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A Novel Three-parameter Weibull Distribution Parameter Estimation Using Chaos Simulated Annealing Particle Swarm Optimization in Civil Aircraft Risk Assessment

  • Research Article-Computer Engineering and Computer Science
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Abstract

In order to improve the parameter estimation accuracy of three-parameter Weibull distribution, a novel parameter estimation method using chaos simulated annealing particle swarm optimization (CSAPSO) algorithm is proposed. The simulated annealing (SA) algorithm is used to update the inertia weight of particle swarm optimization (PSO) algorithm according to the Metropolis acceptance criteria. The Chebyshev mapping is introduced into PSO according to the properties of chaos to make adaptively chaos mutate for premature particle. Moreover, in order to reduce the search range of PSO and improve the speed of parameter estimation, the initial estimation obtained by graphical parameter estimation method is taken as the initial solution of PSO. The proposed CSAPSO algorithm is compared with genetic algorithm (GA), PSO and SAPSO. These four algorithms are used to estimate the parameters of three sets of sample data which are conform to the Weibull distribution. The mean absolute percentage error (MAPE), correlation coefficient \(\rho \), Anderson Darling (AD) test value and the number of convergence step are used as evaluation indexes. The experimental results show that compared with the other three algorithms, the proposed CSAPSO algorithm has best parameter estimation accuracy for different number of samples and different setting parameters of three-parameter Weibull distribution.

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References

  1. Li, Z.; Cui, J.; Li, W.; et al.: Three parameter Weibull distribution estimation based on particle swarm optimization. In: 2018 13th IEEE Conference on Industrial Electronics and Applications (ICIEA); 2018 31 May–2 June; Wuhan, China. IEEE. 1892–1899 (2018)

  2. Fu, Q.; Wang, H.W.; Yan, X.J.: Evaluation of the aero engine performance reliability based on generative adversarial networks and Weibull distribution. Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 233(15), 5717–5728 (2019)

    Article  Google Scholar 

  3. Wang, Y.; Chen, Z.; Zhang, Y., et al.: Remaining useful life prediction of rolling bearings based on the three-parameter Weibull distribution proportional hazards model. Insight-Non-Destr. Test. Cond. Monit. 62, 710–718 (2020)

    Article  Google Scholar 

  4. Violette, M.G.; Safarian, P.; Han, N., et al.: Transport airplane risk analysis. J. Aircr. 52, 395–402 (2015)

    Article  Google Scholar 

  5. Barabadi, A.: Reliability model selection and validation using Weibull probability plot—a case study. Electr. Power Syst. Res. 101, 96–101 (2013)

    Article  Google Scholar 

  6. Jiang, R.: A drawback and an improvement of the classical Weibull probability plot. Reliab. Eng. Syst. Saf. 126, 135–142 (2014)

    Article  Google Scholar 

  7. Ross, R.: Graphical methods for plotting and evaluating Weibull distributed data. In: Proceedings of 1994 4th International Conference on Properties and Applications of Dielectric Materials (ICPADM); 1994 July 3–8; Brisbane, Queensland, Australia. IEEE. 250–253 (1994)

  8. Bain, L.J.; Antle, C.E.: Estimation of parameters in the Weibdl distribution. Technometrics 9, 621–627 (1967)

    MathSciNet  MATH  Google Scholar 

  9. Dubey, S.D.: Asymptotic properties of several estimators of Weibull parameters. Technometrics 7, 423–434 (1965)

    Article  Google Scholar 

  10. Touw, A.E.: Bayesian estimation of mixed Weibull distributions. Reliab. Eng. Syst. Saf. 94, 463–473 (2009)

    Article  Google Scholar 

  11. Lehman, E.H.: Shapes, moments and estimators of the Weibull distribution. IEEE Trans. Rel. R12, 32–38 (1963)

    Article  Google Scholar 

  12. White, J.S.: The moments of Log-Weibull order statistics. Technometrics 11, 373–386 (1969)

    Article  MathSciNet  Google Scholar 

  13. Yang, F.; Ren, H.; Hu, Z.: Maximum likelihood estimation for three-parameter Weibull distribution using evolutionary strategy. Math. Prob. Eng. 2019, 1–8 (2019)

    MathSciNet  MATH  Google Scholar 

  14. Luus, R.; Jamme, M.: Estimation of parameters in 3-parameter Weibull probability distribution functions. Hung. J. Ind. Chem. 33, 1–2 (2005)

    Google Scholar 

  15. Moeini, A.; Jenab, K.; Mohammadi, M., et al.: Fitting the three-parameter Weibull distribution with cross entropy. Appl. Math. Model. 37, 6354–6363 (2013)

    Article  MathSciNet  Google Scholar 

  16. Abbasi, B.; Eshragh Jahromi, A.H.; Arkat, J., et al.: Estimating the parameters of Weibull distribution using simulated annealing algorithm. Appl. Math. Comput. 183, 85–93 (2006)

    MathSciNet  MATH  Google Scholar 

  17. Ismail, A.A.: Estimating the parameters of Weibull distribution and the acceleration factor from hybrid partially accelerated life test. Appl. Math. Model. 36, 2920–2925 (2012)

    Article  MathSciNet  Google Scholar 

  18. Kennedy, J.; Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95—International Conference on Neural Networks. 1995 Nov 27–Dec 1; Perth, WA, Australia. IEEE, 1942–1948 (1995)

  19. Wang, F.; Huang, P.: Implementing particle swarm optimization algorithm to estimate the mixture of two Weibull parameters with censored data. J. Stat. Comput. Simul. 84, 1975–1989 (2014)

    Article  MathSciNet  Google Scholar 

  20. Carneiro, T.C.; Melo, S.P.; Carvalho, P.C.M., et al.: Particle Swarm Optimization method for estimation of Weibull parameters: a case study for the Brazilian northeast region. Renew. Energy 86, 751–759 (2016)

    Article  Google Scholar 

  21. Krohling, R.A.; Campos, M.; Borges, P.: Bare bones particle swarm applied to parameter estimation of mixed Weibull distribution. In: Soft computing in industrial applications, pp. 53–60. Springer, Berlin (2010)

    Chapter  Google Scholar 

  22. Örkcü, H.H.; Özsoy, V.S.; Aksoy, E., et al.: Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: a comprehensive experimental comparison. Appl. Math. Comput. 268, 201–226 (2015)

    MathSciNet  MATH  Google Scholar 

  23. Van den Bergh, F.: Engelbrecht, AP.: Training product unit networks using cooperative particle swarm optimisers. In: IJCNN’01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222); 2001 July 15–19. Washington, DC, USA. IEEE. 892–899 (2001)

  24. Clerc, M.; Kennedy, J.: The particle swarm—explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Computat. 6, 58–73 (2002)

    Article  Google Scholar 

  25. Sengupta, S.; Basak, S.; Peters, R.A.: Particle swarm optimization: a survey of historical and recent developments with hybridization perspectives. Mach. Learn. Knowl. Extr. 1, 157–191 (2019)

    Article  Google Scholar 

  26. Chi, Y.; Sun, F.; Wang, W., et al.: An improved particle swarm optimization algorithm with search space zoomed factor and attractor. Chin. J. Comput. 34, 115–130 (2011)

    Article  Google Scholar 

  27. Zhao, X.: Non-uniform variance fuzzy guided particle swarm algorithm. In: 2009 Fifth International Conference on Natural Computation; 2009 Aug 14–16; Tianjin, China. IEEE. 341–345 (2009)

  28. Yang, X.; Niu, J.; Cai, Z.: Chaotic simulated annealing particle swarm optimization algorithm. In: 2018 2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC); 2018 May 25–27; Xi’an, China. IEEE. 11–19 (2018)

  29. Nancharaiah, B.; Chandra Mohan, B.: MANET link performance using ant colony optimization and particle swarm optimization algorithms. In: 2013 International Conference on Communication and Signal Processing; 2013 April 3–5; Melmaruvathur, India. IEEE. 767–770 (2018)

  30. Sharma, J.; Singhal, RS.: Comparative research on genetic algorithm, particle swarm optimization and hybrid GA-PSO. In: 2015 2nd International Conference on Computing for Sustainable Global Development (INDIACom); 2015 March 11–13; New Delhi, India. IEEE. 110–114 (2015)

  31. Liu, W.; Luo, N.; Pan, G., et al.: Chaos particle swarm optimization algorithm for optimization problems. Int. J. Patt. Recogn. Artif. Intell. 32, 1859019 (2018)

    Article  Google Scholar 

  32. Pan, X.; Xue, L.; Lu, Y., et al.: Hybrid particle swarm optimization with simulated annealing. Multimed Tools Appl. 78, 29921–29936 (2019)

    Article  Google Scholar 

  33. Aarts, E.H.L.: Simulated annealing and Boltzmann machines. Wiley (1989)

    MATH  Google Scholar 

  34. Johnson, D.S.; Aragon, C.R.; McGeoch, L.A., et al.: Optimization by simulated annealing: an experimental evaluation part I, graph partitioning. Oper. Res. 37, 865–892 (1989)

    Article  Google Scholar 

  35. de Sales, M.: Simulated annealing. Nova Science Pub Incorporated (2014)

    Google Scholar 

  36. Levy, D.: Chaos theory and strategy: theory, application, and managerial implications. Strat. Mgmt. J. 15, 167–178 (2007)

    Article  Google Scholar 

  37. Xu, X.; Rong, H.; Trovati, M., et al.: CS-PSO: chaotic particle swarm optimization algorithm for solving combinatorial optimization problems. Soft Comput. 22, 783–795 (2018)

    Article  Google Scholar 

  38. Mokhtari, H.; Noroozi, A.: An efficient chaotic based PSO for earliness/tardiness optimization in a batch processing flow shop scheduling problem. J. Intell. Manuf. 29, 1063–1081 (2018)

    Article  Google Scholar 

  39. Lian, J.F.; Yu, W.T.; Liu, W.R.: A chaotic adaptive particle swarm optimization for robot path planning. In: 2019 Chinese Control Conference (CCC); 2019 July 27–30; Guangzhou, China. IEEE. 4751–4756 (2019)

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Funding

This work was supported by China National Natural Science Foundation (grant numbers U1933202); China Scholarship Council (CSC) (Grant No. 201906830043); Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant Nos. KYCX18_0310 and KYCX18_0265).

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Authors and Affiliations

  1. Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Di Zhou & Hongfu Zuo

  2. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

    Di Zhou & Xiao Zhuang

  3. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Xiao Zhuang

Authors
  1. Di Zhou
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  2. Xiao Zhuang
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  3. Hongfu Zuo
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Correspondence to Xiao Zhuang.

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Zhou, D., Zhuang, X. & Zuo, H. A Novel Three-parameter Weibull Distribution Parameter Estimation Using Chaos Simulated Annealing Particle Swarm Optimization in Civil Aircraft Risk Assessment. Arab J Sci Eng 46, 8311–8328 (2021). https://doi.org/10.1007/s13369-021-05467-0

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  • DOI: https://doi.org/10.1007/s13369-021-05467-0

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