Reconceptualizing the Prognostics Digital Twin for Smart Manufacturing with Data-Driven Evolutionary Models and Adaptive Uncertainty Quantification
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Published
Oct 26, 2023
Jack Murray
Brandon Chamberlain
Nicholas Hemleben
Daniel Ospina-Acero
Indranil Nayak
Andrew VanFossen
Frank Zahiri
Mrinal Kumar
Abstract
This work presents an integrated architecture for a prognostic digital twin for smart manufacturing
subsystems. The specific case of cutting tool wear (flank wear) in a CNC machine is considered, using
benchmark data sets provided by the Prognostics and Health Management (PHM) Society. This paper
emphasizes the role of robust uncertainty quantification, especially in the presence of data-driven
black- and gray-box dynamic models. A surrogate dynamic model is constructed to track the evolution
of flank wear using a reduced set of features extracted from multi-modal sensor time series data. The
digital twin's uncertainty quantification engine integrates with this dynamic model along with a
machine emulator that is tasked with generating future operating scenarios for the machine. The
surrogate dynamic model and emulator are combined in a closed-loop architecture with an adaptive
Monte Carlo uncertainty forecasting framework that allows prediction of quantities of interest
critical to prognostics within user-prescribed bounds. Numerical results using the PHM dataset are
shown illustrating how the adaptive uncertainty forecasting tools deliver a trustworthy forecast by
maintaining predictive error within the prescribed tolerance.
subsystems. The specific case of cutting tool wear (flank wear) in a CNC machine is considered, using
benchmark data sets provided by the Prognostics and Health Management (PHM) Society. This paper
emphasizes the role of robust uncertainty quantification, especially in the presence of data-driven
black- and gray-box dynamic models. A surrogate dynamic model is constructed to track the evolution
of flank wear using a reduced set of features extracted from multi-modal sensor time series data. The
digital twin's uncertainty quantification engine integrates with this dynamic model along with a
machine emulator that is tasked with generating future operating scenarios for the machine. The
surrogate dynamic model and emulator are combined in a closed-loop architecture with an adaptive
Monte Carlo uncertainty forecasting framework that allows prediction of quantities of interest
critical to prognostics within user-prescribed bounds. Numerical results using the PHM dataset are
shown illustrating how the adaptive uncertainty forecasting tools deliver a trustworthy forecast by
maintaining predictive error within the prescribed tolerance.
How to Cite
Murray, J., Chamberlain, B., Hemleben, N., Ospina-Acero, D., Nayak, I., VanFossen, A., Zahiri, F., & Kumar, M. (2023). Reconceptualizing the Prognostics Digital Twin for Smart Manufacturing with Data-Driven Evolutionary Models and Adaptive Uncertainty Quantification. Annual Conference of the PHM Society, 15(1). https://doi.org/10.36001/phmconf.2023.v15i1.3484
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Keywords
Prognostic digital twin, Monte Carlo forecasting, Dynamics learning, Smart manufacturing, Uncertainty quantification
References
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Fang, K.-T., & Lin, D. K. (2003). Ch. 4. uniform experimental designs and their applications in industry. In Statistics in industry (Vol. 22, pp. 131–170). Elsevier.
Grosso, A., Jamali, A., & Locatelli, M. (2009). Finding maximin latin hypercube designs by iterated local search heuristics. European Journal of Operational Research, 197(2), 541–547. Hamilton, J. (1994). Time series analysis. Princeton University
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Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2). Springer.
Hickernell, F. (1998). A generalized discrepancy and quadrature error bound. Mathematics of Computation,
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Janssen, H. (2013). Monte-carlo based uncertainty analysis: Sampling efficiency and sampling convergence. Reliability
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Jimenez, J. J. M., Schwartz, S., Vingerhoeds, R., Grabot, B., &Sala¨un, M. (2020). Towards multi-model approaches
to predictive maintenance: A systematic literature survey on diagnostics and prognostics. Journal of Manufacturing Systems, 56, 539–557.
Lattanzi, L., Raffaeli, R., Peruzzini, M., & Pellicciari, M. (2021). Digital twin for smart manufacturing: A review
of concepts towards a practical industrial implementation. International Journal of Computer Integrated
Manufacturing, 34(6), 567–597.
Li, L., Lei, B., & Mao, C. (2022). Digital twin in smart manufacturing. Journal of Industrial Information Integration, 26, 100289. doi: https://doi.org/10.1016/j.jii.2021.100289
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Integrated Manufacturing, 61, 101837. doi: https://doi.org/10.1016/j.rcim.2019.101837
Menon, S., Shah, S., & Coutroubis, A. (2018). An overview of smart manufacturing for competitive and digital global supply chains. In 2018 ieee international conference on technology management, operations and decisions (ictmod) (p. 178-183). doi: 10.1109/ITMC.2018.8691224
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Qi, Q., & Tao, F. (2018). Digital twin and big data towards smart manufacturing and industry 4.0: 360 degree comparison. IEEE Access, 6, 3585-3593. doi: 10.1109/ACCESS.2018.2793265
Ramakrishna, S., Khong, T. C., & Leong, T. K. (2017). Smart manufacturing. Procedia Manufacturing, 12, 128-131. (International Conference on Sustainable and Intelligent Manufacturing, RESIM 2016, 14-17 December
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Simpson, T., Poplinski, J., Koch, P. N., & Allen, J. (2001). Metamodels for computer-based engineering design: Survey and recommendations. Engineering with Computers, 17, 129–150.
Tao, F., Zhang, M., & Nee, A. Y. C. (2019). Digital twin driven smart manufacturing. Academic Press.
Thelen, A., Zhang, X., Fink, O., Lu, Y., Ghosh, S., Youn, B. D., and Zhen Hu, C. H. (Aug, 2022). A comprehensive
review of digital twin - part 2: Roles of uncertainty quantification and optimization, a battery digital twin, and perspectives. arXiv:2208.12904v1.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society:
Series B (Methodological), 58(1), 267-288.
Vanfossen, A. W., & Kumar, M. (2023). Efficient adaptive monte carlo uncertainty forecasting for high dimensional
nonlinear dynamic systems. IEEE Access, 11, 12119-12138.
Vogl, G.W.,Weiss, B. A., & Helu, M. (2019). A review of diagnostic and prognostic capabilities and best practices
for manufacturing. Journal of Intelligent Manufacturing, 30(1), 79–95.
Wright, L., & Davidson, S. (2020). How to tell the difference between a model and a digital twin. Advanced Modeling
and Simulation in Engineering Sciences, 7(1), 1– 13.
Yang, C., Buck, K., & Kumar, M. (2015). An evaluation of monte carlo for nonlinear initial uncertainty propagation in keplerian mechanics. In 2015 18th international conference on information fusion (fusion) (p. 119-125).
Yang, C., & Kumar, M. (2019a). An adaptive monte carlo method for uncertainty forecasting in perturbed twobody
dynamics. Acta Astronautica, 155, 369–378.
Yang, C., & Kumar, M. (2019b). Closed-loop adaptive monte carlo framework for uncertainty forecasting in nonlinear dynamic systems. Journal of Guidance, Control, and Dynamics, 42(6), 1218-1236.
Errandonea, I., Beltran, S., & Arrizabalaga, S. (2020). Digital twin for maintenance: A literature review. Computers in Industry, 123, 103316.
Fang, K.-T., & Lin, D. K. (2003). Ch. 4. uniform experimental designs and their applications in industry. In Statistics in industry (Vol. 22, pp. 131–170). Elsevier.
Grosso, A., Jamali, A., & Locatelli, M. (2009). Finding maximin latin hypercube designs by iterated local search heuristics. European Journal of Operational Research, 197(2), 541–547. Hamilton, J. (1994). Time series analysis. Princeton University
Press.
Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2). Springer.
Hickernell, F. (1998). A generalized discrepancy and quadrature error bound. Mathematics of Computation,
67(221), 299–322.
Janssen, H. (2013). Monte-carlo based uncertainty analysis: Sampling efficiency and sampling convergence. Reliability
Engineering & System Safety, 109, 123–132.
Jimenez, J. J. M., Schwartz, S., Vingerhoeds, R., Grabot, B., &Sala¨un, M. (2020). Towards multi-model approaches
to predictive maintenance: A systematic literature survey on diagnostics and prognostics. Journal of Manufacturing Systems, 56, 539–557.
Lattanzi, L., Raffaeli, R., Peruzzini, M., & Pellicciari, M. (2021). Digital twin for smart manufacturing: A review
of concepts towards a practical industrial implementation. International Journal of Computer Integrated
Manufacturing, 34(6), 567–597.
Li, L., Lei, B., & Mao, C. (2022). Digital twin in smart manufacturing. Journal of Industrial Information Integration, 26, 100289. doi: https://doi.org/10.1016/j.jii.2021.100289
Lu, Y., Liu, C., Wang, K. I.-K., Huang, H., & Xu, X. (2020). Digital twin-driven smart manufacturing: Connotation, reference model, applications and research issues. Robotics and Computer-
Integrated Manufacturing, 61, 101837. doi: https://doi.org/10.1016/j.rcim.2019.101837
Menon, S., Shah, S., & Coutroubis, A. (2018). An overview of smart manufacturing for competitive and digital global supply chains. In 2018 ieee international conference on technology management, operations and decisions (ictmod) (p. 178-183). doi: 10.1109/ITMC.2018.8691224
Niederreiter, H. (1978). Quasi-monte carlo methods and pseudo-random numbers. Bulletin of the American
Mathematical Society, 84(6), 957–1041.
Øksendal, B. (2003). Stochastic differential equations: An introduction with applications (6th ed.). Springer-Verlag Berlin Heidelberg.
Qi, Q., & Tao, F. (2018). Digital twin and big data towards smart manufacturing and industry 4.0: 360 degree comparison. IEEE Access, 6, 3585-3593. doi: 10.1109/ACCESS.2018.2793265
Ramakrishna, S., Khong, T. C., & Leong, T. K. (2017). Smart manufacturing. Procedia Manufacturing, 12, 128-131. (International Conference on Sustainable and Intelligent Manufacturing, RESIM 2016, 14-17 December
2016, Leiria, Portugal)
Simpson, T., Poplinski, J., Koch, P. N., & Allen, J. (2001). Metamodels for computer-based engineering design: Survey and recommendations. Engineering with Computers, 17, 129–150.
Tao, F., Zhang, M., & Nee, A. Y. C. (2019). Digital twin driven smart manufacturing. Academic Press.
Thelen, A., Zhang, X., Fink, O., Lu, Y., Ghosh, S., Youn, B. D., and Zhen Hu, C. H. (Aug, 2022). A comprehensive
review of digital twin - part 2: Roles of uncertainty quantification and optimization, a battery digital twin, and perspectives. arXiv:2208.12904v1.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society:
Series B (Methodological), 58(1), 267-288.
Vanfossen, A. W., & Kumar, M. (2023). Efficient adaptive monte carlo uncertainty forecasting for high dimensional
nonlinear dynamic systems. IEEE Access, 11, 12119-12138.
Vogl, G.W.,Weiss, B. A., & Helu, M. (2019). A review of diagnostic and prognostic capabilities and best practices
for manufacturing. Journal of Intelligent Manufacturing, 30(1), 79–95.
Wright, L., & Davidson, S. (2020). How to tell the difference between a model and a digital twin. Advanced Modeling
and Simulation in Engineering Sciences, 7(1), 1– 13.
Yang, C., Buck, K., & Kumar, M. (2015). An evaluation of monte carlo for nonlinear initial uncertainty propagation in keplerian mechanics. In 2015 18th international conference on information fusion (fusion) (p. 119-125).
Yang, C., & Kumar, M. (2019a). An adaptive monte carlo method for uncertainty forecasting in perturbed twobody
dynamics. Acta Astronautica, 155, 369–378.
Yang, C., & Kumar, M. (2019b). Closed-loop adaptive monte carlo framework for uncertainty forecasting in nonlinear dynamic systems. Journal of Guidance, Control, and Dynamics, 42(6), 1218-1236.
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Technical Research Papers
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