IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v230y2023ics0951832022005142.html
   My bibliography  Save this article

Probabilistic physics-informed machine learning for dynamic systems

Author

Listed:
  • Subramanian, Abhinav
  • Mahadevan, Sankaran

Abstract

This paper develops a physics-informed machine learning approach for response prediction in dynamic systems, by augmenting a physics-based model with a machine learning model for model error; both models are probabilistic. The physics-based dynamic system model has discrepancy in the predicted output (due to incomplete physics or model form error in the physics-based model) when compared against observation data. The model form error is quantified using Bayesian state estimation with observation data, and a probabilistic machine learning model is trained to predict the output discrepancy for untrained inputs. Two different computational options are developed to implement this overall approach, with different levels of sophistication and computational effort. The methods are developed for problems with stationary and non-stationary, and Gaussian and non-Gaussian random process inputs. Strategies for computational effort reduction at different stages, such as model training, model error quantification, and reliability prediction, are discussed. The proposed approach is demonstrated using two numerical illustrations: (a) a deep beam subjected to dynamic loading (a single physics system), and (b) hypersonic flow over a flexible aircraft panel (a multi-physics system).

Suggested Citation

  • Subramanian, Abhinav & Mahadevan, Sankaran, 2023. "Probabilistic physics-informed machine learning for dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
  • Handle: RePEc:eee:reensy:v:230:y:2023:i:c:s0951832022005142
    DOI: 10.1016/j.ress.2022.108899
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832022005142
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2022.108899?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kim, Wongon & Lee, Guesuk & Son, Hyejeong & Choi, Hyunhee & Youn, Byeng D., 2022. "Estimation of fatigue crack initiation and growth in engineering product development using a digital twin approach," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    2. Jiang, Chen & Vega, Manuel A. & Todd, Michael D. & Hu, Zhen, 2022. "Model correction and updating of a stochastic degradation model for failure prognostics of miter gates," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    3. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    4. Hajiha, Mohammadmahdi & Liu, Xiao & Lee, Young M. & Ramin, Moghaddass, 2022. "A physics-regularized data-driven approach for health prognostics of complex engineered systems with dependent health states," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    5. Zhang, Qiongfang & Xu, Nan & Ersoy, Daniel & Liu, Yongming, 2022. "Manifold-based Conditional Bayesian network for aging pipe yield strength estimation with non-destructive measurements," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Oster, Matthew R. & King, Ethan & Bakker, Craig & Bhattacharya, Arnab & Chatterjee, Samrat & Pan, Feng, 2023. "Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    2. Phan, Hieu Chi & Dhar, Ashutosh Sutra & Bui, Nang Duc, 2023. "Reliability assessment of pipelines crossing strike-slip faults considering modeling uncertainties using ANN models," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    3. Yang, Chen & Lu, Wanze & Xia, Yuanqing, 2023. "Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis," Reliability Engineering and System Safety, Elsevier, vol. 237(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Khakifirooz, Marzieh & Fathi, Michel & Lee, I-Chen & Tseng, Sheng-Tsaing, 2023. "Neural ordinary differential equation for sequential optimal design of fatigue test under accelerated life test analysis," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    2. Wang, Ying & Zheng, Xueke & Wang, Le & Lu, Gavin & Jia, Yixing & Li, Kezhi & Li, Mian, 2023. "Sensor fault detection of vehicle suspension systems based on transmissibility operators and Neyman–Pearson test," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    3. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    4. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    5. Xiaoyu Xiong & Benjamin D. Youngman & Theodoros Economou, 2021. "Data fusion with Gaussian processes for estimation of environmental hazard events," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    6. Petropoulos, G. & Wooster, M.J. & Carlson, T.N. & Kennedy, M.C. & Scholze, M., 2009. "A global Bayesian sensitivity analysis of the 1d SimSphere soil–vegetation–atmospheric transfer (SVAT) model using Gaussian model emulation," Ecological Modelling, Elsevier, vol. 220(19), pages 2427-2440.
    7. Drignei, Dorin, 2011. "A general statistical model for computer experiments with time series output," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 460-467.
    8. Yuan, Jun & Ng, Szu Hui, 2013. "A sequential approach for stochastic computer model calibration and prediction," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 273-286.
    9. Edward Boone & Jan Hannig & Ryad Ghanam & Sujit Ghosh & Fabrizio Ruggeri & Serge Prudhomme, 2022. "Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study," Stats, MDPI, vol. 5(4), pages 1-17, November.
    10. Abokersh, Mohamed Hany & Vallès, Manel & Cabeza, Luisa F. & Boer, Dieter, 2020. "A framework for the optimal integration of solar assisted district heating in different urban sized communities: A robust machine learning approach incorporating global sensitivity analysis," Applied Energy, Elsevier, vol. 267(C).
    11. Campbell, Katherine, 2006. "Statistical calibration of computer simulations," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1358-1363.
    12. Perrin, G., 2016. "Active learning surrogate models for the conception of systems with multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 130-136.
    13. Antony M. Overstall & David C. Woods, 2016. "Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 483-505, August.
    14. Na, Wei & Wang, Mingming, 2022. "A Bayesian approach with urban-scale energy model to calibrate building energy consumption for space heating: A case study of application in Beijing," Energy, Elsevier, vol. 247(C).
    15. Andrew White & Malachi Tolman & Howard D Thames & Hubert Rodney Withers & Kathy A Mason & Mark K Transtrum, 2016. "The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-26, December.
    16. MacKenzie, Cameron A. & Hu, Chao, 2019. "Decision making under uncertainty for design of resilient engineered systems," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    17. Huang, Xucong & Peng, Zhaoqin & Tang, Diyin & Chen, Juan & Zio, Enrico & Zheng, Zaiping, 2024. "A physics-informed autoencoder for system health state assessment based on energy-oriented system performance," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    18. Pasanisi, Alberto & Keller, Merlin & Parent, Eric, 2012. "Estimation of a quantity of interest in uncertainty analysis: Some help from Bayesian decision theory," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 93-101.
    19. White, Staci A. & Herbei, Radu, 2015. "A Monte Carlo approach to quantifying model error in Bayesian parameter estimation," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 168-181.
    20. Jun Yuan & Haowei Wang & Szu Hui Ng & Victor Nian, 2020. "Ship Emission Mitigation Strategies Choice Under Uncertainty," Energies, MDPI, vol. 13(9), pages 1-20, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:230:y:2023:i:c:s0951832022005142. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.