A Bayesian deep learning framework for interval estimation of remaining useful life in complex systems by incorporating general degradation characteristics

References

• Bengio, Y., Simard, P. and Frasconi, P. (1994) Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5(2), 157–166.
   PubMed Web of Science ®Google Scholar
• Bian, L. and Gebraeel, N. (2014) Stochastic modeling and real-time prognostics for multi-component systems with degradation rate interactions. IIE Transactions, 46(5), 470–482.
   Web of Science ®Google Scholar
• Chehade, A., Bonk, S. and Liu, K. (2017) Sensory-based failure threshold estimation for remaining useful life prediction. IEEE Transactions on Reliability, 66(3), 939–949.
   Web of Science ®Google Scholar
• Chehade, A., Song, C., Liu, K., Saxena, A. and Zhang, X. (2018) A data-level fusion approach for degradation modeling and prognostic analysis under multiple failure modes. Journal of Quality Technology, 50(2), 150–165.
   Web of Science ®Google Scholar
• Gal, Y. (2016) Uncertainty in deep learning. PhD Thesis, University of Cambridge, Cambridge, UK.
   Google Scholar
• Gal, Y. and Ghahramani, Z. (2016) Dropout as a Bayesian approximation: Representing model uncertainty in deep learning, in Proceedings of the 33rd International Conference on Machine Learning - Volume 48. pp. 1050–1059. PMLR, New York, NY, USA
   Google Scholar
• Garga, A.K., McClintic, K.T., Campbell, R.L., Yang, C.-C., Lebold, M.S., Hay, T.A. and Byington, C.S. (2001) Hybrid reasoning for prognostic learning in CBM systems, in IEEE Aerospace Conference Proceedings. pp. 2957–2969. IEEE, Big Sky, MT, USA.
   Google Scholar
• Gebraeel, N. (2006) Sensory-updated residual life distributions for components with exponential degradation patterns. IEEE Transactions on Automation Science and Engineering, 3(4), 382–393.
   Web of Science ®Google Scholar
• Gebraeel, N. and Pan, J. (2008) Prognostic degradation models for computing and updating residual life distributions in a time-varying environment. IEEE Transactions on Reliability, 57(4), 539–550.
   Web of Science ®Google Scholar
• Gebraeel, N.Z. and Lawley, M.A. (2008) A neural network degradation model for computing and updating residual life distributions. IEEE Transactions on Automation Science and Engineering, 5(1), 154–163.
   Web of Science ®Google Scholar
• Gers, F.A., Schmidhuber, J. and Cummins, F. (2000) Learning to forget: Continual prediction with LSTM. Neural Computation, 12(10), 2451–2471.
   PubMed Web of Science ®Google Scholar
• Graves, A. (2011) Practical variational inference for neural networks, in Advances in Neural Information Processing Systems 24. pp. 2348–2356. Available from: Curran Associates Inc., Granada, Spain.
   Google Scholar
• Graves, A. (2012) Supervised Sequence Labelling with Recurrent Neural Networks, Springer, Heidelberg, Germany.
   Google Scholar
• Guo, L., Li, N., Jia, F., Lei, Y. and Lin, J. (2017) A recurrent neural network based health indicator for remaining useful life prediction of bearings. Neurocomputing, 240, 98–109.
   Web of Science ®Google Scholar
• Hinton, G.E., Srivastava, N., Krizhevsky, A., Sutskever, I. and Salakhutdinov, R.R. (2012) Improving neural networks by preventing co-adaptation of feature detectors. arXiv preprint arXiv:1207.0580.
   Google Scholar
• Hochreiter, S. and Schmidhuber, J. (1997) Long short-term memory. Neural Computation, 9(8), 1–32.
   PubMed Web of Science ®Google Scholar
• Huang, C.G., Huang, H.Z. and Li, Y.F. (2019) A bi-directional LSTM prognostics method under multiple operational conditions. IEEE Transactions on Industrial Electronics, 66(11), 8792–8802.
   Web of Science ®Google Scholar
• Huang, C.G., Yin, X., Huang, H.Z. and Li, Y.F. (2019) An enhanced deep learning-based fusion prognostic method for RUL prediction. IEEE Transactions on Reliability (early access), 1–13. doi: 10.1109/TR.2019.2948705
   Web of Science ®Google Scholar
• Khan, S. and Yairi, T. (2018) A review on the application of deep learning in system health management. Mechanical Systems and Signal Processing, 107, 241–265.
   Web of Science ®Google Scholar
• Kim, M., Song, C. and Liu, K. (2019) A generic health index approach for multisensor degradation modeling and sensor selection. IEEE Transactions on Automation Science and Engineering, 16(3), 1426–1437.
   Web of Science ®Google Scholar
• LeCun, Y., Boser, B., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W. and Jackel, L.D. (1989) Backpropagation applied to handwritten zip code recognition. Neural Computation, 1(4), 541–551.
   Web of Science ®Google Scholar
• Le Guennec, A., Malinowski, S. and Tavenard, R. (2016) Data augmentation for time series classification using convolutional neural networks, in ECML/PKDD Workshop on Advanced Analytics and Learning on Temporal Data. Available from: Riva del Garda, Italy.
   Google Scholar
• Lei, Y. and Zuo, M.J. (2009) Gear crack level identification based on weighted K nearest neighbor classification algorithm. Mechanical Systems and Signal Processing, 23(5), 1535–1547.
   Web of Science ®Google Scholar
• Li, X., Ding, Q. and Sun, J. (2018) Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability Engineering & System Safety, 172, 1–11.
   Web of Science ®Google Scholar
• Liao, L., Jin, W. and Pavel, R. (2016) Enhanced restricted Boltzmann machine with prognosability regularization for prognostics and health assessment. IEEE Transactions on Industrial Electronics, 63(11), 7076–7083.
   Web of Science ®Google Scholar
• Liu, K., Chehade, A. and Song, C. (2017) Optimize the signal quality of the composite health index via data fusion for degradation modeling and prognostic analysis. IEEE Transactions on Automation Science and Engineering, 14(3), 1504–1514.
   Web of Science ®Google Scholar
• Liu, K., Gebraeel, N.Z. and Shi, J. (2013) A data-level fusion model for developing composite health indices for degradation modeling and prognostic analysis. IEEE Transactions on Automation Science and Engineering, 10(3), 652–664.
   Web of Science ®Google Scholar
• Liu, K. and Huang, S. (2016) Integration of data fusion methodology and degradation modeling process to improve prognostics. IEEE Transactions on Automation Science and Engineering, 13(1), 344–354.
   Web of Science ®Google Scholar
• Lu, C.J. and Meeker, W.Q. (1993) Using degradation measures to estimate a time-to-failure distribution. Technometrics, 35(2), 161–174.
   Web of Science ®Google Scholar
• MacKay, D.J.C. (1992) Bayesian methods for adaptive models. Ph.D. thesis, California Institute of Technology, Pasadena, CA.
   Google Scholar
• Osband, I., Blundell, C., Pritzel, A., van Roy, B. (2016) Deep exploration via bootstrapped DQN, in Advances in Neural Information Processing Systems 29. pp. 4026–4034. Available from: Curran Associates, Inc., Barcelona, Spain.
   Google Scholar
• Peng, W., Hong, L. and Ye, Z. (2017) Degradation-based reliability modeling of complex systems in dynamic environments, in Statistical Modeling for Degradation Data. pp. 81–103. Available from: Springer, Singapore.
   Google Scholar
• Peng, W., Ye, Z.S. and Chen, N. (2020) Bayesian deep-learning-based health prognostics toward prognostics uncertainty. IEEE Transactions on Industrial Electronics, 67(3), 2283–2293.
   Web of Science ®Google Scholar
• Sateesh Babu, G., Zhao, P. and Li, X.-L. (2016) Deep convolutional neural network based regression approach for estimation of remaining useful life, in Proceedings of the International Conference on Database Systems for Advanced Applications. pp. 214–228. Springer, Cham, Switzerland.
   Google Scholar
• Saxena, A. and Goebel, K. (2008) Turbofan engine degradation simulation data set. NASA Ames Prognostics Data Repository (http://ti.arc.nasa.gov/project/prognostic-data-repository), NASA Ames Research Center, Moffett Field, CA.
   Google Scholar
• Si, X.S., Wang, W., Hu, C.H., Zhou, D.H. and Pecht, M.G. (2012) Remaining useful life estimation based on a nonlinear diffusion degradation process. IEEE Transactions on Reliability, 61(1), 50–67.
   Web of Science ®Google Scholar
• Song, C. and Liu, K. (2018) Statistical degradation modeling and prognostics of multiple sensor signals via data fusion: A composite health index approach. IISE Transactions, 50(10), 853–867.
   Web of Science ®Google Scholar
• Song, C., Liu, K. and Zhang, X. (2017) Integration of data-level fusion model and kernel methods for degradation modeling and prognostic analysis. IEEE Transactions on Reliability, 67(2), 640–650.
   Web of Science ®Google Scholar
• Song, C., Liu, K. and Zhang, X. (2019) A generic framework for multisensor degradation modeling based on supervised classification and failure surface. IISE Transactions, 51(11), 1288–1302.
   Web of Science ®Google Scholar
• Soudry, D., Hubara, I. and Meir, R. (2014) Expectation backpropagation: Parameter-free training of multilayer neural networks with continuous or discrete weights, in Advances in Neural Information Processing Systems 27. pp. 963–971. Available from: Curran Associates, Inc., Montreal, Canada.
   Google Scholar
• Springenberg, J.T., Klein, A., Falkner, S. and Hutter, F. (2016) Bayesian optimization with robust Bayesian neural networks, in Advances in Neural Information Processing Systems 29. pp. 4134–4142. Available from: Curran Associates, Inc., Barcelona, Spain.
   Google Scholar
• Tian, Z., Wong, L. and Safaei, N. (2010) A neural network approach for remaining useful life prediction utilizing both failure and suspension histories. Mechanical Systems and Signal Processing, 24(5), 1542–1555.
   Web of Science ®Google Scholar
• Tieleman, T. and Hinton, G. (2012) Lecture 6.5-rmsprop: Divide the Gradient by a Running Average of Its Recent Magnitude. COURSERA: Neural Networks for Machine Learning, 4, 26–31.
   Google Scholar
• Tran, V.T., Yang, B.-S., Oh, M.-S. and Tan, A.C.C. (2009) Fault diagnosis of induction motor based on decision trees and adaptive neuro-fuzzy inference. Expert Systems with Applications, 36(2), 1840–1849.
   Web of Science ®Google Scholar
• Wang, W. and Christer, A.H. (2000) Towards a general condition based maintenance model for a stochastic dynamic system. Journal of the Operational Research Society, 51(2), 145–155.
   Web of Science ®Google Scholar
• Widodo, A. and Yang, B.-S. (2007) Support vector machine in machine condition monitoring and fault diagnosis. Mechanical Systems and Signal Processing, 21(6), 2560–2574.
   Web of Science ®Google Scholar
• Yan, H., Liu, K., Zhang, X. and Shi, J. (2016) Multiple sensor data fusion for degradation modeling and prognostics under multiple operational conditions. IEEE Transactions on Reliability, 65(3), 1416–1426.
   Web of Science ®Google Scholar
• Zhang, C., Lim, P., Qin, A.K. and Tan, K.C. (2017) Multiobjective deep belief networks ensemble for remaining useful life estimation in prognostics. IEEE Transactions on Neural Networks and Learning Systems, 28(10), 2306–2318.
   PubMed Web of Science ®Google Scholar
• Zhu, J., Chen, N. and Peng, W. (2018) Estimation of bearing remaining useful life based on multiscale convolutional neural network. IEEE Transactions on Industrial Electronics, 66(4), 3208–3216.
   Web of Science ®Google Scholar