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A fast-convergent approach for damage assessment using CMA-ES optimization algorithm and modal parameters

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Abstract

This paper investigates the application and the performance of covariance matrix adaptation-evolution strategy (CMA-ES) in structural damage detection and quantification. Many of the proposed optimization algorithms cannot detect damages accurately when the dimensions of the optimization problems increase. In essence, they stick in local optimum points and need huge amount of time and effort to find the exact solution of the problem. For this study, a novel objective function was proposed for the optimization problem based on natural frequencies and mode shapes. The efficiency of the CMA-ES algorithm has been examined by comparing to results of particle swarm optimization, genetic algorithm, and multi-population genetic algorithm (MPGA). Furthermore, robustness of the method has been evaluated in the presence of noise. The algorithms have been applied to a truss structure and a frame structure with different damage scenarios. The results of the paper demonstrated that the CMA-ES method is able to identify damages with satisfactory precision. Also, it was seen that the CMA-ES optimization algorithm is faster, more accurate, and more reliable than other algorithms.

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References

  1. Majumdar A, Maiti DK, Maity D (2012) Damage assessment of truss structures from changes in natural frequencies using ant colony optimization. Appl Math Comput 218:9759–9772. https://doi.org/10.1016/j.amc.2012.03.031

    Article  MATH  Google Scholar 

  2. Sahoo B, Maity D (2007) Damage assessment of structures using hybrid neuro-genetic algorithm. Appl Soft Comput J 7:89–104. https://doi.org/10.1016/j.asoc.2005.04.001

    Article  Google Scholar 

  3. Cawley P, Adams RD (1979) The location of defects in structures from measurements of natural frequencies. J Strain Anal Eng Des 14:49–57. https://doi.org/10.1243/03093247V142049

    Article  Google Scholar 

  4. Chondros TG, Dimarogonas AD (1980) Identification of cracks in welded joints of complex structures. J Sound Vib 69:531–538. https://doi.org/10.1016/0141-1187(81)90045-6

    Article  Google Scholar 

  5. Hassiotis S, Jeong GD (1995) Identification of stiffness reduction using natural frequencies. J Eng Mech 121:1106–1113. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:10(1106)

    Article  Google Scholar 

  6. Naito H, Bolander JE (2019) Damage detection method for RC members using local vibration testing. Eng Struct 178:361–374. https://doi.org/10.1016/j.engstruct.2018.10.031

    Article  Google Scholar 

  7. Yuen MMF (1985) A numerical study of the Eigen parameters of a damaged cantilever. J Sound Vib 103:301–310. https://doi.org/10.1016/0022-460X(85)90423-7

    Article  Google Scholar 

  8. Talaei S, Beitollahi A, Moshirabadi S, Fallahian M (2018) Vibration-based structural damage detection using twin Gaussian process (TGP). Structures 16:10–19. https://doi.org/10.1016/j.istruc.2018.08.006

    Article  Google Scholar 

  9. Kaveh A, Maniat M (2015) Damage detection based on MCSS and PSO using modal data. Smart Struct Syst 15:1253–1270. https://doi.org/10.12989/sss.2015.15.5.1253

    Article  Google Scholar 

  10. Mares C, Surace C (1996) An application of genetic algorithms to identify damage in elastic structures. J Sound Vib 195:195–215. https://doi.org/10.1006/jsvi.1996.0416

    Article  Google Scholar 

  11. Maity D, Tripathy R (2005) Damage assessment of structures from changes in natural frequencies. Struct Eng Mech 19:21–42. https://doi.org/10.12989/sem.2005.19.1.021

    Article  Google Scholar 

  12. Panigrahi SK, Chakraverty S, Mishra BK (2013) Damage identification of multistory shear structure from sparse modal information. J Comput Civ Eng 27:1–9. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000189

    Article  Google Scholar 

  13. Gomes GF, de Almeida FA, Junqueira DM et al (2019) Optimized damage identification in CFRP plates by reduced mode shapes and GA-ANN methods. Eng Struct 181:111–123. https://doi.org/10.1016/j.engstruct.2018.11.081

    Article  Google Scholar 

  14. Villalba J, Laier J (2012) Localising and quantifying damage by means of a multi-chromosome genetic algorithm. Adv Eng Softw 50:150–157. https://doi.org/10.1016/j.advengsoft.2012.02.002

    Article  Google Scholar 

  15. Wu ZY, Zhou K, Shenton HW III, Chajes MJ (2019) Development of sensor placement optimization tool and application to large-span cable-stayed bridge. J Civ Struct Health Monit 9:77–90. https://doi.org/10.1007/s13349-018-0320-5

    Article  Google Scholar 

  16. Shakya A, Mishra M, Maity D, Santarsiero G (2019) Structural health monitoring based on the hybrid ant colony algorithm by using Hooke–Jeeves pattern search. SN Appl Sci. https://doi.org/10.1007/s42452-019-0808-6

    Article  Google Scholar 

  17. Mohan SC, Maiti DK, Maity D (2013) Structural damage assessment using FRF employing particle swarm optimization. Appl Math Comput 219:10387–10400. https://doi.org/10.1016/j.amc.2013.04.016

    Article  MathSciNet  MATH  Google Scholar 

  18. Kang F, Li J, Xu Q (2012) Damage detection based on improved particle swarm optimization using vibration data. Appl Soft Comput 12:2329–2335. https://doi.org/10.1016/j.asoc.2012.03.050

    Article  Google Scholar 

  19. Nanda B, Maity D, Maiti DK (2014) Modal parameter based inverse approach for structural joint damage assessment using unified particle swarm optimization. Appl Math Comput 242:407–422. https://doi.org/10.1016/j.amc.2014.05.115

    Article  MathSciNet  MATH  Google Scholar 

  20. Mishra M, Gunturi VR, Maity D (2020) Teaching–learning-based optimisation algorithm and its application in capturing critical slip surface in slope stability analysis. Soft Comput 24:2969–2982. https://doi.org/10.1007/s00500-019-04075-3

    Article  Google Scholar 

  21. Mishra M, Ramana GV, Maity D (2020) Multiverse optimisation algorithm for capturing the critical slip surface in slope stability analysis. Geotech Geol Eng 38:459–474. https://doi.org/10.1007/s10706-019-01037-2

    Article  Google Scholar 

  22. Mishra M, Barman SK, Maity D, Maiti DK (2019) Ant lion optimisation algorithm for structural damage detection using vibration data. J Civ Struct Health Monit 9:117–136. https://doi.org/10.1007/s13349-018-0318-z

    Article  Google Scholar 

  23. Kaveh A, Zolghadr A (2015) An improved CSS for damage detection of truss structures using changes in natural frequencies and mode shapes. Adv Eng Softw 80:93–100. https://doi.org/10.1016/j.advengsoft.2014.09.010

    Article  Google Scholar 

  24. Kaveh A, Zolghadr A (2017) Guided modal strain energy-based approach for structural damage identification using tug-of-war optimization algorithm. J Comput Civ Eng. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000665

    Article  Google Scholar 

  25. Jahangiri M, Hadianfard MA (2019) Vibration-based structural health monitoring using symbiotic organism search based on an improved objective function. J Civ Struct Health Monit 9:741–755. https://doi.org/10.1007/s13349-019-00364-5

    Article  Google Scholar 

  26. Mishra M, Barman SK, Maity D, Maiti DK (2020) Performance studies of 10 metaheuristic techniques in determination of damages for large-scale spatial trusses from changes in vibration responses. J Comput Civ Eng. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000872

    Article  Google Scholar 

  27. Hansen N, Muller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol Comput 11:1–18. https://doi.org/10.1162/106365603321828970

    Article  Google Scholar 

  28. Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9:159–195. https://doi.org/10.1162/106365601750190398

    Article  Google Scholar 

  29. Akimoto Y, Nagata Y, Ono I, Kobayashi S (2011) Theoretical foundation for CMA-ES from information geometry perspective. Algorithmica 64:698–716. https://doi.org/10.1007/s00453-011-9564-8

    Article  MathSciNet  MATH  Google Scholar 

  30. Ros R, Hansen N (2008) A simple modification in CMA-ES achieving linear time and space complexity. Lect Notes Comput Sci. https://doi.org/10.1007/978-3-540-87700-4_30

    Article  Google Scholar 

  31. Kern S, Müller SD, Hansen N et al (2004) Learning probability distributions in continuous evolutionary algorithms—a comparative review. Nat Comput 3:77–112. https://doi.org/10.1023/b:naco.0000023416.59689

    Article  MathSciNet  MATH  Google Scholar 

  32. Iruthayarajan MW, Baskar S (2010) Covariance matrix adaptation evolution strategy based design of centralized PID controller. Expert Syst Appl 37:5775–5781. https://doi.org/10.1016/j.eswa.2010.02.031

    Article  Google Scholar 

  33. Baskar S, Alphones A, Suganthan PN (2005) Design of optimal length low-dispersion FBG filter using covariance matrix adapted evolution. IEEE Photonics Technol Lett 17:2119–2121. https://doi.org/10.1109/LPT.2005.854350

    Article  Google Scholar 

  34. Reddy SS, Panigrahi BK, Kundu R, Rohan Mukherjee SD (2013) Energy and spinning reserve scheduling for a wind–thermal power system using CMA-ES with mean learning technique. Electr Power Energy Syst 53:113–122. https://doi.org/10.1016/j.ijepes.2013.03.032

    Article  Google Scholar 

  35. Akbarzadeh V, Ko AHR, Gagné C, Parizeau M (2010) Topography-aware sensor deployment optimization with CMA-ES. Lect Notes Comput Sci (including Subser Lect Notes Artif Intell Lect Notes Bioinformatics) 6239:141–150. https://doi.org/10.1007/978-3-642-15871-1_15

    Article  Google Scholar 

  36. Ghosh S, Das S, Roy S et al (2012) A differential covariance matrix adaptation evolutionary algorithm for real parameter optimization. Inf Sci (Ny) 182:199–219. https://doi.org/10.1016/j.ins.2011.08.014

    Article  MathSciNet  Google Scholar 

  37. Hansen N (2005) The CMA Evolution Strategy: A Tutorial [Online]. http://www.lri.fr/~hansen/cmatutorial.pdf

  38. Perea R, Ruiz A (2008) A multistage FE updating procedure for damage identification in large-scale structures based on multiobjective evolutionary optimization. Mech Syst Signal Process 22:970–991

    Article  Google Scholar 

  39. Hao H, Xia Y (2002) Vibration-based damage detection of structures by genetic algorithm. J Comput Civ Eng 16:222–229. https://doi.org/10.1061/(ASCE)0887-3801(2002)16:3(222)

    Article  Google Scholar 

  40. MATLAB V (2017) 9.2. 0 (R2017a). The MathWorks Inc., Natick, MA, USA

  41. Chipperfield AJ, Fleming PJ (1995) The MATLAB genetic algorithm toolbox. https://digitallibrary.theiet.org/content/conferences/10.1049/ic_19950061

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Correspondence to Maryam Bitaraf.

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Ghahremani, B., Bitaraf, M. & Rahami, H. A fast-convergent approach for damage assessment using CMA-ES optimization algorithm and modal parameters. J Civil Struct Health Monit 10, 497–511 (2020). https://doi.org/10.1007/s13349-020-00397-1

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  • DOI: https://doi.org/10.1007/s13349-020-00397-1

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