Evidence Theory based Uncertainty Design Optimization for Planetary Gearbox in Wind Turbine


Evidence theory
Interval variables
Random variables
Planetary gearbox

How to Cite

Yang, S., Wang , J. ., & Yang, H. . (2022). Evidence Theory based Uncertainty Design Optimization for Planetary Gearbox in Wind Turbine. Journal of Advances in Applied & Computational Mathematics, 9, 86–102. https://doi.org/10.15377/2409-5761.2022.09.7


The planetary gearbox is an important part of the wind turbine. There are many random uncertain factors in the process of design, production, installation, and use, and these uncertain factors greatly influence the service life and reliability of the planetary gearbox. Therefore, the influence of uncertain factors needs to be considered in the design process to reduce the risk of failure. In this paper, an uncertainty design optimization method based on evidence theory is proposed, which can consider both interval variables and random variables in the optimization process. Then the megawatt wind turbine planetary gearbox is taken as the research object to analyze its uncertainty sources. Finally, the planetary gearbox is optimized by the proposed method. By comparing the results, the design scheme obtained by the method proposed in this paper is more reliable.



Qian G. Overview of hydro-wind-solar power complementation development in China. Global Energy Interconnection, 2019; 2(4): 285-289. https://doi.org/10.1016/j.gloei.2019.11.011

Wang T, Han Q, Chu F, Feng Z. Vibration based condition monitoring and fault diagnosis of wind turbine planetary gearbox: A review. Mechanical Systems and Signal Processing, 2019; 126: 662-685. https://doi.org/10.1016/j.ymssp.2019.02.051

Li G, Liu W, Su X. The Sun and Planetary Gear Design of a 1.5-MW Wind Turbine. Journal of Vibration Engineering & Technologies, 2018; 6(6): 495-501. https://doi.org/10.1007/s42417-018-0066-8

Yang Y, Li H, Yao J, Gao W, Peng H. Analysis on the force and life of gearbox in double-rotor wind turbine. Energies, 2019; 12(21): 4220. https://doi.org/10.3390/en12214220

Chen X, Yang X, Zuo MJ, Tian Z. Planetary gearbox dynamic modeling considering bearing clearance and sun gear tooth crack. Sensors, 2021; 21(8): 2638. https://doi.org/10.3390/s21082638

Hazbavi Z, Baartman JE, Nunes JP, Keesstra SD, Sadeghi SH. Changeability of reliability, resilience and vulnerability indicators with respect to drought patterns. Ecological Indicators, 2018; 87: 196-208. https://doi.org/10.1016/j.ecolind.2017.12.054

Monsef H, Naghashzadegan M, Farmani R, Jamali A. Deficiency of reliability indicators in water distribution networks. Journal of Water Resources Planning and Management, 2019; 145(6): 04019022. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001053

Meng D, Lv Z, Yang S, Wang H, Xie T, Wang Z. A time-varying mechanical structure reliability analysis method based on performance degradation. Structures, 2021; 34: 3247-3256. https://doi.org/10.1016/j.istruc.2021.09.085

Abd Rahim AA, Abdullah S, Singh SSK, Nuawi MZ. Reliability assessment on automobile suspension system using wavelet analysis. International Journal of Structural Integrity, 2019; 10(5): 602-611. https://doi.org/10.1108/IJSI-04-2019-0035

Yang YJ, Wang G, Zhong Q, Zhang H, He J, Chen H. Reliability analysis of gas pipeline with corrosion defect based on finite element method. International Journal of Structural Integrity, 2021; 12(6): 854-863. https://doi.org/10.1108/IJSI-11-2020-0112

Xi, Z. Model-based reliability analysis with both model uncertainty and parameter uncertainty. Journal of Mechanical Design, 2019; 141(5): 051404. https://doi.org/10.1115/1.4041946

Schietzold FN, Leichsenring F, Götz M, Graf W, Kaliske M. Robustness versus Performance-Nested Inherence of Objectives in Optimization with Polymorphic Uncertain Parameters. Advances in Engineering Software, 2021; 156: 102932. https://doi.org/10.1016/j.advengsoft.2020.102932

Ding S. Uncertain random quadratic bottleneck assignment problem. Journal of Ambient Intelligence and Humanized Computing, 2020; 11(8): 3259-3264. https://doi.org/10.1007/s12652-019-01510-z

Mourelatos ZP, Zhou J. A design optimization method using evidence theory. Journal of Mechanical Design, 2005; 128(4): 901-908. https://doi.org/10.1115/1.2204970

Keshtegar B, Seghier MEAB, Zhu SP, Abbassi R, Trung NT. Reliability analysis of corroded pipelines: Novel adaptive conjugate first order reliability method. Journal of Loss Prevention in the Process Industries, 2019; 62: 103986. https://doi.org/10.1016/j.jlp.2019.103986

Al-Ani A, Deriche M. A new technique for combining multiple classifiers using the Dempster-Shafer theory of evidence. Journal of Artificial Intelligence Research, 2002; 17: 333-361. https://doi.org/10.1613/jair.1026

Zhang J, Xiao M, Gao L, Qiu H, Yang Z. An improved two-stage framework of evidence-based design optimization. Structural and Multidisciplinary Optimization, 2018; 58(4): 1673-1693. https://doi.org/10.1007/s00158-018-1991-6

Han Y, Liu S, Geng Z, Gu H, Qu Y. Energy analysis and resources optimization of complex chemical processes: Evidence based on novel DEA cross-model. Energy, 2021; 218: 119508. https://doi.org/10.1016/j.energy.2020.119508

Liu P, Liu X, Ma G, Liang Z, Wang C, Alsaadi FE. A multi-attribute group decision-making method based on linguistic intuitionistic fuzzy numbers and Dempster-Shafer evidence theory. International Journal of Information Technology & Decision Making, 2020; 19(02): 499-524. https://doi.org/10.1142/S0219622020500042

Du YW, Zhong JJ. Generalized combination rule for evidential reasoning approach and Dempster-Shafer theory of evidence. Information Sciences, 2021; 547: 1201-1232. https://doi.org/10.1016/j.ins.2020.07.072

Meng Z, Guo L, Wang X. A general fidelity transformation framework for reliability-based design optimization with arbitrary precision. Structural and Multidisciplinary Optimization, 2022; 65(1): 1-16. https://doi.org/10.1007/s00158-021-03091-y

Montonen J, Nerg J, Polikarpova M, Pyrhönen J. Integration principles and thermal analysis of an oil-cooled and-lubricated permanent magnet motor planetary gearbox drive system. IEEE Access, 2019; 7: 69108-69118. https://doi.org/10.1109/ACCESS.2019.2919506

Yuan R, Li H, Wang Q. An enhanced genetic algorithm-based multi-objective design optimization strategy. Advances in Mechanical Engineering, 2018; 10(7): 1687814018784836. https://doi.org/10.1177/1687814018784836

Vlami V, Danek J, Zogaris S, Gallou E, Kokkoris IP, Kehayias G, Dimopoulos P. Residents' Views on Landscape and Ecosystem Services during a Wind Farm Proposal in an Island Protected Area. Sustainability, 2020; 12(6): 2442. https://doi.org/10.3390/su12062442

Keshavarzzadeh V, Ghanem RG, Tortorelli D. A. Shape optimization under uncertainty for rotor blades of horizontal axis wind turbines. Computer Methods in Applied Mechanics and Engineering, 2019; 354: 271-306. https://doi.org/10.1016/j.cma.2019.05.015

Ding F, Tian,Z. Integrated Prognosis for Wind Turbine Gearbox Condition-Based Maintenance Considering Time-Varying Load and Crack Initiation Time Uncertainty. International Journal of Reliability, Quality and Safety Engineering, 2021; 28(04): 2150024. https://doi.org/10.1142/S0218539321500248

Behera SK, Meena H, Chakraborty S, Meikap BC. Application of response surface methodology (RSM) for optimization of leaching parameters for ash reduction from low-grade coal. International Journal of Mining Science and Technology, 2018; 28(4): 621-629. https://doi.org/10.1016/j.ijmst.2018.04.014

Guiling H. Reliability Optimization Design of Transmission Mechanism of Automobile Mechanical Transmission Based on Feature Extraction. Solid State Technology, 2020; 63(4): 8603-8611.

Yingcheng X, Nengling T. Review of contribution to frequency control through variable speed wind turbine. Renewable energy, 2011; 36(6): 1671-1677. https://doi.org/10.1016/j.renene.2010.11.009

Lu L, He Y, Ruan Y, Yuan W. Wind turbine planetary gearbox condition monitoring method based on wireless sensor and deep learning approach. IEEE Transactions on Instrumentation and Measurement, 2020; 70: 1-16. https://doi.org/10.1109/TIM.2021.3118092

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Copyright (c) 2022 Shiyuan Yang, Jiapeng Wang , Hengfei Yang