Data processing and analysis involves transforming raw data into meaningful information through structured steps such as collecting, organizing, analyzing, and interpreting data using manual or automatic processes to generate valuable insights for decision making. The data processing and analysis category represents the most research area among the publications reviewed, accounting for 50.3% of the included studies.
3.4.6. Displacement Analysis/Estimation
The Leica Nova MS50 MultiStation, an image-assisted total station, is potentially utilized as a modern geodetic measurement system capable of precise vibration and displacement analysis [
83]. The outcome of the experiments demonstrates that the Leica MS50 is capable of precisely estimating the deflection and movement characteristics under 5 Hz [
83].
In another displacement analysis research, Xu et al. [
84] presented an economical visual recognition method for multiple location vibration acquisition, leveraging a regular consumer camera for video recording and a specifically designed method for motion picture analysis. The research validated the technique on a pedestrian bridge by measuring the structural deformation of the deck and cable vibrations caused by human load [
84]. The analysis results of both measured parameters allow for precise prediction of the eigenfrequencies, and the results can be utilized to study divergences in eigenfrequencies under different human loading conditions [
84].
Fradelos et al. [
47] suggested that a simplified algorithm to process standard video imagery can revamp the two-dimensional movement dynamic of elastic footbridges. Fradelos et al. [
47] applied this technique to a timber bridge with managed forced vibrations, where the footbridge was vertically rigid but exhibited significant lateral flexibility due to accumulated damage.
Figure 13 displays the chronological data of calculated deformations for the reference positions. The research produced precise predictions of the eigenfrequency and the attenuation of the footbridge and was matched with predictions extracted by using other sensing devices [
47].
Yu et al. [
85] introduced a novel hybrid device, the “smartstation”, for monitoring displacements of footbridges. Full-scale investigations were carried out on a footbridge to assess the method’s viability using the composite instrument [
85]. Yu et al. [
85] reported that in experiments within the range of 5.7–10.0 mm and 1.3–2.5 mm, the technique precisely recognized almost stationary and active vibrations.
Ma et al. [
86] proposed a technique for deflection prediction for structures that combines datasets from a frequency-modulated continuous-wave millimeter wave radar (FMCW) and an accelerometer.
Figure 14 shows the overview of the design and flowchart. The deflection was predicted on-the-fly using the radar data with a phase-unwrapping algorithm with the aid of an accelerometer if the radar wavelength is smaller than the structure deflection [
86]. The proposed technique produced an enhanced deflection estimation precisely [
86].
3.4.7. Dynamic Assessment/Monitoring/Response
He et al. [
87] concentrated on vibration recognition and FEM of a footbridge in the investigation. In between ranges of frequencies of 3.59 to 14.92 Hz, He et al. [
87] discovered several consistent modes linked with dominant bending and twisting distortions using a highly synchronous tri-axial WSN, which later led to the design of four distinct FEMs [
87]. According to He et al. [
87], the conclusive FEM is suitable as a reference for continuous tracking and provides recommendations to scholars for analyzing and modeling this type of footbridge.
Huang et al. [
88]’s research focused on OMA on a stress-ribbon footbridge. Huang et al. [
88] determined the bond failure of the hollow steel profiles filled with concrete and the concrete elasticity modulus using ultrasonic instruments and rebound hammers, respectively. By comparing the identified FE model with non-destructive testing methods, Huang et al. [
88] reported that the non-destructive testing methods provide crucial supplementary information to the SHM.
Colmenares et al. [
89]’s dynamic assessment of the KTH Royal Institute of Technology’s concrete footbridge using the FEM and three-dimensional solid FEM in autumn and winter weather identified that the weather conditions significantly influence differences in eigenfrequencies of the studied footbridge. Colmenares et al. [
89] reported that the findings will help minimize the ambiguities linked with an FEM.
Li et al. [
90] presented a technique to determine a footbridge’s frequencies with pedestrians by analyzing the vibrations of a shared scooter. An innovative FEM consisting of four independent directions of motion was presented to simulate a rider and a scooter. The study highlighted several additional engineering factors between the vehicle and the bridge, which warrant further investigation.
The investigation of the patterns of vibration caused by human motion in footbridges with elevated vibrational frequencies and the assessment of the viability in a Tuned Liquid Damper (TLD) to dampen vibrations was conducted by Lu et al. [
91]. Using a simple pure water TLD to test and analyze the feasibility of vibration control, Lu et al. [
91] identified that the TLD decreases the bridge’s primary frequency and raises the attenuation ratio which provides relevant data for SHM and vibration control for similar structures under human-induced vibration.
Bassoli et al. [
92] aimed to characterize the time-dependent response of a steel curved pedestrian bridge for ambient vibrations and pedestrian-induced loads while assessing the impact of temperature variations on structural modal properties using an SHM established on MEMS sensors. The structural motion-related properties are determined with the use of the classical Enhanced Frequency Domain Decomposition (EFDD) method [
92]. The experiments found that the value of the vertical accelerations induced by wind reached about 3–5 mg while a crowd of walkers produced vertical accelerations higher than 100 mg as illustrated in
Figure 15 [
92]. Bassoli et al. [
92] reported that a model updating procedure is needed to match the experimental results. The numerical dynamic investigation was conducted after refining the FEM to reproduce pedestrian dynamic loads [
92].
Cunha et al. [
93] described two dynamic monitoring systems installed on lively footbridges to characterize their dynamic behavior and response, with the potential to detect damage at early stages. By using LabVIEW software, Cunha et al. [
93] developed a Continuous Structural Modal Identification framework for tracking of deviation of modal characteristics in both footbridges. The experiments presented results from the automated data analysis of the monitored footbridges, highlighting the possibility of constant vibration tracking [
93].
Moutinho et al. [
7]’s research work involved the numerical and experimental dynamic analysis of a very flexible pedestrian bridge in Porto, where it received a high level of vibrations reported by the users. The research begins with the description of the bridge and identification of its dynamic properties, followed by experimental and numerical simulations of various pedestrian loading scenarios exciting the bridge [
7]. Using a dynamic monitoring system to characterize vibration levels, the results revealed that a single pedestrian walking under resonance conditions induced maximum acceleration on the footbridge exceeding 0.5 m/s
2, which approaches the limit specified in several codes [
7].
Bai et al. [
94] presented an innovative framework to track bridge behavior, employing distinct camera locations and several image processing methods to achieve economical yet highly efficient results. The framework incorporates a deep-learning-based data processing and analysis technique, verified through an optical motion tracking technique for movement monitoring [
94]. The framework incorporates a deep-learning-based data processing and analysis approach that demonstrated its accuracy in capturing motions in the laboratory and real-life footbridges [
94].
A non-invasive, low-cost, vision-based technique proposed by Ponsi et al. [
95] using image-based techniques for the vibrations tracking of footbridge demonstrated satisfying results. However, Ponsi et al. [
95] also concluded that there are real conditions such as camera shakes, lighting, field of view and camera synchronization drawbacks that could potentially affect the results are areas for future studies.
Gamino et al. [
96] employed a computational modeling approach incorporating a soil-structure interaction methodology to represent the vibration characteristics of a timber-concrete pedestrian bridge. The monitoring conducted with ground-based radar interferometry and video motion amplification highlights the significance of incorporating the soil-structure interaction approach to accurately represent the bridge’s dynamic behavior and develop reliable models for assessing its structural responses.
In the research, Ponsi et al. [
97] investigated vision-based techniques based on target tracking for dynamic monitoring and identification of a steel footbridge. The vibration outcomes from the image-based technique, when corresponding with accelerometer data, show satisfactory agreement in time-space and frequency-space, resulting in the identification of three eigenmodes of the footbridge, demonstrating the possibility of the image-based approaches.
In a study of a pedestrian bridge by Miskiewicz et al. [
98] that includes computational modeling, on-site vibrational loading experiments and an SHM system, the pedestrian bridge was found to possibly have structural dynamics problems based on the numerical simulation results. During dynamic loading, the deck exhibited movements with accelerations reaching as high as 4.5 m/s
2, consistent with the findings of the computational simulations [
98]. The repair project involved installing TMDs on the deck’s external girders at its mid-span, a design validated through numerical simulations and analysis [
98]. The result before TMDs and after TMDs is illustrated in
Figure 16. Repeated dynamic tests performed on the bridge following the repair work confirmed the positive outcome [
98].
In a footbridge response characterization study, Kromanis [
99] presents the findings on surveying distortions of a pedestrian bridge with loading from cyclists using an altered GoPro camera equipped with a lens that is zoomable. Kromanis [
99] reported employing techniques such as visual data processing, de-noising recorded data, interpretation of vertical displacements, and the derivation of influence lines. The method can detect stationary and active motions of footbridges, and vertical deflections calculation in sub-millimeter accuracy from the camera recording [
99].
Kromanis and Elias [
100] used the templating recognition method to estimate the subject’s pixel motion, from which precise reference deflections can be obtained. These displacements are utilized to determine the frequencies of the movements and generate the shape of the first vertical oscillation mode [
100]. In conclusion, Kromanis and Elias [
100] reported that despite being able to gauge high-mode vibrations, determining oscillation mode shape is challenging when using 1/10 pixel resolution data.
3.4.10. Load Prediction
Identifying walking patterns and predicting pedestrian loads on a footbridge is challenging due to the complex ground reaction forces generated by human-induced vibrations [
103]. Sadhu et al. [
103] performed an investigation demonstrating a wavelet-based time-frequency decomposition technique for extracting pedestrian walking patterns using video cameras and vibration sensors. Full-scale investigations and experiments suggested that the technique has accuracy in identifying walking patterns [
103].
Hassoun et al. [
104] presented a novel technique for continuous crowd load prediction on pedestrian bridges, focusing on high-density crowds using FBG fiber optic sensors and machine learning (ML) to generate prediction models. Hassoun et al. [
104] investigated different types of bridge loading scenarios to predict the weight of individuals and groups of people and the continuous flow of people’s activities in the laboratory and on a scaled bridge model [
104].
Figure 18 reveals the result of the groups of people for fast and slow activities. The findings highlighted the capability to estimate the total load weight with a mean error of 10 kg and determine activity speed with over 90% accuracy [
104].
Mustapha et al. [
105], focusing on pedestrian load prediction, introduced effective methods for estimating crowd flow and bridge loads by leveraging cutting-edge AI and measurements collected from structure sensing devices and body-worn sensors. The AI approaches, including Convolutional Neural Networks (CNN) and Support Vector Machines (SVM), were initially used in individual sensing sources, such as FBGs and accelerometers, and later extended to enable multi-sensor measurements integration [
105]. The results demonstrate the monitoring solution’s effectiveness, achieving 98% precision for one movement type speed identification, 91% for multiple movement type speed and loading assessment, and a minimum 9% error in load behavior prediction [
105].
3.4.11. Method Validation
Liang et al. [
106] presented a technique utilizing 3D imaging with laser for assessing mechanical performance. Initially, the study derives a reverse analysis approach alongside a conceptual model for evaluating the physical characteristics of pedestrian bridges [
106]. The study develops a point-based model of the footbridge to extract alignment and key parameters, deduces forces on key components using back analysis, and verifies the precision of the outcomes by corresponding them with the inner force measurements [
106]. When compared to traditional single-point measurements, the results present an alternative and efficient approach for the assessment of the mechanical behavior in complex bridges [
106].
To overcome the limitations of wired solutions and costly equipment, Casciati et al. [
107] proposed an innovative method using a measurement integration method based on Kalman filtering, integrating reactions from a GPS and an acceleration sensor. GPS accuracy is improved by utilizing satellite refinements from a single base reference using the Real Time Kinematics method [
107]. The method was validated on the “Tesa” cable-stayed pedestrian bridge [
107].
The study by Ngeljaratan and Moustafa [
108] explored marker tracing digital image correlation in the role of contactless data acquisition technique. The method was validated through a large-scale laboratory application, monitoring the reaction of a footbridge subjected to two-directional earthquake movements [
108]. The digital image correlation method validation successfully captured the footbridge’s deck rotaional movement and deflection caused by varying grades of seismic severity [
108].
Barros and Paiva [
109] proposed a non-intrusive radar interferometry method for SHM and validated the method on four different bridges in Portugal. The radar sensor used in their study, the IDS IBIS-FS system, is an industrial-grade microwave interferometer that includes a sensing device, a personal computer, and an electrical energy source [
109]. The method was validated for natural and excitation frequencies to produce high accuracy, portability, and ease of use of the non-intrusive radar interferometry technique [
109].
A temperature compensation methodology developed by Weil et al. [
110] has laid the foundation for Particle Filter-based temperature compensation of FBG strain data. This Particle Filter-based implementation, compared with the Kalman Filter, was validated to have improved results by modeling the strain events as an asymmetric Weibull Distribution.
In Ponsi et al. [
111]’s research, the method of fusing Global Navigation Satellite Systems (GNSS) data with accelerometers was validated on a steel footbridge. The data-fusion outcomes demonstrate that the technique is able to mitigate the constraints of single sensing devices and deliver better displacement estimates precisely.
3.4.12. Modal Identification
Abasi and Sadhu [
112]’s study evaluated and compared Time-Varying Filtering Empirical Mode Decomposition (TVF-EMD) and Second-Order Blind Identification (SOBI) on a large-scale footbridge and a wind rotor blade with diverse dynamic characteristics. Abasi and Sadhu [
112] reported that the outcomes indicate that TVF-EMD achieves higher precision in modal analysis than SOBI. Nevertheless, SOBI offers greater computational efficiency over TVF-EMD when the sensor number is equal to or larger than the modes of interest’s number.
Brownjohn et al. [
113] detailed using wireless inertial measurement units as sensors, developed for biomechanical movement analysis, in the vibration assessment experiment of a footbridge. Brownjohn et al. [
113] used the sensors to determine the modal frequencies and damping parameters in an output-only dynamic assessment and to measure the inertial responses of a jumping person, correlating them with the deck’s dynamics. The mode-specific mass predictions of the footbridge, when compared with those acquired from a hammer with a force transducer and specified mass configurations, demonstrate uniformity throughout the investigation results [
113].
Górski et al. [
114] performed an investigation on monitoring the vertical direction of a glass fiber-reinforced polymer (GFRP) footbridge. The research included mode shape recognition and vibration-based experiments with several specific vibrational inputs based on ambient vibration tests [
114]. Górski et al. [
114] identified seven eigenfrequencies reaching as high as 21 Hz, associated vibration modes, and energy dissipation ratios of the pedestrian bridge.
Figure 19 illustrates the results from the experiments ranging up to 21 Hz. The outcomes delivered valuable information for the SHM of identical structures subjected to comparable loading situations [
114].
Jiang et al. [
115] presented an innovative approach for dynamic response reconstruction of structure and virtual sensing in SHM, utilising a sequential modeling method. This method leverages space-time dependence in sequential measurements to enhance data transfer, significantly improving reconstruction performance and demonstrated to be effective [
115].
To fully utilize the potential of decentralized implementation, Sadhu et al. [
116] developed new algorithms that leverage sparsity concepts and wavelet transformation under the blind source separation (BSS) approach. The identification challenge is framed under the underspecified BSS framework, applying measurement transformations to the time-frequency domain to achieve a compressed approximation [
116]. The proposed methods experimented on a live infrastructure using WSN in a decentralized deployment successfully recognized the structure modes of the subjected bridge with only very little data in a decentralized manner [
116].
To overcome challenges in contactless image-based dynamic mode analysis techniques for SHM, Banerjee and Saravanan [
117] proposed a blind system determination method to retrieve eigenfrequencies and modal shapes from the acquired video recordings.
Figure 20 illustrates an outline of the proposed methods. The computation inaccuracies were verified below 1%, making it highly applicable and dependable for SHM [
117].
Domaneschi et al. [
118]’s study focused on the vibration mode characterization of a pedestrian bridge by output-based method. The investigation utilizes measurements from an extended-gauge fiber optic stress sensing device implanted throughout the pedestrian bridge, with the spectral power distribution of the dispersed extended-gauge vibration-induced curvature being employed [
118]. Comparison with previous studies in the literature validates this presented technique, although observing narrowly reduced frequency measurements [
118].
To leverage advancements in SHM and explore their use case for lightweight footbridges, Wang et al. [
119] presented a case study of an aluminium alloy footbridge in a high pedestrian activity area. Acceleration time series at specified structural joints were collected for OMA, along with recordings of pedestrian traffic on the structure [
119]. The prototype study concluded that the applied methods are effective for data processing, modal identification, and model updating in lightweight footbridges [
119].
In Ozer [
120]’s research, a medium-term vibration data set from smartphones handheld on a bridge performing different tasks was presented. The result demonstrated that the dataset observations are discontinuous but may still provide insights into the long-term impacts that could have caused fluctuations in the bridge’s natural frequency.
Feng et al. [
121] proposed a modal identification utilizing the drive-by method using smartphones and application-specific accelerometers installed on electric scooters and bicycles. Validation on a pedestrian bridge showed that smartphone sensors can deliver precise output comparable to application-specific accelerometers. The footbridge’s eigenfrequencies were extracted from stationary and moving scooters and bicycles using variational mode decomposition and filtering techniques.
Hacıefendioğlu et al. [
122] introduces an advanced model identification method by combining multiple visual recognition methods. The result shows substantial improvements in distant and contactless SHM.
Qiao et al. [
123]’s research aims to investigate a lightweight synchronization concept using two long-range (LoRa) wireless sensing modules for mode shape and frequency extraction. The test results demonstrated that the synchronized LoRa nodes can rapidly and accurately obtain an average synchronization precision of the principal mode of the beam vibrations of 4.5 ms.
3.4.13. Model Development/Prediction/Validation
He et al. [
124] performed an OMA on a footbridge kept on a butterfly arch. A precisely timed three-axis WSN was deployed for the capturing of the footbridge’s environmental movement responses induced by the breeze and light pedestrian traffic [
124]. The experiment results obtained through the subspace-based system identification technique revealed that the experimentally obtained mode shapes exhibited in-phase and out-of-phase vertical deformation, along with some torsional dynamic modes [
124]. He et al. [
124] reported that a model refined by a sensitivity-based method may operate as a reference instance for extended tracking of the footbridge’s health.
Venuti et al. [
125] presented and validated 2 separate FEM of the Streicker pedestrian bridge. Venuti et al. [
125] first developed the 3D beam-based model based on the detailed drawings. Thereafter, an enhanced discretization of the footbridge deck was implemented using shell-based elements [
125]. The footbridge FEM was verified using pre-recorded SHM measurements from stationary and active experiments [
125]. The results indicate that the S model surpasses the B model in accurately capturing the bridge’s stationary and active behavior, particularly between the primary span and supports, and is more satisfactory in representing the geospatial spread of human loads [
125].
Catbas et al. [
126] investigated digital recording and model design for infrastructures lacking reference materials by using data from LiDAR technology to acquire the datasets of a footbridge. The datasets were analyzed for the generation of geometrical and structure divisions. The investigation demonstrated that the datasets generated return favorable outcomes specifically for footbridges lacking reference materials.
Li et al. [
127] proposed an improved hierarchical Bayesian modeling framework to address issues with high computational costs in the hierarchical Bayesian modeling framework. The results verified via the investigation of a footbridge demonstrate that the framework provides a higher precision assessment of uncertainty in structural parameters and shows increased computational performance analogized with the hierarchical Bayesian modeling framework.
While FEM refinement methods were widely investigated recently, investigations established on deterministic techniques still dominate existing academic work, failing to take into consideration the unpredictable consequences in the process of model refinement [
128]. Yin [
128] proposed a functional approach for FEM refinement and estimation using Bayesian regularization with insufficient datasets. The approach was anticipated to increase the performance of model refinement and estimation [
128].
Ao et al. [
129] proposed a low-cost sensor, highlighted the impact of input parameters, proposed a modified Principal Component Analysis (PCA) model optimization method and explored data models developed with limited data set. Ao et al. [
129] reported successfully detecting damage using the single-class SVM AI method that leverages results from data modeling.
Castle Cornet Bridge is a nine-span reinforced concrete bridge subjected to corrosion and deterioration described in the study of Lutton et al. [
130]. FEA modeling of the footbridge was conducted before the load test, with Structural Health Monitoring (SHM) implemented using the FBG sensing device to acquire the bridge’s structural reaction during the test [
130]. Lutton et al. [
130] used the SHM data obtained from FBG sensors in comparison to the FEA model for the validation of the theoretical model [
130].
3.4.15. Operational Modal
Analysis
Komarizadehasl et al. [
132] sought to overcome common challenges in low-cost SHM solutions by installing 4 LARAs as illustrated in
Figure 21, on a short-span footbridge to conduct experiments. The study focused on automating data acquisition and management, as well as creating a digital model in SAP2000 established on available illustrations and physical properties [
132]. The bridge’s OMA was conducted using the FDD and Covariance Stochastic Subspace Identification methods [
132]. Komarizadehasl et al. [
132] documented that the footbridge’s eigenfrequencies measured using an ultra-precise sensor, the HI-INC, closely matched those obtained using LARA.
Sun et al. [
133] further explored the traditional transmissibility-based operational modal analysis technique, which uses data with various load situations, and the power spectral density transmissibility technique, which relies on multi-reference outputs subjected to a one-load situation. Sun et al. [
133] proposed that addressing uncertainties is crucial for enhancing the reliability of recognition outcomes and improving algorithm precision. Limited research has addressed the unpredictability effects of the power spectral density transmissibility technique, highlighting the need for future unpredictability investigation in this area [
133].
In the study, Fontan and Guerineau [
134] utilized new and standard sensors on a 70-year-old retired concreted footbridge to conduct OMA. The measurements were assessed and contrasted with several formulas, including SSI and EFDD, and these formulas were subsequently used to fine-tune an FEM of the footbridge with the MAC matrix [
134]. Fontan and Guerineau [
134] reported that incorporating dynamic properties enhances the understanding of the structure and helps prevent incorrect conclusions regarding the use of the aging bridge.
3.4.20. Structural Evaluation/Identification/Material and
Response
Prediction
Górski et al. [
144] presented a study on the changes in modal parameters and rigidity of the Fiberline Bridge, a cable-stayed structure constructed completely with Glass fiber-reinforced polymer hybrid, which had been in use for 20 years and exposed to extreme environments. The eigenfrequencies and eigenmodes of the footbridge in its initial condition were assessed using the FEM, which was developed based on geometric and material characteristics acquired using the blueprints and bending or flexing experiment outcomes conducted in 1997 [
144]. The study reported that the revised FEM precisely reflects the responses of the footbridge and is an appropriate reference FEM for extended tracking to assess the all-around responses in operational loading situations [
144].
In the study, Catbas et al. [
145] explored vision-based technologies for practical, low-cost and effective methods in non-destructive structural evaluation. A framework for image-based structural identification was proposed to determine structural parameters using a fully non-contact and non-target method based on vision-related techniques [
145]. The overview of this non-target deflection acquisition technique is shown in
Figure 22. The camera system also identified traffic over the bridge and classification of the vehicle weight estimation [
145]. The input effects, including vehicle loadings, vehicle locations, and output displacements of the bridge structures, can be used to determine a series of displacement unit influence surfaces [
145]. Quantitative analysis of the unit influence surfaces has confirmed its consistency and reliability, making it suitable for applications in damage detection and localization [
145].
In the study by Dong et al. [
146], a fully non-contact structural identification system was proposed, primarily aimed at identifying a footbridge’s unit influence line (UIL) in functional traffic conditions. The study solely used cameras and machine vision methods to obtain the placement of traffic as input and deflections as output [
146]. The UILs were identified in laboratory experiments and on a footbridge [
146]. The bridge user’s loading was predicted using the derived UIL, and the estimated bridge users’ weights were within acceptable ranges [
146].
Dong and Catbas [
147] proposed a visual structure characterization system for footbridges that integrates visual deflection acquisition with the loading localization of image-based vehicles. The study extracted the UIL as a metric of structural characterization and validated the presented techniques on a pedestrian bridge [
147]. The experiment extracted the filtered UIL using fast Fourier transform, which shows the structural behavior of the footbridges and the load capacity was identified [
147]. The study reported that the proposed framework is promising and can complement conventional SHM systems.
Zhao et al. [
148] used MIDAS Civil software to specify an FEM based on the eigenfrequency acquired from the vibration experiments of a live footbridge together with ML prediction of the structural material parameters.
Figure 23 illustrates the two structures of the neural networks. The experiment outcomes indicate that the footbridge model founded on MIDAS Civil software exhibited precision, but did not satisfy the essential requirements until it was updated using the backpropagation technique, which produced results closely aligned with the sensor measurements [
148].
Seon Park et al. [
149] proposed an extended stress forecast approach for concrete buildings using meteorological information and stress measurements with a CNN. The study used meteorological information as the input and stress measurements from the fiber-optic sensors as the output layer of the CNN [
149]. The study reported that it establishes a useful approach for forecasting stress in concrete buildings using the presented method [
149].
3.4.21. System Identification
Ali et al. [
8] conducted system identification (SI) on a pedestrian bridge by capturing the vibration data of the footbridge with six economical triaxial micro-electromechanical systems (MEMS) accelerometers. Ali et al. [
8] used an output-only method of modal analysis, the FDD algorithm, for the derivation of modal characteristics, eigenfrequencies and modes. The study identified three mode shapes and frequencies through system identification and compared them with the bridge’s FEM created with Abaqus software [
8]. The study observed a tight association between the FEM and system identification outcomes, with a frequency difference of approximately 10% and a modal assurance criterion (MAC) exceeding 0.80 for experimental and analytical mode shapes [
8]. This result demonstrates a close match despite the limited number of accelerometers and the simplifications and idealizations in the FEM [
8].
In the study, Duarte and Ortiz [
150] performed a viability investigation using economical data collection equipment, smartphones, and Raspberry Pi for system identification using the Bayesian Spectral Density method to determine the model characteristics and the associated unpredictability regarding probability distributions. The approach was verified on a steel pedestrian bridge with a traditional approach of highly sensitive piezoelectric accelerometers for comparison [
150]. The results show that all three devices consistently recognized the eigenfrequency, with minimal discrepancies lower than 0.01% mean and variation, thus confirming that economical data collection equipment can accurately determine the structure’s eigenfrequency, yielding results comparable to traditional acquisition systems [
150].
Efficiently addressing the multi-parameter recognition challenge for live structures while precisely quantifying ambiguities for determining model characteristics and revising FEM remains a significant challenge [
151]. An innovative Bayesian approach utilizing the Markov Chain Monte Carlo method was presented by Liu et al. [
151] to tackle these challenges. The proposed framework’s effectiveness was demonstrated through multi-configuration atmospheric vibration experiments on a high-traffic pedestrian bridge, with accelerations measured at specific points [
151]. The study reported successfully identifying the prevailing modal behavior and modal characteristics of the pedestrian bridge concurrently with the related ambiguities using the presented method [
151].
Most bridge system identification methods currently use output-only approaches, assuming dynamic loads are white noise due to the challenges of measuring them, leading to considerable flaws [
152]. Lim and Yoon [
152] sought to create a system characterization technique for footbridges that utilized AI and visual recognition methods to estimate the position, extent of the human loading and the vibration reactions of the bridge [
152]. The validation outcomes showed that the presented technique successfully evaluated the vibration characteristics of the footbridge with anticipation of serving as an efficient and effective tool for SHM [
152].
In the research work, Fábry et al. [
153] concentrated on characterizing footbridges by non-invasive dynamic assessment. Several numerical models were developed to facilitate comparison, examining how the rigidity of the parapet affects the overall structure’s rigidity [
153]. Outcomes from the experiment revealed that the FBG FS6500 optoelectronic sensor and the PCB393B31 piezo acceleration sensor produced a fairly matching result, thus forming a foundation for the characterization of the footbridge but it is not yet possible to verify structural damage [
153].
Donnelly et al. [
154] sought to comprehensively investigate the vibration characteristics of the Ha’penny pedestrian bridge by using the associated model in SHM and damage detection. The study initially developed a preliminary finite element model using MATLAB, followed by the use of the modes derived from this analysis to support an OMA conducted with strain gauges attached to the structure [
154]. The study reported that after updating and calibrating the FEM, an accurate representation of the bridge is within acceptable limits [
154].
3.4.23. Vibration Analysis/Modeling
In this research, Omidalizarandi et al. [
157] suggested a reliable and automated dynamic assessment method, a time-based modal analysis recognition technique. This method is innovative in its ability to automatically and reliably identify initial eigenfrequencies, even those that are closely spaced, while reliably and precisely predicting the characterizations of a footbridge with the use of a small number of budget MEMS acceleration sensing device [
157]. The dynamic assessment technique demonstrated that magnitudes could be evaluated with precision within a fraction of a millimeter, the precision of frequencies finer than 0.1 Hz, and damping parameters with accuracies finer than 0.1% for modal damping and 0.2% for overall damping [
157].
In the study, Casciati et al. [
158] presented and analyzed data collected from a pedestrian timber bridge under various “moving” load configurations using a time-frequency decomposition technique to model human-induced vibrations. The motion rates of pedestrians movement on the footbridge were recorded using accelerometers and analyzed to identify the footbridge’s characteristics, followed by the implementation of the numerical model of the pedestrian’s loads [
158]. The study reported that the outcomes acquired from the presented model strongly correspond with the field measurements [
158].
Kadota et al. [
159] conducted a vibration modeling study utilizing 3D acceleration measurements and high-resolution FEM analysis of the joining part of the stairs and main girder of a pedestrian overpass, which exhibited actual damage. The analytical results of this study did not align perfectly with the measured results across multiple natural modes, indicating the need for a thorough review of the analytical framework, including member and material characteristics [
159].
Ngan et al. [
160] designed an FEM for the assessment of the vibration characteristics of a new pultruded GFRP floor system, which, due to its lightweight and low damping characteristics, is prone to excessive vibrations caused by human dynamic loading. The edge constraints of the end support and beams of the footbridge serve as a solid validation reference for a comparable unidirectional spanning GFRP flooring design [
160]. While the verification was conducted on a small collection of results, the investigation highlights the possibility of FE modeling to accurately estimate the vibration properties of the subjected floor design [
160].