Document Open Access Logo

A Study on Redundancy and Intrinsic Dimension for Data-Driven Fault Diagnosis

Authors Daniel Jung , David Axelsson

PDF
Thumbnail PDF

File

OASIcs.DX.2024.4.pdf
  • Filesize: 1.06 MB
  • 17 pages

Document Identifiers

Author Details

Daniel Jung
  • Linköping University, Sweden
David Axelsson
  • Linköping University, Sweden

Funding

  • Jung, Daniel: D. Jung is partially funded by the Swedish excellence center ELLIIT.

Cite As Get BibTex

Daniel Jung and David Axelsson. A Study on Redundancy and Intrinsic Dimension for Data-Driven Fault Diagnosis. In 35th International Conference on Principles of Diagnosis and Resilient Systems (DX 2024). Open Access Series in Informatics (OASIcs), Volume 125, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/OASIcs.DX.2024.4

Abstract

Data-driven fault diagnosis of technical systems use training data from nominal and faulty operation to train machine learning models to detect and classify faults. However, data-driven fault diagnosis is complicated by the fact that training data from faults is scarce. The fault diagnosis task is often treated as a standard classification problem. There is a need for methods to design fault detectors using only nominal data. In model-based diagnosis, the ability construct fault detectors depends on analytical redundancy properties. While analytical redundancy is a model property, it describes the diagnosability properties of the system. In this work, the connection between analytical redundancy and the distribution of observations from the system on low-dimensional manifolds in the observation space is studied. It is shown that the intrinsic dimension can be used to identify signal combinations that can be used for constructing residual generators. A data-driven design methodology is proposed where data-driven residual generators candidates are identified using the intrinsic dimension. The method is evaluated using two case studies: a simulated model of a two-tank system and data collected from a fuel injection system. The results demonstrate the ability to diagnose abnormal system behavior and reason about its cause based on selected signal combinations.

Subject Classification

ACM Subject Classification
  • Computing methodologies
Keywords
  • Data-driven diagnosis
  • intrinsic dimension
  • model-based diagnosis
  • structural methods

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. A. Abid, M. Khan, and J. Iqbal. A review on fault detection and diagnosis techniques: basics and beyond. Artificial Intelligence Review, 54:3639-3664, 2021. URL: https://doi.org/10.1007/S10462-020-09934-2.
  2. N. Allansson, A. Mohammadi, D. Jung, and M. Krysander. Fuel injection fault diagnosis using structural analysis and data-driven residuals. IFAC-PapersOnLine, 58(4):360-365, 2024. Google Scholar
  3. L. Amsaleg, O. Chelly, T. Furon, S. Girard, M. Houle, K. Kawarabayashi, and M. Nett. Extreme-value-theoretic estimation of local intrinsic dimensionality. Data Mining and Knowledge Discovery, 32(6):1768-1805, 2018. URL: https://doi.org/10.1007/S10618-018-0578-6.
  4. J. Bac, E. Mirkes, A. Gorban, I. Tyukin, and A. Zinovyev. Scikit-dimension: a python package for intrinsic dimension estimation. Entropy, 23(10):1368, 2021. URL: https://doi.org/10.3390/E23101368.
  5. R. Bennett. The intrinsic dimensionality of signal collections. IEEE Transactions on Information Theory, 15(5):517-525, 1969. URL: https://doi.org/10.1109/TIT.1969.1054365.
  6. F. Camastra and A. Staiano. Intrinsic dimension estimation: Advances and open problems. Information Sciences, 328:26-41, 2016. URL: https://doi.org/10.1016/J.INS.2015.08.029.
  7. X. Dai and Z. Gao. From model, signal to knowledge: A data-driven perspective of fault detection and diagnosis. IEEE Transactions on Industrial Informatics, 9(4):2226-2238, 2013. URL: https://doi.org/10.1109/TII.2013.2243743.
  8. D. Eriksson, E. Frisk, and M. Krysander. A method for quantitative fault diagnosability analysis of stochastic linear descriptor models. Automatica, 49(6):1591-1600, 2013. URL: https://doi.org/10.1016/J.AUTOMATICA.2013.02.045.
  9. M. Fan, N. Gu, H. Qiao, and B. Zhang. Intrinsic dimension estimation of data by principal component analysis. arxiv. Preprint]. doi, 10, 2010. Google Scholar
  10. E. Frisk, M. Krysander, and D. Jung. A toolbox for analysis and design of model based diagnosis systems for large scale models. IFAC-PapersOnLine, 50(1):3287-3293, 2017. Google Scholar
  11. E. Frisk and M. Nyberg. A minimal polynomial basis solution to residual generation for fault diagnosis in linear systems. Automatica, 37(9):1417-1424, 2001. URL: https://doi.org/10.1016/S0005-1098(01)00078-4.
  12. K. Fukunaga and D. Olsen. An algorithm for finding intrinsic dimensionality of data. IEEE Transactions on computers, 100(2):176-183, 1971. URL: https://doi.org/10.1109/T-C.1971.223208.
  13. G. Haro, G. Randall, and G. Sapiro. Translated poisson mixture model for stratification learning. International Journal of Computer Vision, 80:358-374, 2008. URL: https://doi.org/10.1007/S11263-008-0144-6.
  14. T. Hastie, R. Tibshirani, and J. Friedman. The elements of statistical learning: data mining, inference, and prediction, 2017. Google Scholar
  15. D. Jung. Isolation and localization of unknown faults using neural network-based residuals. In Annual Conference of the PHM Society, volume 11, 2019. Google Scholar
  16. D. Jung, M. Krysander, and A. Mohammadi. Fault diagnosis using data-driven residuals for anomaly classification with incomplete training data. IFAC-PapersOnLine, 56(2):2903-2908, 2023. Google Scholar
  17. M. Krysander, J. Åslund, and M. Nyberg. An efficient algorithm for finding minimal overconstrained subsystems for model-based diagnosis. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 38(1):197-206, 2007. URL: https://doi.org/10.1109/TSMCA.2007.909555.
  18. M. Krysander and E. Frisk. Sensor placement for fault diagnosis. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 38(6):1398-1410, 2008. URL: https://doi.org/10.1109/TSMCA.2008.2003968.
  19. E. Levina and P. Bickel. Maximum likelihood estimation of intrinsic dimension. Advances in neural information processing systems, 17, 2004. Google Scholar
  20. L. Ljung. System identification (2nd ed.): theory for the user. Prentice Hall PTR, USA, 1999. Google Scholar
  21. A. Mohammadi, M. Krysander, and D. Jung. Analysis of grey-box neural network-based residuals for consistency-based fault diagnosis. IFAC-PapersOnLine, 55(6):1-6, 2022. Google Scholar
  22. A. Rehman, W. Jiao, J. Sun, H. Pan, and T. Yan. Open set recognition methods for fault diagnosis: A review. In 2023 15th International Conference on Advanced Computational Intelligence (ICACI), pages 1-8. IEEE, 2023. Google Scholar
  23. W. Rheinboldt. On the computation of multi-dimensional solution manifolds of parametrized equations. Numerische Mathematik, 53(1):165-181, 1988. Google Scholar
  24. C. Sankavaram, A. Kodali, K. Pattipati, and S. Singh. Incremental classifiers for data-driven fault diagnosis applied to automotive systems. IEEE access, 3:407-419, 2015. URL: https://doi.org/10.1109/ACCESS.2015.2422833.
  25. A. Savitzky and M. Golay. Smoothing and differentiation of data by simplified least squares procedures. Analytical chemistry, 36(8):1627-1639, 1964. Google Scholar
  26. A. Theissler, J. Pérez-Velázquez, M. Kettelgerdes, and G. Elger. Predictive maintenance enabled by machine learning: Use cases and challenges in the automotive industry. Reliability engineering & system safety, 215:107864, 2021. URL: https://doi.org/10.1016/J.RESS.2021.107864.
  27. L. Travé-Massuyès. Bridging control and artificial intelligence theories for diagnosis: A survey. Engineering Applications of Artificial Intelligence, 27:1-16, 2014. URL: https://doi.org/10.1016/J.ENGAPPAI.2013.09.018.
  28. M. Verleysen and D. François. The curse of dimensionality in data mining and time series prediction. In International work-conference on artificial neural networks, pages 758-770. Springer, 2005. Google Scholar
  29. Y. Xu, S. Kohtz, J. Boakye, P. Gardoni, and P. Wang. Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges. Reliability Engineering & System Safety, 230:108900, 2023. URL: https://doi.org/10.1016/J.RESS.2022.108900.
  30. Z. Xu and J. Saleh. Machine learning for reliability engineering and safety applications: Review of current status and future opportunities. Reliability Engineering & System Safety, 211:107530, 2021. URL: https://doi.org/10.1016/J.RESS.2021.107530.
  31. T. Zhang, J. Chen, F. Li, K. Zhang, H. Lv, S. He, and E. Xu. Intelligent fault diagnosis of machines with small & imbalanced data: A state-of-the-art review and possible extensions. ISA transactions, 119:152-171, 2022. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact