Finite element model updating of a geared rotor system using particle swarm optimization for condition monitoring

Document Type: Invited by Hamid Ahmadian


School of Mechanical Engineering,College of Engineering, University of Tehran, Tehran, Iran



In this paper, condition monitoring of a geared rotor system using finite element (FE) model updating and particle swarm optimization (PSO) method is onsidered. For this purpose, employing experimental data from the geared rotor system, an updated FE model is obtained. The geared rotor system under study consists of two shafts, four bearings, and two gears. To get the experimental data,  iezoelectric accelerometers are mounted on the bearings to extract the natural frequencies. Also, mass, stiffness and gyroscopic matrices can be obtained using FE method. By extracting these matrices, natural frequencies and mode shapes are also obtained from solutions of an eigenvalue problem. Having the first flexural four natural frequencies from experimental modal analysis as the objective, FE model of the geared rotor structure is to be updated. Solving sensitivity equations iteratively, model updating is performed to predict the required changes in parameters of the model. In the next stage, some defects are introduced into the experimental setup and the resulting natural frequencies are set as the reference for model updating purpose. Therefore, the changes in the model parameter with respect to a healthy system is monitored. Using PSO method, fault detection in a geared rotor system is performed. Model updating and PSO are able to predict the types and values of damages created in the geared rotor system. In general, the model updating method is simpler and computationally more efficient for industrial equipment. However, particle swarm optimization provides more accurate results with higher computations.


  • Condition monitoring of a geared rotor was performed by FE model updating and PSO.
  • Experimental data was used to update the FE model.
  • Optimization method predicted the parameters more accurately than model updating.
  • Changes of natural frequencies for gear faults ranged from 0.7 to 5 percent


Main Subjects

[1] O.D. Mohammed, M. Rantatalo, J.O. Aidanpää, Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis, Mechanical Systems and Signal Processing, 54 (2015) 293-305.

[2] Z. Feng, M.J. Zuo, F. Chu, Application of regularization dimension to gear damage assessment, Mechanical Systems and Signal Processing, 24 (2010) 1081-1098.

[3] Z. Feng, M.J. Zuo, Fault diagnosis of planetary gearboxes via torsional vibration signal analysis, Mechanical Systems and Signal Processing, 36 (2013) 401-421.

[4] W. Bartelmus, Object and operation supported maintenance for mining equipment, Mining Science, 21 (2014) 7--21.

[5] W. Bartelmus, R. Zimroz, Vibration spectra characteristic frequencies for condition monitoring of mining machinery compound and complex gearboxes, Mining Science, 133 (2011) 17.

[6] M. Inalpolat, A. Kahraman, A theoretical and experimental investigation of modulation sidebands of planetary gear sets, Journal of sound and vibration, 323 (2009) 677-696.

[7] Z. Feng, M.J. Zuo, Vibration signal models for fault diagnosis of planetary gearboxes, Journal of Sound and Vibration, 331 (2012) 4919-4939.

[8] R. Patrick, A.l. Ferri, G. Vachtsevanos, Effect of planetary gear carrier-plate cracks on vibration spectrum, Journal of vibration and acoustics, 134 (2012).

[9] A. Parey, N. Tandon, Spur gear dynamic models including defects: A review, The Shock and Vibration Digest, 35 (2003) 465-478.

[10] W. Bartelmus, Supporting diagnostic inference by mathematical modelling from one-stage to planetary gearbox systems, Diagnostyka, 30 (2004) 31-38.

[11] Y. Lei, J. Lin, M.J. Zuo, Z. He, Condition monitoring and fault diagnosis of planetary gearboxes: A review, Measurement, 48 (2014) 292-305.

[12] H. Ma, J. Zeng, R. Feng, X.u. Pang, Q. Wang, B. Wen, Review on dynamics of cracked gear systems, Engineering Failure Analysis, 55 (2015) 224-245.

[13] A.S. Lee, J.W. Ha, D.-H. Choi, Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system, Journal of Sound and Vibration, 263 (2003) 725-742.

[14] M.l. Friswell, J.E. Mottershead, Finite element model updating in structural dynamics, Springer Science & Business Media, 2013.

[15] T. Marwala, Finite element model updating using computational intelligence techniques: applications to structural dynamics, Springer Science & Business Media, 2010.

[16] E. Simoen, G. De Roeck, G. Lombaert, Dealing with uncertainty in model updating for damage assessment: A review, Mechanical Systems and Signal Processing, 56 (2015) 123-149.

[17] A. Teughels, G. De Roeck, Damage detection and parameter identification by finite element model updating, Revue européenne de génie civil, 9 (2005) 109-158.

[18] J.E. Mottershead, M. Link, M.I. Friswell, The sensitivity method in finite element model updating: a tutorial, Mechanical systems and signal processing, 25 (2011) 2275-2296.

[19] J. Kennedy, R.C. Eberhart, Particle swarm optimizationProceedings of IEEE International Conference on Neural Networks, Perth, WA, Australia), Vol. 4, pp 1942–1948, IEEE Service Center, Piscataway, NJ, (1995).

[20] R. Poli, Analysis of the publications on the applications of particle swarm optimisation, Journal of Artificial Evolution and Applications, 2008 (2008).

[21] S.-W. Lin, K.-C. Ying, S.-C. Chen, Z.-J. Lee, Particle swarm optimization for parameter determination and feature selection of support vector machines, Expert systems with applications, 35 (2008) 1817-1824.

[22] Y. Ishida, T. Yamamoto, Linear and nonlinear rotordynamics, Wiley Online Library, 2012.

[23] Q. Han, J. Zhao, F. Chu, Dynamic analysis of a geared rotor system considering a slant crack on the shaft, Journal of Sound and Vibration, 331 (2012) 5803-5823.

[24] A. Esfandiari, F. Bakhtiari-Nejad, A. Rahai, Theoretical and experimental structural damage diagnosis method using natural frequencies through an improved sensitivity equation, International Journal of Mechanical Sciences, 70 (2013) 79-89.

[25] S. Hassiotis, G.D. Jeong, Identification of stiffness reductions using natural frequencies, Journal of engineering mechanics, 121 (1995) 1106-1113.