The Determination of Instants of the Change of Modes of a Dynamic System Using the Indicator Function of the Number of States
Authors: Tukmakov A.L., Tukmakova N.A. | Published: 08.10.2018 |
Published in issue: #9(702)/2018 | |
Category: Mechanical Engineering and Machine Science | Chapter: Methods and Devices for Monitoring and Diagnosing Materials, Products, Substances | |
Keywords: dynamic system, acoustic signal, temporary realization, phase space, set of states, window function, change of dynamic mode, indicator function |
When operating and testing technical devices, including turbines of rocket and aviation engines, there can be a need for diagnostics of the process of change of their dynamic modes, for the determination of the current type of the dynamic mode and the instants or the time interval of the event onset. Along with the spectral methods, a method based on the analysis of conditions of the dynamic system in a discrete phase space can be applied to solve this problem. The authors examine a method and an algorithm that describes the behavior of the dynamic system based on the analysis of the evolution of the indicator function of the number of states, determined in a temporary window and summing up the quantity of the differing conditions of the system in a discrete phase space. A model of the two-dimensional phase space is constructed, in which discrete conditions of the analyzed dynamic process are determined. A method to build a basic discrete set of states of the dynamic system and the indicator function behaviour are described while creating a basic set of states and subsequently identifying discrete conditions of the dynamic process. It is shown that an increase in the indicator function occurs when changing the dynamic mode, leading to the emergence of new states in relation to the conditions of the window of a given width, which is displaced along a time axis. As an example, by analyzing the acoustic signal, the authors examine a change in the dynamic behavior of the system represented by a rotating shaft onto which a thrust force containing constant and pulse components is applied.
References
[1] Akhtyamov A.M., Safina G.F. Vibration-proof conduit fastening. Journal of Applied Mechanics and Technical Physics, 2008, vol. 49, no. 1, pp. 114–121.
[2] Akhtyamov A.M., Yamilova L.S., Muftakhov A.V. Identification of the type and parameters of fastening from the natural frequencies of a fastened rod. Acoustical Physics, 2008, vol. 54, no. 2, pp. 146–152.
[3] Ahtyamov A.M., Ayupova A.R. O reshenii zadachi diagnostirovaniya defektov v vide maloy polosti v sterzhne [On solving the problem of diagnosing defects in a small cavity in the rod]. Zhurnal Srednevolzhskogo matematicheskogo obshchestva [Mid-Volga Mathematical Society]. 2010, vol. 12, no. 3, pp. 37–42.
[4] Kazakov O.N., Sayfutdinov M.I., Strizhkov S.A., Shemyakin V.V. Effektivnost’ primeneniya metoda akusticheskoy emissii pri diagnostike magistral’nyh nefteprovodov [Efficiency of application of the acoustic emission method in the diagnosis of oil trunk pipelines]. Bezopasnost’ truda v promyshlennosti [Occupational safety in industry]. 2000, no. 4, pp. 25–28.
[5] Dudakov S.V. Ob akusticheskoy diagnostike zhelezobetonnyh izdeliy [About acoustic diagnostics of reinforced concrete products]. Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of Irkutsk State Technical University]. 2007, no. 2–2, pp. 90–93.
[6] Buylo S.I. Diagnostika predrazrushayushchego sostoyaniya po amplitudnym i vremennym invariantam potoka aktov akusticheskoy emissii [Diagnostics of the pre-destructive state by amplitude and time invariants of the flow of acoustic emission acts]. Defektoskopiya [Russian Journal of Nondestructive Testing]. 2004, no. 8, pp. 79–83.
[7] Tukmakov A.L., Aksenov I.B. Identifikaciya ob"ektov na osnove analiza funkcii chisla sostoyaniy akusticheskogo otklika [Identification of objects based on the analysis of the function of the number of states of acoustic response]. Zhurnal tekhnicheskoy fiziki [Technical Physics. The Russian Journal of Applied Physics]. 2003, vol. 73, is. 10, pp. 130−133.
[8] Tukmakov A.L. O diagnostike regulyarnyh i haoticheskih rezhimov dvizheniya dinamicheskoy sistemy pri pomoshchi funkcii chisla sostoyaniy [On diagnose regular and chaotic regimes of motion for a function of the number of states of a dynamic system]. Pis’ma v zhurnal tekhnicheskoy fiziki [Applied Physics Letters]. 2002, vol. 28, no. 6, pp. 18−22.
[9] Bigus G.A., Travkin A.A., Daniev Yu.F. Veyvlet-analiz signalov akusticheskoy emissii pri diagnostike konstrukciy [Wavelet analysis of acoustic emission signals in the diagnosis of structures]. Svarka i diagnostika [Welding and Diagnostics]. 2012, no. 4, pp. 34–38.
[10] Solov’ev A.N., Sobol’ B.V., Vasil’ev P.V. Ultrasonic location of inner crack defects in a compound elastic cylinder using an artificial neural-network apparatus. Russian Journal of Nondestructive Testing, 2016, vol. 52, no. 3, pp. 119–124.
[11] Krasnoshchekov A.A. Identifikaciya defektov v uprugih elementah konstrukciy na osnove iskusstvennyh neyronnyh setey [Identification of defects in elastic structures based on artificial neural networks]. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo [Vestnik of Lobachevsky University of Nizhni Novgorod]. 2011, no. 4, pp. 1549–1551.
[12] Zaharov S.I. Povyshenie dostovernosti znacheniy iznosa detaley mashin pri akusticheskoy diagnostike [Raising the authenticity level of the machinery wear at acoustic diagnostics]. Vestnik mashinostroeniya [Russian Engineering research]. 2008, no. 11, pp. 89–91.
[13] Tsallis C. Computational applications of nonextensive statistical mechanics. Journal of Computational and Applied Mathematics, 2009, vol. 227, no. 1, pp. 51–58.
[14] Shuster G. Determinirovannyy haos [Deterministic chaos]. Moscow, Mir publ., 1988. 240 p.
[15] Berzhe P., Pomo I., Vidal’ K. Poryadok v haose. O deterministskom podhode k turbulentnosti [Order in chaos. On the deterministic approach to turbulence]. Moscow, Mir publ., 1991. 368 p.
[16] Jardine A.K.S., Lin D., Banjevic D. A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 2006, vol. 20, is. 7, pp. 1483–1510.
[17] Xu G.Y., Zhu W.D., Emory B.H. Experimental and Numerical Investigation of Structural Damage Detection Using Changes in Natural Frequencies. Journal of Vibration and Acoustics, Transactions of the ASME, 2007, vol. 129(6), pp. 686–700, doi:10.1115/1.2731409.
[18] Ruqiang Yan, Robert X. Gao, Xuefeng Chen. Wavelets for fault diagnosis of rotary machines: A review with applications. Signal Processing, 2014, vol. 96, Part A, pp. 1–15.