Over-height Vehicle Impact Severity Assessment for Through-Plate Girder Railroad Bridges

Over-height Vehicle Impact Severity Assessment for Through-Plate Girder Railroad Bridges | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Over-height Vehicle Impact Severity Assessment for Through-Plate Girder Railroad Bridges Omobolaji Lawal, Shaik Althaf V.Shajihan, Thomas Golecki, Kirill Mechitov, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5994795/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Low clearance railroad bridges in the United States are prone to frequent impacts from over-height vehicles, which can lead to structural damage and disruptions in railroad bridge service. Current practice mandates the closure of bridges after an impact is reported. However, this approach results in traffic delays and loss of revenue for railroad owners in cases of minor impacts, which occur far more frequently than major ones. While researchers have developed approaches to detect such impacts using acceleration responses obtained from sensors mounted on the bridge, the severity is generally difficult to ascertain. Therefore, there is a need for a reliable method to assess both the occurrence and severity of impacts. Although previous studies have used permanent displacement thresholds to rate impact severity, measuring permanent displacement is challenging and too expensive to be scalable. To address these challenges, this study proposes the use of an artificial neural network model to assess impact severity based on the impact impulse, peak acceleration, and spectral energy of detected impacts. The performance of the model is further validated using both simulated and field-collected impact data from a through-plate girder railroad bridge in northern Illinois. The results demonstrate that the developed approach reliably detects and determines the severity of impacts. This solution allows railroad owners to better prioritize the allocation of limited resources towards the inspection of bridges after major impacts. railroad bridge impacts impact severity assessment impact impulse artificial neural network Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Approximately half of the 100,000 railroad bridges in the United States are over 100 years old, being built at a time when vertical clearance standards were lower than they are today and making them vulnerable to impact by over-height vehicles [ 1 , 2 ]. Indeed, impacts can occur frequently on such bridges. For example, Joy et al. [ 3 ] reported that nearly 50% of the railroad bridge service interruptions between January 1999 and March 2010 were the result of over-height vehicle impacts. Additionally, a study by Agrawal et al. [ 4 ], showed that 284 documented bridge impacts in New York between 2005 and 2008 involved railroad bridges. These impacts can lead to both structural damage and service disruptions, posing risks to public safety and potentially causing significant financial losses for railroad owners [ 5 ]. Therefore, detecting these impacts is crucial. Several researchers have developed systems capable of detecting impacts on railroad bridges. The most common approach involves monitoring bridge vibrations with accelerometers where impacts are identified if vibration levels exceed a set threshold. For example, Fu et al.[ 6 ] developed a wireless monitoring system that detects impacts on long-span bridges based on predefined vibration thresholds. Additionally, some researchers have also proposed the use of machine learning for impact detection. Sitton et al.[ 7 ] proposed a simple neural network model for distinguishing between train crossings and impact events on railroad bridges. The approach was further enhanced by employing an ensemble of neural networks to improve detection accuracy [ 5 ]. Lawal et al.[ 8 ] developed an artificial neural network (ANN) system to classify events on railroad bridges using data obtained from an event-triggered wireless sensor. The system was later implemented at the edge in wireless smart sensors [ 9 ]. Khresat et al.[ 10 ] proposed a parallel heterogenous data fusion convolutional neural network for detecting impacts and classifying events on railroad bridges using acceleration and tilt data. Once impacts are detected, railroads are mandated by the Federal Railroad Administration regulations to carry out inspections, irrespective of the impact severity [ 11 ]. Visual inspection is the traditional approach for railroad bridge condition assessment and ensuring proper maintenance [ 12 ]. However, this strategy has numerous challenges, such as potential errors in human judgment and inability to perform continuous condition assessment. Moreover, the inspections of railroad bridges after impact events often involve restrictions on bridge traffic and sometimes even total closure of the bridge. If the detected impact is minor, service interruptions due to the inspection process can lead to unnecessary traffic delays for the public and loss of revenue for railroad owners. For example, the estimated minimum cost following a minor impact that results in service interruption is around $ 10,000 [ 3 ]. Consequently, the railroad industry is interested in ways of rapidly assessing the severity of over-height vehicle impacts on railroad bridges. To that end, Vemuganti et al.[ 13 ] proposed an approach for rating the severity of impacts using permanent deflection threshold limits. However, the challenge with this approach is that such permanent deformations are difficult and costly to measure, thus impractical for large-scale deployment. In this paper, a low-cost and scalable impact severity assessment strategy is proposed for through-plate girder (TPG) railroad bridges, which are the most common type of bridge impacted [ 14 ]. The proposed strategy utilizes an ANN model to assess impact severity by evaluating the impact impulse, peak acceleration, and spectral energy of simulated impacts. The performance of the strategy is also assessed using field-collected data from railroad bridge impact events. The remainder of the paper is organized as follows: Section 2 proposes and validates the robustness of the selected impact severity assessment metrics through finite element (FE) simulations of impacts on a representative railroad bridge model. Section 3 develops an approach for indirect estimation of the metrics from measured acceleration responses as well as a neural network to estimate impact severity. Section 4 validates the proposed strategy numerically and with field data. In summary, the solution proposed in this study will enable more effective deployment of limited inspection resources by railroad owners. 2. Impact Severity Assessment Metrics This section proposes metrics for impact severity assessment. First, the development of a representative railroad bridge FE model is discussed. Subsequently, different impacts are simulated to create varying levels of damage and establish reliable metrics for determining impact severity. 2.1. Finite Element Model Development This study focuses on single-span TPG bridges (see Fig. 1 ), which were chosen because this type of bridge has the highest number of impacts per Ozdagli et al. [ 14 ], presumably because short-span bridges often have lower vertical clearances. A FE model for a representative TPG bridge is developed in Ansys [ 15 ] based on the experimental bridge models used in the studies by Ozdagli et al. [ 14 ] and Xu et al. [ 16 ]. The bridge is 5 m wide and 24 m long. Note that crash beams are not modeled, because few bridges of this type have crash beams installed [ 16 ]. The finite element model serves three purposes: (i) to simulate over-height vehicle impacts on railroad bridges, (ii) to obtain impact severity assessment metrics for different levels of impact severity, and (iii) to create a training database for the impact severity assessment neural network development. To consider material non-linearity, bilinear isotropic hardening is employed for steel components [ 13 ]. The elastic modulus is set to 200 GPa while the yield strength and tangent modulus are 250 MPa and 1450 MPa respectively. The components of the bridge, e.g., girders and cross beams, are modelled using shell elements. A pin-roller boundary condition system is used, which is common for such TPG bridges. For the impact severity assessment in this study, we ignored the contribution of other bridge components (e.g., ballast, track, etc.) and assumed that the steel deck plate contribution is insignificant [ 14 , 16 ]. A detailed mesh analysis was conducted; the final mesh chosen has a total of 9242 elements, with an average element size of 500 mm, providing a balance of computational efficiency and accuracy with respect to the global performance of the bridge. Additionally, stiffness-proportional damping was employed to incorporate the damping behavior of the bridge with the damping ratio randomly varied between 0.5 % and 5 % for the first mode, ased oncommonly assumed ranges for steel railroad bridges [ 14 , 17 , 18 ]. Impacts can occur in various forms (i.e., perpendicular to the bridge girder or skewed at an angle) and at various locations along a bridge span, as well as by vehicles with different local geometry and stiffness. However, for this research, the impact modeled is assumed to be perpendicular and occurs at the elevation level of the bottom flange. In test cases using vehicles of different widths, impact response metrics were similar, i.e., insensitive to vehicle dimensions. As a result, the response of the impacting vehicle is not the focus of this study and is modelled as a rigid body using 3-dimensional solid elements. The illustration of the FE model for impact analysis is shown in Fig. 2 . The focus of this study is bridges spanning over two-lane roads, and for such bridges, impacts are assumed to occur at either 8 m (¼ span) or 16 m (¾ span) from the left support. Due to symmetry, only over-height vehicle impacts at ¾ span are considered. An example of the transverse acceleration response at the highlighted node (see Fig. 2 ) to impact at this location is shown in Figs. 3 and 4 in both the time and frequency domains, respectively. Note, the responses from both the flange and web at the chosen location were found to be approximately the same. In this study, focus is placed on the global response of the TPG, and the response measurement was taken from the web, as this location is more realistic for practical implementations. The name of this location is the response node and will serve as the global response of the TPG. To validate the simulation output, the developed model was scaled down by a factor of 5 to match the experimental set up of Ozdagli et al. [ 14 ]. Since the experimental study reported displacement rather than acceleration, displacement response was obtained from the model to enable a direct comparison. These experiments analyzed the effectiveness of crash beams in mitigating impact from over-height vehicle collisions with TPGs. The test setup was designed such that a scaled TPG bridge model was subjected to impacts from a steel block (see Fig. 5). Temposonics position sensors [ 20 ] were utilized to capture the dynamic displacement response of the bridge during impact events. A series of impact tests were performed with and without the presence of crash beams and the structural deformations were recorded and analyzed. Simulated impact responses from the developed model were compared to the experimental data from the no crash-beam case to assess the numerical model’s ability to replicate realistic structural behavior under over-height vehicle impact loading. (b) (b) Figure 5 Experimental set up (a) bridge model (b) steel impact block Figure 6 shows the responses due to an impact impulse of 0.05 kN-s. Peak dynamic displacements of 20.91 mm and 21.304 mm were obtained from simulation and experimental study, respectively. Furthermore, both experimental and simulation responses are dominated by a single mode of approximately 8 Hz and 9 Hz, respectively. The fact that the simulated responses are consistent with the experimental ones gives confidence in the output of the model. Based on these results, the model is used as a surrogate for the impact severity of a real structure. (b) Figure 6 Comparison of impact response (a) simulation (b) experimental 2.2. Proposed Severity Assessment Metrics The most common approach for detecting impacts and quantifying their severity involves using acceleration measurements. However, the sole use of peak acceleration is not sufficient for assessing the severity of detected impacts because of the difficulty in establishing a suitable threshold for distinguishing between different severity categories. In this subsection, impact impulse, spectral energy, and peak acceleration are investigated as metrics for determining the severity of detected impacts. The impact impulse is proposed instead of the peak impact force because the impulse takes into consideration both magnitude and time, therefore being more suitable for assessing damage. Note that in this study, damage refers to the permanent displacement in the web of the impacted bridge girder. An analysis was conducted using Ansys to simulate impacts that cause different levels of damage. The damage level is determined using the permanent displacement limits proposed by Vemuganti et al. [ 13 ]. Herein, three categories of damage are considered, i.e., negligible, moderate, and significant damage. Permanent displacements less than 10 mm are categorized as negligible damage, while displacements greater than 60 mm are considered significant damage. Moderate damage is defined as permanent displacements between the above-mentioned limits. Next, three different impacts were simulated by changing vehicle speed to cause negligible damage (i.e., the impact resulted in ~ 4 mm permanent displacement), medium damage (i.e., the impact resulted in ~ 45 mm permanent displacement) and significant damage (i.e., the impact resulted in ~ 140 mm permanent displacement), respectively. The impact impulse is calculated as the area under the impact force vs time curve, while the spectral energy is computed by integrating the power spectral density magnitudes across the frequency domain. The computed metrics from the three impact simulation cases are shown in Table 1 . The results from this analysis show that these metrics can be expected to be higher in cases of non-minor impacts, which cause damage, as compared to minor impacts, which do not cause any or result in negligible damage and thus can be used to offer a reliable solution for impact severity assessment. While the peak acceleration and spectral energy are easily obtainable from acceleration measurements, impact impulse is not. The next section investigates an approach for indirect estimation of impact impulse from acceleration measurements and develops a neural network for impact severity assessment. Table 1 Metrics computed from three impact simulation cases Metrics Negligible Damage Medium Damage Significant Damage Impact Impulse (kN-s) 35.76 88.63 183.65 Spectral Energy (m 2 /s 4 ) 68.86 493.82 534.29 Peak Acceleration (m/s 2 ) 21.95 43.10 87.74 3. Impact Severity Assessment Approach This section presents an ANN-based approach to determine the severity of detected impacts on railroad bridges. First, the simulation of different impacts to create a training database for the ANN is discussed. Subsequently, an approach for indirect estimation of impact impulse from acceleration measurements is presented. Finally, the neural network for impact severity assessment is developed. 3.1. Dataset Development In this study, the model described in Section 2.1 is utilized. Three different masses of vehicles are considered to represent light, medium, and heavy weight over-height vehicles respectively. The mass of the vehicle for these weight categories is set to 6750 kg, 27475 kg, and 40000 kg respectively [ 13 , 21 ]. The impacting vehicle speed is selected within the range of 1 m/s to 10 m/s. These values are selected to represent the typical range of speed for these types of vehicles on local roads as well as include both undamaged and damaged scenarios in the training database. Furthermore, to represent different bridge conditions, the damping ratio varies between 0.5 % and %. Theeafter, simulations were carried out by randomly varying the damping ratio as well as the speed of the impacting vehicle within the ranges specified above for all three vehicle categories. A total of 600 simulations were carried out to obtain the ANN training database, covering a wide range of representative vehicle speeds. For each simulation, acceleration is recorded in three directions (longitudinal, vertical and lateral) at 100 Hz for a total duration of 6 s. Finally, the impact force time history is also recorded and used for verification of the impact impulse estimation approach discussed in the next subsection. 3.2. Neural Network for Impact Severity Assessment The response of a railroad bridge to vehicle impacts is influenced by several factors, including bridge geometry, material properties, impact force and energy dissipation mechanisms [ 8 , 22 ]. These relationships are highly nonlinear and difficult to model using traditional analytical methods. Therefore, an ANN is employed in this study to learn the complex correlations between impact response features and impact severity. The ANN approach also enables efficient classification of impacts into different severity categories by leveraging key features extracted from acceleration responses. 3.2.1. Neural Network Architecture Cascaded neural networks are a multi-stage machine learning model in which the output of one network serves as an input to another. In this study, a cascaded neural network is used to estimate the impact impulse, which is then used as a feature to predict the impact severity. Note that the impact impulse is the area under the curve of the impact force with respect to time. However, as mentioned above, the most common impact detection strategies only require accelerometers. Therefore, acceleration responses are typically measured on bridges and not the impact force. Thus, there is a need to employ an indirect approach to estimate the impact impulse from measured acceleration. To this end, an ANN model is used to estimate the impact impulse. To identify an optimal ANN, different architectures are trained and tested. The chosen architecture which optimized the ANN performance is illustrated in Fig. 7 . 3.2.2. First Subnetwork The first subnetwork is trained to estimate the impact impulse and consists of 4 hidden layers with 128, 64, 32 and 16 neurons respectively. Furthermore, the rectified linear unit (ReLU) activation function is applied to all hidden layers [ 23 ]. The developed ANN follows the impact processing strategies proposed in previous studies [ 6 , 24 , 25 ]. The features are extracted from the acceleration response of simulated impacts. These inputs include: (i) maximum acceleration record, (ii) time at maximum acceleration record, (iii) the maximum value of detailed coefficients after discrete wavelet transform (WT) using level 4 Daubechies wavelet (db4), and (iv) the maximum value of approximated coefficients of WT (db4). These features have been found to be effective for estimating impact impulse [ 6 ]. Each of the four features is extracted from the three directions of acceleration, making a total of twelve inputs into the ANN. The use of all three acceleration directions was found to increase the accuracy of the impact impulse estimation. For training, the loss function minimized is the mean squared error, and the mean absolute error metric is used to evaluate the model’s performance. 3.2.3. Second Subnetwork The second subnetwork, which determines the impact severity, uses a two-stage classification approach. This approach is selected to ensure high performance in the model’s ability to distinguish between different categories of impact, particularly focusing on accurately identifying major impacts which potentially result in structural damage. The three impact severity categories of interest considered are: minor, moderate, and major impacts. Note that minor impacts occur far more frequently than major impacts. In the first stage, the model distinguishes between minor impacts and non-minor impacts (a combination of moderate and major impacts). In the second stage, the model is run only on non-minor impacts and is trained to differentiate between moderate and major impacts. The models used for both stages have two hidden layers with 16 neurons each. In addition, the ReLU activation function is applied to all layers. The Sigmoid activation function, which is commonly used to handle binary classification problems and outputs a probability (i.e., a number between 0 and 1) [ 26 ], was used for the output layers. The simulated impacts are labelled into one of the categories of interest based on the permanent displacement and using the guidelines proposed in Vemuganti et al. [ 13 ]. The inputs into the ANN include the impact impulse estimated in the first subnetwork, the peak acceleration, and spectral energy. The peak acceleration and spectral energy are extracted from all three acceleration directions. For training, the loss function minimized in both stages is binary cross-entropy. This function is used for binary classification problems and computes the entropy between actual and predicted labels. The two subnetworks are trained independently. The created dataset is randomly split into 75% training and 25% testing data. Furthermore, 20% of the training data is held out for validation during the training process. The ANN was developed in Python using the Keras Sequential Applications Program Interface [ 27 ]. Having discussed the development of the ANN for impact severity assessment, the next section shows the results obtained from testing. 4. Results In this section, the accuracy of the ANN model is validated through evaluation of the test data for both impact impulse estimation and impact severity assessment. The accuracy and robustness of the impact severity assessment model is validated using both simulation and field-collected data. 4.1. Impact Impulse Estimation Results In training ANNs, an epoch represents one complete pass through the entire training dataset. During each epoch, the model processes batches of data, computes the loss, and updates the weights through backpropagation to minimize the loss function. By repeatedly iterating through the data over multiple epochs, the model learns patterns and relationships in the dataset. Figure 8 shows the training loss curve for the ANN model described in Section 3.2 , which demonstrates its performance for predicting impact impulse. Both training and validation losses decrease progressively with an increasing number of epochs and eventually converge to a reasonable value of 2.77 kN-s. The error value is considered reasonable as this falls within the predefined target of 5 kN-s. The reduction in losses demonstrates that the chosen number of epochs was sufficient and that the model has the potential for strong performance after training. The number of epochs was selected by closely analyzing the behavior of the training and validation loss curves. The accuracy of the ANN model was assessed through the mean absolute error. An average error of 3.77 kN-s was obtained from the held-out test data, which corresponds to an approximate error of 14%. Note that identifying major impacts which can cause damage to railroad bridges holds higher importance to engineers compared to identifying minor ones. To address this priority, the model was specifically tested with a focus on major impacts. In this case, an approximate error of 8% was obtained from the test data. 4.2. Impact Severity Classification Results 4.2.1. Model Training Performance The two-stage impact severity classification model was trained using simulated data. Figure 9 presents the training loss curves for stage 1 (minor vs non-minor impact classification) and stage 2 (moderate vs major impact classification) of the two-stage model. Both sets of losses decrease as the number of epochs increases and converge to a very low level. The training performance shows that the stage 1 model effectively learns the decision boundary between minor and non-minor impacts. The stage 2 losses start and converge to a slightly higher value than in stage 1. This higher loss indicates that the stage 2 task is more complex, likely due to overlapping features between moderate and major impacts, creating a more challenging decision boundary. (b) Figure 9 Training and validation loss curves for impact severity ANN classifier from (a) stage 1 model (b) stage 2 model 4.2.2. Validation Using Field-Collected Impact Data Two types of impacts are of interest: (i) scrapes, where vehicles scrape underneath bridges and (ii) head-on impacts. In practice, scrapes occur more often than head-on impacts. For the classification strategy developed in this paper, scrapes should be classified as minor impacts as they cause negligible or no damage. The proposed impact severity assessment model is first validated on scrapes using data previously collected in the study of Lawal et al.[ 8 ] from a railroad bridge in northern Illinois (see Fig. 10 ). The bridge is a short single-span steel plate girder bridge, which is the type focused on in this study. Data was gathered over a 44-week period during 2021–2022 using two Xnode wireless sensors [ 28 – 31 ], one on each side of the bridge. The Xnode is a wireless smart sensor platform that has been effectively utilized for structural health monitoring in civil infrastructure. During this period, the bridge experienced 105 impacts from over-height vehicles, as detailed in Lawal et al. [ 8 ]. All data was consistently sampled at 100 Hz, ensuring data uniformity and facilitating machine learning implementations. This dataset captures a broad range of impact events, providing a comprehensive view of bridge impacts over nearly a year. Note that all the impact data collected were scrapes, which occurred 1–2 times a week on average. The model successfully classified all field-collected impact data (scrapes) as minor impacts. 4.2.3. Validation Using Simulated Impacts Because head-on impacts did not occur on the instrumented bridge, held-out test data from simulation was used to validate the model performance for this type of impact. Figure 11 shows the performance of the model on simulated head-on impacts using a confusion matrix. The ANN classifier achieved 96.71% accuracy on the held-out test data. Additionally, other metrics were also used to evaluate the performance of the model. First, the area under the curve (AUC) of the receiver operating characteristic (ROC) curve was computed. The ROC curve is a plot of the false positive rate versus the true positive rate for different decision threshold values. The AUC score represents the model’s ability to distinguish between classes. An AUC score of 0.95 was obtained from the test data, showing that the model is highly likely to positively identify major impacts. Other useful metrics to calculate include precision and recall values. For this problem, precision and recall give an indication of how good the model is at identifying major impacts as well as the false positive rate. The F1 score, which is the harmonic average of the recall and precision was computed during testing, The obtained F1 score of 0.95 shows the model has a low false positive rate as well as the capability of identifying severe impacts when they occur. These results are summarized in Table 2 . Table 2 Model evaluation scores Metric Score Accuracy 0.9671 ROC AUC 0.9466 F1 0.9529 A 10-fold cross-validation method was used for validation to assess the model’s robustness further [ 32 ]. This technique divides the dataset into 10 equal parts. In each iteration, one part is used for testing while the model is trained on the remaining nine. This process is repeated 10 times, allowing each subset to act as the test set once. The model achieved an average accuracy of 93.19% across the 10 iterations. The standard deviation of 0.0334 shows that the model does not exhibit overfitting. 5. Conclusion Frequent collisions with over-height vehicles have been a persistent challenge, often leading to structural damage and disruptions in service for low-clearance railroad bridges. The traditional response of mandatory bridge inspections after all reported impacts results in significant traffic delays and financial losses for railroad owners, especially since most impacts cause negligible damage. To address these issues, this study presented a novel, low-cost approach for assessing the severity of impacts on low-clearance railroad bridges. An artificial neural network was developed to evaluate impact severity using features such as impact impulse, peak acceleration, and spectral energy. The ANN was trained on a diverse simulated impact dataset comprising of different severity categories. A two-stage classification strategy was employed to ensure high accuracy by first distinguishing minor impacts from non-minor ones and then classifying non-minor impacts into moderate or major categories. The results demonstrate that the proposed method reliably classifies impacts into different severity categories. The robustness of the model was confirmed by a 10-fold cross validation with an accuracy of 93.19% and low standard deviation suggesting minimal risk of overfitting. The proposed approach can be implemented by bridge owners by instrumenting a bridge with just a single accelerometer and leveraging the impact detection ANN developed by Lawal et al. [ 8 ] alongside the severity assessment ANN developed in this paper. Moreover, the model is robust and also applicable to bridges that are slightly different from the finite element model used in this study, as was demonstrated in Section 4.2 . The developed method is not intended to replace inspections but rather complement them by enabling railroad owners to prioritize resources efficiently by focusing inspections on bridges with significant impacts, thereby reducing service delays and costs. Future research will focus on the assessment of railroad bridge conditions after severe impacts are detected. Overall, the developed model showed significant promise for widespread development, enhancing public safety and preventing loss of revenue for railroad authorities. Declarations Data availability All field-collected and simulation data, and code to generate figures for this study are available from the corresponding author upon reasonable request. Conflict of interest The authors declare that they have no conflict of interest. References Ozdagli, A.I.; Gomez, J.A.; Moreu, F. Real-Time Reference-Free Displacement of Railroad Bridges during Train-Crossing Events. 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Efficient and High-Precision Time Synchronization for Wireless Monitoring of Civil Infrastructure Subjected to Sudden Events. Struct Control Health Monit 2021, 28 , doi:10.1002/stc.2643. Fu, Y.; Mechitov, K.; Hoang, T.; Kim, J.R.; Lee, D.H.; Spencer, B.F. Development and Full-Scale Validation of High-Fidelity Data Acquisition on a next-Generation Wireless Smart Sensor Platform. Advances in Structural Engineering 2019, 22 , 3512–3533, doi:10.1177/1369433219866093. Shajihan, S.A.V.; Chow, R.; Mechitov, K.; Fu, Y.; Hoang, T.; Spencer, B.F. Development of Synchronized High-Sensitivity Wireless Accelerometer for Structural Health Monitoring. Sensors (Switzerland) 2020, 20 , 1–20, doi:10.3390/s20154169. Spencer, B.F.; Park, J.W.; Mechitov, K.A.; Jo, H.; Agha, G. Next Generation Wireless Smart Sensors Toward Sustainable Civil Infrastructure. In Proceedings of the Procedia Engineering; Elsevier Ltd, 2017; Vol. 171, pp. 5–13. A Gentle Introduction to K-Fold Cross-Validation Available online: https://machinelearningmastery.com/k-fold-cross-validation/ (accessed on 30 July 2022). Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5994795","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":413327731,"identity":"7a154e3d-48aa-446a-ad60-efc55d20d9b7","order_by":0,"name":"Omobolaji Lawal","email":"","orcid":"","institution":"University of Illinois at Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Omobolaji","middleName":"","lastName":"Lawal","suffix":""},{"id":413327732,"identity":"217946dc-0787-4bdb-bb5a-6342c8da08ef","order_by":1,"name":"Shaik Althaf V.Shajihan","email":"","orcid":"","institution":"University of Illinois at Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Shaik","middleName":"Althaf","lastName":"V.Shajihan","suffix":""},{"id":413327733,"identity":"104e954f-f89b-4798-9f18-c74b5414c81b","order_by":2,"name":"Thomas Golecki","email":"","orcid":"","institution":"University of Illinois at Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Golecki","suffix":""},{"id":413327734,"identity":"20876b38-ee8d-4e94-acc5-2bdb045254d8","order_by":3,"name":"Kirill Mechitov","email":"","orcid":"","institution":"StructureIQ","correspondingAuthor":false,"prefix":"","firstName":"Kirill","middleName":"","lastName":"Mechitov","suffix":""},{"id":413327735,"identity":"e4ff0a9f-ad9d-40c1-bc9d-5577955ef372","order_by":4,"name":"Fernando Moreu","email":"","orcid":"","institution":"University of New Mexico","correspondingAuthor":false,"prefix":"","firstName":"Fernando","middleName":"","lastName":"Moreu","suffix":""},{"id":413327736,"identity":"43f7a87b-4dbe-4c5a-aaff-8f347e6f38b7","order_by":5,"name":"Billie Spencer Jr.","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYBACA+YDjA8SCix4GBgYG4B8ZiK0sCUwGyQYSJCmhU2CwUACxidCizkb+7OKBwYSMubszc0fGCqsExsIabFs4zG7AXKYZc/BNgmGM+mEtRjc72EDazG4kdjGwNh2mAgtx9ifFUC1NH9g/EeUFgYzBqiWBgnGBiK0AP1iLAHWcgbol4Rj6cYEtQBD7OHHHxU29gbH2x9/+FBjLUtQCypIIE35KBgFo2AUjAJcAABSMjoOsKuBOQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Illinois at Urbana-Champaign","correspondingAuthor":true,"prefix":"","firstName":"Billie","middleName":"","lastName":"Spencer","suffix":"Jr."}],"badges":[],"createdAt":"2025-02-10 01:36:23","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5994795/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5994795/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":76010283,"identity":"af036174-594b-408c-91f3-cbfb7c95f38a","added_by":"auto","created_at":"2025-02-11 12:07:20","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":306720,"visible":true,"origin":"","legend":"\u003cp\u003eTypical single-span TPG railroad bridge, elevation view [19]\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/74b9f96ea020a2b82d52b95d.png"},{"id":76010329,"identity":"af1412d5-2bee-46d8-a2ef-60487ff59662","added_by":"auto","created_at":"2025-02-11 12:07:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":340639,"visible":true,"origin":"","legend":"\u003cp\u003eFE model of railroad bridge with impact at ¼ span\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/368886cea8cc7d952956d959.png"},{"id":76011244,"identity":"5e692b2a-f41d-4dfa-9ac6-c7553976baa1","added_by":"auto","created_at":"2025-02-11 12:15:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":89243,"visible":true,"origin":"","legend":"\u003cp\u003eResponse to simulated impact at ¼ span in time domain (a) full acceleration response (b) zoomed-in view\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/40bc0300e6a0d9abcd1e4181.png"},{"id":76010285,"identity":"9c0f9e11-749f-4ae4-93fd-523f3833fb38","added_by":"auto","created_at":"2025-02-11 12:07:20","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":49978,"visible":true,"origin":"","legend":"\u003cp\u003eResponse to simulated impact at ¼ span in frequency domain\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/30516f923648ebd1f391bdb8.png"},{"id":76010294,"identity":"1f465282-eda1-4343-ba3b-8f5d9335674a","added_by":"auto","created_at":"2025-02-11 12:07:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":482277,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental set up (a) bridge model (b) steel impact block\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/8f2640e43726b15efbbbaee5.png"},{"id":76010302,"identity":"eaf1c818-d159-4187-a33d-e42e8e23781c","added_by":"auto","created_at":"2025-02-11 12:07:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":112967,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of impact response (a) simulation (b) experimental\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/b30f8344799a8ef69fef0bfa.png"},{"id":76010327,"identity":"c42770e7-8f10-49f4-8873-f36f5149024e","added_by":"auto","created_at":"2025-02-11 12:07:22","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":151310,"visible":true,"origin":"","legend":"\u003cp\u003eANN architecture for impact severity assessment\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/e88278d794bb02f118303467.png"},{"id":76010287,"identity":"ad1e993f-061b-492c-a68e-243b7aec8c61","added_by":"auto","created_at":"2025-02-11 12:07:20","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":58850,"visible":true,"origin":"","legend":"\u003cp\u003eANN training and validation loss curves for impact impulse estimation\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/504c766ec8bc2851e80a5af9.png"},{"id":76010308,"identity":"d39d7fe9-413d-4ac0-a235-9d4a1c23d26f","added_by":"auto","created_at":"2025-02-11 12:07:21","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":73754,"visible":true,"origin":"","legend":"\u003cp\u003eTraining and validation loss curves for impact severity ANN classifier from (a) stage 1 model (b) stage 2 model\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/52d3f5a49bab16f40aa55bf9.png"},{"id":76011246,"identity":"887f3093-1d6c-4bb5-ba7c-48c2b43e3bf0","added_by":"auto","created_at":"2025-02-11 12:15:21","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":289387,"visible":true,"origin":"","legend":"\u003cp\u003eSingle span steel plate girder railroad bridge instrumented with the Xnode [8]\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/dccda9e512e73247d872512a.png"},{"id":76010328,"identity":"79897310-704b-4206-8945-ac0ef777951f","added_by":"auto","created_at":"2025-02-11 12:07:22","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":33710,"visible":true,"origin":"","legend":"\u003cp\u003eConfusion Matrix for test examples (0 = minor impact, 1 = moderate impact, 2 = major impact)\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/4808ecf83abd0e0d264f6fae.png"},{"id":76014380,"identity":"1ef27bbc-cb11-4b89-b793-79fd23c7eede","added_by":"auto","created_at":"2025-02-11 12:39:22","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2910484,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5994795/v1/8eb4debd-57f0-417f-ae3a-660477e207f3.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOver-height Vehicle Impact Severity Assessment for Through-Plate Girder Railroad Bridges\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eApproximately half of the 100,000 railroad bridges in the United States are over 100 years old, being built at a time when vertical clearance standards were lower than they are today and making them vulnerable to impact by over-height vehicles [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Indeed, impacts can occur frequently on such bridges. For example, Joy et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] reported that nearly 50% of the railroad bridge service interruptions between January 1999 and March 2010 were the result of over-height vehicle impacts. Additionally, a study by Agrawal et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], showed that 284 documented bridge impacts in New York between 2005 and 2008 involved railroad bridges. These impacts can lead to both structural damage and service disruptions, posing risks to public safety and potentially causing significant financial losses for railroad owners [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Therefore, detecting these impacts is crucial.\u003c/p\u003e \u003cp\u003eSeveral researchers have developed systems capable of detecting impacts on railroad bridges. The most common approach involves monitoring bridge vibrations with accelerometers where impacts are identified if vibration levels exceed a set threshold. For example, Fu et al.[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] developed a wireless monitoring system that detects impacts on long-span bridges based on predefined vibration thresholds. Additionally, some researchers have also proposed the use of machine learning for impact detection. Sitton et al.[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] proposed a simple neural network model for distinguishing between train crossings and impact events on railroad bridges. The approach was further enhanced by employing an ensemble of neural networks to improve detection accuracy [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Lawal et al.[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] developed an artificial neural network (ANN) system to classify events on railroad bridges using data obtained from an event-triggered wireless sensor. The system was later implemented at the edge in wireless smart sensors [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Khresat et al.[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] proposed a parallel heterogenous data fusion convolutional neural network for detecting impacts and classifying events on railroad bridges using acceleration and tilt data. Once impacts are detected, railroads are mandated by the Federal Railroad Administration regulations to carry out inspections, irrespective of the impact severity [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Visual inspection is the traditional approach for railroad bridge condition assessment and ensuring proper maintenance [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. However, this strategy has numerous challenges, such as potential errors in human judgment and inability to perform continuous condition assessment. Moreover, the inspections of railroad bridges after impact events often involve restrictions on bridge traffic and sometimes even total closure of the bridge. If the detected impact is minor, service interruptions due to the inspection process can lead to unnecessary traffic delays for the public and loss of revenue for railroad owners. For example, the estimated minimum cost following a minor impact that results in service interruption is around \u003cspan\u003e$\u003c/span\u003e10,000 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Consequently, the railroad industry is interested in ways of rapidly assessing the severity of over-height vehicle impacts on railroad bridges. To that end, Vemuganti et al.[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] proposed an approach for rating the severity of impacts using permanent deflection threshold limits. However, the challenge with this approach is that such permanent deformations are difficult and costly to measure, thus impractical for large-scale deployment.\u003c/p\u003e \u003cp\u003eIn this paper, a low-cost and scalable impact severity assessment strategy is proposed for through-plate girder (TPG) railroad bridges, which are the most common type of bridge impacted [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The proposed strategy utilizes an ANN model to assess impact severity by evaluating the impact impulse, peak acceleration, and spectral energy of simulated impacts. The performance of the strategy is also assessed using field-collected data from railroad bridge impact events. The remainder of the paper is organized as follows: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e proposes and validates the robustness of the selected impact severity assessment metrics through finite element (FE) simulations of impacts on a representative railroad bridge model. Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3\u003c/span\u003e develops an approach for indirect estimation of the metrics from measured acceleration responses as well as a neural network to estimate impact severity. Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e4\u003c/span\u003e validates the proposed strategy numerically and with field data. In summary, the solution proposed in this study will enable more effective deployment of limited inspection resources by railroad owners.\u003c/p\u003e"},{"header":"2. Impact Severity Assessment Metrics","content":"\u003cp\u003eThis section proposes metrics for impact severity assessment. First, the development of a representative railroad bridge FE model is discussed. Subsequently, different impacts are simulated to create varying levels of damage and establish reliable metrics for determining impact severity.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Finite Element Model Development\u003c/h2\u003e \u003cp\u003eThis study focuses on single-span TPG bridges (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), which were chosen because this type of bridge has the highest number of impacts per Ozdagli et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], presumably because short-span bridges often have lower vertical clearances. A FE model for a representative TPG bridge is developed in Ansys [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] based on the experimental bridge models used in the studies by Ozdagli et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and Xu et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The bridge is 5 m wide and 24 m long. Note that crash beams are not modeled, because few bridges of this type have crash beams installed [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The finite element model serves three purposes: (i) to simulate over-height vehicle impacts on railroad bridges, (ii) to obtain impact severity assessment metrics for different levels of impact severity, and (iii) to create a training database for the impact severity assessment neural network development. To consider material non-linearity, bilinear isotropic hardening is employed for steel components [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The elastic modulus is set to 200 GPa while the yield strength and tangent modulus are 250 MPa and 1450 MPa respectively. The components of the bridge, e.g., girders and cross beams, are modelled using shell elements. A pin-roller boundary condition system is used, which is common for such TPG bridges. For the impact severity assessment in this study, we ignored the contribution of other bridge components (e.g., ballast, track, etc.) and assumed that the steel deck plate contribution is insignificant [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. A detailed mesh analysis was conducted; the final mesh chosen has a total of 9242 elements, with an average element size of 500 mm, providing a balance of computational efficiency and accuracy with respect to the global performance of the bridge. Additionally, stiffness-proportional damping was employed to incorporate the damping behavior of the bridge with the damping ratio randomly varied between 0.5 % and 5 % for the first mode, ased oncommonly assumed ranges for steel railroad bridges [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eImpacts can occur in various forms (i.e., perpendicular to the bridge girder or skewed at an angle) and at various locations along a bridge span, as well as by vehicles with different local geometry and stiffness. However, for this research, the impact modeled is assumed to be perpendicular and occurs at the elevation level of the bottom flange. In test cases using vehicles of different widths, impact response metrics were similar, i.e., insensitive to vehicle dimensions. As a result, the response of the impacting vehicle is not the focus of this study and is modelled as a rigid body using 3-dimensional solid elements. The illustration of the FE model for impact analysis is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The focus of this study is bridges spanning over two-lane roads, and for such bridges, impacts are assumed to occur at either 8 m (\u0026frac14; span) or 16 m (\u0026frac34; span) from the left support. Due to symmetry, only over-height vehicle impacts at \u0026frac34; span are considered. An example of the transverse acceleration response at the highlighted node (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) to impact at this location is shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e in both the time and frequency domains, respectively. Note, the responses from both the flange and web at the chosen location were found to be approximately the same. In this study, focus is placed on the global response of the TPG, and the response measurement was taken from the web, as this location is more realistic for practical implementations. The name of this location is the response node and will serve as the global response of the TPG.\u003c/p\u003e \u003cp\u003eTo validate the simulation output, the developed model was scaled down by a factor of 5 to match the experimental set up of Ozdagli et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Since the experimental study reported displacement rather than acceleration, displacement response was obtained from the model to enable a direct comparison. These experiments analyzed the effectiveness of crash beams in mitigating impact from over-height vehicle collisions with TPGs. The test setup was designed such that a scaled TPG bridge model was subjected to impacts from a steel block (see Fig.\u0026nbsp;5). Temposonics position sensors [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] were utilized to capture the dynamic displacement response of the bridge during impact events. A series of impact tests were performed with and without the presence of crash beams and the structural deformations were recorded and analyzed. Simulated impact responses from the developed model were compared to the experimental data from the no crash-beam case to assess the numerical model\u0026rsquo;s ability to replicate realistic structural behavior under over-height vehicle impact loading.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e(b)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e(b)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;5\u003c/b\u003e Experimental set up (a) bridge model (b) steel impact block\u003c/p\u003e \u003cp\u003eFigure 6 shows the responses due to an impact impulse of 0.05 kN-s. Peak dynamic displacements of 20.91 mm and 21.304 mm were obtained from simulation and experimental study, respectively. Furthermore, both experimental and simulation responses are dominated by a single mode of approximately 8 Hz and 9 Hz, respectively. The fact that the simulated responses are consistent with the experimental ones gives confidence in the output of the model. Based on these results, the model is used as a surrogate for the impact severity of a real structure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e(b)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;6\u003c/b\u003e Comparison of impact response (a) simulation (b) experimental\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Proposed Severity Assessment Metrics\u003c/h2\u003e \u003cp\u003eThe most common approach for detecting impacts and quantifying their severity involves using acceleration measurements. However, the sole use of peak acceleration is not sufficient for assessing the severity of detected impacts because of the difficulty in establishing a suitable threshold for distinguishing between different severity categories. In this subsection, impact impulse, spectral energy, and peak acceleration are investigated as metrics for determining the severity of detected impacts. The impact impulse is proposed instead of the peak impact force because the impulse takes into consideration both magnitude and time, therefore being more suitable for assessing damage. Note that in this study, damage refers to the permanent displacement in the web of the impacted bridge girder. An analysis was conducted using Ansys to simulate impacts that cause different levels of damage. The damage level is determined using the permanent displacement limits proposed by Vemuganti et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Herein, three categories of damage are considered, i.e., negligible, moderate, and significant damage. Permanent displacements less than 10 mm are categorized as negligible damage, while displacements greater than 60 mm are considered significant damage. Moderate damage is defined as permanent displacements between the above-mentioned limits. Next, three different impacts were simulated by changing vehicle speed to cause negligible damage (i.e., the impact resulted in ~\u0026thinsp;4 mm permanent displacement), medium damage (i.e., the impact resulted in ~\u0026thinsp;45 mm permanent displacement) and significant damage (i.e., the impact resulted in ~\u0026thinsp;140 mm permanent displacement), respectively. The impact impulse is calculated as the area under the impact force vs time curve, while the spectral energy is computed by integrating the power spectral density magnitudes across the frequency domain. The computed metrics from the three impact simulation cases are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The results from this analysis show that these metrics can be expected to be higher in cases of non-minor impacts, which cause damage, as compared to minor impacts, which do not cause any or result in negligible damage and thus can be used to offer a reliable solution for impact severity assessment. While the peak acceleration and spectral energy are easily obtainable from acceleration measurements, impact impulse is not. The next section investigates an approach for indirect estimation of impact impulse from acceleration measurements and develops a neural network for impact severity assessment.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMetrics computed from three impact simulation cases\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetrics\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNegligible Damage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMedium Damage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSignificant Damage\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eImpact Impulse (kN-s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e88.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e183.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpectral Energy (m\u003csup\u003e2\u003c/sup\u003e/s\u003csup\u003e4\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e68.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e493.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e534.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePeak Acceleration (m/s\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e21.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e43.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e87.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Impact Severity Assessment Approach","content":"\u003cp\u003eThis section presents an ANN-based approach to determine the severity of detected impacts on railroad bridges. First, the simulation of different impacts to create a training database for the ANN is discussed. Subsequently, an approach for indirect estimation of impact impulse from acceleration measurements is presented. Finally, the neural network for impact severity assessment is developed.\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Dataset Development\u003c/h2\u003e \u003cp\u003eIn this study, the model described in Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e2.1\u003c/span\u003e is utilized. Three different masses of vehicles are considered to represent light, medium, and heavy weight over-height vehicles respectively. The mass of the vehicle for these weight categories is set to 6750 kg, 27475 kg, and 40000 kg respectively [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The impacting vehicle speed is selected within the range of 1 m/s to 10 m/s. These values are selected to represent the typical range of speed for these types of vehicles on local roads as well as include both undamaged and damaged scenarios in the training database. Furthermore, to represent different bridge conditions, the damping ratio varies between 0.5 % and %. Theeafter, simulations were carried out by randomly varying the damping ratio as well as the speed of the impacting vehicle within the ranges specified above for all three vehicle categories. A total of 600 simulations were carried out to obtain the ANN training database, covering a wide range of representative vehicle speeds. For each simulation, acceleration is recorded in three directions (longitudinal, vertical and lateral) at 100 Hz for a total duration of 6 s. Finally, the impact force time history is also recorded and used for verification of the impact impulse estimation approach discussed in the next subsection.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Neural Network for Impact Severity Assessment\u003c/h2\u003e \u003cp\u003eThe response of a railroad bridge to vehicle impacts is influenced by several factors, including bridge geometry, material properties, impact force and energy dissipation mechanisms [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. These relationships are highly nonlinear and difficult to model using traditional analytical methods. Therefore, an ANN is employed in this study to learn the complex correlations between impact response features and impact severity. The ANN approach also enables efficient classification of impacts into different severity categories by leveraging key features extracted from acceleration responses.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1. Neural Network Architecture\u003c/h2\u003e \u003cp\u003eCascaded neural networks are a multi-stage machine learning model in which the output of one network serves as an input to another. In this study, a cascaded neural network is used to estimate the impact impulse, which is then used as a feature to predict the impact severity. Note that the impact impulse is the area under the curve of the impact force with respect to time. However, as mentioned above, the most common impact detection strategies only require accelerometers. Therefore, acceleration responses are typically measured on bridges and not the impact force. Thus, there is a need to employ an indirect approach to estimate the impact impulse from measured acceleration. To this end, an ANN model is used to estimate the impact impulse. To identify an optimal ANN, different architectures are trained and tested. The chosen architecture which optimized the ANN performance is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2. First Subnetwork\u003c/h2\u003e \u003cp\u003eThe first subnetwork is trained to estimate the impact impulse and consists of 4 hidden layers with 128, 64, 32 and 16 neurons respectively. Furthermore, the rectified linear unit (ReLU) activation function is applied to all hidden layers [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The developed ANN follows the impact processing strategies proposed in previous studies [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The features are extracted from the acceleration response of simulated impacts. These inputs include: (i) maximum acceleration record, (ii) time at maximum acceleration record, (iii) the maximum value of detailed coefficients after discrete wavelet transform (WT) using level 4 Daubechies wavelet (db4), and (iv) the maximum value of approximated coefficients of WT (db4). These features have been found to be effective for estimating impact impulse [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Each of the four features is extracted from the three directions of acceleration, making a total of twelve inputs into the ANN. The use of all three acceleration directions was found to increase the accuracy of the impact impulse estimation. For training, the loss function minimized is the mean squared error, and the mean absolute error metric is used to evaluate the model\u0026rsquo;s performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3. Second Subnetwork\u003c/h2\u003e \u003cp\u003eThe second subnetwork, which determines the impact severity, uses a two-stage classification approach. This approach is selected to ensure high performance in the model\u0026rsquo;s ability to distinguish between different categories of impact, particularly focusing on accurately identifying major impacts which potentially result in structural damage. The three impact severity categories of interest considered are: minor, moderate, and major impacts. Note that minor impacts occur far more frequently than major impacts.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eIn the first stage, the model distinguishes between minor impacts and non-minor impacts (a combination of moderate and major impacts).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIn the second stage, the model is run only on non-minor impacts and is trained to differentiate between moderate and major impacts.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe models used for both stages have two hidden layers with 16 neurons each. In addition, the ReLU activation function is applied to all layers. The Sigmoid activation function, which is commonly used to handle binary classification problems and outputs a probability (i.e., a number between 0 and 1) [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], was used for the output layers. The simulated impacts are labelled into one of the categories of interest based on the permanent displacement and using the guidelines proposed in Vemuganti et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The inputs into the ANN include the impact impulse estimated in the first subnetwork, the peak acceleration, and spectral energy. The peak acceleration and spectral energy are extracted from all three acceleration directions. For training, the loss function minimized in both stages is binary cross-entropy. This function is used for binary classification problems and computes the entropy between actual and predicted labels.\u003c/p\u003e \u003cp\u003eThe two subnetworks are trained independently. The created dataset is randomly split into 75% training and 25% testing data. Furthermore, 20% of the training data is held out for validation during the training process. The ANN was developed in Python using the Keras Sequential Applications Program Interface [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Having discussed the development of the ANN for impact severity assessment, the next section shows the results obtained from testing.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cp\u003eIn this section, the accuracy of the ANN model is validated through evaluation of the test data for both impact impulse estimation and impact severity assessment. The accuracy and robustness of the impact severity assessment model is validated using both simulation and field-collected data.\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Impact Impulse Estimation Results\u003c/h2\u003e \u003cp\u003eIn training ANNs, an epoch represents one complete pass through the entire training dataset. During each epoch, the model processes batches of data, computes the loss, and updates the weights through backpropagation to minimize the loss function. By repeatedly iterating through the data over multiple epochs, the model learns patterns and relationships in the dataset. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the training loss curve for the ANN model described in Section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, which demonstrates its performance for predicting impact impulse. Both training and validation losses decrease progressively with an increasing number of epochs and eventually converge to a reasonable value of 2.77 kN-s. The error value is considered reasonable as this falls within the predefined target of 5 kN-s. The reduction in losses demonstrates that the chosen number of epochs was sufficient and that the model has the potential for strong performance after training. The number of epochs was selected by closely analyzing the behavior of the training and validation loss curves. The accuracy of the ANN model was assessed through the mean absolute error. An average error of 3.77 kN-s was obtained from the held-out test data, which corresponds to an approximate error of 14%. Note that identifying major impacts which can cause damage to railroad bridges holds higher importance to engineers compared to identifying minor ones. To address this priority, the model was specifically tested with a focus on major impacts. In this case, an approximate error of 8% was obtained from the test data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Impact Severity Classification Results\u003c/h2\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e4.2.1. Model Training Performance\u003c/h2\u003e \u003cp\u003eThe two-stage impact severity classification model was trained using simulated data. Figure\u0026nbsp;9 presents the training loss curves for stage 1 (minor vs non-minor impact classification) and stage 2 (moderate vs major impact classification) of the two-stage model. Both sets of losses decrease as the number of epochs increases and converge to a very low level. The training performance shows that the stage 1 model effectively learns the decision boundary between minor and non-minor impacts. The stage 2 losses start and converge to a slightly higher value than in stage 1. This higher loss indicates that the stage 2 task is more complex, likely due to overlapping features between moderate and major impacts, creating a more challenging decision boundary.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e(b)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;9\u003c/b\u003e Training and validation loss curves for impact severity ANN classifier from (a) stage 1 model (b) stage 2 model\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2. Validation Using Field-Collected Impact Data\u003c/h2\u003e \u003cp\u003eTwo types of impacts are of interest: (i) scrapes, where vehicles scrape underneath bridges and (ii) head-on impacts. In practice, scrapes occur more often than head-on impacts. For the classification strategy developed in this paper, scrapes should be classified as minor impacts as they cause negligible or no damage. The proposed impact severity assessment model is first validated on scrapes using data previously collected in the study of Lawal et al.[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] from a railroad bridge in northern Illinois (see Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e10\u003c/span\u003e). The bridge is a short single-span steel plate girder bridge, which is the type focused on in this study. Data was gathered over a 44-week period during 2021\u0026ndash;2022 using two Xnode wireless sensors [\u003cspan additionalcitationids=\"CR29 CR30\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], one on each side of the bridge. The Xnode is a wireless smart sensor platform that has been effectively utilized for structural health monitoring in civil infrastructure. During this period, the bridge experienced 105 impacts from over-height vehicles, as detailed in Lawal et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. All data was consistently sampled at 100 Hz, ensuring data uniformity and facilitating machine learning implementations. This dataset captures a broad range of impact events, providing a comprehensive view of bridge impacts over nearly a year. Note that all the impact data collected were scrapes, which occurred 1\u0026ndash;2 times a week on average. The model successfully classified all field-collected impact data (scrapes) as minor impacts.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e4.2.3. Validation Using Simulated Impacts\u003c/h2\u003e \u003cp\u003eBecause head-on impacts did not occur on the instrumented bridge, held-out test data from simulation was used to validate the model performance for this type of impact. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the performance of the model on simulated head-on impacts using a confusion matrix. The ANN classifier achieved 96.71% accuracy on the held-out test data. Additionally, other metrics were also used to evaluate the performance of the model. First, the area under the curve (AUC) of the receiver operating characteristic (ROC) curve was computed. The ROC curve is a plot of the false positive rate versus the true positive rate for different decision threshold values. The AUC score represents the model\u0026rsquo;s ability to distinguish between classes. An AUC score of 0.95 was obtained from the test data, showing that the model is highly likely to positively identify major impacts. Other useful metrics to calculate include precision and recall values. For this problem, precision and recall give an indication of how good the model is at identifying major impacts as well as the false positive rate. The F1 score, which is the harmonic average of the recall and precision was computed during testing, The obtained F1 score of 0.95 shows the model has a low false positive rate as well as the capability of identifying severe impacts when they occur. These results are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel evaluation scores\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScore\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9671\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eROC AUC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9466\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9529\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eA 10-fold cross-validation method was used for validation to assess the model\u0026rsquo;s robustness further [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. This technique divides the dataset into 10 equal parts. In each iteration, one part is used for testing while the model is trained on the remaining nine. This process is repeated 10 times, allowing each subset to act as the test set once. The model achieved an average accuracy of 93.19% across the 10 iterations. The standard deviation of 0.0334 shows that the model does not exhibit overfitting.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eFrequent collisions with over-height vehicles have been a persistent challenge, often leading to structural damage and disruptions in service for low-clearance railroad bridges. The traditional response of mandatory bridge inspections after all reported impacts results in significant traffic delays and financial losses for railroad owners, especially since most impacts cause negligible damage. To address these issues, this study presented a novel, low-cost approach for assessing the severity of impacts on low-clearance railroad bridges. An artificial neural network was developed to evaluate impact severity using features such as impact impulse, peak acceleration, and spectral energy. The ANN was trained on a diverse simulated impact dataset comprising of different severity categories. A two-stage classification strategy was employed to ensure high accuracy by first distinguishing minor impacts from non-minor ones and then classifying non-minor impacts into moderate or major categories. The results demonstrate that the proposed method reliably classifies impacts into different severity categories. The robustness of the model was confirmed by a 10-fold cross validation with an accuracy of 93.19% and low standard deviation suggesting minimal risk of overfitting.\u003c/p\u003e \u003cp\u003eThe proposed approach can be implemented by bridge owners by instrumenting a bridge with just a single accelerometer and leveraging the impact detection ANN developed by Lawal et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] alongside the severity assessment ANN developed in this paper. Moreover, the model is robust and also applicable to bridges that are slightly different from the finite element model used in this study, as was demonstrated in Section \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e4.2\u003c/span\u003e. The developed method is not intended to replace inspections but rather complement them by enabling railroad owners to prioritize resources efficiently by focusing inspections on bridges with significant impacts, thereby reducing service delays and costs. Future research will focus on the assessment of railroad bridge conditions after severe impacts are detected. Overall, the developed model showed significant promise for widespread development, enhancing public safety and preventing loss of revenue for railroad authorities.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll field-collected and simulation data, and code to generate figures for this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eOzdagli, A.I.; Gomez, J.A.; Moreu, F. 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In Proceedings of the Procedia Engineering; Elsevier Ltd, 2017; Vol. 171, pp. 5\u0026ndash;13.\u003c/li\u003e\n \u003cli\u003eA Gentle Introduction to K-Fold Cross-Validation Available online: https://machinelearningmastery.com/k-fold-cross-validation/ (accessed on 30 July 2022).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Illinois at Urbana-Champaign","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"railroad bridge, impacts, impact severity assessment, impact impulse, artificial neural network","lastPublishedDoi":"10.21203/rs.3.rs-5994795/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5994795/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLow clearance railroad bridges in the United States are prone to frequent impacts from over-height vehicles, which can lead to structural damage and disruptions in railroad bridge service. Current practice mandates the closure of bridges after an impact is reported. However, this approach results in traffic delays and loss of revenue for railroad owners in cases of minor impacts, which occur far more frequently than major ones. While researchers have developed approaches to detect such impacts using acceleration responses obtained from sensors mounted on the bridge, the severity is generally difficult to ascertain. Therefore, there is a need for a reliable method to assess both the occurrence and severity of impacts. Although previous studies have used permanent displacement thresholds to rate impact severity, measuring permanent displacement is challenging and too expensive to be scalable. To address these challenges, this study proposes the use of an artificial neural network model to assess impact severity based on the impact impulse, peak acceleration, and spectral energy of detected impacts. The performance of the model is further validated using both simulated and field-collected impact data from a through-plate girder railroad bridge in northern Illinois. The results demonstrate that the developed approach reliably detects and determines the severity of impacts. This solution allows railroad owners to better prioritize the allocation of limited resources towards the inspection of bridges after major impacts.\u003c/p\u003e","manuscriptTitle":"Over-height Vehicle Impact Severity Assessment for Through-Plate Girder Railroad Bridges","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-11 12:07:15","doi":"10.21203/rs.3.rs-5994795/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3282dace-fdf1-40c3-993b-c5bba1db42e8","owner":[],"postedDate":"February 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-02-11T12:07:16+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-11 12:07:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5994795","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5994795","identity":"rs-5994795","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}