Accessible Requires Authentication Published by De Gruyter May 26, 2013

A Crack Identification Approach for Beam-Like Structures under Moving Vehicle using Particle Swarm Optimization

Ein Ansatz zur Rissidentifizierung für balkenartige Strukturen unter bewegten Fahrzeugen mittels Particle Swarm Optimization
Hakan Gökdağ
From the journal Materials Testing


A crack identification method for beam type structures under moving vehicle is proposed. The basic of the method is to formulate damage detection as an inverse problem, and solve for damage locations and extents. With respect to this, an objective function is defined based on the difference of damaged beam dynamic response and the response calculated by the mathematical model of the beam. The optimization problem is solved by the particle swarm optimization (PSO) with linearly increasing inertia weight to obtain crack locations and their depths. By the numerical simulations, it was observed that cracks with depth ratio of 0.1 can be identified with reasonable error by the present method in spite of noise interference of 3 %.


Ein Verfahren zur Identifizierung von Rissen in balkenartigen Strukturen unter bewegten Fahrzeugen wird in dem vorliegenden Beitrag dargestellt. Die Basis dieses Verfahrens bildet die Formulierung der Rissdetektion als inverses Problem und dessen Lösung für die Schädigungsorte und -ausmaße. Diesbezüglich wurde eine objektive Funktion definiert, die auf der Differenz basiert, die sich zwischen der dynamischen Antwort des geschädigten Balkens und der Antwort ergibt, die mittels des mathematischen Balkenmodells berechnet wurde. Die Optimierungsaufgabe wurde mittels Particle Swarm Optimization (PSO) mit linear wachsendem Massenträgheitsmoment gelöst, um die entsprechenden Rissorte und deren Tiefe zu erhalten. Mittels der numerischen Simulationen wurde beobachtet, dass Risse mit einem Tiefenverhältnis von 0,1 mit diesem Verfahren innerhalb eines vernünftigen Fehlers identifiziert werden können, trotz einer Rauschinterferenz von 3 %.

Hakan Gökdağ has been assistant professor of Mechanical Engineering at Bursa Technical University, Turkey ( for about a year. Before, he was research assistant at Uludağ University, Turkey (, where he received his diploma (MSc) in 20 0 5 on applications of linear theory of vibrations, and PhD in 20 10 on wavelet transform based structural damage detection. From 20 0 9 to 20 10 he was visitor researcher at Mechanical Engineering, Imperial College London, UK. His research interests include applications of linear and nonlinear vibrations, experimental modal analysis, structural damage detection, wavelet transform and its applications, applied mathematics, and signal processing for sound and vibration applications.


1 L.Fryba: Vibration of Solids and Structures Under Moving Loads, Telford, London (1999) Search in Google Scholar

2 Y. B.Yang, J. D.Yau, Y. S.Wu: Vehicle-Bridge Interaction Dynamics With Applications in High-Speed Railways, World Scientific Publishing Co. Pte. Ltd., Singapore (2004) Search in Google Scholar

3 M. A.Mahmoud: Effect of cracks on the dynamic response of a simple beam subject to a moving load, Proceedings of the Institution of Mechanical Engineers215 (2001), pp. 207215 Search in Google Scholar

4 C.Bilello, L. A.Bergman: Vibration of damaged beam under a moving mass: theory and experimental validation, Journal of Sound and Vibration274 (2004), pp. 567582 Search in Google Scholar

5 S. S.Law, X. Q.Zhu: Dynamic behaviour of damaged concrete bridge structures under moving vehicular loads, Engineering Structures26 (2004), pp. 12791293 Search in Google Scholar

6 A.Ariaei, S.Ziaei-Rad, M.Ghayour: Vibration analysis of beams with open and breathing cracks subjected to moving masses, Journal of Sound and Vibration326 (2009), pp. 709724 Search in Google Scholar

7 X. Q.Zhu, S. S.Law: Wavelet-based crack identification of bridge beam from operational deflection time history, International Journal of Solids and Structures43 (2006), pp. 22992317 Search in Google Scholar

8 D.Hester, A.Gonzalez: A wavelet-based damage detection algorithm based on bridge acceleration response to a vehicle, Mechanical Systems and Signal Processing (2011), pp. 145166 Search in Google Scholar

9 K. V.Nguyen, H. T.Tran: Multi-crack detection of a beam-like structure based on the on-vehicle vibration signal and wavelet analysis, Journal of Sound and Vibration329 (2010), pp. 44554465 Search in Google Scholar

10 A.Khorram, F.Bakhtiari-Nejad, M.Rezaeian: Comparison studies between two waveletbased crack detection methods of a beam subjected to a moving load, International Journal of Engineering Science51 (2012), pp. 204215 Search in Google Scholar

11 H.Gökdag: Wavelet-based damage detection method for a beam-type structure carrying moving mass, Structural Engineering and Mechanics, 38 (2011), No. 1, pp. 8197 Search in Google Scholar

12 F. S.Buezas, M. B.Rosales, C. P.Filipich: Damage detection with genetic algorithms taking into account a crack contact model, Engineering Fracture Mechanics78 (2011), pp. 695712 Search in Google Scholar

13 O.Begambre, J. E.Laier: A hybrid particle swarm optimization – simplex algorithm (PSOS) for structural damage identification, Advances in Engineering Software40 (2009), pp. 883891 Search in Google Scholar

14 S.Moradi, P.Razi, L.Fatahi: On the application of bees algorithm to the problem of crack detection, Computers and Structures89 (2011), pp. 21692175 Search in Google Scholar

15 S. M.Seyedpoor: A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization, International Journal of Non-Linear Mechanics47 (2012), pp. 18 Search in Google Scholar

16 J.Kennedy, R.Eberhart: Particle swarm optimization, Proceedings of the 4th IEEE International Conference on Neural Networks4 (1995), pp. 19421948 Search in Google Scholar

17 K. E.Parsopoulos, M. N.Vrahatis: Particle Swarm Optimization and Intelligence: Advances and Applications, IGI Global, Hershey PA (2010) Search in Google Scholar

18 H.Gökdag, A. R.Yildiz: Structural damage detection using modal parameters and particle swarm optimization, Materials Testing54 (2012), pp. 416420 Search in Google Scholar

19 R. W.Clough, J.Penzien: Dynamics of Structures, Computers & Structures, Inc., Berkeley, CA (1995) Search in Google Scholar

20 S. Q.Wu, S. S.Law: Vehicle axle load identification on bridge deck with irregular road surface profile, Engineering Structures33 (2011), pp. 591601 Search in Google Scholar

21 M.Clerc, J.Kennedy: The particle swarmexplosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computation6 (2002), No. 1, pp. 5873 Search in Google Scholar

22 Y. L.Zheng, L. H.Ma, L. Y.Zhang, J. X.Qian: On the convergence analysis and parameter selection in particle swarm optimization, Proc. of the 2nd International Conference on Machine Learning and Cybernetics 03 (2003), pp. 18021807 Search in Google Scholar

23 I. C.Trelea: The particle swarm optimization algorithm: Convergence analysis and parameter selection, Information Processing Letters 85 (2003), pp. 317325 Search in Google Scholar

24 B.Trentadue, A.Messina, N. I.Giannoccaro: Damage detecting through the processing of dynamic shapes measured by a psd-tri angular laser sensor, International Journal of Solids and Structures 44 (2007), pp. 55545575 Search in Google Scholar

25 A.Alvandi, C.Cremona: Assessment of vibration-based damage identification techniques, Journal of Sound and Vibration 292 (2006), pp. 179202 Search in Google Scholar

Published Online: 2013-05-26
Published in Print: 2013-02-01

© 2013, Carl Hanser Verlag, München