A data-driven method based on deep belief networks for backlash error prediction in machining centers

  • Zhe LiEmail author
  • Yi Wang
  • Kesheng Wang


Backlash error occurs in a machining center may lead to a series of changes in the geometry of the components and subsequently deteriorate the overall performance of the equipment. Due to the uncertainty of mechanical wear between kinematic pairs, it is challenging to predict backlash error through physical models directly. An alternative method is to leverage data-driven models to map the degradation. This paper proposes a data-driven method for backlash error predication through Deep Belief Network (DBN). The proposed method focuses on the assessment of both current and future geometric errors for backlash error prediction and subsequent maintenance in machining centers. During the process of prognosis, a DBN via stacking Restricted Boltzmann Machines is constructed for backlash error prediction. Energy-based models enable DBN to mine information hidden behind highly coupled inputs, which makes DBN a feasible method for fault diagnosis and prognosis when the target condition is beyond the historical data. In the experiment, to confirm the effectiveness of deep learning for backlash error prediction, similar popular regression methods, including Support Vector Machine Regression and Back Propagation Neural Network, are employed to present a comprehensive comparison in both diagnosis and prognosis. The experimental results show that the performances of all these regression methods are acceptable in the diagnostic stage. In the prognostic stage, DBN demonstrates its superiority and significantly outperforms the other models for backlash error prediction in machining centers.


Data mining Machining centers Data-driven method Deep belief network Backlash error 


  1. Aydın, İ., Karaköse, M., & Akın, E. (2015). Combined intelligent methods based on wireless sensor networks for condition monitoring and fault diagnosis. Journal of Intelligent Manufacturing, 26(4), 717–729.CrossRefGoogle Scholar
  2. Bengio, Y. (2009). Learning deep architectures for AI. Foundations and Trends® in Machine Learning, 2(1), 1–127.CrossRefGoogle Scholar
  3. Carreira-Perpinan, M. A., & Hinton, G. (2005). On contrastive divergence learning. In AISTATS (Vol. 10, pp. 33–40). CiteseerGoogle Scholar
  4. Chen, C., Liu, Z., Zhang, Y., Chen, C. P., & Xie, S. (2016). Actuator backlash compensation and accurate parameter estimation for active vibration isolation system. IEEE Transactions on Industrial Electronics, 63(3), 1643–1654.CrossRefGoogle Scholar
  5. Cheng, Q., Zhao, H., Zhang, G., Gu, P., & Cai, L. (2014). An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis. The International Journal of Advanced Manufacturing Technology, 75(1–4), 107–121.CrossRefGoogle Scholar
  6. Cheng, Q., Zhao, H., Zhao, Y., Sun, B., & Gu, P. (2015). Machining accuracy reliability analysis of multi-axis machine tool based on Monte Carlo simulation. Journal of Intelligent Manufacturing.
  7. Ciodaro, T., Deva, D., De Seixas, J., & Damazio, D. (2012). Online particle detection with neural networks based on topological calorimetry information. In Journal of physics: Conference series (Vol. 368, pp. 012030). IOP PublishingGoogle Scholar
  8. Deng, L., & Yu, D. (2014). Deep learning: Methods and applications. Foundations and Trends® in Signal Processing, 7(3–4), 197–387. Scholar
  9. Er, M. J., Zhang, Y., Wang, N., & Pratama, M. (2016). Attention pooling-based convolutional neural network for sentence modelling. Information Sciences, 373, 388–403.CrossRefGoogle Scholar
  10. Fines, J. M., & Agah, A. (2008). Machine tool positioning error compensation using artificial neural networks. Engineering Applications of Artificial Intelligence, 21(7), 1013–1026.CrossRefGoogle Scholar
  11. Gan, M., & Wang, C. (2016). Construction of hierarchical diagnosis network based on deep learning and its application in the fault pattern recognition of rolling element bearings. Mechanical Systems and Signal Processing, 72, 92–104.CrossRefGoogle Scholar
  12. Helmstaedter, M., Briggman, K. L., Turaga, S. C., Jain, V., Seung, H. S., & Denk, W. (2013). Connectomic reconstruction of the inner plexiform layer in the mouse retina. Nature, 500(7461), 168–174.CrossRefGoogle Scholar
  13. Hermann, M., Pentek, T., & Otto, B. (2015). Design principles for Industrie 4.0 scenarios: A literature review. Dortmund: Technische Universität Dortmund.Google Scholar
  14. Hinton, G. (2010). A practical guide to training restricted Boltzmann machines. Momentum, 9(1), 926.Google Scholar
  15. Hinton, G. E. (2002). Training products of experts by minimizing contrastive divergence. Neural Computation, 14(8), 1771–1800.CrossRefGoogle Scholar
  16. Hinton, G., Deng, L., Yu, D., Dahl, G. E., Mohamed, A.-R., Jaitly, N., et al. (2012). Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Processing Magazine, 29(6), 82–97.CrossRefGoogle Scholar
  17. Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18(7), 1527–1554.CrossRefGoogle Scholar
  18. Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504–507.CrossRefGoogle Scholar
  19. Kao, J., Yeh, Z.-M., Tarng, Y., & Lin, Y. (1996). A study of backlash on the motion accuracy of CNC lathes. International Journal of Machine Tools and Manufacture, 36(5), 539–550.CrossRefGoogle Scholar
  20. Keyvanrad, M. A., & Homayounpour, M. M. (2014). A brief survey on deep belief networks and introducing a new object oriented MATLAB toolbox (DeeBNet V2. 1). arXiv preprint arXiv:1408.3264.
  21. Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012). Imagenet classification with deep convolutional neural networks. In Paper presented at the proceedings of the 25th international conference on neural information processing systems (Vol. 1). Lake Tahoe, Nevada.Google Scholar
  22. Kusiak, A. (2017). Smart manufacturing must embrace big data. Nature, 544(7648), 23.CrossRefGoogle Scholar
  23. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436–444.CrossRefGoogle Scholar
  24. LeCun, Y., Bottou, L., Bengio, Y., & Haffner, P. (1998). Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11), 2278–2324.CrossRefGoogle Scholar
  25. Lee, K.-I., & Yang, S.-H. (2013). Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar. International Journal of Machine Tools and Manufacture, 70, 45–52.CrossRefGoogle Scholar
  26. Li, J., Tao, F., Cheng, Y., & Zhao, L. (2015). Big data in product lifecycle management. The International Journal of Advanced Manufacturing Technology, 81(1–4), 667–684.CrossRefGoogle Scholar
  27. Liu, H., Xue, X., & Tan, G. (2010). Backlash error measurement and compensation on the vertical machining center. Engineering, 2(06), 403.CrossRefGoogle Scholar
  28. Mosallam, A., Medjaher, K., & Zerhouni, N. (2016). Data-driven prognostic method based on Bayesian approaches for direct remaining useful life prediction. Journal of Intelligent Manufacturing, 27(5), 1037–1048.CrossRefGoogle Scholar
  29. O’Connor, P., Neil, D., Liu, S.-C., Delbruck, T., & Pfeiffer, M. (2013). Real-time classification and sensor fusion with a spiking deep belief network. Frontiers in Neuroscience, 7, 178.
  30. Prasanga, D. K., Tanida, K., Mizoguchi, T., & Ohnishi, K. (2013). Evaluation of a backlash compensation method using two parallel thrust wires. In IEEE international symposium on industrial electronics (ISIE) (pp. 1–6). IEEEGoogle Scholar
  31. Ribeiro, B., Gonçalves, I., Santos, S., & Kovacec, A. (2011). Deep learning networks for off-line handwritten signature recognition. In C. San Martin & S.-W. Kim (Eds.), Proceedings of progress in pattern recognition, image analysis, computer vision, and applications: 16th Iberoamerican Congress, CIARP 2011, Pucón, Chile, November 15–18, 2011 (pp. 523–532). Berlin, Heidelberg: Springer Berlin Heidelberg.Google Scholar
  32. Sainath, T. N., Mohamed, A.-R., Kingsbury, B., & Ramabhadran, B. (2013). Deep convolutional neural networks for LVCSR. In 2013 IEEE International conference on acoustics, speech and signal processing (pp. 8614–8618). IEEEGoogle Scholar
  33. Schmidhuber, J. (2015). Deep learning in neural networks: An overview. Neural Networks, 61, 85–117.CrossRefGoogle Scholar
  34. Schwenke, H., Knapp, W., Haitjema, H., Weckenmann, A., Schmitt, R., & Delbressine, F. (2008). Geometric error measurement and compensation of machines: An update. CIRP Annals-Manufacturing Technology, 57(2), 660–675.CrossRefGoogle Scholar
  35. Seltzer, M. L., Yu, D., & Wang, Y. (2013 ). An investigation of deep neural networks for noise robust speech recognition. In 2013 IEEE international conference on acoustics, speech and signal processing (pp. 7398–7402). IEEEGoogle Scholar
  36. Siguenza-Guzman, L., Saquicela, V., Avila-Ordóñez, E., Vandewalle, J., & Cattrysse, D. (2015). Literature review of data mining applications in academic libraries. The Journal of Academic Librarianship, 41(4), 499–510.CrossRefGoogle Scholar
  37. Slamani, M., Nubiola, A., & Bonev, I. A. (2012). Modeling and assessment of the backlash error of an industrial robot. Robotica, 30(07), 1167–1175.CrossRefGoogle Scholar
  38. Stryczek, R. (2016). A metaheuristic for fast machining error compensation. Journal of Intelligent Manufacturing, 27(6), 1209–1220.Google Scholar
  39. Tao, F., Cheng, J., Qi, Q., Zhang, M., Zhang, H., & Sui, F. (2017). Digital twin-driven product design, manufacturing and service with big data. The International Journal of Advanced Manufacturing Technology.
  40. Tompson, J., Jain, A., LeCun, Y., & Bregler, C. (2014). Joint training of a convolutional network and a graphical model for human pose estimation. In Paper presented at the proceedings of the 27th international conference on neural information processing systems (Vol. 1). Montreal, Canada.Google Scholar
  41. Wang, C., & Jiang, P. (2017). Deep neural networks based order completion time prediction by using real-time job shop RFID data. Journal of Intelligent Manufacturing.
  42. Wang, K.-S., Li, Z., Braaten, J., & Yu, Q. (2015). Interpretation and compensation of backlash error data in machine centers for intelligent predictive maintenance using ANNs. Advances in Manufacturing, 3(2), 97–104.CrossRefGoogle Scholar
  43. Xiong, H. Y., Alipanahi, B., Lee, L. J., Bretschneider, H., Merico, D., Yuen, R. K., et al. (2015). The human splicing code reveals new insights into the genetic determinants of disease. Science, 347(6218), 1254806.CrossRefGoogle Scholar
  44. Yu, D., & Deng, L. (2011). Deep learning and its applications to signal and information processing [exploratory dsp]. IEEE Signal Processing Magazine, 28(1), 145–154.CrossRefGoogle Scholar
  45. Zhang, Y., Er, M. J., Zhao, R., & Pratama, M. (2017). Multiview convolutional neural networks for multidocument extractive summarization. IEEE Transactions on Cybernetics, 47(10), 3230–3242.CrossRefGoogle Scholar
  46. Zhang, Y., Yang, J., & Zhang, K. (2013). Geometric error measurement and compensation for the rotary table of five-axis machine tool with double ballbar. The International Journal of Advanced Manufacturing Technology, 65(1–4), 275–281.CrossRefGoogle Scholar
  47. Zhong, G., Wang, C., Yang, S., Zheng, E., & Ge, Y. (2015). Position geometric error modeling, identification and compensation for large 5-axis machining center prototype. International Journal of Machine Tools and Manufacture, 89, 142–150.CrossRefGoogle Scholar
  48. Zhou, S., Chen, Q., & Wang, X. (2010). Discriminative Deep Belief networks for image classification. In 2010 IEEE international conference on image processing (pp. 1561–1564). IEEEGoogle Scholar
  49. Zhu, S., Ding, G., Qin, S., Lei, J., Zhuang, L., & Yan, K. (2012). Integrated geometric error modeling, identification and compensation of CNC machine tools. International Journal of Machine Tools and Manufacture, 52(1), 24–29.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Production and Quality EngineeringNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.School of BusinessPlymouth UniversityPlymouth DevonUK

Personalised recommendations