Application of moving vehicle response and variational mode decomposition (VMD) for indirect damage detection in bridges

Document Type : Original Research

Authors
S. Khalkhali Shandiz
H. Khezrzadeh
Faculty of Civil and Environmental Engineering, Tarbiat Modares University
Abstract
Regarding the importance of bridges as one of the most critical infrastructures, their maintenance, and health monitoring is of high priority. Interaction between the moving vehicles and bridges is amongst the fields of study that have been investigated in depth by numerous researchers in the field of bridge engineering. Among different proposed methods of structural health monitoring of bridges, the indirect methods that do not need the healthy structure response are of high interest because of their ease and low maintenance costs.

The response of a moving mass passing through a bridge can be analyzed for the indirect prediction of the beamchr('39')s mechanical properties. This can lead to the detection of possible damages or degradations in the structure. By mounting high precision accelerometers on the moving vehicle and recording the corresponding signals, it is possible to capture the sudden change of mechanical properties pertaining to the existence of damage in the bridge.

In the current study, an FE code is developed in order to analyze the moving vehicle response. In this code, the bridge is modeled as an Euler-Bernoulli beam, and a complete model comprising stiffness and damping of the suspension system of moving vehicle is built. In order to verify the results of the code, comparisons are made with the outcomes of modal analysis. The sensitivity of the FE results with respect to the number of elements is examined. These comparisons clearly show that both methods reach the same values for a sufficiently high number of elements for the moving vehicle response.

Following verification of the code, a brief review of the concepts underlying the variational mode decomposition (VMD) method is given for a self-contained representation. The VMD can be used to decompose a signal into a number of signals with limited bandwidth. Although it has found many applications in different signal processing cases (e.g. in the field of electronics, mechanical vibrations of machines, or even in the analysis of economic and financial time series), extending its application to the field of structural health monitoring is entirely a recent and ongoing topic of research.

After the introduction of the VMD, damage in the beams is implemented by using fracture mechanics concepts. Different damage scenarios are applied in order to check the reliability and robustness of using VMD as a damage detection method. These include different damage locations (single, dual) and damage severity represented in terms of crack depth. By having a reliable means for the analysis, the novel variational mode decomposition (VMD) is applied to analyze the signals recorded from the vehiclechr('39')s back axel in search of any possible irregularity in the signal properties. By monitoring results attained for several damage cases, the following conclusions can be given:

• The variational mode decomposition (VMD) can highlight the presence of irregularities in mechanical properties that can be reached directly from decomposed signals.

• The location of these signal irregularities coincides with the presumed location(s) of the crack(s).

• The severity of the signal irregularity and corresponding instantaneous energy is proportional to the degree of damage imposed on the beam.

• The moving vehiclechr('39')s natural frequency plays an essential role in the bridgeschr('39') structural health monitoring. The signal processing results exhibit amplified abrupt changes for the vehicles with the natural frequencies close to the beamchr('39')s fundamental frequencies.

Regarding the above conclusions, analyzing moving mass response with the VMD can be a reliable damage detection technique.

Keywords

Subjects

A. Yavari, M. Nouri, and M. Mofid, "Discrete element analysis of dynamic response of Timoshenko beams under moving mass," Advances in engineering software, vol. 33, no. 3, pp. 143-153, 2002.
A. Nikkhoo, A. Farazandeh, and M. E. Hassanabadi, "On the computation of moving mass/beam interaction utilizing a semi-analytical method," Journal of the Brazilian Society of Mechanical Sciences and Engineering vol. 38, no. 3, pp. 761-771, 2016.
A. Nikkhoo, F. Rofooei, and M. Shadnam, "Dynamic behavior and modal control of beams under moving mass," Journal of Sound and Vibration, vol. 306, no. 3-5, pp. 712-724, 2007.
A. Ghannadiasl and S. K. Ajirlou, "Forced vibration of multi-span cracked Euler–Bernoulli beams using dynamic Green function formulation," Applied Acoustics, vol. 148, pp. 484-494, 2019.
H. Khezrzadeh and H. Jafari, "Analytical study of steel-FRP bridges vibration subjected to moving mass," (in eng), Modares Civil Engineering journal, vol. 18, no. 4, pp. 57-70, 2018.
Y.-B. Yang, C. Lin, and J. Yau, "Extracting bridge frequencies from the dynamic response of a passing vehicle," Journal of Sound Vibration vol. 272, no. 3-5, pp. 471-493, 2004.
P. J. McGetrick, A. Gonzlez, and E. J. OBrien, "Theoretical investigation of the use of a moving vehicle to identify bridge dynamic parameters," Insight-Non-Destructive Testing Condition Monitoring vol. 51, no. 8, pp. 433-438, 2009.
C. Lin and Y. Yang, "Use of a passing vehicle to scan the fundamental bridge frequencies: An experimental verification," Engineering Structures, vol. 27, no. 13, pp. 1865-1878, 2005.
A. Malekjafarian and E. J. OBrien, "Identification of bridge mode shapes using short time frequency domain decomposition of the responses measured in a passing vehicle," Engineering Structures, vol. 81, pp. 386-397, 2014.
J. Bu, S. Law, and X. Zhu, "Innovative bridge condition assessment from dynamic response of a passing vehicle," Journal of engineering mechanics, vol. 132, no. 12, pp. 1372-1379, 2006.
K. V. Nguyen and H. T. Tran, "Multi-cracks detection of a beam-like structure based on the on-vehicle vibration signal and wavelet analysis," Journal of Sound and Vibration, vol. 329, no. 21, pp. 4455-4465, 2010.
K. V. Nguyen, "Comparison studies of open and breathing crack detections of a beam-like bridge subjected to a moving vehicle," Engineering Structures, vol. 51, pp. 306-314, 2013.
K. V. Nguyen, "Dynamic analysis of a cracked beam-like bridge subjected to earthquake and moving vehicle," Advances in Structural Engineering, vol. 18, no. 1, pp. 75-95, 2015.
S.-H. Yin and C.-Y. Tang, "Identifying cable tension loss and deck damage in a cable-stayed bridge using a moving vehicle," Journal of Vibration Acoustics vol. 133, no. 2, 2011.
M. E. Hassanabadi, A. Heidarpour, S. E. Azam, and M. Arashpour, "Recursive principal component analysis for model order reduction with application in nonlinear Bayesian filtering," Computer Methods in Applied Mechanics and Engineering, vol. 371, p. 113334, 2020.
E. J. OBrien, A. Malekjafarian, and A. González, "Application of empirical mode decomposition to drive-by bridge damage detection," European Journal of Mechanics-A/Solids, vol. 61, pp. 151-163, 2017.
A. ElHattab, N. Uddin, and E. OBrien, "Drive-by bridge damage detection using non-specialized instrumented vehicle," Bridge Structures, vol. 12, no. 3-4, pp. 73-84, 2017.
J. Li, X. Zhu, S.-S. Law, and B. Samali, "A two-step drive-by bridge damage detection using Dual Kalman Filter," International Journal of Structural Stability Dynamics, 2020.
K. Kildashti, M. M. Alamdari, C. Kim, W. Gao, and B. Samali, "Drive-by-bridge inspection for damage identification in a cable-stayed bridge: Numerical investigations," Engineering Structures, vol. 223, p. 110891, 2020.
P. Mario, "Structural Dynamics Theory and Computation," ed, 2004.
K. Youcef, T. Sabiha, D. El Mostafa, D. Ali, and M. Bachir, "Dynamic analysis of train-bridge system and riding comfort of trains with rail irregularities," Journal of Mechanical Science Technology, vol. 27, no. 4, pp. 951-962, 2013.
H. Tada, P. C. Paris, G. R. Irwin, and H. Tada, The stress analysis of cracks handbook. ASME press New York, 2000.
K. Dragomiretskiy and D. Zosso, "Variational mode decomposition," IEEE transactions on signal processing, vol. 62, no. 3, pp. 531-544, 2013.
M. Bertero, T. A. Poggio, and V. Torre, "Ill-posed problems in early vision," Proceedings of the IEEE, vol. 76, no. 8, pp. 869-889, 1988.
A. N. Tihonov, "Solution of incorrectly formulated problems and the regularization method," Soviet Math, vol. 4, pp. 1035-1038, 1963.
N. Wiener, Extrapolation, interpolation, and smoothing of stationary time series: with engineering applications. MIT press, 1950.
E. Bedrosian, "A product theorem for Hilbert transforms," 1962.
I. ISO, "Mechanical vibration—Road surface profiles—Reporting of measured data," ed, 1995.
Z. Wang et al., "Application of parameter optimized variational mode decomposition method in fault diagnosis of gearbox," IEEE Access, vol. 7, pp. 44871-44882, 2019.
Y. Wang, R. Markert, J. Xiang, and W. Zheng, "Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system," Mechanical Systems and Signal Processing, vol. 60, pp. 243-251, 2015.
Modares Civil Engineering journal
Volume 21, Issue 1
March and April 2021
Pages 31-46