Skip to main content
Log in

An active learning hybrid reliability method for positioning accuracy of industrial robots

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

Popsitioning accuracy is an important index for evaluating the capacity of industrial robots. As a mechanism with multi-degree of freedom, the uncertainties of industrial robots are diverse and analyzing the positioning accuracy reliability is time consuming. To improve computation efficiency, a new active learning method based on Kriging model is proposed for hybrid reliability analysis of positioning accuracy with random and interval variables. In this study, the updated samples were selected through U learning function in the vicinity of limit-state function. A new stopping criterion based on expected risk function was exploited to judge whether the accuracy of Kriging model is enough. Two numerical examples and one engineering example were provided to verify the efficiency and accuracy of the proposed method. The results indicate that the proposed method is accurate and efficient.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Wu, X. Han and Y. Tao, Kinematic response of industrial robot with uncertain-but-bounded parameters using interval analysis method, Journal of Mechanical Science and Technology, 33(1) (2019) 333–340.

    Google Scholar 

  2. M. Pandey and X. Zhang, System reliability analysis of the robotic manipulator with random joint clearances, Mechanism and Machine Theory, 58 (2012) 137–152.

    Google Scholar 

  3. J. Wu, D. Zhang, J. Liu and X. Han, A moment approach to positioning accuracy reliability analysis for industrial robots, IEEE Transactions on Reliability, 69(2) (2020) 699–714.

    Google Scholar 

  4. J. Wu, D. Zhang, J. Liu, X. Jia and X. Han, A computational framework of kinematic accuracy reliability analysis for industrial robots, Applied Mathematical Modelling, 82 (2020) 189–216.

    MathSciNet  MATH  Google Scholar 

  5. G. Cui, H. Zhang, D. Zhang and F. Xu, Analysis of the kinematic accuracy reliability of a 3-DOF parallel robot manipulator, International Journal of Advanced Robotic Systems, 12(2) (2015) 15.

    Google Scholar 

  6. R. Kluz and T. Trzepieciński, The repeatability positioning analysis of the industrial robot arm, Assembly Automation, 34(3) (2014) 285–295.

    Google Scholar 

  7. D. Zhang and X. Han, Kinematic reliability analysis of robotic manipulator, Journal of Mechanical Design, 142 (4) (2020).

  8. M. Yang, D. Zhang and X. Han, New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization, Computer Methods in Applied Mechanics and Engineering, 366 (2020) 113018.

    MathSciNet  MATH  Google Scholar 

  9. P. Hao, Y. Wang, C. Liu, B. Wang and H. Wu, A novel non-probabilistic reliability-based design optimization algorithm using enhanced chaos control method, Computer Methods in Applied Mechanics and Engineering, 318 (2017) 572–593.

    MathSciNet  MATH  Google Scholar 

  10. Z. Meng, Y. Pang, Y. Pu and X. Wang, New hybrid reliability-based topology optimization method combining fuzzy and probabilistic models for handling epistemic and aleatory uncertainties, Computer Methods in Applied Mechanics and Engineering, 363 (2020) 112886.

    MathSciNet  MATH  Google Scholar 

  11. C. Jiang, Z. Zhang, X. Han and J. Liu, A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty, Computers & Structures, 129 (2013) 1–12.

    Google Scholar 

  12. C. Jiang, X. Han, G. Lu, J. Liu, Z. Zhang and Y. Bai, Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique, Computer Methods in Applied Mechanics and Engineering, 200(33–36) (2011) 2528–2546.

    MATH  Google Scholar 

  13. C. Jiang, R. Bi, G. Lu and X. Han, Structural reliability analysis using non-probabilistic convex model, Computer Methods in Applied Mechanics and Engineering, 254 (2013) 83–98.

    MathSciNet  MATH  Google Scholar 

  14. Z. Meng, Z. Zhang and H. Zhou, A novel experimental data-driven exponential convex model for reliability assessment with uncertain-but-bounded parameters, Applied Mathematical Modelling, 77 (2020) 773–787.

    MathSciNet  MATH  Google Scholar 

  15. C. Jiang, G. Y. Lu, X. Han and L. X. Liu, A new reliability analysis method for uncertain structures with random and interval variables, International Journal of Mechanics and Materials in Design, 8(2) (2012) 169–182.

    Google Scholar 

  16. D. Zhang, X. Han, C. Jiang, J. Liu and X. Long, The interval PHI2 analysis method for time-dependent reliability, SCIENTIA SINICA Physica, Mechanica & Astronomica, 45(5) (2015) 054601–054601.

    Google Scholar 

  17. F. Li, J. Liu, Y. Yan, J. Rong, J. Yi and G. Wen, A time-variant reliability analysis method for non-linear limit-state functions with the mixture of random and interval variables, Engineering Structures, 213 (2020) 110588.

    Google Scholar 

  18. H. Li, Reliability-based design optimization via high order response surface method, Journal of Mechanical Science and Technology, 27(4) (2013) 1021–1029.

    MathSciNet  Google Scholar 

  19. D. Zhang, X. Han, C. Jiang, J. Liu and Q. Li, Time-dependent reliability analysis through response surface method, Journal of Mechanical Design, 139 (4) (2017).

  20. D. Zhou, X. Zhang and Y. Zhang, Reliability analysis of the traction unit of a shearer mechanism with response surface method, Journal of Mechanical Science and Technology, 31(10) (2017) 4679–4689.

    Google Scholar 

  21. H. Dai, W. Zhao, W. Wang and Z. Cao, An improved radial basis function network for structural reliability analysis, Journal of Mechanical Science and Technology, 25(9) (2011) 2151.

    Google Scholar 

  22. Z. Guo, L. Song, C. Park, J. Li and R. T. Haftka, Analysis of dataset selection for multi-fidelity surrogates for a turbine problem, Structural and Multidisciplinary Optimization, 57(6) (2018) 2127–2142.

    Google Scholar 

  23. P. Hao, S. Feng, K. Zhang, Z. Li, B. Wang and G. Li, Adaptive gradient-enhanced kriging model for variable-stiffness composite panels using Isogeometric analysis, Structural and Multidisciplinary Optimization, 58(1) (2018) 1–16.

    MathSciNet  Google Scholar 

  24. Z. Meng, Z. Zhang, G. Li and D. Zhang, An active weight learning method for efficient reliability assessment with small failure probability, Structural and Multidisciplinary Optimization, 61(3) (2020) 1157–1170.

    MathSciNet  Google Scholar 

  25. M. Xiao, Y. Yi, J. Zhang and W. Li, An effective method for quantifying and incorporating uncertainty in metamodel selection, Journal of Mechanical Science and Technology, 33(3) (2019) 1279–1291.

    Google Scholar 

  26. L. Hong, H. Li, K. Peng and H. Xiao, A novel kriging based active learning method for structural reliability analysis, Journal of Mechanical Science and Technology, 34 (2020) 1545–1556.

    Google Scholar 

  27. N. Xiao, K. Yuan and C. Zhou, Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables, Computer Methods in Applied Mechanics and Engineering, 359 (2020) 112649.

    MathSciNet  MATH  Google Scholar 

  28. K. Yuan, N. Xiao, Z. Wang and K. Shang, System reliability analysis by combining structure function and active learning kriging model, Reliability Engineering & System Safety, 195 (2020) 106734.

    Google Scholar 

  29. B. J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan and J. M. McFarland, Efficient global reliability analysis for nonlinear implicit performance functions, AIAA Journal, 46(10) (2008) 2459–2468.

    Google Scholar 

  30. B. Echard, N. Gayton and M. Lemaire, AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation, Structural Safety, 33(2) (2011) 145–154.

    Google Scholar 

  31. B. Echard, N. Gayton, M. Lemaire and N. Relun, A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models, Reliability Engineering & System Safety, 111 (2013) 232–240.

    Google Scholar 

  32. F. Cadini, F. Santos and E. Zio, An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability, Reliability Engineering & System Safety, 131 (2014) 109–117.

    Google Scholar 

  33. C. Tong, Z. Sun, Q. Zhao, Q. Wang and S. Wang, A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling, Journal of Mechanical Science and Technology, 29(8) (2015) 3183–3193.

    Google Scholar 

  34. X. Huang, J. Chen and H. Zhu, Assessing small failure probabilities by AK-SS: An active learning method combining Kriging and subset simulation, Structural Safety, 59 (2016) 86–95.

    Google Scholar 

  35. J. Zhang, M. Xiao and L. Gao, An active learning reliability method combining kriging constructed with exploration and exploitation of failure region and subset simulation, Reliability Engineering & System Safety, 188 (2019) 90–102.

    Google Scholar 

  36. Z. Meng, Z. Zhang, D. Zhang and D. Yang, An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization, Computer Methods in Applied Mechanics and Engineering, 357 (2019) 112570.

    MathSciNet  MATH  Google Scholar 

  37. Z. Meng, D. Zhang, G. Li and B. Yu, An importance learning method for non-probabilistic reliability analysis and optimization, Structural and Multidisciplinary Optimization, 59(4) (2019) 1255–1271.

    Google Scholar 

  38. M. Xiao, J. Zhang and L. Gao, A system active learning Kriging method for system reliability-based design optimization with a multiple response model, Reliability Engineering & System Safety, 199 (2020) 106935.

    Google Scholar 

  39. C. Jiang, D. Wang, H. Qiu, L. Gao, L. Chen and Z. Yang, An active failure-pursuing Kriging modeling method for time-dependent reliability analysis, Mechanical Systems and Signal Processing, 129 (2019) 112–129.

    Google Scholar 

  40. C. Jiang, H. Qiu, L. Gao, D. Wang, Z. Yang and L. Chen, Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis, Applied Mathematical Modelling, 77 (2020) 82–98.

    MathSciNet  MATH  Google Scholar 

  41. X. Yang, Y. Liu, Y. Gao, Y. Zhang and Z. Gao, An active learning kriging model for hybrid reliability analysis with both random and interval variables, Structural and Multidisciplinary Optimization, 51(5) (2014) 1003–1016.

    MathSciNet  Google Scholar 

  42. J. Zhang, M. Xiao, L. Gao and J. Fu, A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables, Computer Methods in Applied Mechanics and Engineering, 341 (2018) 32–52.

    MathSciNet  MATH  Google Scholar 

  43. J. Zhang, M. Xiao, L. Gao and S. Chu, A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities, Computer Methods in Applied Mechanics and Engineering, 344 (2019) 13–33.

    MathSciNet  MATH  Google Scholar 

  44. M. Xiao, J. Zhang, L. Gao, S. Lee and A. T. Eshghi, An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability, Structural and Multidisciplinary Optimization, 59(6) (2019) 2077–2092.

    MathSciNet  Google Scholar 

  45. B. Birge, PSOt-a particle swarm optimization toolbox for use with Matlab, Proceedings of the 2003 IEEE Swarm Intelligence Symposium, IEEE (2003) 182–186.

  46. S. N. Lophaven, H. B. Nielsen and J. Sandergaard, DACE: A Matlab Kriging Toolbox, CiteSeer (2002).

  47. X. Du, Unified uncertainty analysis by the first order reliability method, Journal of Mechanical Design, 130(9) (2008) 091401.

    Google Scholar 

  48. P. I. Corke, A robotics toolbox for MATLAB, IEEE Robotics & Automation Magazine, 3(1) (1996) 24–32.

    Google Scholar 

  49. H. Lim, D. Kim, S. Kim and H. Kang, A practical approach to enhance positioning accuracy for industrial robots, ICCAS-SICE, IEEE (2009) 2268–2273.

Download references

Acknowledgments

This work was financially supported by the National Key R&D Program of China (Grant No. 2017YFB1301300), the National Natural Science Foundation of China (Grant No. 51905146), the Key R&D Plan Program of Hebei Province (Grant No. 19211808D) and the Research Program of Education Bureau of Hebei Province (Grant No. QN2019141).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dequan Zhang.

Additional information

Recommended by Editor Ja Choon Koo

Dequan Zhang is an Assistant Professor of Mechanical Engineering, Hebei University of Technology, Tianjin, China. He received the Ph.D. in Mechanical Engineering from Hunan University, Hunan, China, in 2018. His research interests are in the area of reliability analysis, design under uncertainty and robotics.

Song Liu is a master’s student in Mechanical Engineering, Hebei University of Technology, Tianjin, China. His research interests are in the area of reliability analysis and error compensation for industrial robot.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, D., Liu, S., Wu, J. et al. An active learning hybrid reliability method for positioning accuracy of industrial robots. J Mech Sci Technol 34, 3363–3372 (2020). https://doi.org/10.1007/s12206-020-0729-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-0729-8

Keywords

Navigation