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AK-GWO: a novel hybrid optimization method for accurate optimum hierarchical stiffened shells

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Abstract

The efficiency as computational efforts and accuracy as optimum design condition are two major changes in hybrid intelligent optimization methods for hierarchical stiffened shells (HSS). In this current work, a novel hybrid optimization coupled by adaptive modeling framework is proposed to improve the accuracy of the predicted optimum results of load-carrying capacity for HSS by combining active Kriging (AK) and grey wolf optimizer (AK-GWO) for optimization. In the active learning process, two data sets are introduced to train Kriging model, where active points given from initial data and adaptive points simulated based on optimal point using radial samples. The ability for accuracy of AK-GWO optimization method is compared with several soft computing models including Kriging, response surface method and support vector regression combined by GWO. The accurate results are extracted for simulating the load-carrying strength of HSS using the proposed AK-GWO method. The AK-GWO method is enhanced about 10% the accuracy of optimum load-carrying capacity with superior optimum design condition compared to other models, while the load-carrying using AK-GWO is increased about 2% compared the Kriging model.

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References

  1. Singh K, Zhao W, Jrad M, Kapania RK (2019) Hybrid optimization of curvilinearly stiffened shells using parallel processing. J Aircr 56(3):1068–1079. https://doi.org/10.2514/1.c035069

    Article  Google Scholar 

  2. Wagner HNR, Hühne C, Niemann S, Tian K, Wang B, Hao P (2018) Robust knockdown factors for the design of cylindrical shells under axial compression: analysis and modeling of stiffened and unstiffened cylinders. Thin-Walled Struct 127:629–645. https://doi.org/10.1016/j.tws.2018.01.041

    Article  Google Scholar 

  3. Bagheri M, Jafari AA, Sadeghifar M, Fortin-Simpson J (2016) Comparisons of buckling-to-weight behavior of cylindrical shells with composite and metallic stiffeners. Mech Adv Mater Struct 23(3):353–361. https://doi.org/10.1080/15376494.2014.981611

    Article  Google Scholar 

  4. Duc ND, Tuan ND, Tran P, Cong PH, Nguyen PD (2016) Nonlinear stability of eccentrically stiffened S-FGM elliptical cylindrical shells in thermal environment. Thin-Walled Struct 108:280–290. https://doi.org/10.1016/j.tws.2016.08.025

    Article  Google Scholar 

  5. Ning X, Pellegrino S (2015) Imperfection-insensitive axially loaded thin cylindrical shells. Int J Solids Struct 62:39–51. https://doi.org/10.1016/j.ijsolstr.2014.12.030

    Article  Google Scholar 

  6. Shahgholian-Ghahfarokhi D, Rahimi G (2019) Buckling analysis of composite lattice sandwich shells under uniaxial compression based on the effective analytical equivalent approach. Compos B Eng 174:106932. https://doi.org/10.1016/j.compositesb.2019.106932

    Article  Google Scholar 

  7. Shahgholian-Ghahfarokhi D, Rahimi G (2018) Buckling load prediction of grid-stiffened composite cylindrical shells using the vibration correlation technique. Compos Sci Technol 167:470–481. https://doi.org/10.1016/j.compscitech.2018.08.046

    Article  Google Scholar 

  8. Wang B, Hao P, Li G, Zhang J-X, Du K-F, Tian K, Wang X-J, Tang X-H (2014) Optimum design of hierarchical stiffened shells for low imperfection sensitivity. Acta Mech Sin 30:391–402. https://doi.org/10.1007/s10409-014-0003-3

    Article  Google Scholar 

  9. Wang B, Tian K, Zhou C, Hao P, Zheng Y, Ma Y, Wang J (2017) Grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity. Aerosp Sci Technol 62:114–121. https://doi.org/10.1016/j.ast.2016.12.002

    Article  Google Scholar 

  10. Zeng M, Zhou H (2018) New target performance approach for a super parametric convex model of non-probabilistic reliability-based design optimization. Comput Methods Appl Mech Eng 339:644–662

    Article  MathSciNet  Google Scholar 

  11. Wu H, Lai C, Sun F, Li M, Ji B, Wei W, Liu D, Zhang X, Fan H (2018) Carbon fiber reinforced hierarchical orthogrid stiffened cylinder: fabrication and testing. Acta Astronaut 145:268–274. https://doi.org/10.1016/j.actaastro.2018.01.064

    Article  Google Scholar 

  12. Tian K, Wang B, Hao P, Waas AM (2018) A high-fidelity approximate model for determining lower-bound buckling loads for stiffened shells. Int J Solids Struct 148:14–23

    Article  Google Scholar 

  13. Wang B, Zhu S, Hao P, Bi X, Du K, Chen B, Ma X, Chao YJ (2018) Buckling of quasi-perfect cylindrical shell under axial compression: a combined experimental and numerical investigation. Int J Solids Struct 130:232–247

    Article  Google Scholar 

  14. Tian K, Wang B, Zhang K, Zhang J, Hao P, Wu Y (2018) Tailoring the optimal load-carrying efficiency of hierarchical stiffened shells by competitive sampling. Thin-Walled Struct 133:216–225

    Article  Google Scholar 

  15. Wang B, Tian K, Zhao H, Hao P, Zhu T, Zhang K, Ma Y (2017) Multilevel optimization framework for hierarchical stiffened shells accelerated by adaptive equivalent strategy. Appl Compos Mater 24(3):575–592

    Article  Google Scholar 

  16. Keshtegar B, Hao P, Wang Y, Hu Q (2018) An adaptive response surface method and Gaussian global-best harmony search algorithm for optimization of aircraft stiffened panels. Appl Soft Comput 66:196–207

    Article  Google Scholar 

  17. Hao P, Wang B, Li G, Meng Z, Tian K, Tang X (2014) Hybrid optimization of hierarchical stiffened shells based on smeared stiffener method and finite element method. Thin-Walled Struct 82:46–54

    Article  Google Scholar 

  18. Zhao Y, Chen M, Yang F, Zhang L, Fang D (2017) Optimal design of hierarchical grid-stiffened cylindrical shell structures based on linear buckling and nonlinear collapse analyses. Thin-Walled Struct 119:315–323

    Article  Google Scholar 

  19. Tian K, Zhang J, Ma X, Li Y, Sun Y, Hao P (2019) Buckling surrogate-based optimization framework for hierarchical stiffened composite shells by enhanced variance reduction method. J Reinf Plast Compos 38(21–22):959–973

    Article  Google Scholar 

  20. Tian K, Li Z, Ma X, Zhao H, Zhang J, Wang B (2020) Toward the robust establishment of variable-fidelity surrogate models for hierarchical stiffened shells by two-step adaptive updating approach. Struct Multidisc Optim 61:1515–1528

    Article  Google Scholar 

  21. Keshtegar B, Hao P, Wang Y, Li Y (2017) Optimum design of aircraft panels based on adaptive dynamic harmony search. Thin-Walled Struct 118:37–45

    Article  Google Scholar 

  22. Gao L, Xiao M, Shao X, Jiang P, Nie L, Qiu H (2012) Analysis of gene expression programming for approximation in engineering design. Struct Multidiscip Optim 46(3):399–413. https://doi.org/10.1007/s00158-012-0767-7

    Article  Google Scholar 

  23. Zhang Y, Gao L, Xiao M (2020) Maximizing natural frequencies of inhomogeneous cellular structures by Kriging-assisted multiscale topology optimization. Comput Struct 230:106197

    Article  Google Scholar 

  24. Lu C, Feng Y-W, Fei C-W, Bu S-Q (2020) Improved decomposed-coordinated Kriging modeling strategy for dynamic probabilistic analysis of multicomponent structures. IEEE Trans Reliab 69(2):440–457

    Article  Google Scholar 

  25. Li H, Liu T, Wang M, Zhao D, Qiao A, Wang X, Gu J, Li Z, Zhu B (2017) Design optimization of stent and its dilatation balloon using Kriging surrogate model. Biomed Eng Online 16(1):13. https://doi.org/10.1186/s12938-016-0307-6

    Article  Google Scholar 

  26. Kolahchi R, Zhu S-P, Keshtegar B, Trung N-T (2020) Dynamic buckling optimization of laminated aircraft conical shells with hybrid nanocomposite martial. Aerosp Sci Technol 98:105656

    Article  Google Scholar 

  27. Xiao M, Zhang J, Gao L, Lee S, Eshghi AT (2019) An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability. Struct Multidiscip Optim 59(6):2077–2092

    Article  MathSciNet  Google Scholar 

  28. Zhang J, Xiao M, Gao L, Chu S (2019) A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities. Comput Methods Appl Mech Eng 344:13–33

    Article  MathSciNet  Google Scholar 

  29. Zhang J, Xiao M, Gao L, Fu J (2018) A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables. Comput Methods Appl Mech Eng 341:32–52

    Article  MathSciNet  Google Scholar 

  30. Seghier MEAB, Keshtegar B, Correia JA, Lesiuk G, De Jesus AM (2019) Reliability analysis based on hybrid algorithm of M5 model tree and Monte Carlo simulation for corroded pipelines: Case of study X60 Steel grade pipes. Eng Fail Anal 97:793–803

    Article  Google Scholar 

  31. Sun Z, Wang J, Li R, Tong C (2017) LIF: A new Kriging based learning function and its application to structural reliability analysis. Reliab Eng Syst Saf 157:152–165. https://doi.org/10.1016/j.ress.2016.09.003

    Article  Google Scholar 

  32. Keshtegar B, Kisi O (2018) RM5Tree: radial basis M5 model tree for accurate structural reliability analysis. Reliab Eng Syst Saf 180:49–61. https://doi.org/10.1016/j.ress.2018.06.027

    Article  Google Scholar 

  33. Fei C-W, Lu C, Liem RP (2019) Decomposed-coordinated surrogate modeling strategy for compound function approximation in a turbine-blisk reliability evaluation. Aerosp Sci Technol 95:105466

    Article  Google Scholar 

  34. Xiao M, Zhang J, Gao L (2020) A system active learning Kriging method for system reliability-based design optimization with a multiple response model. Reliab Eng Syst Saf 199:106935. https://doi.org/10.1016/j.ress.2020.106935

    Article  Google Scholar 

  35. Zhang J, Gao L, Xiao M (2020) A new hybrid reliability-based design optimization method under random and interval uncertainties. Int J Numer Methods Eng. https://doi.org/10.1002/nme.6440

    Article  MathSciNet  Google Scholar 

  36. Fei C-W, Li H, Liu H-T, Lu C, Keshtegar B (2020) Multilevel nested reliability-based design optimization with hybrid intelligent regression for operating assembly relationship. Aerosp Sci Technol 103:105906. https://doi.org/10.1016/j.ast.2020.105906

    Article  Google Scholar 

  37. Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. arXiv preprint. arXiv:10031409

  38. Cai Y, Zhang L, Gu J, Yue Y, Wang Y (2018) Multiple meta-models based design space differentiation method for expensive problems. Struct Multidiscip Optim 57(6):2249–2258. https://doi.org/10.1007/s00158-017-1854-6

    Article  MathSciNet  Google Scholar 

  39. Keshtegar B, Meng D, Ben Seghier MEA, Xiao M, Trung N-T, Bui DT (2020) A hybrid sufficient performance measure approach to improve robustness and efficiency of reliability-based design optimization. Eng Comput. https://doi.org/10.1007/s00366-019-00907-w

    Article  Google Scholar 

  40. Xiao N-C, Yuan K, Zhou C (2020) Adaptive Kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables. Comput Methods Appl Mech Eng 359:112649

    Article  MathSciNet  Google Scholar 

  41. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  42. Keshtegar B, Bagheri M, Meng D, Kolahchi R, Trung N-T (2020) Fuzzy reliability analysis of nanocomposite ZnO beams using hybrid analytical-intelligent method. Eng Comput. https://doi.org/10.1007/s00366-020-00965-5

    Article  Google Scholar 

  43. Jayakumar N, Subramanian S, Ganesan S, Elanchezhian E (2016) Grey wolf optimization for combined heat and power dispatch with cogeneration systems. Int J Electr Power Energy Syst 74:252–264

    Article  Google Scholar 

  44. Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J South Afr Inst Min Metall 52(6):119–139

    Google Scholar 

  45. Heddam S, Keshtegar B, Kisi O (2020) Predicting total dissolved gas concentration on a daily scale using Kriging interpolation, response surface method and artificial neural network: case study of Columbia river Basin Dams, USA. Nat Resour Res 29:1801–1818

    Article  Google Scholar 

  46. Sakata S, Ashida F, Zako M (2003) Structural optimization using Kriging approximation. Comput Methods Appl Mech Eng 192(7–8):923–939

    Article  Google Scholar 

  47. Huang D, Allen TT, Notz WI, Miller RA (2006) Sequential Kriging optimization using multiple-fidelity evaluations. Struct Multidiscip Optim 32(5):369–382

    Article  Google Scholar 

  48. Jiang C, Qiu H, Gao L, Wang D, Yang Z, Chen L (2020) Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis. Appl Math Model 77:82–98. https://doi.org/10.1016/j.apm.2019.06.035

    Article  MathSciNet  MATH  Google Scholar 

  49. Yun W, Lu Z, Jiang X (2018) An efficient reliability analysis method combining adaptive Kriging and modified importance sampling for small failure probability. Struct Multidiscip Optim 58(4):1383–1393. https://doi.org/10.1007/s00158-018-1975-6

    Article  MathSciNet  Google Scholar 

  50. Zhang J, Xiao M, Gao L (2019) A new method for reliability analysis of structures with mixed random and convex variables. Appl Math Model 70:206–220

    Article  MathSciNet  Google Scholar 

  51. Zhang J, Xiao M, Gao L, Chu S (2019) Probability and interval hybrid reliability analysis based on adaptive local approximation of projection outlines using support vector machine. Comput Aided Civ Infrastruct Eng 34(11):991–1009

    Article  Google Scholar 

  52. Dubourg V, Sudret B, Bourinet J-M (2011) Reliability-based design optimization using Kriging surrogates and subset simulation. Struct Multidiscip Optim 44(5):673–690

    Article  Google Scholar 

  53. Meng Z, Zhang D, Li G, Yu B (2019) An importance learning method for non-probabilistic reliability analysis and optimization. Struct Multidiscip Optim 59(4):1255–1271. https://doi.org/10.1007/s00158-018-2128-7

    Article  Google Scholar 

  54. Lu C, Feng Y-W, Liem RP, Fei C-W (2018) Improved Kriging with extremum response surface method for structural dynamic reliability and sensitivity analyses. Aerosp Sci Technol 76:164–175

    Article  Google Scholar 

  55. Li Y, Wu Y, Zhao J, Chen L (2017) A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points. J Glob Optim 67(1):343–366. https://doi.org/10.1007/s10898-016-0455-z

    Article  MathSciNet  MATH  Google Scholar 

  56. Kowsar R, Keshtegar B, Miyamoto A (2019) Understanding the hidden relations between pro-and anti-inflammatory cytokine genes in bovine oviduct epithelium using a multilayer response surface method. Sci Rep 9(1):1–17

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Reza Kolahchi

  2. Faculty of Civil Engineering, Duy Tan University, Da Nang, 550000, Vietnam

    Reza Kolahchi

  3. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China

    Kuo Tian & Zengcong Li

  4. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Behrooz Keshtegar & Nguyen- Thoi Trung

  5. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Behrooz Keshtegar & Nguyen- Thoi Trung

  6. Department of Civil and Environmental Engineering, Sejong University, 98 Gunja-dong, Gwangjin-gu, Seoul, 143-747, South Korea

    Duc-Kien Thai

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  1. Reza Kolahchi
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  2. Kuo Tian
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  3. Behrooz Keshtegar
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Correspondence to Behrooz Keshtegar.

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Kolahchi, R., Tian, K., Keshtegar, B. et al. AK-GWO: a novel hybrid optimization method for accurate optimum hierarchical stiffened shells. Engineering with Computers 38 (Suppl 1), 29–41 (2022). https://doi.org/10.1007/s00366-020-01124-6

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