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Inverse problem based multiobjective sunflower optimization for structural health monitoring of three-dimensional trusses

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Abstract

Truss-type structures are widely used in engineering, with several applications in different sectors such as construction, aeronautics/aerospace, telecommunications and energy fields. In all these situations they are generally large-scale structures, posing difficulties to take advantage of some direct inspection techniques to locate and identify structural damage. In case these inspections are not performed properly, the likelihood of occurrence of accidents will be very high. In this sense, structural health monitoring techniques based on the use of optimization algorithms appear as a promising and non-destructive methodology. In this study, an inverse damage identification problem is formulated and solved in order to identify damages in large-scale lattice-type structures. The direct problem is numerically formulated using finite element method considering a 72-bar truss where the modal response is obtained. A recent new metaheuristic SunFlower Optimization algorithm is used to solve the inverse damage problem formulated in terms of multiple damage sites and two independent objective functions (based on natural frequencies and mode shapes). Numerical results have shown that the inclusion of mode shapes in a multiobjective formulation improves the ability to accurately identify the damage in terms of its location and severity. The multi-object SFO algorithm showed results strictly superior to the NSGAII.

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Abbreviations

SHM :

Structural health monitoring

SFO :

SunFlower optimization

SFOMO :

SunFlower optimization multi objective

\(P_i\) :

Population individual

F(X):

Mathematical function

h(x):

Equality constraint

g(x):

Non-linear constraint

\(w_i\) :

Weights

\(F_{ws}\) :

Weighted sum objective function

a :

Dimension of the truss

\(J_{\omega }\) :

Objective function composed by natural frequencies

\(J_{\phi }\) :

Objective function composed by mode shapes

\(J_{mo}\) :

Objective function composed by both natural frequencies and mode shapes

\(\omega\) :

Natural frequencies

\(\phi\) :

Mode shape vector

\(N_{var}\) :

Number of design variables

\(N_e\) :

Damaged element number (location)

\(\alpha\) :

Damage severity (stiffness reduction)

FEM :

Finite element method

E :

Young modulus

\(\nu\) :

Poisson ratio

\(p_p\) :

Pollination rate

\(p_s\) :

Survivor rate

\(m_p\) :

Mortality rate

\(J(\overrightarrow{X})\) :

Objective function

\(\overrightarrow{X}\) :

Design vector

References

  1. Abraham A, Jain L (2005) Evolutionary multiobjective optimization. In: Evolutionary multiobjective optimization, pp 1–6. Springer

  2. Ahmadi M, Arabi M, Hoag DL, Engel BA (2013) A mixed discrete-continuous variable multiobjective genetic algorithm for targeted implementation of nonpoint source pollution control practices. Water Resour Res 49(12):8344–8356

    Article  Google Scholar 

  3. Alkayem NF, Cao M (2018) Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison. Eng Optim 50(10):1695–1714

    Article  MATH  Google Scholar 

  4. Bhandari J, Khan F, Abbassi R, Garaniya V, Ojeda R (2015) Modelling of pitting corrosion in marine and offshore steel structures-a technical review. J Loss Prev Process Ind 37:39–62

    Article  Google Scholar 

  5. Bureerat S, Pholdee N (2018) Inverse problem based differential evolution for efficient structural health monitoring of trusses. Appl Soft Comput 66:462–472

    Article  Google Scholar 

  6. Cai Y, Xie Q, Xue S, Hu L, Kareem A (2019) Fragility modelling framework for transmission line towers under winds. Eng Struct 191:686–697

    Article  Google Scholar 

  7. Cawley P (2018) Structural health monitoring: closing the gap between research and industrial deployment. Struct Health Monit 17(5):1225–1244

    Article  Google Scholar 

  8. Chawla M, Duhan M (2018) Levy flights in metaheuristics optimization algorithms: a review. Appl Artif Intell 32(9–10):802–821

    Article  Google Scholar 

  9. Connor JJ, Faraji S (2016) Fundamentals of structural engineering. Springer, Berlin

  10. de Paula TI, Gomes GF, de Freitas Gomes JH, de Paiva AP (2019) A mixture design of experiments approach for genetic algorithm tuning applied to multi-objective optimization, pp 600–610

  11. De Roeck G (2019) Model-based methods of damage identification of structures under seismic excitation. In: Seismic structural health monitoring, pp 237–259. Springer

  12. Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: Nsga-II. In: International conference on parallel problem solving from nature, pp 849–858. Springer

  13. Dinh-Cong D, Nguyen-Thoi T, Nguyen DT. A two-stage multi-damage detection approach for composite structures using mkecr-tikhonov regularization iterative method and model updating procedure. Appl Math Model 90:114–130

  14. Doebling SW, Farrar CR, Prime MB et al (1998) A summary review of vibration-based damage identification methods. Shock Vib Digest 30(2):91–105

    Article  Google Scholar 

  15. Donoso Y, Fabregat R (2016) Multi-objective optimization in computer networks using metaheuristics. Auerbach Publications

  16. Erazo K, Sen D, Nagarajaiah S, Sun L (2019) Vibration-based structural health monitoring under changing environmental conditions using Kalman filtering. Mech Syst Signal Process 117:1–15

    Article  Google Scholar 

  17. Fan W, Qiao P (2011) Vibration-based damage identification methods: a review and comparative study. Struct Health Monit 10(1):83–111

    Article  Google Scholar 

  18. Francisco MB, Junqueira DM, Oliver GA, Pereira JLJ, da Cunha Jr Jr SS, Gomes GF (2020) Design optimizations of carbon fibre reinforced polymer isogrid lower limb prosthesis using particle swarm optimization and lichtenberg algorithm. Eng Optim, pp 1–24

  19. Francisco MB, Pereira JLJ, Oliver GA, da Silva FHS, da Cunha Jr SS, Gomes GF (2021) Multiobjective design optimization of cfrp isogrid tubes using sunflower optimization based on metamodel. Comput Struct 249:106508

    Article  Google Scholar 

  20. Friswell MI (2006) Damage identification using inverse methods. Philos Trans R Soc A: Math Phys Eng Sci 365(1851):393–410

    Article  Google Scholar 

  21. Gomes GF, da Cunha SS, Ancelotti AC (2019) A sunflower optimization (sfo) algorithm applied to damage identification on laminated composite plates. Eng Comput 35(2):619–626

    Article  Google Scholar 

  22. Gomes GF, de Almeida FA (2020) Tuning metaheuristic algorithms using mixture design: application of sunflower optimization for structural damage identification. Adv Eng Softw 149:102877

    Article  Google Scholar 

  23. Gomes GF, de Almeida FA, Alexandrino PdSL, da Cunha SS, de Sousa BS, Ancelotti AC (2019) A multiobjective sensor placement optimization for shm systems considering fisher information matrix and mode shape interpolation. Eng Comput 35(2):519–535

  24. Gomes GF, de Almeida FA, Junqueira DM, da Cunha Jr SS, Ancelotti AC Jr (2019) Optimized damage identification in cfrp plates by reduced mode shapes and ga-ann methods. Eng Struct 181:111–123

    Article  Google Scholar 

  25. Gomes GF, Giovani RS (2020) An efficient two-step damage identification method using sunflower optimization algorithm and mode shape curvature (msdbi-sfo). Eng Comput, pp 1–20

  26. Gomes GF, Mendez YAD, Alexandrino PdSL, da Cunha SS, Ancelotti AC (2019) A review of vibration based inverse methods for damage detection and identification in mechanical structures using optimization algorithms and ann. Arch Comput Methods Eng 26(4):883–897

  27. Hu C, Dai L, Yan X, Gong W, Liu X, Wang L (2020) Modified nsga-iii for sensor placement in water distribution system. Inf Sci 509:488–500

    Article  MathSciNet  Google Scholar 

  28. Imam BM, Chryssanthopoulos MK (2012) Causes and consequences of metallic bridge failures. Struct Eng Int 22(1):93–98

    Article  Google Scholar 

  29. Jahangiri M, Najafgholipour M, Dehghan S, Hadianfard M (2019) The efficiency of a novel identification method for structural damage assessment using the first vibration mode data. J Sound Vib

  30. Jaimes AL, Martınez SZ, Coello CAC (2009) An introduction to multiobjective optimization techniques. Optim Polym Process, pp 29–57

  31. Kaveh A, Vaez SH, Hosseini P, Fathali M (2019) A new two-phase method for damage detection in skeletal structures. Iran J Sci Technol Trans Civil Eng 43(1):49–65

    Article  Google Scholar 

  32. 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

    Article  Google Scholar 

  33. Lin J-F, Xu Y-L, Zhan S (2019) Experimental investigation on multi-objective multi-type sensor optimal placement for structural damage detection. Struct Health Monit 18(3):882–901

    Article  Google Scholar 

  34. Maczak J (2012) The concept of the distributed diagnostic system for structural health monitoring of critical elements of infrastructure objects. In: Asset condition, information systems and decision models, pp 125–131. Springer

  35. Mishra M, Barman SK, Maity D, Maiti DK (2019) Ant lion optimisation algorithm for structural damage detection using vibration data. J Civ Struct Heal Monit 9(1):117–136

    Article  Google Scholar 

  36. Nguyen K-D, Chan TH, Thambiratnam DP, Nguyen A (2019) Damage identification in a complex truss structure using modal characteristics correlation method and sensitivity-weighted search space. Struct Health Monit 18(1):49–65

    Article  Google Scholar 

  37. Oliver GA, Ancelotti AC, Gomes GF (2021) Neural network-based damage identification in composite laminated plates using frequency shifts. Neural Comput Appl 33(8):3183–3194

    Article  Google Scholar 

  38. Ostachowicz W, Soman R, Malinowski P (2019) Optimization of sensor placement for structural health monitoring: a review. Struct Health Monit 18(3):963–988

    Article  Google Scholar 

  39. Pereira JLJ, Francisco MB, da Cunha Jr SS, Gomes GF (2021) A powerful lichtenberg optimization algorithm: a damage identification case study. Eng Appl Artif Intell 97:104055

    Article  Google Scholar 

  40. Pereira JLJ, Francisco MB, Diniz CA, Oliver GA, Cunha SS Jr, Gomes GF (2021) Lichtenberg algorithm: a novel hybrid physics-based meta-heuristic for global optimization. Expert Syst Appl 170:114522

    Article  Google Scholar 

  41. Perera R, Ruiz A, Manzano C (2009) Performance assessment of multicriteria damage identification genetic algorithms. Comput Struct 87(1–2):120–127

    Article  Google Scholar 

  42. Pytel A, Kiusalaas J (2016) Engineering mechanics: dynamics. Nelson Education

  43. Rao SS (2019) Engineering optimization: theory and practice. Wiley, London

  44. Ruina AL, Pratap R (2002) Introduction to statics and dynamics. Pre-print for Oxford University Press

  45. Sarrafi A, Poozesh P, Niezrecki C, Mao Z (2019) Detection of natural frequency and mode shape correspondence using phase-based video magnification in large-scale structures. In: Structural health monitoring, photogrammetry & DIC, volume 6, pp 81–87. Springer

  46. Smith CB, Hernandez EM (2019) Non-negative constrained inverse eigenvalue problems-application to damage identification. Mech Syst Signal Process 129:629–644

    Article  Google Scholar 

  47. Tan Y, Zhang L (2020) Computational methodologies for optimal sensor placement in structural health monitoring: a review. Struct Health Monit 19(4):1287–1308

    Article  Google Scholar 

  48. Toğan V, Durmaz M, Daloğlu A. Failure investigation of a roof truss in the eastern black sea region due to the snow load. Int J Eng Appl Sci 1(3):30–42

  49. Tripathy L, Lu WF (2018) Evaluation of axially-crushed cellular truss structures for crashworthiness. Int J Crashworthiness 23(6):680–696

    Article  Google Scholar 

  50. Wang S, Xu M, Xia Z, Li Y (2019) A novel tikhonov regularization-based iterative method for structural damage identification of offshore platforms. J Mar Sci Technol 24(2):575–592

    Article  Google Scholar 

  51. Williams PJ, Kendall WL, Hooten MB (2019) Selecting ecological models using multi-objective optimization. Ecol Model 404:21–26

    Article  Google Scholar 

  52. Xiao F, Fan J, Chen GS, Hulsey JL (2019) Bridge health monitoring and damage identification of truss bridge using strain measurements. Adv Mech Eng 11(3):1687814019832216

    Article  Google Scholar 

  53. Xu M, Wang S, Jiang Y (2019) Iterative two-stage approach for identifying structural damage by combining the modal strain energy decomposition method with the multiobjective particle swarm optimization algorithm. Struct Control Health Monit 26(2):e2301

    Article  Google Scholar 

  54. Yang X-S (2014) Nature-inspired optimization algorithms. Elsevier

  55. Zeng J, Chen K, Ma H, Duan T, Wen B (2019) Vibration response analysis of a cracked rotating compressor blade during run-up process. Mech Syst Signal Process 118:568–583

    Article  Google Scholar 

  56. Zhang J, Xie Q (2019) Failure analysis of transmission tower subjected to strong wind load. J Constr Steel Res 160:271–279

    Article  Google Scholar 

  57. Zhou G-D, Xie M-X, Yi T-H, Li H-N (2019) Optimal wireless sensor network configuration for structural monitoring using automatic-learning firefly algorithm. Adv Struct Eng 22(4):907–918

    Article  Google Scholar 

  58. Zhou G-D, Yi T-H, Xie M-X, Li H-N, Xu J-H (2021) Optimal wireless sensor placement in structural health monitoring emphasizing information effectiveness and network performance. J Aerosp Eng 34(2):04020112

    Article  Google Scholar 

  59. Zhou G-D, Yi T-H, Zhang H, Li H-N (2015) Energy-aware wireless sensor placement in structural health monitoring using hybrid discrete firefly algorithm. Struct Control Health Monit 22(4):648–666

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the financial support from the Brazilian agencies CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico, CAPES – Coordenação de Aperfeiçoamento de Pessoal de Nível Superior and FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais (APQ-00385-18)

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Authors and Affiliations

  1. Mechanical Engineering Institute, Universidade Federal de Itajubá, Itajubá, Brazil

    Evandro Gabriel Magacho

  2. Post Graduate Program in Integrity of Engineering Materials, Universidade de Brasília, Brasília, Brazil

    Ariosto Bretanha Jorge

  3. Mechanical Engineering Institute, Universidade Federal de Itajubá, Itajubá, Brazil

    Guilherme Ferreira Gomes

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  1. Evandro Gabriel Magacho
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Correspondence to Guilherme Ferreira Gomes.

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Magacho, E.G., Jorge, A.B. & Gomes, G.F. Inverse problem based multiobjective sunflower optimization for structural health monitoring of three-dimensional trusses. Evol. Intel. 16, 247–267 (2023). https://doi.org/10.1007/s12065-021-00652-4

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