An Effective Approach for Damage Identification in Beam-Like Structures Based on Modal Flexibility Curvature and Particle Swarm Optimization

Document Type : Regular Paper


1 Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Center of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science & Technology

3 Department of Civil Engineering, Payame Noor University


In this paper, a computationally simple approach for damage localization and quantification in beam-like structures is proposed. This method is in consonance with applying modal flexibility curvature (MFC) and particle swarm optimization (PSO) algorithm. Analytical studies in the literature have revealed that changes in the modal flexibility curvature can be considered as a sensitive and suitable criterion for identifying damage in the beam-like structures. Modal flexibility curvature can be calculated utilizing central difference approximation, based on entries of the modal flexibility matrix. The PSO algorithm, as a powerful optimization tool, is employed in order to minimize the error function which is formulated as an error function between the measured modal flexibility curvatures of the damaged structure and those calculated from the analytical structure. To demonstrate the efficiency of the method, two beam-like structures under different damage scenarios are studied. In addition, the robustness of presented method is investigated only when the first several modal data are available. It is observed that the proposed approach is able to localize and quantify various damage cases only by a few lower vibrational modes and also, it is low-sensitive to measurement noise.


Main Subjects

[1]     Abdo, M.A.B. (2012). “Parametric study of using only static response in structural damage detection”. Engineering Structures, Vol. 34, pp. 124-131.
[2]     Pandey, A.K., Biswas, M., Samman, M.M. (1991). “Damage detection from changes in curvature mode shapes”. Journal of Sound and Vibration, Vol. 145, pp. 321-333.
[3]     Abdel Wahab, M.M., DeRoeck, G. (1999). “Damage detection in bridges using modal curvatures: application to a real damage scenario”. Journal of Sound and Vibration, Vol. 226, No. 2, pp. 217-235.
[4]     Lin, R.J., Cheng, F.P. (2008). “Multiple crack identification of a free-free beam with uniform material property variation and varied noised frequency”. Engineering Structures, Vol. 30, pp. 909-929.
[5]     Lu, X.B., Liu, J.K., Lu, Z.R. (2013). “A two-step approach for crack identification in beam”. Journal of Sound and Vibration, Vol. 332, pp. 282-293.
[6]     Tomaszewska, A. (2010). “Influence of statistical errors on damage detection based on structural flexibility and mode shape curvature”. Computers & Structures, Vol. 88, pp. 154-164.
[7]     Lu, Q., Ren, G., Zhao, Y. (2002). “Multiple damage location with flexibility curvature and relative frequency change for beam structures”. Journal of Sound and Vibration, Vol. 253, No. 5, pp. 1101-1114.
[8]     Wong, F.S., Thint, M.P., Tung, A.T. (1997). “On-line detection of structural damage using neural networks”. Civil Engineering and Environmental Systems, Vol. 14, pp. 167–197.
[9]     Sahin, M., Shenoi, R.A. (2003). “Quantification and localization of damage in beam-like structures by using artificial neural networks with experimental validation”. Engineering Structures, Vol. 25, pp. 1785-1802.
[10]    Vinayak, H.K., Kumar, A., Agarwal, P., Thakkar, S.K. (2010). “Neural network-based damage detection from transfer function changes”. Journal of Earthquake Engineering, Vol. 14, pp. 771–787.
[11]    Lee, J. (2009). “Identification of multiple cracks in a beam using vibration amplitudes”. Journal of Sound and vibration, Vol. 326, pp. 205-212.
[12]    Lopes, P.S., Jorge, A.B., Cunha Jr, S.S. (2010). “Detection of holes in a plate using global optimization and parameter identification techniques”. Inverse Problems in Science and Engineering, Vol. 18, No. 4, pp. 439-463.
[13]    Meruane, V., Heylen, W. (2011). “An hybrid real genetic algorithm to detect structural damage using modal properties”. Mechanical Systems and Signal Processing, Vol. 25, pp. 1559-1573.
[14]    Na, C., Kim, S.P., Kwak, H.G. (2011). “Structural damage evaluation using genetic algorithm”. Journal of Sound Vibration, Vol. 330, pp. 2772-2783.
[15]    Mehrjoo, M., Khaji, N., Ghafory-Ashtiany, M. (2013). “Application of genetic algorithm in crack detection of beam-like structures using a new cracked Euler–Bernoulli beam element”. Applied Soft Computing, Vol. 13, pp. 867-880.
[16]    Zare Hosseinzadeh, A., Bagheri, A., Ghodrati Amiri, G. (2013). “Two-stage method for damage localization and quantification in high-rise shear frames based on the first mode shape slope”. International journal of optimization in civil engineering, Vol. 3, No. 4, pp. 653-672.
[17]    Tabrizian, Z., Ghodrati Amiri, G., Hossein Ali Beigy, M. (2014). “Charged system search algorithm utilized for structural damage detection”. Shock and Vibration, Vol. 2014, 13 pages, Article ID: 194753.
[18]    Ghodrati Amiri, G., Zare Hosseinzadeh, A., Seyed Razzaghi, S.A. (2015). “Generalized flexibility based model updating approach via democratic particle swarm optimization algorithm for structural damage prognosis”. International Journal of Optimization in Civil Engineering, Vol. 5, No. 4, pp. 44-65
[19]    Zare Hosseinzadeh, A., Ghodrati Amiri, G., Seyed Razzaghi, S.A. (2017). “Model-based identification of damage from sparse sensor measurements using Neumann series expansion”. Inverse Problems in Science and Engineering, Vol. 25, No. 2, pp. 239-259.
[20]    Kaveh, A., Hoseini Vaez, S.R., Hosseini, P. (2019). “Enhanced vibrating particles system algorithm for damage identification of truss structures”. Scientia Iranica, Vol. 26, No. 1, pp. 246-256.
[21]    Kennedy, J., Eberhart, R. (1995). “Particle swarm optimization”. In: Proceedings of the IEEE international conference on neural networks, Vol. 4, pp. 1942-1948.
[22]    Golbon-Haghighi, M.H., Saeidi-Manesh, H., Zhang, G., Zhang, Y. (2018). “Pattern synthesis for the cylindrical polarimetric phased array radar (CPPAR)”. Progress in Electromagnetics Research M, Vol. 66, pp. 87-98.
[23]    Shi, Y., Eberhart, R.C. (1998). “A modified particle swarm optimizer”. Proceedings IEEE International Conference on Evolutionary Computation, pp. 69-73.
[24]    Shi, Y., Eberhart, R.C. (1999). “Empirical study of particle swarm optimization”. Proceedings of the Congress on Evolutionary Computation, Vol. 3, pp. 1945-1950.