# Deep-Learning-Based Drive-by Damage Detection System for Railway Bridges

## Abstract

**:**

## 1. Introduction

## 2. Description of the Damage Detection System

#### 2.1. TTB Numerical Model

^{2}at the maximum damage level of 55% and is 0.0097 m/s

^{2}at 5% damage.

#### 2.2. Deep Leaning Architecture

#### 2.3. Bayesian Optimisation

**,**${y}_{i}=f({\mathit{\theta}}_{i})+{\u03f5}_{i}$, $\mathbf{Y}={\left\{{y}_{i}\right\}}_{i=1}^{n},\Theta ={\left\{{\mathit{\theta}}_{i}\right\}}_{i=1}^{n}$, $\mathit{\theta}=\left\{{\theta}_{1},\dots ,{\theta}_{d}\right\}$, $d$ is dimension of the hyperparameter vector and${\u03f5}_{i}~\mathcal{N}\left(0,{\sigma}_{noise}^{2}\right)$, the posterior process of $f({\mathit{\theta}}_{n+1})|{\mathcal{D}}_{n}$ is a Gaussian Process with a mean expressed as Equation (5):

^{−4}to 1 and the epochs can vary from 30 to 80.

^{−4}, epochs of 31 and dropout probability of 55% result in the maximum number of the optimum objective function values.

## 3. Results

#### Recommendations for Future Work

## 4. Conclusions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Hajializadeh, D.; OBrien, E.J.; O’Connor, A.J. Virtual Structural Health Monitoring and Remaining Life Prediction of Steel Bridges. Can. J. Civ. Eng.
**2017**, 44, 264–273. [Google Scholar] [CrossRef] [Green Version] - HekmatiAthar, S.; Taheri, M.; Secrist, J.; Taheri, H. Neural Network for Structural Health Monitoring with Combined Direct and Indirect Methods. J. Appl. Remote Sens.
**2020**, 14, 014511. [Google Scholar] [CrossRef] - Ni, Y.Q.; Ye, X.W.; Ko, J.M. Monitoring-Based Fatigue Reliability Assessment of Steel Bridges: Analytical Model and Application. J. Struct. Eng.
**2010**, 136, 1563–1573. [Google Scholar] [CrossRef] - Yang, Y.B.; Yau, J.D.; Yao, Z.; Wu, Y.S. Vehicle-Bridge Interaction Dynamics: With Applications to High-Speed Railways; World Scientific: Singapore, 2004. [Google Scholar]
- Lin, C.W.; Yang, Y.B. Use of a Passing Vehicle to Scan the Fundamental Bridge Frequencies: An Experimental Verification. Eng. Struct.
**2005**, 27, 1865–1878. [Google Scholar] [CrossRef] - Yang, Y.B.; Chang, K.C. Extraction of Bridge Frequencies from the Dynamic Response of a Passing Vehicle Enhanced by the EMD Technique. J. Sound Vib.
**2009**, 322, 718–739. [Google Scholar] [CrossRef] - Oshima, Y.; Yamaguchi, T.; Kobayashi, Y.; Sugiura, K. Eigenfrequency Estimation for Bridges Using the Response of a Passing Vehicle with Excitation System. In Proceedings of the Fourth International Conference on Bridge Maintenance, Safety and Management, Seoul, Korea, 13–17 July 2008; pp. 3030–3037. [Google Scholar]
- Yang, Y.B.; Yang, J.P. State-of-the-Art Review on Modal Identification and Damage Detection of Bridges by Moving Test Vehicles. Int. J. Struct. Stab. Dyn.
**2018**, 18, 1850025. [Google Scholar] [CrossRef] - Malekjafarian, A.; McGetrick, P.J.; OBrien, E.J. A Review of Indirect Bridge Monitoring Using Passing Vehicles. Shock Vib.
**2015**, 2015, 286139. [Google Scholar] [CrossRef] [Green Version] - Yang, Y.B.; Li, Y.C.; Chang, K.C. Using Two Connected Vehicles to Measure the Frequencies of Bridges with Rough Surface: A Theoretical Study. Acta Mech.
**2012**, 223, 1851–1861. [Google Scholar] [CrossRef] - McGetrick, P.J.; Gonzlez, A.; OBrien, E.J. Theoretical Investigation of the Use of a Moving Vehicle to Identify Bridge Dynamic Parameters. Insight-Non-Destr. Test. Cond. Monit.
**2009**, 51, 433–438. [Google Scholar] [CrossRef] [Green Version] - Yang, J.; Lam, H.F.; Hu, J. Ambient Vibration Test, Modal Identification and Structural Model Updating Following Bayesian Framework. Int. J. Struct. Stab. Dyn.
**2015**, 15, 1540024. [Google Scholar] [CrossRef] - McGetrick, P.J.; Kim, C.W. An Indirect Bridge Inspection Method Incorporating a Wavelet-Based Damage Indicator and Pattern Recognition. In Proceedings of the International Conference on Structural Dynamics EURODYN 2014, Porto, Portugal, 30 June 2014. [Google Scholar]
- Hester, D.; González, A. A Bridge-Monitoring Tool Based on Bridge and Vehicle Accelerations. Struct. Infrastruct. Eng.
**2015**, 11, 619–637. [Google Scholar] [CrossRef] [Green Version] - Fitzgerald, P.C.; Malekjafarian, A.; Cantero, D.; OBrien, E.J.; Prendergast, L.J. Drive-by Scour Monitoring of Railway Bridges Using a Wavelet-Based Approach. Eng. Struct.
**2019**, 191, 1–11. [Google Scholar] [CrossRef] - Locke, W.; Sybrandt, J.; Redmond, L.; Safro, I.; Atamturktur, S. Using Drive-by Health Monitoring to Detect Bridge Damage Considering Environmental and Operational Effects. J. Sound Vib.
**2020**, 468, 115088. [Google Scholar] [CrossRef] - Worden, K.; Manson, G.; Allman, D. Experimental Validation of a Structural Health Monitoring Methodology: Part I. Novelty Detection on a Laboratory Structure. J. Sound Vib.
**2003**, 259, 323–343. [Google Scholar] [CrossRef] - Farrar, C.R.; Worden, K. Structural Health Monitoring: A Machine Learning Perspective, 1st ed.; John Wiley & Sons: Chichester, UK, 2013; ISBN 9781119994336. [Google Scholar]
- Bull, L.; Worden, K.; Manson, G.; Dervilis, N. Active Learning for Semi-Supervised Structural Health Monitoring. J. Sound Vib.
**2018**, 437, 373–388. [Google Scholar] [CrossRef] - Deraemaeker, A.; Worden, K. A Comparison of Linear Approaches to Filter out Environmental Effects in Structural Health Monitoring. Mech. Syst. Signal Process.
**2018**, 105, 1–15. [Google Scholar] [CrossRef] - Liu, Y.Y.; Ju, Y.F.; Duan, C.D.; Zhao, X.F. Structure Damage Diagnosis Using Neural Network and Feature Fusion. Eng. Appl. Artif. Intell.
**2011**, 24, 87–92. [Google Scholar] [CrossRef] - Zhu, L.; Malekjafarian, A. On the Use of Ensemble Empirical Mode Decomposition for the Identification of Bridge Frequency from the Responses Measured in a Passing Vehicle. Infrastructures
**2019**, 4, 32. [Google Scholar] [CrossRef] [Green Version] - Antoniadou, I.; Cross, E.J.; Worden, K. Cointegration and the Empirical Mode Decomposition for the Analysis of Diagnostic Data. Key Eng. Mater.
**2013**, 569–570, 884–891. [Google Scholar] [CrossRef] - OBrien, E.J.; Malekjafarian, A.; González, A. Application of Empirical Mode Decomposition to Drive-by Bridge Damage Detection. Eur. J. Mech. A/Solids
**2017**, 61, 151–163. [Google Scholar] [CrossRef] [Green Version] - Zhang, T.; Biswal, S.; Wang, Y. SHMnet: Condition Assessment of Bolted Connection with beyond Human-Level Performance. Struct. Health Monit.
**2019**, 19, 1188–1201. [Google Scholar] [CrossRef] - Chun, P.J.; Yamashita, H.; Furukawa, S. Bridge Damage Severity Quantification Using Multipoint Acceleration Measurement and Artificial Neural Networks. Shock Vib.
**2015**, 789384. [Google Scholar] [CrossRef] [Green Version] - Dackermann, U.; Li, J.; Samali, B. Dynamic-Based Damage Identification Using Neural Network Ensembles and Damage Index Method. Adv. Struct. Eng.
**2010**, 13, 1001–1016. [Google Scholar] [CrossRef] [Green Version] - Neves, A.C.; González, I.; Leander, J.; Karoumi, R. Structural Health Monitoring of Bridges: A Model-Free ANN-Based Approach to Damage Detection. J. Civ. Struct. Health Monit.
**2017**, 7, 689–702. [Google Scholar] [CrossRef] [Green Version] - Hakim, S.J.S.; Abdul Razak, H. Modal Parameters Based Structural Damage Detection Using Artificial Neural Networks—A Review. Smart Struct. Syst.
**2014**, 14, 159–189. [Google Scholar] [CrossRef] [Green Version] - Mrugalska, B. Towards Enhanced Performance of Neural-Network-Based Fault Detection Using an Sequential D-Optimum Experimental Design. Appl. Sci.
**2018**, 8, 1290. [Google Scholar] [CrossRef] [Green Version] - Hakim, S.J.S.; Abdul Razak, H. Adaptive Neuro Fuzzy Inference System (ANFIS) and Artificial Neural Networks (ANNs) for Structural Damage Identification. Struct. Eng. Mech.
**2013**, 45, 779–802. [Google Scholar] [CrossRef] [Green Version] - Kim, P. MATLAB Deep Learning; Apress: Seoul, Korea, 2017; ISBN 9781484228449. [Google Scholar]
- Tang, Z.; Chen, Z.; Bao, Y.; Li, H. Convolutional Neural Network-Based Data Anomaly Detection Method Using Multiple Information for Structural Health Monitoring. Struct. Control Health Monit.
**2019**, 26, 1–22. [Google Scholar] [CrossRef] [Green Version] - Cha, Y.J.; Choi, W.; Büyüköztürk, O. Deep Learning-Based Crack Damage Detection Using Convolutional Neural Networks. Comput. Civ. Infrastruct. Eng.
**2017**, 32, 361–378. [Google Scholar] [CrossRef] - Mohtasham Khani, M.; Vahidnia, S.; Ghasemzadeh, L.; Ozturk, Y.E.; Yuvalaklioglu, M.; Akin, S.; Ure, N.K. Deep-Learning-Based Crack Detection with Applications for the Structural Health Monitoring of Gas Turbines. Struct. Health Monit.
**2020**, 19, 1440–1452. [Google Scholar] [CrossRef] - Tong, Z.; Gao, J.; Zhang, H. Recognition, Location, Measurement, and 3D Reconstruction of Concealed Cracks Using Convolutional Neural Networks. Constr. Build. Mater.
**2017**, 146, 775–787. [Google Scholar] [CrossRef] - Kim, B.; Cho, S. Image-Based Concrete Crack Assessment Using Mask and Region-Based Convolutional Neural Network. Struct. Control Health Monit.
**2019**, 26, e2381. [Google Scholar] [CrossRef] - Nex, F.; Duarte, D.; Tonolo, F.G.; Kerle, N. Structural Building Damage Detection with Deep Learning: Assessment of a State-of-the-Art CNN in Operational Conditions. Remote Sens.
**2019**, 11, 2765. [Google Scholar] [CrossRef] [Green Version] - Sony, S.; Gamage, S.; Sadhu, A.; Samarabandu, J. Multiclass Damage Identification in a Full-Scale Bridge Using Optimally Tuned One-Dimensional Convolutional Neural Network. J. Comput. Civ. Eng.
**2022**, 36, 4021035. [Google Scholar] [CrossRef] - Khodabandehlou, H.; Pekcan, G.; Fadali, M.S. Vibration-Based Structural Condition Assessment Using Convolution Neural Networks. Struct. Control Health Monit.
**2019**, 26, e2308. [Google Scholar] [CrossRef] - Yu, Y.; Wang, C.; Gu, X.; Li, J. A Novel Deep Learning-Based Method for Damage Identification of Smart Building Structures. Struct. Health Monit.
**2019**, 18, 143–163. [Google Scholar] [CrossRef] [Green Version] - Ferrara, R. A Numerical Model to Predict Train Induced Vibrations and Dynamic Overloads. Ph.D. Thesis, University of Reggio Calabria, Reggio Calabria, Italy, University Montpellier 2, Montpellier, France, 2014. [Google Scholar]
- Zhang, B.; Qian, Y.; Wu, Y.; Yang, Y.B. An Effective Means for Damage Detection of Bridges Using the Contact-Point Response of a Moving Test Vehicle. J. Sound Vib.
**2018**, 419, 158–172. [Google Scholar] [CrossRef] - Cantero, D.; Arvidsson, T.; OBrien, E.; Karoumi, R. Train–Track–Bridge Modelling and Review of Parameters. Struct. Infrastruct. Eng.
**2016**, 12, 1051–1064. [Google Scholar] [CrossRef] - Fryba, L. Dynamics of Railway Bridges; Thomas Telford: London, UK, 1996. [Google Scholar]
- Hamid, A.; Rasmussen, K.; Baluja, M.; Yang, T.L. Analytical Descriptions of Track Geometry Variations; Federal Railroad Adminitration: Washington, DC, USA, 1983.
- Martino, D. Train-Bridge Interaction on Freight Railway Lines. MSc Thesis; KTH Royal Institute of Technology: Stockholm, Sweden, 2011. [Google Scholar]
- Lei, X.; Zhang, B. Influence of Track Stiffness Distribution on Vehicle and Track Interactions in Track Transition. Proc. Inst. Mech. Eng.
**2010**, 224, 592–604. [Google Scholar] [CrossRef] - Lou, P. Finite Element Analysis for Train-Track-Bridge Interaction System. Arch. Appl. Mech.
**2007**, 77, 707–728. [Google Scholar] [CrossRef] - Dinh, V.N.; Du Kim, K.; Warnitchai, P. Dynamic Analysis of Three-Dimensional Bridge-High-Speed Train Interactions Using a Wheel-Rail Contact Model. Eng. Struct.
**2009**, 31, 3090–3106. [Google Scholar] [CrossRef] - Lilly, J.M.; Olhede, S.C. Higher-Order Properties of Analytic Wavelets. IEEE Trans. Signal Process.
**2009**, 57, 146–160. [Google Scholar] [CrossRef] [Green Version] - Medhi, M.; Dandautiya, A.; Raheja, J.L. Real-Time Video Surveillance Based Structural Health Monitoring of Civil Structures Using Artificial Neural Network. J. Nondestruct. Eval.
**2019**, 38, 1–16. [Google Scholar] [CrossRef] - Szegedy, C.; Liu, W.; Jia, Y.; Sermanet, P.; Reed, S. Going Deeper with Convolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA, 7 June 2015; pp. 1–9. [Google Scholar]
- Lin, M.; Chen, Q.; Yan, S. Network in Network. arXiv
**2013**, arXiv:1312.4400. [Google Scholar] - Arora, S.; Bhaskara, A.; Ge, R.; Ma, T. Provable Bounds for Learning Some Deep Representations. In Proceedings of the 31st International Conference on Machine Learning (ICML 2014), Beijing, China, 21 June 2014; Volume 1, pp. 883–891. [Google Scholar]
- Snoek, J.; Larochelle, H.; Adams, R.P. Practical Bayesian Optimization of Machine Learning Algorithms. Adv. Neural Inf. Process. Syst.
**2012**, 25, 2951–2959. [Google Scholar] [CrossRef] - Wan, H.-P.; Ni, Y.-Q. A New Approach for Interval Dynamic Analysis of Train-Bridge System Based on Bayesian Optimization. J. Eng. Mech.
**2020**, 146, 04020029. [Google Scholar] [CrossRef] - Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning; MIT Press: Cambridge, MA, USA, 2006. [Google Scholar]
- Selvaraju, R.R.; Cogswell, M.; Das, A.; Vedantam, R.; Parikh, D.; Batra, D. Grad-Cam: Visual Explanations from Deep Networks via Gradient-Based Localization. In Proceedings of the IEEE International Conference on Computer Vision 2017, Venice, Italy, 22–29 October 2017; Volume 17, pp. 618–626. [Google Scholar]
- Maaten, L.V.D.; Hinton, G. Visualizing Data Using T-SNE. J. Mach. Learn. Res.
**2008**, 9, 2579–2605. [Google Scholar] [CrossRef]

**Figure 3.**A sample of acceleration signals for front (1st) and rear (2nd) bogies for different damage levels at mid-span at the speed of 105 kph.

**Figure 5.**Difference between the real-valued CWT coefficients of healthy and six damage levels under speed of 105 kph.

**Figure 7.**Inception layer with dimensionality reduction (adapted from [54]).

**Figure 8.**Bayesian Optimisation results for hyperparameters of learning rate, maximum number of epochs and dropout probability.

**Figure 9.**An example of discriminating cues from CWT images: (

**a**) original image; (

**b**) highlighted sensitive features.

**Figure 10.**An example of discriminating cues from CWT images: (

**a**) original image; (

**b**) activating features in max pool layer 3 × 3; (

**c**) activating features in inception (5b).

**Figure 11.**An example of network behaviour from first pooling activation layer to final softmax activations.

**Figure 12.**Prediction accuracy of damage detection algorithm for different levels of damage and different locations.

Vehicle Properties [47] | Track Properties [48] | ||||
---|---|---|---|---|---|

Parameter | Symbol | Value | Parameter | Symbol | Value |

Carriage body mass (kg) | ${m}_{c}$ | 61,560 | Rail Young’s modulus (N/m^{2}) | ${E}_{r}$ | 206 × 10^{9} |

Carriage body moment of inertia (kg·m^{2}) | ${J}_{c}$ | 9.11 × 10^{6} | Rail cross-sectional area (m^{2}) | ${A}_{r}$ | 15.38 |

Bogie mass (kg) | ${m}_{br},{m}_{bf}$ | 5200 | Rail second moment of area (m^{4}) | ${I}_{r}$ | 6.43 × 10^{−5} |

Bogie moment of inertia (kg·m^{2}) | ${J}_{br},{J}_{bf}$ | 5900 | Rail mass per unit length (kg/m) | ${\rho}_{r}$ | 120 |

Wheelset mass (kg) | ${m}_{wr},{m}_{wf}$ | 1510 | Rail pad stiffness (N/m) | ${k}_{rp}$ | 80 × 10^{6} |

Primary suspension stiffness (N/m) | ${k}_{1r}^{v},{k}_{1f}^{v}$ | 4.96 × 10^{6} | Rail pad damping (N.s/m) | ${c}_{rp}$ | 60 × 10^{3} |

Secondary suspension stiffness (N/m) | ${k}_{2r}^{v},{k}_{2f}^{v}$ | 1.9 × 10^{6} | Mass of sleeper (kg) | ${m}_{s}$ | 340 |

Primary suspension damping (kN·s/m) | ${c}_{1r}^{v},{c}_{1f}^{v}$ | 108 | Sleeper spacing (m) | ${L}_{s}$ | 0.57 |

Secondary suspension damping (kN·s/m) | ${c}_{2r}^{v},{c}_{2f}^{v}$ | 152 | Ballast stiffness (N/m) | ${k}_{ba}$ | 120 × 10^{6} |

Distance between axles (m) | ${L}_{ar},{L}_{af}$ | 2.7 | Ballast damping (N·s/m) | ${c}_{ba}$ | 60 × 10^{3} |

Horizontal distance between centre of mass of main body and bogie (m) | ${L}_{cr},{L}_{cf}$ | 3.81 | Ballast mass | ${m}_{ba}$ | 2718 |

Sub-ballast stiffness (N/m) | ${k}_{sb}$ | 60 × 10^{6} | |||

Sub-ballast damping (N/m) | ${c}_{sb}$ | 90 × 10^{3} |

Type |
---|

convolution layer 7 × 7 and stride [2,2] |

max pool layer 3 × 3 and stride [2,2] |

convolution layer 3 × 3 and stride [1,1] |

max pool layer 3 × 3 and stride [2,2] |

inception (3a) |

inception (2b) |

max pool layer 3 × 3 and stride [2,2] |

inception (4a) |

inception (4b) |

inception (4c) |

inception (4d) |

inception (4e) |

max pool layer 3 × 3 and stride [2,2] |

inception (5a) |

inception (5b) |

average pool layer 7 × 7 and stride [1,1] |

dropout layer with probability of 55% |

fully connected layer |

softmax |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hajializadeh, D.
Deep-Learning-Based Drive-by Damage Detection System for Railway Bridges. *Infrastructures* **2022**, *7*, 84.
https://doi.org/10.3390/infrastructures7060084

**AMA Style**

Hajializadeh D.
Deep-Learning-Based Drive-by Damage Detection System for Railway Bridges. *Infrastructures*. 2022; 7(6):84.
https://doi.org/10.3390/infrastructures7060084

**Chicago/Turabian Style**

Hajializadeh, Donya.
2022. "Deep-Learning-Based Drive-by Damage Detection System for Railway Bridges" *Infrastructures* 7, no. 6: 84.
https://doi.org/10.3390/infrastructures7060084