] first introduced a formulation for assessing the mode shapes of a simply supported bridge in which the excitation is provided only by the passage of the vehicle. The authors demonstrated analytically that the mode shape can be extracted from the instantaneous amplitude, which is computed as the modulus of the analytical signal derived from the Hilbert transform of the part of the vehicle response related to the natural frequency of the bridge. This method implies the use of dedicated techniques to identify the frequency of the bridge and filter the signal to isolate only the portion related to the bridge. The authors applied the method to a case study involving a simply supported bridge and a sprung mass vehicle. From this study, two major drawbacks of the method became evident. Firstly, its accuracy, especially for higher order modes, seems to strongly rely on the use of very low speeds, on the order of 2 m/s, which would impose operational constraints from the practical point of view. Besides that, the results for higher-order modes have shown to be deeply affected by track irregularities which is another obstacle to be overcome to enable practical applications if the identification of higher-order modes is required.

A recent study conducted by Tan et al. [29] further investigated the methodology proposed by Yang et al. [30] for different values of the bridge’s damping ratio. As presented in Figure 8a, the damping significantly distorts the mode shape, shifting it to the left. Based on an analytical formulation of the bridge vehicle interaction model considering the damping, the authors proposed a correction factor for the original formulation which is a function of the bridge’s natural frequency and damping ratio. As can be seen in Figure 8b, the proposed correction can significantly improve the results; however, some distortion is still present for high damping values, which the authors claim can be corrected by applying a smooth operation to the instantaneous amplitudes.

Malekjafarian and OBrien [31] introduced the Short Time Frequency Domain Decomposition (STFDD) technique for mode shape assessment. This method is based on the application of the Frequency Domain Decomposition (FDD) [49] method to the signals measured in consecutive axles of the vehicle. The bridge is divided into equal-length segments (see Figure 9) and the measurement is performed in stages where each axle is over one of the segments. For each stage, a modal ordinate vector with two elements is obtained by the FDD, and since each stage has overlapping segments, the global mode shape vector can be reconstructed by a progressive rescaling procedure. The authors achieved satisfactory results under the influence of track irregularities by combining the STFDD with the method of subtracting the signal from consecutive axles. The performance of the method was not evaluated as a function of the vehicle speed; however, very low speeds (in the order of 1 m/s) were used in the presented case study. Although it has not been tested, it is possible to infer that the increase in speed will be harmful to the method since there will be a significant reduction in the acquisition time and, consequently, in the frequency resolution obtained with the FFTs.

So far, most of the studies involving drive-by methodologies for mode shape extraction have been based only on the SDOF models without any experimental validation. Seeking to further advance in this topic, Zhou et al. [50] proposed a methodology for bridge mode shape extraction based on the vertical acceleration of a two-axle vehicle crossing a bridge. Firstly, the FFT of the acceleration signal was taken and the peaks corresponding to bridge frequencies were isolated from the rest of the response by frequency domain filtering. Then, the time-domain response corresponding to the bridge contribution was recovered and the mode shapes were estimated based on the signal’s envelope. The method has proved to be effective for speeds up to 20 m/s and with different vehicle parameters and bridge damping values; however, track irregularities and noise had a negative impact on its accuracy. A scaled laboratory test was conducted, and the bridge’s first two mode shapes were successfully identified for a low level of irregularities. In another study involving scaled experimental validation, Eshkevari et al. [51] proposed the Crowdsourced Modal Identification using the Continuous Wavelet (CMICW) technique for the extraction of the mode shapes of a bridge. This technique relies on the use of the Continuous Wavelet Transform (CTW) method averaged for a large number of vehicles (crowd) to extract the absolute value of the mode shapes, as it is presented in the flowchart of Figure 10a. The use of a large number of vehicle passages contributes for reducing the influence of track irregularities, measurement noise, and other sources of interference. The authors validated their methodology using a reduced-scale bridge and vehicles made of Lego^® to measure vertical acceleration. The results obtained for the five first mode shapes are depicted in Figure 10b.

3.1.3. Damping Ratio Evaluation

Besides being less widespread, some studies are found to involve damping estimation using the drive-by concept. González et al. [28] were one of the pioneers in this type of development. They proposed the damping estimation by reverse modeling to derive the track irregularities profile under each of the two wheels of the 2D model from acceleration at the vehicle’s axles. The process is performed by a series of assumed damping ratios. The bridge damping ratio is taken as the one which provides the lower squared error between the estimated profiles under each wheel since, in theory, they should be the same as the wheels cross the same path. The method was validated numerically and performed very well for a wide range of vehicle velocities (10 to 30 m/s) and track irregularities. However, some difficulties were found in dealing with short-span bridges since its higher stiffness results in lower excitation levels. Tan et al. [29] proposed the use of the same correction function applied to extract the bridge’s mode shapes, as mentioned in Section 3.1.2, to estimate the bridge’s damping. The method proposed by the authors involves finding for the correction function the damping value which provides the better mode shape estimative, that is, the highest MAC value with the actual mode shape. However, one of the disadvantages of this methodology is that it requires previous knowledge of the true mode shape.

3.1.4. Summary of the Discussed Literature on Bridge Modal Identification

In

Table 2. Summary of the presented works in drive-by modal identification.

Reference	Modal Parameter	Study Type	Methodology
Yang et al. [32]	NF	A/N	Analytical solution by single-mode approximation validated by FEM. Frequency derived from Fourier transform of vehicle response.
Yang and Lin [33]	NF	A/N	Analytical solution by mode superposition validated by FEM. Frequency derived from Fourier transform of vehicle response.
Yang and Lee [34]	NF	N	Vehicle response signal decomposition by the EMD and assessment of the suspension damping influence on the identification.
Lin and Yang [36]	NF	E	FFT of the vehicle’s acceleration measured while crossing a bridge.
Yang et al. [37]	NF	N	Residual frequency spectrum from consecutive vehicles.
Kong et al. [38]	NF/MS	N	Calculation of time-domain residual response from consecutive vehicles and the FFT and STFT.
Yang et al. [39]	NF	N	Bandpass filter and singular spectrum analysis.
Yang et al. [40]	NF/MS	A/N	Contact-point response from closed-form solutions verified by FEM.
Corbally and Malekjafarian [41]	NF	A/N	Expressions derived for the contact-point response from in-vehicle data. Natural frequency extraction from FFT spectrum.
Yang et al. [42]	NF	A/N	FFT of contact response derived from analytical expressions validated by FEM.
He and Yang [43]	NF	A/N	Residual frequency spectrum calculated from the contact-point responses.
Erduran et al. [23]	NF	N	FFT and CWT coefficients of the bogie’s responses at candidate frequencies.
Zhan et al. [24]	NF	N	FFT of the time-domain residual response.
Zhan et al. [25]	NF	N	Combined residual response of several consecutive vehicles.
Yang and Chang [45]	NF	N	Frequency content of IMFs derived from the EMD of the vehicle’s response.
Zhu and Malekjafarian [46]	NF	N	Frequency content of IMFs derived from the EEMD of the vehicle’s response.
Malekjafarian et al. [26]	NF	E	HHT of measured bogie acceleration responses of several train crossings.
Lorenzen et al. [27]	NF	N/E	NN trained based on the FFT of wheelset acceleration responses.
Zhang et al. [48]	MS	A/N/E	Acceleration response of a vehicle equipped with a sinusoidal exciter.
Yang et al. [30]	MS	A/N	Amplitude of the analytical signal derived from the HT of the bridge-related components of the vehicle response.
Tan et al. [29]	MS/DR	A/N/E	HT of vehicle response combined with a correction function for bridge damping.
Malekjafarian and OBrien [31]	MS	N	Short-Time Frequency Domain Decomposition technique.
Zhou et al. [50]	MS	N/E	Acceleration signal envelop of bridge-related components of vehicle response.
Eshkevari et al. [51]	MS	A/E	CWT of the response of a crowd of sensors.
González et al. [28]	DR	N	Reverse dynamic modeling to derive the damping ratio which provides the lower squared error between the estimated irregularity profiles under each wheel.

Abbreviations: Natural frequency (NF), mode shapes (MS), damping ratio (DR), analytical (A), numerical (N), and experimental (E).

, a summary of the main references discussed in the previous sections regarding modal identification is presented. Aspects such as the estimated modal parameter, study type, and main techniques used are highlighted for a better consolidation of the contents presented.

3.2. Bridge Damage Identification

3.2.1. Overview

The identification of bridge damage is an indispensable task that demands a comprehensive approach to guarantee the safety and operational efficiency of bridges. The criticality of this procedure lies in its ability to determine necessary maintenance or repair actions, which can prevent catastrophic failures from occurring [52]. Furthermore, early detection of any structural abnormalities enables stakeholders to implement measures that will help mitigate potential economic losses and physical harm.

The process of bridge damage detection involves the meticulous examination and analysis of various indicators that could reveal potential defects or structural impairments. This comprehensive inspection entails not only visual inspections, but also non-destructive testing techniques such as ultrasound technology, infrared thermography and acoustic emission monitoring to scrutinize different components including beams, columns and decks for shreds of evidence of deterioration [53]. The gathered data from these examinations are then evaluated using advanced analytical tools which provide insights into possible weaknesses in the structure’s integrity, allowing engineers to determine appropriate measures necessary for addressing any detected issues.

Over the years, technological advancements have played a significant role in enhancing the accuracy and reliability of bridge health monitoring systems [54,55,56,57], making it easier than ever before for experts to detect even minor damages with precision [58]. By facilitating prompt interventions and effective maintenance activities through sophisticated strategies that include a comprehensive sensor network and smart algorithms, optimal functionality throughout the lifespan of any given bridge structure can be ensured.

Several researchers have developed many bridge damage detection strategies for SHM in recent decades which include vibration-based approaches, model update strategies, and neural network applications [59,60,61,62,63,64,65,66]. In addition to the secondary studies discussed in Section 1 (Table 1) of this paper, which are focused on drive-by applications, Karimi and Mirza [66] carried out a comprehensive review of the literature on damage identification in bridge structures. The authors critically evaluated different methods that have been proposed to detect damages in different bridges and concluded that there is still a long way to go in the field of bridge damage detection, and this requires the construction of a comprehensive information model for bridges.

Aligned with the main topic of this paper, the latest research studies have focused on monitoring bridge health using sensors mounted on moving vehicles, a field of study often known as indirect bridge health monitoring. The first work based on this type of monitoring was published by Yang et al. [32]. In their study, the equation of motion combining the dynamic properties of both the vehicle and the bridge was analyzed before representing the passing vehicle’s acceleration as a function of the bridge’s dynamic qualities. By applying Fourier transform on the acceleration of the vehicle, the bridge’s frequencies were detected. Afterwards, indirect health monitoring became an active research field, and the developed approaches that led to breakthrough improvements in this area are discussed in the following subsections. Figure 11 depicts the topics covered, which focus on the main approaches regarding bridge damage identification.

Firstly, Section 3.2.2 presents several signal processing techniques that are used to extract features from response measurements. These features are defined as damage indexes that allow assessing the structural condition of bridges, and their extraction and selection is a crucial step in signal-based damage detection. Frequency-domain methods extract features from the frequency-domain signals such as natural frequencies, mode shapes, damping ratios, modal strain, and modal curvature. These methods which rely on structural properties formed the basis of vibration-based damage detection and have acquired extensive applications in past decades. Time-frequency features can describe local details of measurements both in the time and frequency domain, and thus are able to detect damage-induced variations in a timely manner, even with nonstationary signals. This category of features is commonly extracted by short-time Fourier transform, Hilbert-Huang transform, and wavelet transform, among others. Time-series approaches fit the structural response with autoregressive (AR) models or their variants such as autoregressive with exogenous input (ARX) using the model coefficients as features to detect damage.

Afterwards, the implementation of comprehensive machine learning methodologies, which include not only the extraction of features but also their normalization, fusion, and classification, is discussed in Section 3.2.3.

3.2.2. Feature Extraction

Regarding drive-by railway bridge inspection, Bowe et al. [21] proposed a damage detection method using the analysis of vehicle accelerations resulting from a numerical 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.

Quirke 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.

Yang 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.

Fitzgerald 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. While no field testing has been conducted, the scour indicator has performed well in the two evaluated numerical models, which incorporated measurement errors and train–bridge interaction effects.

Carnevale et al. [70] investigated the dynamic response of a train crossing a bridge to identify structural damage. A moving window root mean square (RMS) damage diagnosis technique is used to analyze the spectral components of axle box and bogies accelerations from healthy and damaged bridges. A damage localization error index (DLE) is introduced to quantify the accuracy of damage localization using sensors deployed in different train positions. Numerical simulations of the train–track–bridge interaction compared scenarios with varying bridge span lengths, damage levels, damage locations, train speeds, and bogie arrangement types. The magnitude of the acceleration to be measured to distinguish between a healthy and a damaged structure (i.e., the damage component) and the accuracy of damage localization are used to evaluate the proposed approach. The strategy worked well for localizing anomalies in commuter train velocity ranges. However, the damage component to be measured is in the order of 10⁻² or 10⁻³ m/s², which is a challenge for implementation in a real railway scenario where track imperfections might reduce the signal-to-noise ratio. The carried-out analyses implied that the acceleration recorded on the leading bogie is best for damage identification, and the algorithm assessing the quasi-static response of the bridge performs better, enabling more precise damage localization and reduced sensitivity to track irregularities. The shortest bridges result in the greatest amounts of damaged components. The damage component increases with train speed, up to 140 km/h, and with damage level, although the best localization accuracy is achieved at lower train speeds and damage levels.

A novel method for indirectly monitoring the structural health of railway bridges was proposed by Keenahan et al. [71], in which direct integration techniques are applied to determine the bridge’s apparent profile by an optimization procedure, directly from the vehicle accelerations. Using the apparent profile, Bridge Displacement Profile Difference (BDPD) is calculated and used as an indicator of temperature change and bridge damage. The frequency of BDPD is demonstrated to be effective through both numerical simulations and experimental studies on a laboratory-scale railway bridge model. The authors show that their method can accurately detect and quantify changes in the structural response of the bridge due to damage or deterioration and can provide useful information for the maintenance and repair of the bridge.

A railway damage detection approach was presented by Martinez et al. [72] for calculating the flexural rigidity of bridges (FR) by measuring the deflections of the bridge using a drive-by method. The method involves using a model of a vehicle equipped with a high-speed laser scanning system (Traffic Speed Deflectometer and Doppler Vibrometers at eight different locations) to measure the deflection of the bridge as the vehicle crosses it. The relation between FR and deflection is given by the Unit Load Method, which is used to extract a damage index with the concept of Ratio of Spatial Standard Deviation (SSTD), i.e., spatial variability in calculated FR. The Blackman filter is also applied to regularize the system of equations as the bending moment matrix relating deflections to FR is ill-conditioned and sensitive to measurement noise. The results of the study show that the proposed method can accurately calculate the flexural stiffness of the bridge, and the calculated results are consistent with the results obtained using traditional inspection methods. In conclusion, the authors suggest that their proposed method has the potential to be a reliable and cost-effective tool for calculating the flexural stiffness of bridges, especially in situations where traditional inspection methods are not feasible.

In their paper, Bernardini et al. [22] analyzed the performance of two time-frequency algorithms in identifying damages in a short-span Warren truss bridge by using a FE 3D model to simulate the dynamic interaction of the track–train–bridge system. Numerical investigation is conducted, and two types of damage are simulated, the first of which involves the connection between the lower chord and the side diagonal member, and the second of which involves the connection between the cross-girder and the lower chord. Then, two different time-frequency algorithms, continuous wavelet transform (CWT) and the Hilbert–Huang transform (HHT), are used to analyze the vibration response of the train bogie. The performance of the two algorithms is then compared in terms of their ability to identify the location and severity of the damage. The results show that both the CWT and HHT algorithms can identify the location of the damage in the bridge model, but the HHT algorithm is found to be more accurate in identifying the severity of the damage. Figure 13 shows the position–frequency map of the difference between the damaged and healthy CWT coefficients and the HHT values. The damaged area may be identified by the index maxima in both instances, even if the HHT instantaneous energy peak is near the right edge. The authors discussed the limitations of the study, including the use of a simplified bridge model and the assumption of linear behavior in the vibration response of the bridge. Additionally, the article suggests possible avenues for future research in this area, including the use of more complex bridge models and the development of more robust time-frequency algorithms.

Lan [73] presented a drive-by inspection approach using vehicle parameter optimization and vehicle displacement as a damage indicator. The displacement difference profile of vehicle is obtained by subtracting the vehicle’s time histories between the baseline and the damaged bridge, where the baseline is derived from the first run over the bridge in good condition. Through several simulations, it was determined that the occurrence of damages may be effectively detected as the peak in the displacement difference profile, whilst the damage level was considered to be the rise in displacement difference. This work provided an approach of parameter optimization aimed at enhancing the vehicle displacement profile difference and minimizing the noises from vehicle dynamics to increase the accuracy and sensitivity of detection findings. The findings suggested that the optimal vehicle characteristics may significantly enhance the inspection performance for all damage situations. Using Monte Carlo techniques, the optimal parameters were established by running several simulations under various damage scenarios. Based on the vehicle displacement profile, the results demonstrated that bridge defects may be identified efficiently and precisely by applying the ideal vehicle characteristics.

The work presented by Micu et al. [74] investigated the potential of using repeated dynamic measurements taken on a passing train to determine the condition of a bridge. The paper presented a full-scale field study of drive-by bridge monitoring using acceleration measurements on an instrumented train. Ensemble responses of the traversing train signals were indicative of the existence and location of a stiffer part of the viaduct where two spans were replaced. 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 Ren 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.

Souza 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.

3.2.3. Machine Learning Methodologies

The main challenge in applying drive-by methodologies for damage identification is that the signals collected on drive-by vehicles also include signatures from the vehicle and the rail profile; in addition, they are easily influenced by environmental and operational effects such as vehicle speed, traffic, temperature, or surface roughness [77]. Therefore, for drive-by health monitoring to be feasible, the variabilities in dynamic measurements caused by environmental and operational variations (EOVs) need to be considered and the algorithms implemented should be able to remove or reduce their influence. Furthermore, most current drive-by damage identification systems rely on prior knowledge of the vehicle or bridge dynamic characteristics, which has led to the limited application of the concept in practice so far. Since the works mentioned in Section 3.2.2 are still in the preliminary stage of research, these conditions were not considered, therefore the feature extraction algorithms were not tested in the most realistic environment. On the other hand, feature extraction as an isolated approach does not allow automatic damage identification (without user intervention). In line with this, to allow a robust, efficient and automatic drive-by damage identification on bridges, the path seems to be the implementation of a complete methodology with several steps that group different techniques. Due to the scarcity of works that follow approaches for drive-by condition assessment of railway bridges, this research was also extended to damage identification based on dynamic responses measured on the bridge. However, because vehicles and bridges create a coupled system, their application in a drive-by approach is very promising.

Meixedo et al. [57,78] and Santos et al. [79] showed that damage identification methodologies must resort to four main operations after data acquisition: (i) feature extraction, (ii) feature normalization, (iii) data fusion and (iv) feature classification.

Feature extraction is often required as raw data are not informative enough about the occurrence of damage. As mentioned in Section 3.2.2, Hilbert Transform and Continuous Wavelet Transform are examples of methods effectively implemented as extractors of damage-sensitive features in drive-by applications. In applications based on acceleration measurements, time series alone provide little information regarding the structural behavior whose appropriate characterization requires the extraction of damage-sensitive features. In this context, autoregressive (AR) models and autoregressive exogenous (ARX) models have been widely reported [57,78,80]. Meixedo et al. [78] implemented an unsupervised data-driven SHM based on a continuous online procedure for damage identification using train-induced dynamic bridge responses. For extract features, the authors applied AR models. Figure 14 shows 30 AR features calculated with the measurements from an accelerometer located at the second mid-span of the concrete slab (Ac1) for baseline and damaged conditions. Baseline scenarios include the variability of temperature actions, train type, speed, and loads. Damaged scenarios were defined based on simulated stiffness reductions (5%, 10% and 20%) in the diaphragm, concrete slab, and arches, as well as friction increases in the movements of the bearing devices. Comparing undamaged (Figure 14a) and damaged features (Figure 14b), the AR parameters present a higher variability in the presence of a range of environmental and operational variations. This behavior reveals the difficulty in distinguishing damaged and undamaged scenarios as variations in EOVs result in similar or greater changes in the parameters.

Feature normalization is key to prevent false alarm detections since, as mentioned above, environmental variations (e.g., temperature) or operational actions (e.g., trains crossing at different speeds) may inflict greater changes than those occurring due to damage. Two approaches are usually mentioned in the literature and in the practice of feature normalization: (i) input–output, based on linear or nonlinear regression models or (ii) output-only, based on latent variable techniques such as Principal Component Analysis (PCA) [81]. The former removes the effects of EOVs, establishing relationships between measured structural responses and measured actions (e.g., traffic, speed, temperature). When monitoring systems do not include sensors to measure EOVs, latent variable methods can be applied. This approach can reduce the influence of independent actions using only structural measurements. Due to the need of suppressing nonlinear effects induced by EOVs, models such as auto-encoder have recently been implemented with high accuracy with regard to feature normalization [82,83].

Data fusion aims to reduce the volume of data while maintaining their most important information. This procedure may merge features from a single sensor, features from spatially distributed sensors or even heterogeneous data types. In all approaches, the goal of data fusion is to achieve a new type of information with less volume and a similar or greater ability to define the measured phenomena when compared to that reached when using any of the original information sources alone. The Mahalanobis Distance has been widely used in this context due to its ability to represent the variability in multivariate data sets [84]. Meixedo et al. [57] show that the Mahalanobis Distance is generic enough to be used to identify any damage while granting a weighting that is completely unsupervised and thus independent of the type of structure, the actions imposed on it, and the human intervention. It consists of a weighted damage indicator in which the weights are determined by the covariance structure. In addition, and as an important advantage, the weighting proportional to the covariance structure grants an additional layer of feature normalization.

While time-series analysis and distance measures can help perform data analysis and indicate the existence of different damages within a data set, employing online and automatic bridge health monitoring procedures must rely on machine learning approaches. These algorithms can autonomously decide whether one or more distinct damages are being observed from patterns in the features. Machine learning is one of the applications of artificial intelligence (AI) where machines are not explicitly programmed to perform certain tasks; rather, they learn and improve from experience automatically. Deep learning is a subset of machine learning based on artificial neural networks for predictive analysis. There are several machine learning algorithms, such as supervised learning or unsupervised learning.

In this sense, feature classification as the last step of the methodology can be implemented to automatically discriminate the extracted features into healthy or damaged using supervised or unsupervised algorithms. If training data are available from undamaged and damaged structures, supervised learning algorithms can be implemented. Artificial neural networks (ANN) [85,86], Support Vector Machines (SVM) [87], or deep Convolutional Neural Networks (CNN) are examples of promising algorithms for supervised strategies. As data collected from damaged civil engineering structures are scarce, unsupervised learning algorithms have been increasingly observed in the literature. This approach is generally based on training machine learning algorithms with baseline references of extracted features, where the structure is assumed to be undamaged and unchanged. New features are then analyzed by the pre-trained machine-learning algorithms to assess whether the structure’s behavior remains unchanged. Most of unsupervised techniques are based on outlier detection [78]. Cluster analysis can be seen as an alternative to these techniques as it allows distinguishing different groups in the data without any previous knowledge or known reference baseline [57].

Hajializadeh et al. [77] implemented deep learning algorithms to perform damage identification using measurements from an instrumented train. Therefore, a deep CNN was built, optimized, trained, and tested to detect damage based only on acceleration signals acquired from the train. The authors concluded that to harness the power of 2D CNN, time-frequency analyses offer powerful images with more distinctive features for classifying train-borne acceleration signals. Among different approaches, the time-frequency spectrogram of the signals was found to provide the best high-level damage sensitive feature. The hyperparameters of the algorithm were optimized using the Bayesian optimization technique. For validation purposes, the method was applied to measurements acquired on a model instrumented train travelling on a simply supported model steel bridge. The algorithm showed good accuracy when experimentally tested for four damage scenarios (combination of two different locations and intensity) and three different travelling speeds. Figure 15 presents a spectrogram of acceleration responses for the benchmark and four damage scenarios under an average speed of 4 miles/h. In this figure, the far-left column corresponds to the sample of five sets of measurements for healthy scenarios. The other four columns denote samples with different damage intensities and locations. The difference between healthy and the damage scenarios is relatively noticeable; however, the pattern does not appear to be consistent all the time.

3.2.4. Summary of the Main Discussed Literature on Bridge Damage Detection

In

Table 3. Summary of the main presented works in bridge damage identification.

Reference	Scope	Study Type	Methodology
Bowe et al. [21]	FE	N	A numerical method using wavelet transform to detect and locate damage in railway bridges by analyzing the change in pseudo frequency.
Quirke et al. [67]	FE	N	A method employing optimization and CE to identify and locate damage in railway bridges by comparing profiles pre- and post-damage.
Yang et al. [68]	FE	N	A numerical method using ht to detect and locate damage in railway bridges by calculating the IAS from the contact-point response.
Fitzgerald et al. [69]	FE	N	A numerical method using CWT to detect and locate scour in railway bridges by calculating the difference in average CWT coefficients between healthy and scoured batches of railway crossings.
Carnevale et al. [70]	FE	N	A method utilizing RMS damage diagnosis technique examines spectral components of accelerations from axle box and bogies to detect and locate damage in railway bridges.
Keenahan et al. [71]	FE	N	Direct integration techniques to determine bridge’s apparent profile from vehicle accelerations using BDPD as indicator of damage.
Martinez et al. [72]	FE	N	Drive-by method using a model of a vehicle equipped with a high-speed laser scanning system to measure the deflection of the bridge and calculate the FR using the Unit Load Method.
Bernardini et al. [22]	FE	N	Two time-frequency algorithms, CWT and HHT, are used to analyze the vibration response of the train bogie to identify the location and severity of damage in a short-span Warren truss bridge.
Lan [73]	FE	N	Drive-by inspection approach using vehicle parameter optimization and vehicle displacement as a damage indicator.
Micu et al. [74]	FE	E	Full-scale field study of drive-by bridge monitoring using acceleration measurements on an instrumented train.
Ren et al. [75]	FE	N	Novel method to determine AP of the track and detect railway bridge condition using sensors on in-service trains.
Souza et al. [76]	FE	N	Feasibility of applying MFCC to the indirect damage detection in high-speed railway bridges by onboard sensors.
Hajializadeh [77]	ML	N	Drive-by health monitoring of railway bridges using machine learning considering environmental and operational variations.
Meixedo et al. [57]	ML	N	Unsupervised data-driven SHM based on a continuous online procedure for damage detection identification based on train-induced dynamic bridge responses. AR models were used to extract features.
Meixedo et al. [78]	ML	N	Application of the Mahalanobis Distance (MD) for damage identification.

Abbreviations: Feature extraction (FE), machine learning methodologies (ML), numerical (N), and experimental (E).

, a summary of the main references discussed in the previous sections regarding bridge damage detection is presented. Aspects such as the feature extraction and machine learning approach, study type, and main techniques used are highlighted for a better consolidation of the contents presented.

4. Conclusions

This article presents and discusses various studies that focus on formulating approaches for evaluating the condition of railway bridges through indirect structural health monitoring (SHM) via drive-by methods. Recent advances in drive-by monitoring have made it possible to evaluate the condition of railway bridges in a non-invasive manner providing more reliable and accurate data, whether by modal parameter-based techniques or non-modal parameter-based techniques. When it comes to damage identification, robust feature extraction methods and machine learning algorithms have shown their effectiveness in processing the measured data and detecting damages thus being well-suited for the drive-by monitoring of railway bridges. However, further research is needed to establish these methods as a practical SHM tool for railway bridges.

It is worth noting that, in the context of damage identification using train-borne signals, careful consideration must be given to the feature extraction procedures due to the dynamic nature of the train–track–bridge interaction and the complexity of the collected data. While these features capture important information about the condition of railway bridges, they may also be sensitive to environmental factors such as weather conditions, track irregularities, and train speed. To provide a more comprehensive analysis, machine learning methods can incorporate such external factors into damage detection processes. Therefore, the article highlights the development and application of feature extraction and machine learning techniques for evaluating the condition of railway bridges through drive-by monitoring.

Despite the aforementioned advancements, most of the developed work relies on simplified numerical models in which the complexity of the effects of dynamic vehicle–track–structure interaction is not properly included. Thus, the potential of the methods developed so far needs to be further evaluated, either in field experiments or in numerical models that include VTBI models in which, although the need for prior knowledge about the dynamic characteristics of the vehicle and the bridge represents an added difficulty in their practical implementation, it is possible to evaluate the robustness of these methodologies against environmental and operational effects. In addition, increased speeds, particularly for high-speed bridges, may result in shorter measurement durations and, therefore, a lower frequency resolution. Many of these factors provide additional challenges for applications requiring high-speed vehicles.

Several promising avenues are suggested for further development in this area. First, the development of more robust and accurate feature extraction methods is essential. Current methods are sensitive to environmental factors such as weather conditions, track geometry, and train speed. Improving the robustness and accuracy of feature extraction methods will significantly improve the performance of drive-by monitoring systems. Second, the development of more efficient and effective machine learning algorithms is critical. The existing algorithms can be computationally expensive and struggle to handle the large amounts of data collected by drive-by monitoring systems. The development of more efficient and effective machine learning algorithms will make drive-by monitoring systems more practical for field use. Finally, there is a need to develop more comprehensive numerical models that accurately capture the dynamic vehicle–roadway–structure interaction. Current numerical models often oversimplify the complexity of the real-world scenario. By developing more comprehensive numerical models, the accuracy of underride monitoring systems can be improved.