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2025 | OriginalPaper | Chapter

5. Statistical Assessment of Diagnostic Parameters

Authors : Vitalii Babak, Sergii Babak, Artur Zaporozhets

Published in: Statistical Diagnostics of Electric Power Equipment

Publisher: Springer Nature Switzerland

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Abstract

This chapter presents a comprehensive exploration of statistical methods for the estimation and analysis of diagnostic signals in a variety of contexts, ranging from spectral analysis to parameter estimation and hypothesis testing. Beginning with numerical parameters of diagnostic signals, the discussion extends to spectral correlation analysis, focusing on the calculation of moments, the power spectral density, and the correlation function from signal samples. The utilization of the Goertzel algorithm for efficient spectral density estimation highlights the chapter's contribution to spectral analysis techniques. Further, the application of Pearson's system of curves for empirical data distribution approximation underscores the chapter’s innovative approach to statistical analysis. The extract also delves into stationarity testing methods (F-test, t-test, and Kolmogorov–Smirnov test) critical for diagnostic reliability and defect identification, illustrating the chapter's diagnostic focus. In addressing statistical hypothesis testing, the chapter introduces a method based on the maximum likelihood principle for distinguishing hypotheses about the parameters of a multidimensional Gaussian distribution, demonstrating the chapter's depth in statistical methodology. Lastly, it explores the use of the Neyman-Pearson criterion in planning diagnostic tests, offering a practical framework for hypothesis distinction regarding system states. This exploration underscores the chapter’s significant contribution to both the theoretical and practical aspects of diagnostic signal analysis, providing valuable insights and methods for researchers and practitioners in the field.

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Babak, V., Eremenko, V., Zaporozhets, A.: Research of diagnostic parameters of composite materials using Johnson distribution. Int. J. Comput. 18(4), 483–494 (2019)CrossRef

Eremenko, V., Zaporozhets, A., Isaienko, V., Babikova, K.: Application of wavelet transform for determining diagnostic signs. In: Proceedings of the 15th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, vol. 1, pp. 12–15 (2019)

Zaporozhets, A.A., Eremenko, V.S., Serhiienko, R.V., Ivanov, S.A.: Development of an intelligent system for diagnosing the technical condition of the heat power equipment. In: 2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT), vol. 1, pp. 48–51. IEEE (2018)

Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M.: Technical provision of diagnostic systems. Diagnostic Syst. Energy Equipm. 91–133 (2020)

Furse, C.M., Kafal, M., Razzaghi, R., Shin, Y.J.: Fault diagnosis for electrical systems and power networks: a review. IEEE Sens. J. 21(2), 888–906 (2020)CrossRef

Gyzhko, Y., Myslovych, M., Sysak, R.: To use of spectral windows in analysis of vibration signals. Przeglad Electrotechnichny 89(2A), 294–296 (2013)

Tytarenko, V., Tychkov, D., Bilokin, S., Bondarenko, M., Andriienko, V.: Development of a simulation model of an information-measuring system of electrical characteristics of the functional coatings of electronic devices. Math. Model. 4(2), 68–71 (2020)

Tymchuk, S.O., Abramenko, I.G., Zahumenna, K.V., Miroshnyk, O.O., Shchur, T.G., Tomporowski, A., Kruszelnicka, W.: Determination of the discretion interval of the temporal series of the technological process parameter measurement in ACS TP in the noises conditions. In Journal of Physics: Conference Series, vol. 1781, No. 1, p. 012017. IOP Publishing (2021)

Tempelman, A.: Generalization of the Glivenko-Cantelli theorem to finite-dimensional distributions of ergodic homogeneous random fields. Statist. Probab. Lett. 195, 109767 (2023)MathSciNetCrossRef

10.

Babak, V., Zaporozhets, A., Kuts, Y., Myslovych, M., Fryz, M., Scherbak, L.: Models and characteristics of identification of noise stochastic signals of research objects. In: CEUR Workshop Proceedings, vol. 3309, pp. 349–362 (2022)

11.

Babak, V., Scherbak, L., Kuts, Y., Zaporozhets, A.: Information and measurement technologies for solving problems of energy informatics. In: The 1st International Workshop on Information Technologies: Theoretical and Applied Problems 2021. CEUR Workshop Proceedings, vol. 3039, pp. 24–31 (2021)

12.

Khanıev, T.A., Unver, İ., Maden, S.: On the semi-Markovian random walk with two reflecting barriers (2001)

13.

Liu, T., Zhang, B., Hu, G., Bai, Z.: Revisit of Sheppard corrections in linear regression. SCIENCE CHINA Math. 53, 1435–1451 (2010)MathSciNetCrossRef

14.

Stuart, A., Ord, K.: Kendall's advanced theory of statistics, distribution theory, vol. 1. John Wiley & Sons (2010)

15.

Lal-Jadziak, J.: Accuracy in determination of correlation functions by digital methods. Metrol. Measur. Syst. 8(2), 153–163 (2001)

16.

Murray, L.L., Bellhouse, D.R.: WF Sheppard’s correspondence with Karl Pearson and the development of his tables and moment estimates. Hist. Math. 53, 108–117 (2020)CrossRef

17.

La ïb, N., & Ould-Sa ÏD, E.: A robust nonparametric estimation of the autoregression function under an ergodic hypothesis. Canad. J. Statist. 28(4), 817–828 (2000)MathSciNetCrossRef

18.

Higgins, C.W., Katul, G.G., Froidevaux, M., Simeonov, V., Parlange, M.B.: Are atmospheric surface layer flows ergodic? Geophys. Res. Lett. 40(12), 3342–3346 (2013)CrossRef

19.

Loh, I. Approximation with ergodic processes and testability. J. Appl. Probabil. 1–20 (2024)

20.

Zhao, H., Wu, Z.: Statistical Estimation of Uncertainty in Surface Duct Parameters Inversion. In: 2018 12th International Symposium on Antennas, Propagation and EM Theory (ISAPE), pp. 1–4. IEEE (2018)

21.

Babak, S., Babak, V., Zaporozhets, A., Sverdlova, A.: Method of statistical spline functions for solving problems of data approximation and prediction of objects state. In Proceedings of the Second International Workshop on Computer Modeling and Intelligent Systems (CMIS-2019), Zaporizhzhia, Ukraine, April, pp. 15–19 (2019)

22.

Babak, V., Zaporozhets, A., Kuts, Y., Scherbak, L., Eremenko, V.: Application of material measure in measurements: theoretical aspects. In: Systems, Decision and Control in Energy II, pp. 261–269. Springer International Publishing, Cham (2021)CrossRef

23.

Ruzgas, T., Lukauskas, M., Čepkauskas, G.: Nonparametric multivariate density estimation: case study of cauchy mixture model. Mathematics 9(21), 2717 (2021)CrossRef

24.

Kaipio, J.P., Somersalo, E.: Statistical inversion theory. Statistical Comput. Inverse Probl. 49–114 (2005)

25.

Lupenko, S.A., Osukhivska, H.M., Lutsyk, N.S., Stadnyk, N.B., Zozulia, A.M., Shablii, N.R.: The comparative analysis of mathematical models of cyclic signals structure and processes. Sci. J. TNTU 82(2), 115–127 (2016)

26.

Lupenko, S.: The mathematical model of cyclic signals in dynamic systems as a cyclically correlated random process. Mathematics 10(18), 3406 (2022)CrossRef

27.

Motai, Y.: Data-Variant Kernel Analysis. John Wiley & Sons (2015)CrossRef

28.

Babak, V., Zaporozhets, A., Kovtun, S., Myslovych, M., Kuts, Y., Scherbak, L.: Information support for identification of the technical state of electric power facilities. In: Systems, Decision and Control in Energy V, pp. 129–153. Springer Nature Switzerland, Cham (2023)

29.

Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O.: Models and measures for the diagnosis of electric power equipment. Models Meas. Measurem. Monit. 99–126 (2021)

30.

Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M.: Methods and models for information data analysis. Diagn. Syst. Energy Equipments 23–70 (2020)

31.

Burdzik, R., Konieczny, Ł.: Diagnosing of shock-absorbers of car vehicles at changeable pressure in tires. Diagnostyka, 27–32 (2009)

32.

Cholewa, W., Korbicz, J., Moczulski, W., Timofiejczuk, A.: Methods of signal analysis. Fault Diagnosis: Models, Artif. Intell. Appl. 119–153 (2004)

33.

Kobayashi, H., Mark, B.L., Turin, W.: Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance. Cambridge University Press (2011)CrossRef

34.

Xu, Y., Hespanha, J.P.: Estimation under uncontrolled and controlled communications in networked control systems. In: Proceedings of the 44th IEEE Conference on Decision and Control, pp. 842–847. IEEE (2005)

35.

Hurd, H.L., Miamee, A.: Periodically Correlated Random Sequences: Spectral Theory and Practice, vol. 355. John Wiley & Sons (2007)

36.

Zaporozhets, A.O.: Correlation analysis between the components of energy balance and pollutant emissions. Water Air Soil Pollut. 232, 1–22 (2021)CrossRef

37.

Lucor, D., Su, C.H., Karniadakis, G.E.: Generalized polynomial chaos and random oscillators. Int. J. Numer. Meth. Eng. 60(3), 571–596 (2004)MathSciNetCrossRef

38.

Gray, R.M., Davisson, L.D.: An Introduction to Statistical Signal Processing. Cambridge University Press (2004)CrossRef

39.

Randall, R.B., Antoni, J., Chobsaard, S.: The relationship between spectral correlation and envelope analysis in the diagnostics of bearing faults and other cyclostationary machine signals. Mech. Syst. Signal Process. 15(5), 945–962 (2001)CrossRef

40.

Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M.: Simulation and software for diagnostic systems. Diagnostic Syst. Energy Equipments 71–90 (2020)

41.

Zaporozhets, A., Eremenko, V., Isaenko, V., Babikova, K.: Approach for creating reference signals for detecting defects in diagnosing of composite materials. In: Conference on Computer Science and Information Technologies, pp. 154–172. Springer International Publishing, Cham (2019)

42.

Isermann, R.: Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance. Springer Science & Business Media (2006)

43.

Antoni, J., Randall, R.B.: The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines. Mech. Syst. Signal Process. 20(2), 308–331 (2006)CrossRef

44.

Jardine, A.K., Lin, D., Banjevic, D.: A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mech. Syst. Signal Process. 20(7), 1483–1510 (2006)CrossRef

45.

Li, Y.Y., Lee, Y.W., Ho, T.S., Wei, R.T., Lai, P.Y., Jao, K.S., Huang, S.L.: Interferometry based EUV spectrometer. IEEE Photonics J. 9(4), 1–8 (2017)

46.

Marwan, N., Braun, T.: Power spectral estimate for discrete data. Chaos: an Interdisciplinary J. Nonlinear Sci. 33(5) (2023)

47.

Verma, N.K., Singh, S., Gupta, J.K., Sevakula, R.K., Dixit, S., Salour, A.: Smartphone application for fault recognition. In: 2012 Sixth International Conference on Sensing Technology (ICST), pp. 1–6. IEEE (2012)

48.

Torcal-Milla, F.J., Lobera, J., Lopez, A.M., Palero, V., Andres, N., Arroyo, M.P.: Mach-Zehnder-based measurement of light emitting diodes temporal coherence. Optik 267, 169722 (2022)CrossRef

49.

Tomashin, A., Leonardi, G., Wallot, S.: Four methods to distinguish between fractal dimensions in time series through recurrence quantification analysis. Entropy 24(9), 1314 (2022)MathSciNetCrossRef

50.

Newland, D.E.: An introduction to random vibrations, spectral and wavelet analysis. Courier Corporation (2012)

51.

Grimmett, G., Stirzaker, D.: Probability and Random Processes. Oxford University Press (2020)

52.

Crandall, S.H., Mark, W.D.: Random vibration in mechanical systems. Academic Press (2014)

53.

Bendat, J.S., Piersol, A.G.: Random Data: Analysis and Measurement Procedures. John Wiley & Sons (2011)

54.

Li, T.H.: Laplace periodogram for time series analysis. J. Am. Stat. Assoc. 103(482), 757–768 (2008)MathSciNetCrossRef

55.

Stoica, P., Li, J., He, H.: Spectral analysis of nonuniformly sampled data: a new approach versus the periodogram. IEEE Trans. Signal Process. 57(3), 843–858 (2008)MathSciNetCrossRef

56.

Li, T.H.: A robust periodogram for high-resolution spectral analysis. Signal Process. 90(7), 2133–2140 (2010)CrossRef

57.

Akin, M., Kiymik, M.K.: Application of periodogram and AR spectral analysis to EEG signals. J. Med. Syst. 24, 247–256 (2000)CrossRef

58.

Candan, C., Kutay, M.A., Ozaktas, H.M.: The discrete fractional fourier transform. IEEE Trans. Signal Process. 48(5), 1329–1337 (2000)MathSciNetCrossRef

59.

Babak, V., Zaporozhets, A., Zvaritch, V., Scherbak, L., Myslovych, M., Kuts, Y.: Models and measures in theory and practice of manufacturing processes. IFAC-PapersOnLine 55(10), 1956–1961 (2022)CrossRef

60.

Zaporozhets, A., Redko, O., Babak, V., Eremenko, V., Mokiychuk, V.: Method of indirect measurement of oxygen concentration in the air. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu 5, 105–114 (2018)CrossRef

61.

CusidÓCusido, J., Romeral, L., Ortega, J.A., Rosero, J.A., Espinosa, A.G.: Fault detection in induction machines using power spectral density in wavelet decomposition. IEEE Trans. Industr. Electron. 55(2), 633–643 (2008)CrossRef

62.

Polat, K., Güneş, S.: Classification of epileptiform EEG using a hybrid system based on decision tree classifier and fast fourier transform. Appl. Math. Comput. 187(2), 1017–1026 (2007)MathSciNet

63.

Shirbhate, R., Panse, T., Ralekar, C.: Design of parallel FFT architecture using cooley Tukey algorithm. In: 2015 International Conference on Communications and Signal Processing (ICCSP), pp. 0574–0578. IEEE (2015)

64.

Ratnam, D.V., Pasha, A., Swathi, P., Rao, M.V.G.: Acquisition of GPS L1 signals using Cooley-tukey FFT algorithm. In: 2013 IEEE International Conference on Signal Processing, Computing and Control (ISPCC), pp. 1–4. IEEE (2013)

65.

Voronenko, Y., Puschel, M.: Algebraic signal processing theory: cooley-Tukey type algorithms for real DFTs. IEEE Trans. Signal Process. 57(1), 205–222 (2008)MathSciNetCrossRef

66.

Abbaci, M., & Zmirli, M.O.: Performance evaluation of PMU using modified cooley-tukey algorithm based on GDFT. In: 2018 International Conference on Applied Smart Systems (ICASS), pp. 1–6. IEEE (2018)

67.

Püschel, M., Rtteler, M.: Algebraic signal processing theory: cooley-Tukey type algorithms on the 2-D hexagonal spatial lattice. Appl. Algebra Eng. Commun. Comput. 19(3), 259–292 (2008)MathSciNetCrossRef

68.

Li, C., Du, P., Li, K., Liu, Y., Jiang, H., Quan, Z.: Accurate goertzel algorithm: error analysis, validations and applications. Mathematics 10(11), 1788 (2022)CrossRef

69.

Sysel, P., Rajmic, P.: Goertzel algorithm generalized to non-integer multiples of fundamental frequency. EURASIP J. Adv. Signal Proc. 2012, 1–8 (2012)

70.

Chen, H., Chen, G., Li, J.: The generalized Goertzel algorithm and its parallel hardware implementation. Sci China Ser A Math 51(1), 37–41 (2008)MathSciNetCrossRef

71.

Brown, S., Timoney, J., Lysaght, T.: An evaluation of the Goertzel Algorithm for low-power, embedded systems. In: 25th IET Irish Signals & Systems Conference 2014 and 2014 China-Ireland International Conference on Information and Communications Technologies (ISSC 2014/CIICT 2014), pp. 357–361. IET (2014)

72.

Dabrowski, A., Marciniak, T.: Canonic Goertzel algorithm and drawbacks of various Goertzel algorithm formulations. In: 2017 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA), pp. 259–262. IEEE (2017)

73.

Forbes, C., Evans, M., Hastings, N., Peacock, B.: Statistical distributions. John Wiley & Sons (2011)

74.

Cordeiro, G.M., de Castro, M.: A new family of generalized distributions. J. Stat. Comput. Simul. 81(7), 883–898 (2011)MathSciNetCrossRef

75.

Watanabe, T.: Convolution equivalence and distributions of random sums. Probab. Theory Relat. Fields 142, 367–397 (2008)MathSciNetCrossRef

76.

Devroye, L.: Nonuniform random variate generation. Handbooks Oper. Res. Manage. Sci. 13, 83–121 (2006)CrossRef

77.

Yari, G., Tondpour, Z.: The new Burr distribution and its application. Math. Sci. 11(1), 47–54 (2017)MathSciNetCrossRef

78.

Chakraborty, T., Das, S., Chattopadhyay, S.: A new method for generalizing burr and related distributions. Math. Slovaca 72(1), 241–264 (2022)MathSciNetCrossRef

79.

Pawlas, P., Szynal, D.: Recurrence relations for single and product moments of generalized order statistics from Pareto, generalized Pareto, and Burr distributions. Commun. Stat.-Theo. Methods 30(4), 739–746 (2001)MathSciNetCrossRef

80.

Jamal, F., Abuzaid, A.H., Tahir, M.H., Nasir, M.A., Khan, S., Mashwani, W.K.: New modified burr iii distribution, properties and applications. Math. Comput. Appl. 26(4), 82 (2021)

81.

Nadarajah, S., Pogány, T.K., Saxena, R.K.: On the characteristic function for Burr distributions. Statistics 46(3), 419–428 (2012)MathSciNetCrossRef

82.

Borroni, C.G.: Understanding Karl Pearson’s influence on Italian statistics in the early 20th century. Int. Stat. Rev. 77(1), 81–95 (2009)MathSciNetCrossRef

83.

Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O.: Problems and features of measurements. Models Meas. Meas. Monit. 1–31 (2021)

84.

Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M.: Principles of construction of systems for diagnosing the energy equipment. Diagnost. Syst. Energy Equip. 1–22 (2020)

85.

Xiong, Q., Du, P., Deng, J., Huang, D., Song, G., Qian, L., Luo, Y.: Global sensitivity analysis for nuclear reactor LBLOCA with time-dependent outputs. Reliab. Eng. Syst. Saf. 221, 108337 (2022)CrossRef

86.

Pearson, K.: Mathematical contributions to the theory of evolution on a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc. Royal Soc. london, 60(359–367), 489–498 (1897)

87.

Pearson, K.: Contributions to the mathematical theory of evolution. Philosoph. Trans. Royal Soc. London. A, 185, 71–110 (1894)

88.

Pearson, K.: I. Mathematical contributions to the theory of evolution.—VII. On the correlation of characters not quantitatively measurable. Philosophical Trans. Royal Soc. London. Series A, Containing Papers of a Mathematical or Physical Character, 195(262–273), 1–47 (1900)

89.

Zvarich, V.N., Marchenko, B.G.: Linear autoregressive processes with periodic structures as models of information signals. Radioelectron. Commun. Syst. 54(7), 367–372 (2011)CrossRef

90.

Marchenko, B.G., Tkachuk, R.A., Palamar, M.I.: Harmonic analysis using in human visual system diagnosnics by means of elektroretinograms identification. In: Pattern recognition and information processing (1997)

91.

Guzii, V.I., Marchenko, B.G., Protsenko, L.D.: Transformations providing for detection invariance with changes in the spectral parameters of low-frequency noise. Radioehlektronika 28, 3–10 (1985)

92.

Marchenko, B., Shcherbak, L.: 1975, p. 144. Naukova Dumka, Linear random processes and their applications. Kyiv (1975)

93.

Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O.: Models of measuring signals and fields. Models Meas. Measurements Monit. 33–59 (2021)

94.

Smyth, G.K.: Linear models and empirical bayes methods for assessing differential expression in microarray experiments. Stat. Appl. Genet. Molecular Biol. 3(1) (2004)

95.

Dobson, A.J., Barnett, A.G.: An Introduction to Generalized Linear Models. Chapman and Hall/CRC (2018)

96.

Hommel, G.: Adaptive modifications of hypotheses after an interim analysis. Biomet. J.: J. Mathemat. Methods Biosci. 43(5), 581–589 (2001)MathSciNetCrossRef

97.

Székely, G.J., Rizzo, M.L.: Testing for Equal Distributions in High Dimension. InterStat, 5(16.10), 1249–1272 (2004)

98.

Manoukian, E.B.: Modern Concepts and Theorems of Mathematical Statistics. Springer Science & Business Media (2012)

99.

Dodge, Y.: The Concise Encyclopedia of Statistics. Springer Science & Business Media (2008)

100.

Haeusler, E.H.: How many times do we need an assumption to prove a tautology in minimal logic? examples on the compression power of classical reasoning. Electron. Notes Theoret. Comput. Sci. 315, 31–46 (2015)MathSciNetCrossRef

101.

Kesner, D., Viana, P.: Proceedings seventh workshop on logical and semantic frameworks, with applications (2013). ArXiv preprint arXiv:1303.7136.

102.

Drago, A.: The birth of the non-Euclidean geometries as the more significant crisis in the foundations of modern mathematics. Logic Philos Sci 9(1), 103–110 (2011)

103.

Schmidt-Hieber, J.: The Kolmogorov-Arnold representation theorem revisited. Neural Netw. 137, 119–126 (2021)CrossRef

104.

Köppen, M.: On the training of a kolmogorov network. In: Artificial Neural Networks—ICANN 2002: International Conference Madrid, Spain, August 28–30, 2002 Proceedings 12, pp. 474–479. Springer Berlin Heidelberg (2002)

105.

Arnold, V.I.: Proof of a theorem of AN Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory 1957–1965, 267–294 (2009)CrossRef

106.

Rassokhin, D.N., Agrafiotis, D.K.: Kolmogorov-Smirnov statistic and its application in library design. J. Mol. Graph. Model. 18(4–5), 368–382 (2000)CrossRef

107.

Greenwell, R.N., Finch, S.J.: Randomized rejection procedure for the two-sample Kolmogorov-Smirnov statistic. Comput. Stat. Data Anal. 46(2), 257–267 (2004)MathSciNetCrossRef

108.

Nguyen, H.D.: A Two-sample Kolmogorov-Smirnov-like test for big data. In: Data Mining: 15th Australasian Conference, AusDM 2017, Melbourne, VIC, Australia, August 19–20, 2017, Revised Selected Papers 15, pp. 89–106. Springer Singapore (2018)

109.

Sverdlova, A., Zaporozhets, A.: Predicting anomaly conditions of energy equipment using neural networks. In: E3S Web of Conferences, vol. 280, p. 09005 (2021)

110.

Zaporozhets, A., Eremenko, V., Babak, V., Isaienko, V., Babikova, K.: Using Hilbert transform in diagnostic of composite materials by impedance method. Period. Polytechnica Electr. Eng. Comput. Sci. 64(4), 334–342 (2020)CrossRef

111.

Eremenko, V., Babak, V., Zaporozhets, A.: Method of reference signals creating in non-destructive testing based on low-speed impact. Tekhnichna ElektroDynamika 4, 070 (2021)CrossRef

112.

Babak, V., Bohachev, I., Zaporozhets, A., Khaidurov, V., Havrysh, V., Kalinichenko, A.: Some features of modeling ultrasound propagation in non-destructive control of metal structures based on the magnetostrictive effect. Electronics 12(3), 477 (2023)CrossRef

113.

Zaporozhets, A., Babak, V., Sverdlova, A., Isaienko, V., Babikova, K.: Development of a system for diagnosing heat power equipment based on IEEE 802.11 s. In: Systems, Decision and Control in Energy II, pp. 141–151. Springer International Publishing, Cham (2021)

114.

Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O.: Models and measures for standardless measurements of the composite materials characteristics. Models Meas. Meas. Monit. 157–190 (2021)

115.

Bohachev, I., Babak, V., Zaporozhets, A.: Novel small-aperture transducers based on magnetostrictive effect for diagnostic systems. Tech. Electrodynamics 3, 69–78 (2022)

116.

Santhakumaran, A.: Fundamentals of Testing Statistical Hypotheses. Atlantic Publishers & Dist (2001)

117.

Holický, M.: Testing of statistical hypotheses. Introduction to Probability and Statistics for Engineers, pp. 125–138 (2013)

118.

Kachiashvili, G.K., Kachiashvili, K.J., Mueed, A.: Specific features of regions of acceptance of hypotheses in conditional Bayesian problems of statistical hypotheses testing. Sankhya A 74, 112–125 (2012)MathSciNetCrossRef

119.

He, J., Jones, J.W., Graham, W.D., Dukes, M.D.: Influence of likelihood function choice for estimating crop model parameters using the generalized likelihood uncertainty estimation method. Agric. Syst. 103(5), 256–264 (2010)CrossRef

120.

Rohde, C.A.: Introductory Statistical Inference with the Likelihood Function. Springer, New York (2014)CrossRef

121.

Li, F., Luan, P.: ARMA model for predicting the number of new outbreaks of newcastle disease during the month. In: 2011 IEEE International Conference on Computer Science and Automation Engineering, vol. 4, pp. 660–663. IEEE (2011)

122.

Huang, D., Yang, J., Zhou, D., Litak, G., Liu, H.: Influence of Poisson white noise on the response statistics of nonlinear system and its applications to bearing fault diagnosis. J. Comput. Nonlinear Dyn. 14(3), 031010 (2019)CrossRef

123.

Guo, S.L., Yang, Y.G., Sun, Y.H.: Stochastic response of an energy harvesting system with viscoelastic element under Gaussian white noise excitation. Chaos Solitons Fractals 151, 111231 (2021)MathSciNetCrossRef

Title: Statistical Assessment of Diagnostic Parameters
Authors: Vitalii Babak
Sergii Babak
Artur Zaporozhets
Publisher: Springer Nature Switzerland
Book: Statistical Diagnostics of Electric Power Equipment
Print ISBN: 978-3-031-76252-9

Electronic ISBN: 978-3-031-76253-6

Copyright Year: 2025
DOI: https://doi.org/10.1007/978-3-031-76253-6_5