|Article title||USING THE METHOD OF NORMALIZED EXPANSION TO ANALYZE THE BEHAVIOR OF A TECHNICAL OBJECT PARAMETER|
|Authors||S. I. Klevtsov|
|Section||SECTION III. METHODS AND MEANS OF MANAGEMENT AND CONTROL|
|Month, Year||06, 2018 @en|
|Abstract||The condition of the technical object is determined on the basis of the assessment of its parameters, current and forecast. The object is affected by various external factors that lead to degradation of the object parameters. If changing the parameters becomes invalid for the operating mode of the object, it can fail, and this can lead to an emergency. To prevent this, it is necessary not only to control the parameters during operation, but also to predict their values one step and more forward along the time axis. However, a reliable and satisfying forecast is possible if the behavior of the parameter is determined by the background, that is, by the data that are currently known, and the trend for the time series of the parameter retains the character of monotony for some time. To analyze the possible behavior of the time series of the parameter, including the assessment of trend stability, determining the points of change in its dynamics, the method of normalized Hurst scope was used. The normalized-scale method does not put an additional condition for the analysis of compliance with the normal law of distribution. For time series of parameters, this condition is practically not met. On the basis of determining the value of the Hurst exponent ranks are classified on antipersistent, random and persistent. If a series is classified as anti-persistent, it has pronounced fractal properties, and if it is persistent, then its trend has a "historical" memory and for its prediction you can use conventional time series methods. With the help of the Hurst exponent, it is possible to determine not only the estimation of the ratio of the strength of the trend to the noise level, but the magnitude of the index. thread the necessity of implementing procedures for filtering a noise component of the signal. On the basis of data processing about acceleration of the technical object by the method of normalized amplitude a conclusion about expediency of application of the Hurst exponent in the solution of problems of forecasting parameters of technical objects. The higher the Hurst indicator from the range (0.5÷1.0) for the considered series, the more accurate the forecast of the parameter values can be. For values of the Hurst exponent approaching the value of 0.5, additional data processing is required before the forecasting procedure to reduce the error in estimating the series values.|
|Keywords||Time series; model; forecasting; technical parameter; Hurst exponent; method of normalized amplitude.|
|References||1. Yaroshenko I.V. Matematicheskaya model' i metod klassifikatsii tekhnicheskogo sostoyaniya vysokovol'tnykh mekhatronnykh moduley [Mathematical model and method of classification of technical condition of high-voltage mechatronic modules], Inzhenernyy vestnik Dona [Engineering journal of Don], 2014, No. 2. Available at: ivdon.ru/ru/magazine/archive/n2y2014/2330.
2. Klevtsova A.B. Parametricheskaya zonnaya otsenka sostoyaniya tekhnicheskogo ob"ekta s ispol'zovaniem rezhimnoy karty [Parametric conditioning assessment of the condition of a technical object with the use of a modal map], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2010, No. 5 (106), pp. 107-111.
3. Detlev W. Gross. Partial Discharge Measurement and Monitoring on Rotating Machines, IEEE Int. Sym. On Elect. Insul, Boston MAUSA, April 7-10, 2002, pp. 33-41.
4. Klevtsova A.B., Klevtsov G.S. Modeli parametricheskoy ekspress-otsenki sostoyaniya tekhnicheskogo ob"ekta [Models of parametric Express assessment of the state of a technical object], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2008, No. 11 (88), pp. 15-19.
5. Klevtsov S.I. Identification of the State of Technical Objects Based on Analyzing a Limited Set of Parameters, 2016 International Siberian Conference on Control and Communications, SIBCON 2016 - Proceedings. 2016, pp. 749-752.
6. Klevtsov S.I., Klevtsova A.B., Burinov S.V. Model' parametricheskoy kachestvennoy ierarkhicheskoy otsenki sostoyaniya tekhnicheskoy sistemy [A parametric hierarchical model for quality assessment technical systems], Inzhenernyy vestnik Dona [Engineering journal of Don], 2015, No. 3. Available at: ivdon.ru/ru/magazine/archive/n3y2015/3088.
7. Lihua Sun, Yingjun Guo, Haichao Ran. A New Method of Early Real-Time Fault Diagnosis for Technical Process, Electrical and Control Engineering (ICECE), 2010 International Conference. Wuhan, China, 2010, pp. 4912-4915.
8. Klevtsov S.I. Prognozirovanie izmeneniy fizicheskoy velichiny v real'nom vremeni s ispol'zovaniem lineynogo adaptivnogo fil'tra [The prediction of changes of physical quantities in real time using a linear adaptive filter], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 5 (142), pp. 180-185.
9. Darkhovsky B., Brodsky B. Asymptotically Optimal Methods of Early Change-point Detection, Sequential Analysis, 2013, No. 32, pp. 158-181.
10. Matuszewski J. Application of clustering methods for recognition of technical objects, Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET), 2010 International Conference, 2010, pp. 39-40.
11. George E.P. Box, Gwilym M. Jenkins, Gregory C. Reinsel. Time series analysis: forecasting and control. 4th ed. – A JOHN WILEY & SONS, INC., Publication, 2015, 712 p.
12. Feder E. Fraktaly [Fractals]: transl. from engl. Moscow: Mir, 1991, 254 p.
13. Antipov O.I., Neganov V.A. Primenenie metoda normirovannogo razmakha KHersta k analizu stokhasticheskikh vremennykh ryadov v impul'snykh stabilizatorakh napryazheniya [Application of the Hirst normalized range method to the analysis of stochastic time series in pulse voltage stabilizers], Fizika volnovykh protsessov i radiotekhnicheskie sistemy [Physics of wave processes and radio engineering systems], 2009, Vol. 12, No. 3, pp. 78-85.
14. Peter J. Brockwell, Richard A. Davis. ITSM: An Interactive Time Series Modelling Package for the PC. Springer New York. 1991, 105 p.
15. Sidorov S.G., Nikologorskaya A.V. Analiz vremennykh ryadov kak metod postroeniya prognoza potrebleniya elektroenergii [Time series analysis as a method of forecasting electricity consumption], Vestnik IGEU [Vestnik IGEU], 2010, Issue 3, pp. 1-3.
16. Vovk S.P., Ginis L.А. Modelling and forecasting of transitions between levels of hierarchies in Difficult formalized systems, European Researcher, 2012, Vol. (20), No. 5-1, pp. 541-545.
17. Klevtsov S.I. Modelirovanie algoritma kratkosrochnogo prognozirovaniya izmeneniya bystromenyayushcheysya fizicheskoy velichiny v real'nom vremeni [Modeling of algorithm of short-term forecasting of change of rapidly changing physical quantity in real time], Inzhenernyy vestnik Dona [Engineering journal of Don], 2012, No. 3 (21), pp. 199-205.
18. Darkhovsky B., Piratinska A. Novel Methodology for Segmentation of Time Series Generated by Different Mechanisms, Proceedings of International work-conference on Time Series (ITISE-2014). Iss. 1. Granada: Copicentro Granada S.L., 2014, pp. 273-285.
19. Klevtsov S.I. Osobennosti vybora parametrov nastroyki modeli sglazhivayushchego vremennogo ryada dlya osushchestvleniya kratkosrochnogo prognozirovaniya izmeneniya fizicheskoy velichiny [Features choice of model settings smoothing time series for the implementation of short-term forecasting of physical size], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2011, No. 5 (118), pp. 133-138.
20. Lukashin Yu.P. Adaptivnye metody kratkosrochnogo prognozirovaniya vremennykh ryadov [Adaptive methods of short-term time series forecasting]. Moscow: Finansy i statistika, 2003, 416 p.
21. Brillindzher D.R. Vremennye ryady. Obrabotka dannykh i teoriya: monografiya [Time series. Data processing and theory: monograph], ed. by A.N. Kolmogorova: transl. from engl. Moscow, 1980, 536 p.
22. Bichenova N. Vychislenie pokazatelya KHersta dlya dinamiki stoimosti kompanii [Calculation of Hurst index for the dynamics of the company's value], Automated control systems. Transactions. Georgian Technical University, 2015, No. 1 (19).
23. Kuzenkov N.P., Loginov V.M. Ispol'zovanie metoda normirovannogo razmakha pri analize rechevykh patologiy nevrologicheskogo geneza [The use of the normalized scope method in the analysis of speech pathologies of neurological Genesis], Komp'yuternye issledovaniya i modelirovanie [Computer studies and modeling], 2014, Vol. 6, No. 5, pp. 775-791.
24. Bel'kov D.V., Edemskaya E.N., Nezamova L.V. Statisticheskiy analiz setevogo trafika [Statistical analysis of network traffic], Naukovі pratsі DonNTU. Serіya "Іnformatika, kіbernetika ta obchislyuval'na tekhnіka" [Scientific works of DonNTU. Series "Informatics, Cybernetics and computer engineering"], 2011, Issue 13 (185), pp. 66-75.
25. Kirichenko L., Chalaya L. Kompleksnyy podkhod k issledovaniyu fraktal'nykh vremennykh ryadov [An integrated approach to the study of fractal time series], International Journal "Information Technologies & Knowledge", 2014, Vol. 8, No. 1, pp. 22-28.
26. Kalush Yu.A., Loginov V.M. Pokazatel' Khersta i ego skrytye svoystva [Hurst exponent and its hidden properties], Sibirskiy zhurnal industrial'noy matematiki [Siberian journal of industrial mathematics], 2002, Vol. 5, No. 4, pp. 29-37.
27. James B. Bassingthwaighte, Gary M. Raymond. Evaluation of the Dispersional Analysis Method for Fractal Time Series, Ann Biomed Eng., 1995, Vol. 23 (4), pp. 491-505.
28. Roel F. Ceballos, Fe F. LargoOn. The Estimation of the Hurst Exponent Using Adjusted Rescaled Range Analysis, Detrended Fluctuation Analysis and Variance Time Plot: A Case of Exponential Distribution, Imperial Journal of Interdisciplinary Research (IJIR), 2017, Vol. 3, Issue 8, pp. 424-434.
29. Cervantes-De la Torre F., Gonz´alez-Trejo J.I., Real-Ramirez C.A., Hoyos-Reyes L.F. Fractal dimension algorithms and their application to time series associated with natural phenomena, Journal of Physics: Conference Series, 2013, No. 475, pp. 1-10.
30. Klevtsov S.I. Ispol'zovanie modeley vremennykh ryadov dlya kratkosrochnogo prognozirovaniya v mikrokontrollere izmeneniy parametrov ob"ekta [he use of time series models for short-term forecasting in the microcontroller of changes in the parameters of the object], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 11 (148), pp. 194-201.