SpringerLink
Log in

Method of non-stationary random vibration reliability of hydro-turbine generator unit

水轮发电机组非**稳随机振动可靠性方法

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The hydraulic excitation acting on a hydro-turbine generator unit exhibits obvious non-stationary characteristics. In order to account for these characteristics, this study focuses on the non-stationary random vibration reliability of the hydro-turbine generator unit. Firstly, the non-stationary characteristics of the hydraulic excitation are analyzed, and a mathematical expression is constructed using the virtual excitation method. Secondly, a dynamic model of the unit is established to demonstrate the non-stationary random vibration characteristics under hydraulic excitation. Thirdly, an active learning non-stationary vibration reliability analysis method AK-MCS-T-H is proposed combining the Kriging model, the Monte Carlo simulation (MCS) method, and the information entropy learning function H. This method reveals the influence of the non-stationary hydraulic excitation on the random vibration reliability of the hydro-turbine generator unit. Finally, an example is presented to analyze the random vibration reliability. The study shows that the AK-MCS-T-H proposed in this paper can solve the problem of non-stationary random vibration reliability of the Francis hydro-turbine generator unit more effectively.

摘要

水轮发电机组的水流激励具有明显的非**稳特性. 为了研究水流激励的非**稳特性, 本文对水轮发电机组的非**稳随机振动可 靠性方法展开研究. 首先, 分析了水流激励的非**稳特性, 并利用虚拟激励法建立了水流激励的数学表达式. 其次, 建立了水轮发电机 组的动力学模型, 探明了水流激励下机组的非**稳随机振动特性. 再次, 将Kriging模型、蒙特卡罗模拟(MCS)方法和信息熵学**稳振动可靠性分析方法AK-MCS-T-H. 该方法揭示了非**稳水流激励对水轮发电机组随机振 动可靠性的影响. 最后, 通过实例分析了水轮发电机组的随机振动可靠性. 研究表明, 本文提出的AK-MCS-T-H能够有效地解决混流式 水轮发电机组的非**稳随机振动可靠性问题.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

References

  1. N. K. Jhankal, A. Kumar, and M. Mangla, Establishment of correlation for the pressure fluctuations on the low-head Francis turbine in the draft tube cone from the model test, Flow Meas. Instrum. 91, 102360 (2023).

    Article  Google Scholar 

  2. X. **a, H. Luo, S. Li, F. Wang, L. Zhou, and Z. Wang, Characteristics and factors of mode families of axial turbine runner, Int. J. Mech. Sci. 251, 108356 (2023).

    Article  Google Scholar 

  3. X. Zhou, H. Wu, and C. Shi, Numerical and experimental investigation of the effect of baffles on flow instabilities in a Francis turbine draft tube under partial load conditions, Adv. Mech. Eng. 11, 168781401882446 (2019).

    Article  Google Scholar 

  4. J. Feng, Y. Men, G. Zhu, Y. Li, and X. Luo, Cavitation detection in a Kaplan turbine based on multifractal detrended fluctuation analysis of vibration signals, Ocean Eng. 263, 112232 (2022).

    Article  Google Scholar 

  5. X. Li, W. Yang, J. Wei, R. Wang, and Y. Liao, Part-load operation risk assessment of hydropower units in hydro-wind-solar hybrid system considering hydraulic characteristics, Energy Rep. 9, 332 (2023).

    Article  Google Scholar 

  6. H. Cheng, L. Zhou, Q. Liang, Z. Guan, D. Liu, Z. Wang, and W. Kang, A method of evaluating the vortex rope strength in draft tube of Francis turbine, Renew. Energy 152, 770 (2020).

    Article  Google Scholar 

  7. X. Yu, X. Liu, X. Wang, X. Wang, and Y. Wang, Vibration control of improved LQG for wheel drive electric vehicle based on uncertain parameters, Proc. Inst. Mech. Eng. Part D-J. Automob. Eng. 235, 2253 (2021).

    Article  Google Scholar 

  8. X. T. Liu, and S. S. Rao, Vibration analysis in the presence of uncertainties using universal grey system theory, J. Vib. Acoust. 140, 031009 (2018).

    Article  Google Scholar 

  9. X. Liu, X. Yu, J. Tong, X. Wang, and X. Wang, Mixed uncertainty analysis for dynamic reliability of mechanical structures considering residual strength, Reliab. Eng. Syst. Saf. 209, 107472 (2021).

    Article  Google Scholar 

  10. A. Sofi, G. Muscolino, and M. Di Paola, Reliability analysis of structures controlled by external fractional viscoelastic dampers with interval parameters, Acta Mech. Sin. 39, 722486 (2023).

    Article  MathSciNet  Google Scholar 

  11. L. Ji, G. Chen, L. Qian, J. Ma, and J. Tang, An iterative interval analysis method based on Kriging-HDMR for uncertainty problems, Acta Mech. Sin. 38, 521378 (2022).

    Article  MathSciNet  Google Scholar 

  12. Q. Zhan, C. Bai, X. Liu, and Y. Ge, Reduced-order representation and reconstruction of non-stationary flow system using flow-time-history deep learning, Acta Mech. Sin. 39, 322491 (2023).

    Article  Google Scholar 

  13. J. Hu, and J. Wang, First passage dynamic reliability analysis of non-stationary and non-Gaussian buffeting random dynamic responses of long-span suspension bridge, Int. J. Str. Stab. Dyn. 23, 2350199 (2023).

    Article  MathSciNet  Google Scholar 

  14. R. Greco, G. C. Marano, A. Fiore, and I. Vanzi, Nonstationary first threshold crossing reliability for linear system excited by modulated Gaussian process, Shock Vib. 2018, 1 (2018).

    Article  Google Scholar 

  15. T. Sun, M. Lyu, and J. Chen, Property of intrinsic drift coefficients in globally-evolving-based generalized density evolution equation for the first-passage reliability assessment, Acta Mech. Sin. 39, 722471 (2023).

    Article  MathSciNet  Google Scholar 

  16. Z. Li, Y. Liu, F. Liu, and X. Yang, Hybrid reliability model of hydraulic turbine-generator unit based on nonlinear vibration, Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 228, 1880 (2014).

    Article  Google Scholar 

  17. S. R. Zhao, L. H. Liu, W. Zhang, T. H. **ong, and X. B. Wei, Hydraulic turbine vibration testing and its reliability analysis (in Chinese), J. Hydroelectric Eng. 25, 139 (2006).

    Google Scholar 

  18. Z. Li, Y. Liu, H. Long, and Y. Zhang, Nonlinear vibration reliability of hydraulic turbine-generator units with multiple failure modes (in Chinese), J. Mech. Eng. 49, 170 (2013).

    Article  Google Scholar 

  19. Z. J. Li, F. X. Liu, M. Qiu, Y. Peng, and Y. Liu, Non-probabilistic reliability model of Francis hydraulic turbine-generator units (in Chinese), J. Guangxi Univ. (Nat. Sci. Ed.) 39, 258 (2014).

    Google Scholar 

  20. W. Wang, Q. Chen, D. Yan, and D. Geng, A novel comprehensive evaluation method of the draft tube pressure pulsation of Francis turbine based on EEMD and information entropy, Mech. Syst. Signal Process. 116, 772 (2019).

    Article  Google Scholar 

  21. F. Liu, Z. Li, M. Liang, B. Zhao, and J. Ding, Prediction method of non-stationary random vibration fatigue reliability of turbine runner blade based on transfer learning, Reliab. Eng. Syst. Safe. 235, 109215 (2023).

    Article  Google Scholar 

  22. H. Zhang, D. Chen, C. Wu, X. Wang, J. M. Lee, and K. H. Jung, Dynamic modeling and dynamical analysis of pump-turbines in S-shaped regions during runaway operation, Energy Convers. Manage. 138, 375 (2017).

    Article  Google Scholar 

  23. Y. J. Wang, Z. J. Li, T. H. Li, F. X. Liu, and A. J. Fu, A mathematical model of the hydrodynamic pressure acting on a turbine runner blade under the rotor-stator interaction based on the quasi-three-dimensional finite element method, Math. Probl. Eng. 2021, 6657812 (2021).

    Google Scholar 

  24. M. B. Priestley, Power spectral analysis of non-stationary random processes, J. Sound Vib. 6, 86 (1967).

    Article  Google Scholar 

  25. Z. Li, X. Mao, F. Liu, Y. Huang, and X. Heng, A comprehensive reliability evaluation model of turbine runner blades under complex conditions, J Fail. Anal. Preven. 20, 2097 (2020).

    Article  Google Scholar 

  26. Z. Li, G. Zhang, F. Liu, and J. Chen, An on-line monitoring method for the flow excitation in francis hydraulic turbine based on dynamics, J. Vibroeng. 24, 745 (2022).

    Article  Google Scholar 

  27. R. Rosli, W. Shi, B. Aktas, R. Norman, and M. Atlar, Cavitation observations, underwater radiated noise measurements and full-scale predictions of the Hydro-Spinna turbine, Ocean Eng. 210, 107536 (2020).

    Article  Google Scholar 

  28. D. E. Launder, and D. B. Spalding, Lectures in Mathematical Models of Turbulence (Academic Press, London, 1972).

    Google Scholar 

  29. S. F. Masri, J. P. Caffrey, and H. Li, Transient response of MDOF systems with inerters to nonstationary stochastic excitation, J. Appl. Mech. 84, 101003 (2017).

    Article  Google Scholar 

  30. H. P. Wang, Z. Zhang, and Q. Li, Coherence of phase of harmonic superposition components in time domain simulation of road roughness for right and left wheel tracks, Trans. Bei**g Inst. Tech. 39, 1034 (2019).

    Google Scholar 

  31. B. Echard, N. Gayton, and M. Lemaire, AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation, Struct. Saf. 33, 145 (2011).

    Article  Google Scholar 

  32. Z. Liu, Z. Lu, C. Ling, K. Feng, and Y. Hu, An improved AK-MCS for reliability analysis by an efficient and simple reduction strategy of candidate sample pool, Structures 35, 373 (2022).

    Article  Google Scholar 

  33. A. Keprate, N. Bagalkot, M. S. Siddiqui, and S. Sen, Reliability analysis of 15 MW horizontal axis wind turbine rotor blades using fluid-structure interaction simulation and adaptive kriging model, Ocean Eng. 288, 116138 (2023).

    Article  Google Scholar 

  34. W. X. Zhang, and Z. Z. Lü, New stop** criterion of adaptive Kriging method and its application in fatigue life reliability for turbine disk, J. Mech. Eng. 58, 263 (2022).

    Article  Google Scholar 

  35. C. Ling, Z. Lu, and X. Zhang, An efficient method based on AK-MCS for estimating failure probability function, Reliab. Eng. Syst. Saf. 201, 106975 (2020).

    Article  Google Scholar 

  36. J. Zhou, and J. Li, IE-AK: A novel adaptive sampling strategy based on information entropy for Kriging in metamodel-based reliability analysis, Reliab. Eng. Syst. Saf. 229, 108824 (2023).

    Article  Google Scholar 

  37. Y. **ong, and S. Sampath, A fast-convergence algorithm for reliability analysis based on the AK-MCS, Reliab. Eng. Syst. Saf. 213, 107693 (2021).

    Article  Google Scholar 

  38. V. Rouillard, Quantifying the non-stationarity of vehicle vibrations with the run test, Packag. Technol. Sci. 27, 203 (2013).

    Article  Google Scholar 

  39. W. J. Luo, and D. Y. Wang, Ultimate strength reliability analysis of ship plates based on improved AK-MCS method (in Chinese), Chin. J. Ship Res. 15, 123 (2020).

    Google Scholar 

  40. X. Li, H. Zhang, and D. Wang, A lumped mass finite element formulation with consistent nodal quadrature for improved frequency analysis of wave equations, Acta Mech. Sin. 38, 521388 (2022).

    Article  MathSciNet  Google Scholar 

  41. Y. Tang, X. Liu, G. Cai, and X. Liu, Active vibration control of a large space telescope truss based on unilateral saturated cable actuators, Acta Mech. Sin. 38, 522040 (2022).

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51465001 and 51905113) and the Natural Science Foundation of Changsha City (Grant No. kq2208085).

Author information

Authors and Affiliations

  1. College of Civil Engineering and Architecture, Guangxi University, Nanning, 530004, China

    Zhaojun Li  (**兆军) & Fuxiu Liu  (刘福秀)

  2. College of Mechanical Engineering, Guangxi University, Nanning, 530004, China

    Zhaojun Li  (**兆军), Ganwei Cai  (蔡敢为), Jiang Ding  (丁江) & Jiaquan Chen  (陈家权)

  3. School of Construction Machinery, Hunan Sany Polytechnic College, Changsha, 410129, China

    Ganwei Cai  (蔡敢为)

Authors
  1. Zhaojun Li  (**兆军)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fuxiu Liu  (刘福秀)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ganwei Cai  (蔡敢为)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiang Ding  (丁江)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiaquan Chen  (陈家权)
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Author contributions Zhaojun Li conceptualized the research and wrote and revised the manuscript. Fuxiu Liu developed and designed the methodology, wrote the program, and wrote and revised the manuscript. Ganwei Cai helped organize the manuscript and wrote and revised the manuscript. Jiang Ding improved the program, processed the data, and wrote and revised the manuscript. Jiaquan Chen processed the experiment data and wrote and revised the manuscript.

Corresponding author

Correspondence to Fuxiu Liu  (刘福秀).

Ethics declarations

Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Z., Liu, F., Cai, G. et al. Method of non-stationary random vibration reliability of hydro-turbine generator unit. Acta Mech. Sin. 40, 523427 (2024). https://doi.org/10.1007/s10409-024-23427-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-024-23427-x

Search

Navigation