Abstract
In this study, a novel optimization-based method is proposed to determine the parameters of a rotating unbalance in a rotor-bearing system. For that purpose, the weighted sum of squared difference between the analytical and predicted unbalance response due to rotational unbalance is considered as the objective function. A hybrid algorithm integrating salp swarm algorithm and Nelder–Mead algorithms is presented for detecting unbalance magnitude and phase as the unbalance parameters. Parameters of the aforementioned optimization algorithm are determined systematically using the Taguchi design of experiments method. The efficiency of the proposed method is compared with various optimization algorithms in the literature. The optimization method is validated with different unbalances experimentally to consider the real-world conditions. The results show the superiority of the proposed hybrid algorithm in terms of the accuracy of the unbalance parameters and computational efficiency.



















Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
Enquiries about data availability should be directed to the authors.
References
Abbasi A, Firouzi B, Sendur P (2021a) On the application of Harris hawks optimization (HHO) algorithm to the design of microchannel heat sinks. Eng Comput 37(2):1409–1428
Abbasi A, Firouzi B, Sendur P, Heidari AA, Chen H, Tiwari R (2021b) Multi-strategy Gaussian Harris hawks optimization for fatigue life of tapered roller bearings. Eng Comput. https://doi.org/10.1007/s00366-021-01442-3
Abbassi R, Abbassi A, Heidari AA, Mirjalili S (2019) An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers Manag 179:362–372
Arias-Montiel M, Beltrán-Carbajal F, Silva-Navarro G (2014) On-line algebraic identification of eccentricity parameters in active rotor-bearing systems. Int J Mech Sci 85:152–159
Cedillo SGT, Al-Ghazal GG, Bonello P, Pérez JC (2019) Improved non-invasive inverse problem method for the balancing of nonlinear squeeze-film damped rotordynamic systems. Mech Syst Signal Process 117:569–593
Chatzisavvas I, Dohnal F (2015) Unbalance identification using the least angle regression technique. Mech Syst Signal Process 50:706–717
Deepthikumar MB, Sekhar AS, Srikanthan MR (2013) Modal balancing of flexible rotors with bow and distributed unbalance. J Sound Vib 332(24):6216–6233
Dey B, Bhattacharyya B, Srivastava A, Shivam K (2020) Solving energy management of renewable integrated microgrid systems using crow search algorithm. Soft Comput 24(14):10433–10454
Firouzi B, Abbasi A, Sendur P (2021a) Improvement of the computational efficiency of metaheuristic algorithms for the crack detection of cantilever beams using hybrid methods. Eng Optim. https://doi.org/10.1080/0305215X.2021.1919887
Firouzi B, Abbasi A, Sendur P (2021b) Identification and evaluation of cracks in electrostatically actuated resonant gas sensors using Harris Hawk/Nelder Mead and perturbation methods. Smart Struct Syst 28(1):121–142. https://doi.org/10.12989/sss.2021.28.1.121
Hamrock BJ, Schmid SR, Jacobson BO (2004) Fundamentals of fluid film lubrication. CRC Press, Boca Raton
He RS, Hwang SF (2006) Damage detection by an adaptive real-parameter simulated annealing genetic algorithm. Comput Struct 84(31–32):2231–2243
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872
Jalan AK, Mohanty AR (2009) Model based fault diagnosis of a rotor–bearing system for misalignment and unbalance under steady-state condition. J Sound Vib 327(3–5):604–622
Jena PK, Parhi DR (2015a) A modified particle swarm optimization technique for crack detection in cantilever beams. Arab J Sci Eng 40(11):3263–3272
Jena PK, Thatoi DN, Parhi DR (2015b) Dynamically self-adaptive fuzzy PSO technique for smart diagnosis of transverse crack. Appl Artif Intell 29(3):211–232
Khalilpourazari S, Khalilpourazary S (2019) An efficient hybrid algorithm based on WATER CYCLE and moth-flame optimization algorithms for solving numerical and constrained engineering optimization problems. Soft Comput 23(5):1699–1722
Lal M, Tiwari R (2012) Multi-fault identification in simple rotor-bearing-coupling systems based on forced response measurements. Mech Mach Theory 51:87–109
Lees AW, Sinha JK, Friswell MI (2009) Model-based identification of rotating machines. Mech Syst Signal Process 23(6):1884–1893
Li Z, Zhang X, Qin J, He J (2020) A reformative teaching–learning-based optimization algorithm for solving numerical and engineering design optimization problems. Soft Comput 24:1–18
McCallion H (1970) Journal bearings in turbomachinery. DM Smith. Chapman and Hall, London 1969. 176 pp. Illustrated. 60s. Aeronaut J 74(715):597–597
Mehta MS, Singh MB, Gagandeep M (2019) Harris Hawks optimization for solving optimum load dispatch problem in power system. Int J Eng Res Technol 8(6):962–968
Menshikov Y (2013) Identification of rotor unbalance as inverse problem of measurement. Adv Pure Math 3(09):20
Mesbahi T, Khenfri F, Rizoug N, Chaaban K, Bartholomeues P, Le Moigne P (2016) Dynamical modeling of Li-ion batteries for electric vehicle applications based on hybrid particle swarm–nelder–mead (PSO–NM) optimization algorithm. Electr Power Syst Res 131:195–204. https://doi.org/10.1016/j.epsr.2015.10.018
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191
Moezi SA, Zakeri E, Zare A, Nedaei M (2015) On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler–Bernoulli beam. Comput Struct 157:42–50
Moezi SA, Zakeri E, Zare A (2018) Structural single and multiple crack detection in cantilever beams using a hybrid Cuckoo-Nelder-Mead optimization method. Mech Syst Signal Process 99:805–831
Mohanty AR (2018) Machinery condition monitoring: Principles and practices. CRC Press, Boca Raton
Moradi S, Razi P, Fatahi L (2011) On the application of bees algorithm to the problem of crack detection of beam-type structures. Comput Struct 89(23–24):2169–2175
Nauclér P, Söderström T (2010) Unbalance estimation using linear and nonlinear regression. Automatica 46(11):1752–1761
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313. https://doi.org/10.1093/comjnl/7.4.308
Ocampo JC, Wing ESG, Moroyoqui FJR, Pliego AA, Ortega AB, Mayén J (2017) A novel methodology for the angular position identification of the unbalance force on asymmetric rotors by response polar plot analysis. Mech Syst Signal Process 95:172–186
Pavlenko IV, Simonovskiy VI, Demianenko MM (2017) Dynamic analysis of centrifugal machines rotors supported on ball bearings by combined application of 3D and beam finite element models. In: IOP conference series: materials science and engineering, vol 233, no 1. IOP Publishing, pp 012053
Pavlenko I, Simonovskiy V, Ivanov V, Zajac J, Pitel J (2018) Application of artificial neural network for identification of bearing stiffness characteristics in rotor dynamics analysis. In: Ivanov VO, Zabolotnyi O, Liaposhchenko OO, Pavlenko IV, Husak OH, Povstyanoy O (eds) Design, simulation, manufacturing: the innovation exchange. Springer, Cham, pp 325–335
Pavlenko I, Ivanov V, Kuric I, Gusak O, Liaposhchenko O (2019a) Ensuring vibration reliability of turbopump units using artificial neural networks. In: Trojanowska J, Ciszak O, Machado JM, Pavlenko I (eds) Advances in manufacturing II. Springer, Cham
Pavlenko I, Neamtu C, Verbovyi A, Pitel J, Ivanov V, Pop G (2019b) Using computer modeling and artificial neural networks for ensuring the vibration reliability of rotors. In: CMIS. pp 702–716
Pennacchi P (2008) Robust estimate of excitations in mechanical systems using M-estimators—theoretical background and numerical applications. J Sound Vib 310(4–5):923–946
Pennacchi P (2009) Robust estimation of excitations in mechanical systems using M-estimators—experimental applications. J Sound Vib 319(1–2):140–162
Reynolds O (1886) IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil. Philos Trans R Soc Lond 177:157–234
Roy RK (2001) Design of experiments using the Taguchi approach: 16 steps to product and process improvement. Wiley, Hoboken
Sanches FD, Pederiva R (2016) Theoretical and experimental identification of the simultaneous occurrence of unbalance and shaft bow in a Laval rotor. Mech Mach Theory 101:209–221
Sarakhsi MK, Ghomi SF, Karimi B (2016) A new hybrid algorithm of scatter search and Nelder–Mead algorithms to optimize joint economic lot sizing problem. J Computat Appl Math 292:387–401. https://doi.org/10.1016/j.cam.2015.07.027
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47
Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48(10):3462–3481
Sekhar AS (2005) Identification of unbalance and crack acting simultaneously in a rotor system: modal expansion versus reduced basis dynamic expansion. Modal Anal 11(9):1125–1145
Shrivastava A, Mohanty AR (2018) Estimation of single plane unbalance parameters of a rotor-bearing system using Kalman filtering based force estimation technique. J Sound Vib 418:184–199
Singh N, Chiclana F, Magnot JP (2019) A new fusion of salp swarm with sine cosine for optimization of non-linear functions. Eng Comput 36:1–28
Sudhakar GNDS, Sekhar AS (2011) Identification of unbalance in a rotor bearing system. J Sound Vib 330(10):2299–2313
Tiwari R (2017) Rotor systems: analysis and identification. CRC Press, Boca Raton
Tiwari R, Chougale A (2014) Identification of bearing dynamic parameters and unbalance states in a flexible rotor system fully levitated on active magnetic bearings. Mechatronics 24(3):274–286
Torres Cedillo SG, Bonello P (2014) Unbalance identification and balancing of nonlinear rotordynamic systems. In: ASME Turbo Expo 2014: turbine technical conference and exposition. American Society of Mechanical Engineers Digital Collection
Vakil-Baghmisheh MT, Peimani M, Sadeghi MH, Ettefagh MM (2008) Crack detection in beam-like structures using genetic algorithms. Appl Soft Comput 8(2):1150–1160
Yao J, Liu L, Yang F, Scarpa F, Gao J (2018) Identification and optimization of unbalance parameters in rotor-bearing systems. J Sound Vib 431:54–69
Yıldız AR, Yıldız BS, Sait SM, Bureerat S, Pholdee N (2019) A new hybrid Harris hawks–Nelder–Mead optimization algorithm for solving design and manufacturing problems. Mater Test 61(8):735–743
Zou D, Zhao H, Liu G, Ta N, Rao Z (2019) Application of augmented Kalman filter to identify unbalance load of rotor-bearing system: theory and experiment. J Sound Vib 463:114972
Acknowledgements
The authors acknowledge the reviewers’ comments and the editor’s efforts, which significantly enhanced the manuscript greatly.
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abbasi, A., Firouzi, B., Sendur, P. et al. Identification of unbalance characteristics of rotating machinery using a novel optimization-based methodology. Soft Comput 26, 4831–4862 (2022). https://doi.org/10.1007/s00500-022-06872-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-022-06872-9