Evaluation of the type a uncertainty caused by simultaneous influence of random noise and power line interference
DOI:
https://doi.org/10.24425/mms.2025.154340Abstract
The paper presents the type A evaluation of standard uncertainty when the result of measurement is determined by digital averaging of the input signal which is distorted by simultaneous influence of the random uncorrelated noise and power line interference. It was shown that the classical evaluation of uncertainty based on determining of the standard deviation of input observations is not sufficient, because it does not take into account the effect of suppression of the interference by averaging. To correctly evaluate uncertainty, both the amplitude of the interference component and the standard deviation of the random component should be estimated separately. Simple methods of separate estimation of these components are proposed and analysed in detail. The proposed solutions to the uncertainty evaluation were studied when uniform and triangle averaging were used and verified both by Monte Carlo simulations and by experimental tests. The simulation and test results obtained showed very good accordance with theoretical results.References
[1] Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data - Guide to the expression of uncertainty in measurement (JCGM 100:2008). http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf
[2] Keithley (2013). Low Level Measurements Handbook - 7th Edition.
[3] Gerard C.M. Meijer (Ed.). (2008). Smart Sensor Systems. John Wiley and Sons Ltd. https://doi.org/10.1002/9780470866931
[4] Hasse, L., Kołodziejski, J., Konczałowska, A., Spiralski, L. (1995) Zakłócenia w aparaturze elektronicznej. Radioelektronik. (in Polish)
[5] Hyungsuk, K., Chung-Ping Chen, C., (2001) Be Careful of Self and Mutual Inductance Formulae. Technical Report University of Wisconsin-Madison. http://ccf.ee.ntu.edu.tw/~cchen/research/CompInduct9.pdf
[6] National Instruments Corp. (2023, Aug 4). Field Wiring and Noise Considerations for Analog Signals. https://www.ni.com/en/shop/data-acquisition/measurement-fundamentals/field-wiring-and-noise-considerations-for-analog-signals
[7] CENELEC. (1999). Voltage characteristics of electricity supplied by public distribution systems (IEC/EN 50160:1999).
[8] Mindykowski, J., Tarasiuk, T., Szmit, E., & Czarkowski, D. (2006). Diagnostyka izolowanego systemu elektroenergetycznego na przykładzie jednostki pływającej. Diagnostyka’2, 38, 171-176. (in Polish).
[9] Mathur, P., & Raman, S. (2020). Electromagnetic Interference (EMI): measurement and reduction techniques. Journal of Electronic Materials, 49(5), 2975-2998. https://doi.org/10.1007/s11664-020-07979-1
[10] Lucca, G. (2022). 50-60 Hz electromagnetic interference generated by power lines under fault condition: some probabilistic considerations. Electrical Engineering, 104(5), 3487-3496. https://doi.org/10.1007/s00202-022-01568-7
[11] Cohen, M.B., Said, R.K., & Inan, U.S. (2010). Mitigation of 50-60 Hz power line interference in geophysical data. Radio Science, 45(6). https://doi.org/10.1029/2010rs004420
[12] Ponnle, A.A. (2022). Measurement and Assessment of Exposure to 50 Hz Magnetic Fields from Common Home Electrical Appliances. European Journal of Engineering and Technology Research, 7(3), 119-127. https://doi.org/10.24018/ejeng.2022.7.3.2832
[13] National Instruments Corp. (2023, Aug 4). Eliminating Powerline Noise from DC Measurements in NI Software. https://knowledge.ni.com/KnowledgeArticleDetails?id=kA00Z000000P9oBSAS&l=pl-PL
[14] Vale-Cardoso, A.S., & Guimarães, H.N. (2009). The effect of 50/60 Hz notch filter application on human and rat ECG recordings. Physiological Measurement, 31(1), 45-58. https://doi.org/10.1088/0967-3334/31/1/004
[15] Tan, L., & Jiang, J. (2018). Introduction to digital signal processing. In Digital Signal Processing - 3rd Edition (pp. 1-12). https://doi.org/10.1016/b978-0-12-815071-9.00001-4
[16] Strzecha, K., Krakós, M., Więcek, B., Chudzik, P., Tatar, K., Lisowski, G., Mosorov, V., & Sankowski, D. (2021). Processing of EMG Signals with High Impact of Power Line and Cardiac Interferences. Applied Sciences, 11(10), 4625. https://doi.org/10.3390/app11104625
[17] Poularikas, A.D. (1999) Handbook of Formulas and Tables for Signal Processing. CRC Press LLC. https://link.springer.com/book/9783540648345
[18] Zygarlicki, J., Zygarlicka, M., & Mroczka, J. (2020). Fast four-point estimators of sinusoidal signal parameters - numerical optimisations for embedded measuring systems. Metrology and Measurement Systems. 27(3), 465-472. https://doi.org/10.24425/mms.2020.132782
[19] Sienkowski, S., & Krajewski, M. (2023). Single-tone frequency estimation based on reformed covariance for half-length autocorrelation. Metrology and Measurement Systems. 27(3), 473-493. https://doi.org/10.24425/mms.2020.134590
[20] Duda, K., & Zieliński, T. (2023). Fast one-cycle frequency estimation of a single sinusoid in noise using downsampled linear prediction model. Metrology and Measurement Systems. 28(4), 661-672, https://doi.org/10.24425/mms.2021.137701
[21] Kern, G.A., & Korn, T.M. (1968). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. McGraw-Hill.
[22] Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data - Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement” - propagation of distributions using a Monte Carlo method (JCGM 101: 2008). https://www.bipm.org/documents/20126/2071204/JCGM_101_2008_E.pdf
[23] National Instruments Corp. (n.d.) NI-9222. https://www.ni.com/en-us/shop/model/ni-9222.html