The reliability of key components of urban rail transit (URT) plays an important role in the maintenance plans of URT. It is necessary to establish the reliability model of URT trains. In the current research, the reliability model has a limited scope of application and fails to accurately depict the reliability of key components in URT trains. To solve the above problem, a multi-peak type mixture Weibull distribution model is established using several three-parameter Weibull distributions based on fault modes of components sourced from historical lifetime data. Due to the complexity of this model, parameter estimation is challenging. For this purpose, an improved hunter-prey optimization (IHPO) was proposed to improve parameter estimation accuracy. Firstly, an improved Hénon chaos map was introduced to improve the distribution of the initial population. Secondly, the Lévy flight was introduced to increase the probability of the individual spreading to the whole range at the late stage. Lastly, a nonlinear balance factor was proposed to enhance the algorithm’s global search capability. The simulation experiment was carried out with examples of the balanced pressing wheel and the wheelset. The IHPO algorithm-based parameter estimation method shows the highest R-square with values of 0.996 and 0.999, respectively, and the lowest root mean square error with values of 0.019 and 0.008, respectively. The simulation results demonstrate that the stability and optimization of the HPO are improved, and the multi-peak mixture Weibull distribution model based on the IHPO can accurately depict URT trains’ reliability.
JinZHeDWeiZ. Intelligent fault diagnosis of train axle box bearing based on parameter optimization VMD and improved DBN. Eng Appl Artif Intell2022; 110: 104713.
2.
HeDZhangXGeC, et al. A novel reliability-centered opportunistic maintenance strategy for metro train complex systems. IEEE Intell Transp Syst Mag2022; 14: 146–159.
3.
SunHHeDZhongJ, et al. Preventive maintenance optimization for key components of subway train bogie with consideration of failure risk. Eng Fail Anal2023; 154: 107634.
4.
ChenBCaiBShangguanW, et al. Data-driven failure characteristics and reliability analysis for train control on-board subsystem. IEEE Access2019; 7: 126489–126499.
5.
YaoBGeXWangH, et al. Multitimescale reliability evaluation of DC-link capacitor banks in metro traction drive system. IEEE Trans Transp Electrif2020; 6: 213–227.
6.
HuangZChienSZhuW, et al. Scheduling wheel inspection for sustainable urban rail transit operation: a Bayesian approach. Physica A Stat Mech Appl2022; 586: 126454.
7.
YangJ-WWangJ-HHuangQ, et al. Reliability assessment for the solenoid valve of a high-speed train braking system under small sample size. Chin J Mech Eng2018; 31: 47.
8.
ChengHCaoYWangJ, et al. A preventive, opportunistic maintenance strategy for the catenary system of high-speed railways based on reliability. Proc IMechE, Part F: J Rail and Rapid Transit2020; 234: 1149–1155.
9.
CroninJJZarembskiAMPaleseJW. Prediction of rail defect development using parametric bootstrapping modified Weibull equations. Proc I MechE, Part F: J Rail and Rapid Transit2022; 236: 337–349.
10.
LiuDZhangJLiQ, et al. Distributions and fitting of stress amplitude spectra for railway vehicle structures. Proc IMechE, Part F: J Rail and Rapid Transit2020; 234: 43–53.
11.
LinSWangYJiaL. System reliability assessment based on failure propagation processes. Complexity2018; 2018: e9502953.
12.
DongXSunFXuF, et al. Three-parameter estimation method of multiple hybrid Weibull distribution based on the EM optimization algorithm. Mathematics2022; 10: 4337.
13.
GhavijorbozehRHamadaniAZ. Application of the mixed Weibull distribution in machine reliability analysis for a cell formation problem. Int J Qual Reliab Manag2017; 34: 128–142.
14.
YuanZDengJWangD. Reliability Estimation of Aero-engine Based on Mixed Weibull Distribution Model. In: IOP Conference Series: Earth and Environmental Science, Harbin, China, 8–10 December 2017, paper no. 012073, pp 1–9. Bristol: IOP.
15.
XueHLiuBDingD, et al. Diagnosis method based on hidden Markov model and Weibull mixture model for mechanical faults of in-wheel motors. Meas Sci Technol2022; 33: 114002.
16.
YuanZChenXMaL, et al. A segmented load spectrum model for high-speed trains and its inflection stress as an indicator for line quality. International Journal of Fatigue2021; 148: 106221.
17.
KaoJHK. A graphical estimation of mixed Weibull parameters in life-testing of electron tubes. Technometrics1959; 1: 389–407.
18.
JiangSKececiogluD. Maximum likelihood estimates, from censored data, for mixed-Weibull distributions. IEEE Trans Reliab1992; 41: 248–255.
19.
ChengSWFuJC. Estimation of mixed Weibull parameters in life testing. IEEE Trans Reliab1982; R-31: 377–381.
20.
MaqsoodAAslamM. A comparative study to estimate the parameters of mixed-Weibull distribution. Pak J Stat Oper Res2008; 4: 1–8.
21.
KarakocaAErisogluUErisogluM. A comparison of the parameter estimation methods for bimodal mixture Weibull distribution with complete data. J Appl Stat2015; 42: 472–1489.
22.
ÖrkcüHHÖzsoyVSAksoyE, et al. Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: a comprehensive experimental comparison. Appl Math Comput2015; 268: 201–226.
23.
KılıçMBŞahinYKocaMB. Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation. Comput Stat2021; 36: 1219–1242.
24.
ZhongLLiDJiaZ. Nonlinear least squares estimation for parameters of mixed Weibull distributions by using particle swarm optimization. IEEE Access2019; 7: 60545–60554.
25.
TekeliEYükselG. Estimating the parameters of twofold Weibull mixture model in right-censored reliability data by using genetic algorithm. Commun Stat Simul Comput2022; 51: 6621–6634.
26.
NarueiIKeyniaFMolahosseiniAS. Hunter-prey optimization: algorithm and applications. Soft Comput2022; 26: 1279–1314.
27.
MaJLiuF. Bearing fault diagnosis with variable speed based on fractional hierarchical range entropy and hunter–prey optimization algorithm–optimized random forest. Machines2022; 10: 763.
28.
RamadanHAKhanBDiabAAZ. Accurate parameters estimation of three diode model of photovoltaic modules using hunter–prey and wild horse optimizers. IEEE Access2022; 10: 87435–87453.
WangXLiJShaoL, et al. Short-term wind power prediction by an extreme learning machine based on an improved hunter–prey optimization algorithm. Sustainability2023; 15: 991.
31.
HeidariAAMirjaliliSFarisH, et al. Harris hawks optimization: algorithm and applications. Future Gener Comput Syst2019; 97: 849–872.
32.
FaramarziAHeidarinejadMMirjaliliS, et al. Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl2020; 152: 113377.
33.
ZhangLFXieMTangLC. On Weighted least squares estimation for the parameters of Weibull distribution. In: PhamH (ed.) Recent advances in reliability and quality in design. London: Springer, 2008, pp.57–84.
34.
WeiJFanHLiJ. Four-dimensional trajectory planning algorithm for fixed-wing aircraft formation based on improved hunter—prey optimization. Electronics2023; 12: 2820.
35.
HassanMHDaqaqFKamelS, et al. An enhanced hunter-prey optimization for optimal power flow with FACTS devices and wind power integration. IET Gener Transm Distrib2023; 17: 3115–3139.
36.
ZhaoBRenYGaoD, et al. Energy utilization efficiency evaluation model of refining unit Based on Contourlet neural network optimized by improved grey optimization algorithm. Energy2019; 185: 1032–1044.
37.
HeQLanZZhangD, et al. Improved marine predator algorithm for wireless sensor network coverage optimization problem. Sustainability2022; 14: 9944.
38.
WangWTianJ. An improved nonlinear tuna swarm optimization algorithm based on circle chaos map and levy flight operator. Electronics2022; 11: 3678.
39.
AlshathriSAbd ElazizMYousriD, et al. Quantum chaotic honey badger algorithm for feature selection. Electronics2022; 11: 3463.
40.
GaripZ. Parameters estimation of three-diode photovoltaic model using fractional-order Harris Hawks optimization algorithm. Optik2023; 272: 170391.
41.
LeeKKimYChongS, et al. On the critical delays of mobile networks under Lévy walks and Lévy flights. IEEE ACM Trans Netwo2013; 21: 1621–1635.
42.
KarimiBNiakiSTANiknamfarAH, et al. A novel imprecise reliability prediction method for incomplete lifetime data based on two-parameter Weibull distribution. Proc IMechE, Part O J Risk and Reliability2020; 235: 306–328.
43.
RajakumarMPRamyaJMaheswariBU. Health monitoring and fault prediction using a lightweight deep convolutional neural network optimized by Levy flight optimization algorithm. Neural Comput Appl2021; 33: 12513–12534.
44.
MaoXSongSDingF. Optimal BP neural network algorithm for state of charge estimation of lithium-ion battery using PSO with Levy flight. J Energy Storage2022; 49: 104139.
45.
MantegnaRN. Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes. Phys Rev E1994; 49: 4677–4683.
