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1887
Volume 69, Issue 2
  • ISSN: 2056-5135

Abstract

Industry 4.0 is built upon the foundations of converting real world analogue effects into digitised binary data suitable for a computer to process. This needs to be done with care, particularly when the data is ingested by a safety critical system. A numerical study probing the limits of a typical analogue to digital converter (ADC) is presented here, highlighting some potential issues that should be identified. Initially a Monte Carlo approach is used to probe the impact of digitisation on an ADC using traditional experimental error analysis. A constant test signal 2.5 ± 0.01 V is used to understand the optimum level of digitisation. The analogue signal is assumed to have Gaussian noise which is then processed by a 5 V ADC. This investigation suggests an optimum digitisation level should be related to the standard error of a measured signal. The use of Bayesian inferencing using the Python package PyMC is then used to gain a better estimate of the underlying standard deviation when the signal has been digitised at the 8-bit level.

This is an Open Access article distributed in accordance with the Creative Commons Attribution (CC BY 4.0) license. You are free to: share: copy and redistribute the material in any medium or format; adapt: remix, transform, and build upon the material for any purpose, even commercially. Under the following terms: attribution: you must give appropriate credit, provide a link to the license, and indicate if changes were made. See: https://creativecommons.org/licenses/by/4.0/
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2025-04-01
2025-04-15
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References

  1. P. Horowitz, W. Hill, “The Art of Electronics”, 3rd Edn., Cambridge University Press, New York, USA, 2015, 1192 pp
  2. R. H. Walden, IEEE J. Select. Areas Commun., 1999, 17, (4), 539 LINK https://doi.org/10.1109/49.761034
    [Google Scholar]
  3. M. J. M. Pelgrom, ‘Analog-to-Digital Conversion’, in “Analog-to-Digital Conversion”, 2nd Edn., Springer Science and Business Media, New York, USA, 2012, pp. 325418 LINK https://doi.org/10.1007/978-1-4614-1371-4_8
    [Google Scholar]
  4. J. Kim, T.-K. Jang, Y.-G. Yoon, S. Cho, IEEE Trans. Circuits Syst. I: Regul. Pap., 2010, 57, (1), 18 LINK https://doi.org/10.1109/tcsi.2009.2018928
    [Google Scholar]
  5. D. Chen, X. Cui, Q. Zhang, D. Li, W. Cheng, C. Fei, Y. Yang, Micromachines, 2022, 13, (1), 114 LINK https://doi.org/10.3390/mi13010114
    [Google Scholar]
  6. L. F. Rahman, F. A. Rudham, M. B. I. Reaz, M. Marufuzzaman, ‘The Evolution of Digital to Analog Converter’, International Conference on Advances in Electrical, Electronic and Systems Engineering (ICAEES), 14th–16th November, 2016, Putrajaya, Malaysia, The Institute of Electrical and Electronics Engineers Inc, New York, USA, 2016, pp. 151154 LINK https://doi.org/10.1109/icaees.2016.7888028
    [Google Scholar]
  7. M. Jorge, C. Ismael, R. Bibiano, S. Manuel, P. Mario, Future Gener. Comput. Syst., 2016, 63, 123 LINK https://doi.org/10.1016/j.future.2015.11.024
    [Google Scholar]
  8. H. Y. Teh, A. W. Kempa-Liehr, K. I.-K. Wang, J. Big Data, 2020, 7, 11 LINK https://doi.org/10.1186/s40537-020-0285-1
    [Google Scholar]
  9. C. Babbage, “Passages from the Life of a Philosopher”, Longman, Green, Longman, Roberts & Green, London, UK, 1864
  10. J. C. Damasceno, P. R. G. Couto, ‘Methods for Evaluation of Measurement Uncertainty’, in “Metrology”, ed. Anil, ch. 2, IntechOpen, London, UK, 2018, pp. 1028 LINK https://doi.org/10.5772/intechopen.74873
    [Google Scholar]
  11. N. C. Barford, “Experimental Measurements and Precision, Error and Truth”, Addison-Wesley Publishers, London, UK, 1967
  12. D. Goldberg, ACM Comput. Surv., 1991, 23, (1), 5 LINK https://doi.org/10.1145/103162.103163
    [Google Scholar]
  13. M. Templeton, T. Rowe, O. Slotosch, M. Parsons, P. Hampton, “Data Safety Guidance v 3.5”, ed. M. Templeton, The Safety-Critical Systems Club, The Data Safety Initiative Working Group, USA, January, 2023, 224 pp
    [Google Scholar]
  14. D. J. Smith, K. G. L. Simpson, ‘Meeting IEC 61508 Part 2’, in “The Safety Criticial Systems Handbook”, 5th Edn., Elsevier, Oxford, UK, 2020, pp. 5576 LINK https://doi.org/10.1016/b978-0-12-820258-6.00003-6
    [Google Scholar]
  15. M. Rausand, “Reliability of Safety-Critical Systems: Theory and Applications”, John Wiley & Sons Inc, Hoboken, New Jersey, USA, 2014, 466 pp LINK https://doi.org/10.1002/9781118776353
  16. L. E. G. Martins, T. Gorschek, Inf. Softw. Technol., 2016, 75, 71 LINK https://doi.org/10.1016/j.infsof.2016.04.002
    [Google Scholar]
  17. I. Cameron, S. Mannan, E. Németh, S. Park, H. Pasman, W. Rogers, B. Seligmann, Process Saf. Environ. Prot., 2017, 110, 53 LINK https://doi.org/10.1016/j.psep.2017.01.025
    [Google Scholar]
  18. D. J. Hand, “Dark Data: Why What You Don’t Know Matters”, Princeton University Press, Princeton, New Jersey, USA, 2020, 344 pp LINK https://doi.org/10.1515/9780691198859
  19. M. Templeton, T. Rowe, O. Slotosch, M. Parsons, P. Hampton, ‘Appendix K: Dark Data and Safety (Informative)’, in “Data Safety Guidance v3.5”, ed. M. Templeton, The Safety-Critical Systems Club, The Data Safety Initiative Working Group, USA, January, 2023, pp. 141148
    [Google Scholar]
  20. M. Templeton, T. Rowe, O. Slotosch, M. Parsons, P. Hampton, ‘Appendix L: Dazzle Data and Safety (Informative)’, in “Data Safety Guidance v3.5”, ed. M. Templeton, The Safety-Critical Systems Club, The Data Safety Initiative Working Group, USA, January, 2023, pp. 149156
    [Google Scholar]
  21. L. Bengtsson, ‘ADCs and Sampling’, in “Electrical Measurement Techniques”, Springer Nature, Singapore, 2024, pp. 229265 LINK https://doi.org/10.1007/978-981-99-8187-8_11
    [Google Scholar]
  22. M. Templeton, T. Rowe, O. Slotosch, M. Parsons, P. Hampton, ‘Ways that Data Can Cause Problems’, in “Data Safety Guidance v3.5”, ed. M. Templeton, ch. 6.2.2, The Safety-Critical Systems Club, The Data Safety Initiative Working Group, USA, January, 2023, pp. 24
    [Google Scholar]
  23. C. H., J. Am. Stat. Assoc., 1964, 59, (308), 1324 LINK https://doi.org/10.2307/2282672
    [Google Scholar]
  24. E. W. Weisstein, ‘Bessel’s Correction’, MathWorld–A Wolfram Web Resource, Wolfram Research, Inc, Illinois, USA: https://mathworld.wolfram.com/BesselsCorrection.html (Accessed on 24th April 2023)
    [Google Scholar]
  25. R. J. Barlow, “Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences”, eds. F. Mandl, R. J. Ellison, D. J. Sandiford, The Manchester Physics Series, John Wiley and Sons Ltd, West Sussex, UK, 1989, 240 pp
    [Google Scholar]
  26. E. T. Jaynes, “Probability Theory: The Logic of Science”, eds. G. L. Bretthorst, Cambridge University Press, Cambridge, UK, 2003, 727 pp LINK https://doi.org/10.1017/cbo9780511790423
  27. J. P. Kaipio, E. Somersalo, “Statistical and Computational Inverse Problems”, eds. S. S. Antman, J. E. Marsden, L. Sirovich, Applied Mathematical Sciences Series, Springer Science+Business Media Inc, New York, USA, 2005, 340 pp LINK https://doi.org/10.1007/b138659
    [Google Scholar]
  28. S. Malefaki, G. Iliopoulos, Comput. Stat. Data Anal., 2007, 51, (12), 5471 LINK https://doi.org/10.1016/j.csda.2007.03.022
    [Google Scholar]
  29. J. Salvatier, T. V. Wiecki, C. Fonnesbeck, PeerJ Comput. Sci., 2016, 2, e55 LINK https://doi.org/10.7717/peerj-cs.55
    [Google Scholar]
  30. C. Read, “Logic, Deductive and Inductive”, Grant Richards, 1898
  31. P. Martin, Solstice, 2004, 15, (2)
    [Google Scholar]
  32. A. E. Summers, J. Hazard. Mater., 2003, 104, (1–3), 163 LINK https://doi.org/10.1016/S0304-3894(03)00242-5
    [Google Scholar]
  33. R. J. Willey, Procedia Eng., 2014, 84, 12 LINK https://doi.org/10.1016/j.proeng.2014.10.405
    [Google Scholar]
  34. A. M. Dowell III, ISA Trans., 1998, 37, (3), 155 LINK https://doi.org/10.1016/S0019-0578(98)00018-4
    [Google Scholar]
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