Monte Carlo uncertainty analysis of an ANN-based spectral analysis method

  • José Ramón SalinasEmail author
  • Francisco García-Lagos
  • Javier Diaz de Aguilar
  • Gonzalo Joya
  • Francisco Sandoval
IWANN2017: Learning algorithms with real world applications


This work presents the uncertainty analysis of an artificial neural network (ANN)-based method, called multiharmonic ANN fitting method (MANNFM), which is able to obtain, at a metrological level, the spectrum of asynchronously sampled periodical signals. For sinusoidal and harmonic content signals, jitter and quantization noise contributions to uncertainty are considered in order to obtain amplitude and phase uncertainties using Monte Carlo method. The analysis performed identifies also both contributions to uncertainty for different parameters laboratory configurations. The analysis is performed simultaneously with our method and two others: discrete Fourier transform (DFT), for synchronously sampled signals, and multiharmonic sine-fitting method (MSFM), for asynchronously sampled signals, in order to compare them in terms of uncertainty. Regarding asynchronous methods, results show that MANNFM provides the same uncertainties than MSFM, with the advantage of a simpler implementation. Regarding asynchronous and synchronous methods comparison, results for sinusoidal signals show that MANNFM has the same uncertainty as DFT for amplitude and higher uncertainty for phase values; for signals with harmonic content, amplitude conclusions maintain but, regarding phase, both MANNFM and DFT uncertainties become closer as the frequency increases, which implies, in fact, that when synchronous sampling is not possible, spectrum analysis can be performed with asynchronous methods without incurring in uncertainty increases.


Sine-fitting methods Spectral analysis ADALINE Digital measurement Uncertainty Monte Carlo 



This work was partially supported by the Universidad de Malaga - Campus de Excelencia Andalucia-Tech.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Svensson S (1999) Power measurement techniques for nonsinusoidal conditions. Doctoral Thesis, Chalmers University of Technology, SwedenGoogle Scholar
  2. 2.
    Wright PS (1994) Traceability in power/reactive power measurements and assessment tests for ‘IEC555 power analyzers’, using the NPL Mk.III digital sampling wattmeter. IEE Colloquium on Low Frequency Power Measurement and Analysis (Digest No. 1994/203), pp. 1/1–1/6Google Scholar
  3. 3.
    Oppenheim AV, Schafer RW (1999) Discrete-time signal processing. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar
  4. 4.
    Pogliano U (2001) Use of integrative analog-to-digital converters for high-precision measurement of electrical power. IEEE Trans Instrum Meas 50(5):1315–1318CrossRefGoogle Scholar
  5. 5.
    Salinas JR, Lagos FG, Joya G, Sandoval F (2006) New Spanish electrical power standard. In: MELECON 2006—2006 IEEE Mediterranean electrotechnical conference, Malaga, Spain, pp 994–997Google Scholar
  6. 6.
    IEEE standard 1241, 2010 (2010) Waveform Measurement and Analysis Technical committee, IEEE Standard for Terminology and Test Methods for Analog-to-Digital ConvertersGoogle Scholar
  7. 7.
    Ramos PM, Cruz Serra A (2007) Least squares multiharmonic fitting: convergence improvements. IEEE Transactions on Instrumentation and Measurement 56(4):1412–1418CrossRefGoogle Scholar
  8. 8.
    Salinas JR, García-Lagos F, Joya G, Sandoval F (2009) Sine fitting multiharmonic algorithms implemented by artificial neural networks. Neurocomputing 72(16–18):3640–3648CrossRefGoogle Scholar
  9. 9.
    Salinas JR, Lagos FG, Romero ML, Joya G, Raso F, Neira M, Sandoval F (2006) Versatile digital system for high accuracy power measurements. In: Conference on precision electromagnetic measurements (CPEM 2006), pp 98–99Google Scholar
  10. 10.
    Salinas JR, Díaz de Aguilar J, García-Lagos F, Joya G, Sandoval F, Romero ML (2014) Spectrum analysis of asynchronously sampled signals by means of an ANN method. In: Conference on precision electromagnetic measurements (CPEM 2014), pp 422–423Google Scholar
  11. 11.
    Salinas JR, García-Lagos F, de Aguilar JD, Joya G, Lapuh R, Sandoval F (2016) Harmonics and interharmonics spectral analysis by ANN. In: 2016 conference on precision electromagnetic measurements (CPEM 2016), Ottawa, Canada, pp 1–2Google Scholar
  12. 12.
    Salinas JR, García-Lagos F, de Aguilar JD, Joya G, Sandoval F (2017) Uncertainty analysis of ANN-based spectral analysis using monte carlo method. In: Rojas I, Joya G, Catala A (eds) Advances in computational intelligence, IWANN 2017, Lecture Notes in Computer Science, vol 10305. Springer, Cham, pp 269–280Google Scholar
  13. 13.
    JGCM 100:2008. Evaluation of measurement data –Guide to the expression of uncertainty in measurementGoogle Scholar
  14. 14.
    JGCM 101:2008. Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement”—Propagation of distributions using a Monte Carlo methodGoogle Scholar
  15. 15.
    JGCM 102:2011. Evaluation of measurement data—Supplement 2 to the “Guide to the expression of uncertainty in measurement”—Extension to any number of output quantitiesGoogle Scholar
  16. 16.
    Šíra M, Mašláň S (2014) Uncertainty analysis of non-coherent sampling phase meter with four parameter sine wave fitting by means of Monte Carlo. In: 29th conference on precision electromagnetic measurements (CPEM 2014), Rio de Janeiro, pp 334–335Google Scholar
  17. 17.
    Wadgy MF (1987) Effects of ADC quantization errors on some periodic signal measurements. IEEE Trans Instrum Meas 36(4):983–988Google Scholar
  18. 18.
    Wagdy MF, Awad SS (1990) Effect of sampling jitter on some sine wave measurements. IEEE Trans Instrum Meas 39(1):86–89CrossRefGoogle Scholar
  19. 19.
    Jain VK, Collins WL, Davis DC (1979) High-accuracy analog measurements via interpolated FFT. IEEE Trans Instrum Meas 28(2):113–122CrossRefGoogle Scholar
  20. 20.
    EN 50470-3:2006. Electricity metering equipment (a.c.)—Part 3: particular requirements—static meters for active energy (class indexes A, B and C)Google Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Grupo ISIS, Dpto. Tecnología Electrónica, ETSI TelecomunicaciónUniversidad de MálagaMálagaSpain
  2. 2.Centro Español de Metrología (CEM)Tres CantosSpain

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