Acknowledgement
The work was supported by the research project of Beijing Municipal Committee of Education Project KM201810005019, Beijing Natural Science Foundation grant number 8184063, National Natural Science Foundation of China (NSFC) grant number 11872190, 51808017 and 51778028. These financial supports are sincerely appreciated. Besides, the author would like to thank the anonymous reviewers for their detailed and fruitful remarks.
References
- Arora, S. and Anand, P. (2018), "Learning automata-based butterfly optimization algorithm for engineering design problems", Int. J. Comput. Mater. Sci. Eng., 7(4), 1850021. https://doi.org/10.1142/S2047684118500215
- Arora, S. and Singh, S. (2015), "Butterfly algorithm with Levy Flights for global optimization", Proceedings of 2015 International Conference on Signal Processing, Computing and Control (ISPCC), Waknaghat, India, September.
- Arora, S. and Singh, S. (2017a), "An Effective Hybrid Butterfly Optimization Algorithm with Artificial Bee Colony for Numerical Optimization", Int. J. Interact. Multimed. Artif. Intell., 4(4). https://doi.org/10.9781/ijimai.2017.442
- Arora, S. and Singh, S. (2017b), "Node Localization in Wireless Sensor Networks Using Butterfly Optimization Algorithm", Arab. J. Sci. Eng., 42(8), 3325-3335. https://doi.org/10.1007/s13369-017-2471-9
- Arora, S. and Singh, S. (2018), "Butterfly optimization algorithm: a novel approach for global optimization", Soft Comput., 23(3), 715-734. https://doi.org/10.1007/s00500-018-3102-4
- Blair, R.B. and Launer, A.E. (1997), "Butterfly diversity and human land use: Species assemblages along an urban grandient", Biol. Conserv., 80(1), 113-125. https://doi.org/10.1016/S0006-3207(96)00056-0
- Cao, M.S., Radzienski, M., Xu, W. and Ostachowicz, W. (2014), "Identification of multiple damage in beams based on robust curvature mode shapes", Mech. Syst. Signal. Pr., 46(2), 468-480. https://doi.org/10.1016/j.ymssp.2014.01.004
- Chatzi, E.N. and Fuggini, C. (2015), "Online correction of drift in structural identification using artificial white noise observations and an unscented Kalman filter", Smart Struct. Syst., Int. J., 16(2), 295-328. https://doi.org/10.12989/sss.2015.16.2.295
- Chen, C. and Yu, L. (2019), "A hybrid ant lion optimizer with improved Nelder-Mead algorithm for structural damage detection by improving weighted trace lasso regularization", Adv. Struct. Eng., 1-17. https://doi.org/10.1177/1369433219872434
- Dewangan, P., Parey, A., Hammami, A., Chaari, F. and Haddar, M. (2020), "Damage detection in wind turbine gearbox using modal strain energy", Eng. Fail. Anal., 107, 104228. https://doi.org/10.1016/j.engfailanal.2019.104228
- Ding, Z.H., Huang, M. and Lu, Z.R. (2016), "Structural damage detection using artificial bee colony algorithm with hybrid search strategy", Swarm Evol. Comput., 28, 1-13. https://doi.org/10.1016/j.swevo.2015.10.010
- Ding, Z.H, Li, J., Hao, H. and Lu, Z.R. (2019), "Structural damage identification with uncertain modelling error and measurement noise by clustering based tree seeds algorithm", Eng. Struct., 185, 301-314. https://doi.org/10.1016/j.engstruct.2019.01.118
- Ding, Z.H., Li, J. and Hao, H. (2020), "Structural damage identification by sparse deep belief network using uncertain and limited data", Struct. Control. Hlth., 27(5). https://doi.org/10.1002/stc.2522
- Doebling, S.W., Farrar, C.R. and Prime, M.B. (1998), "A summary review of vibration-based damage identification methods", Shock Vib. Dig., 30(2), 91-105. https://doi.org/10.1177/058310249803000201
- He, J. and Zhou, Y. (2019), "A novel mode shape reconstruction method for damage diagnosis of cracked beam", Mech. Syst. Signal. Pr., 122, 433-447. https://doi.org/10.1016/j.ymssp.2018.12.045
- Huang, M., Cheng, S., Zhang, H., Gul, M. and Lu, H. (2019), "Structural Damage Identification Under Temperature Variations Based on PSO-CS Hybrid Algorithm", Int. J. Struct. Stab. Dyn., 19(11), 1950139. https://doi.org/10.1142/S0219455419501396
- Huo, L.S., Li, X., Yang, Y.B. and Li, H.N. (2016), "Damage Detection of Structures for Ambient Loading Based on Cross Correlation Function Amplitude and SVM", Shock Vib., 1-12. https://doi.org/10.1155/2016/3989743
- Kang, F., Li, J.J. and Xu, Q. (2012), "Damage detection based on improved particle swarm optimization using vibration data", Soft. Comput., 12(8), 2329-2335. https://doi.org/10.1016/j.asoc.2012.03.050
- Kaveh, A., Vaez, S.R.H., Hosseini, P. and Fallah, N. (2016), "Detection of damage in truss structures using Simplified Dolphin Echolocation algorithm based on modal data", Smart Struct. Syst., Int. J., 18(5), 983-1004. https://doi.org/10.12989/sss.2016.18.5.983
- Kim, J.T., Park, J.H., Yoon, H.S. and Yi, J.H. (2007), "Vibration-based damage detection in beams using genetic algorithm", Smart Struct. Syst., Int. J., 3(3), 263-280. https://doi.org/10.12989/sss.2007.3.3.263
- Lee, K.J. and Yun, C.B. (2008), "Parameter identification for nonlinear behavior of RC bridge piers using sequential modified extended Kalman filter", Smart Struct. Syst., Int. J., 4(3), 319-342. https://doi.org/10.12989/sss.2008.4.3.319
- Li, G.C., Shuang, F., Zhao, P. and Le, C.Y. (2019), "An Improved Butterfly Optimization Algorithm for Engineering Design Problems Using the Cross-Entropy Method", Symmetry-Basel, 11(8), 1049. https://doi.org/10.3390/sym11081049
- Liang, Y., Feng, Q., Li, H. and Jiang, J. (2019), "Damage detection of shear buildings using frequency-change-ratio and model updating algorithm", Smart Struct. Syst., Int. J., 23(2), 107-122. https://doi.org/10.12989/sss.2019.23.2.107
- Liu, K., Yan, R.J. and Soares, C.G. (2018), "Damage identification in offshore jacket structures based on modal flexibility", Ocean Eng., 170, 171-185. https://doi.org/10.1016/j.oceaneng.2018.10.014
- Lu, Y. and Gao, F. (2005), "A novel time-domain auto-regressive model for structural damage diagnosis", J. Sound. Vib., 283(3-5), 1031-1049. https://doi.org/10.1016/j.jsv.2004.06.030
- Lu, Z.R. and Wang, L. (2017), "An enhanced response sensitivity approach for structural damage identification: convergence and performance", Int. J. Numer. Methods Eng., 111(13), 1231-1251. https://doi.org/10.1002/nme.5502
- Maity, D. and Tripathy, R.R. (2005), "Damage assessment of structures from changes in natural frequencies using genetic algorithm", Struct. Eng. Mech., Int. J., 19(1), 21-42. https://doi.org/10.12989/sem.2005.19.1.021
- Mallipeddi, R., Suganthan, P.N., Pan, Q.-K. and Tasgetiren, M.F. (2011), "Differential evolution algorithm with ensemble of parameters and mutation strategies", Appl. Soft. Comput., 11(2), 1679-1696. https://doi.org/10.1016/j.asoc.2010.04.024
- Mirzaee, A., Shayanfar, M. and Abbasnia, R. (2015), "A novel sensitivity method to structural damage estimation in bridges with moving mass", Struct. Eng. Mech., Int. J., 54(6), 1217-1244. https://doi.org/10.12989/sem.2015.54.6.1217
- Padil, K.H., Bakhary, N., Abdulkareem, M., Li, J. and Hao, H. (2020), "Non-probabilistic method to consider uncertainties infrequency response function for vibration-based damage detection using Artificial Neural Network", J. Sound. Vib., 467. https://doi.org/10.1016/j.jsv.2019.115069
- Pan, C.D., Yu, L., Chen, Z.P., Luo, W.F. and Liu, H.L. (2016), "A hybrid self-adaptive Firefly-Nelder-Mead algorithm for structural damage detection", Smart Struct. Syst., Int. J., 17(6), 957-980. https://doi.org/10.12989/sss.2016.17.6.957
- Raguso, R.A. (2008), "Wake up and smell the roses: the ecology and evolution of floral scent", Annu. Rev. Ecol. Evol. Syst., 39, 549-569. https://doi.org/10.1146/annurev.ecolsys.38.091206.095601
- Seyedpoor, S.M., Ahmadi, A. and Pahnabi, N. (2018a), "Structural damage detection using time domain responses and an optimization method", Inverse Probl. Sci. Eng., 27(5), 669-688. https://doi.org/10.1080/17415977.2018.1505884
- Seyedpoor, S.M., Norouzi, E. and Ghasemi, S. (2018b), "Structural damage detection using a multi-stage improved differential evolution algorithm (Numerical and experimental)", Smart Struct. Syst., Int. J., 21(2), 235-248. https://doi.org/10.12989/sss.2018.21.2.235
- Singh, B. and Anand, P. (2019), "A novel adaptive butterfly optimization algorithm", Int. J. Comput. Mater. Sci. Eng., 7(4), 1850026. https://doi.org/10.1142/s2047684118500264
- Sotoudehnia, E., Shahabian, F. and Sani, A.A. (2019), "An iterative method for damage identification of skeletal structures utilizing biconjugate gradient method and reduction of search space", Smart Struct. Syst., Int. J., 23(1), 45-60. https://doi.org/10.12989/sss.2019.23.1.045
- Stutz, L., Tenenbaum, R. and Correa, R. (2015), "The Differential Evolution method applied to continuum damage identification via flexibility matrix", J. Sound Vib., 345, 86-102. https://doi.org/10.1016/j.jsv.2015.01.049
- Tang, H., Xue, S. and Fan, C. (2008), "Differential evolution strategy for structural system identification", Comput. Struct., 86(21-22), 2004-2012. https://doi.org/10.1016/j.compstruc.2008.05.001
- Trinh, T.N. and Koh, C.G. (2012), "An improved substructural identification strategy for large structural systems", Struct. Control. Hlth., 19(8), 686-700. https://doi.org/10.1002/stc.463
- Vo-Duy, T., Ho-Huu, V., Dang-Trung, H. and Nguyen-Thoi, T. (2016), "A two-step approach for damage detection in laminated composite structures using modal strain energy method and an improved differential evolution algorithm", Compos. Struct., 147, 42-53. https://doi.org/10.1016/j.compstruct.2016.03.027
- Vosoughi, A.R. (2015), "A developed hybrid method for crack identification of beams", Smart Struct. Syst., Int. J., 16(3), 401-414. https://doi.org/10.12989/sss.2015.16.3.401
- Wang, X.J., Zhang, G.C., Wang, X.M. and Ni, P.H. (2020), "Output-only structural parameter identification with evolutionary algorithms and correlation functions", Smart Mater. Struct., 29(3). https://doi.org/10.1088/1361-665X/ab6ce9
- Wickramasinghe, W.R., Thambiratnam, D.P. and Chan, T.H.T. (2020), "Damage detection in a suspension bridge using modal flexibility method", Eng. Fail. Anal., 107, 104194. https://doi.org/10.1016/j.engfailanal.2019.104194
- Yang, J.N., Huang, H.W. and Pan, S.W. (2009), "Adaptive Quadratic Sum-Squares Error for Structural Damage Identification", J. Eng. Mech-Asce., 135(2), 67-77. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:2(67)
- Yi, T.H., Li, H.N. and Zhang, X.D. (2015), "Health monitoring sensor placement optimization for Canton Tower using virus monkey algorithm", Smart Struct. Syst., Int. J.., 15(5), 1373-1392. https://doi.org/10.12989/sss.2015.15.5.1373
- Yi, T.H., Li, H.N. and Wang, C.W. (2016), "Multiaxial sensor placement optimization in structural health monitoring using distributed wolf algorithm", Struct. Control. Hlth., 23(4), 719-734. https://doi.org/10.1002/stc.1806
- Yildizdan, G. and Baykan, O.K. (2020), "A novel modified bat algorithm hybridizing by differential evolution algorithm", Expert Syst. Appl., 141, 112949. https://doi.org/10.1016/j.eswa.2019.112949
- Zhang, X.W., Gao, R.X., Yan, R.Q., Chen, X.F., Sun, C. and Yang, Z.B. (2016), "Multivariable wavelet finite element-based vibration model for quantitative crack identification by using particle swarm optimization", J. Sound Vib., 375, 200-216. https://doi.org/10.1016/j.jsv.2016.04.018
- Zhou, L., Wu, S.Y. and Yang, J.N. (2008), "Experimental Study of an Adaptive Extended Kalman Filter for Structural Damage Identification", J. Infrastruct. Syst., 14(1), 42-51. https://doi.org/10.1061/(ASCE)1076-0342(2008)14:1(42)