Wavelet Analysis of Missile Stability

Mathematica modeling, numerical technique and program complexes


Tochilova O. L.

Military industrial corporation «NPO Mashinostroyenia», 33, Gagarina str., Reutov, Moscow region, 143966, Russia

e-mail: forpoint@yandex.ru


The paper is devoted to development of new statistical data processing technologies obtained during simulation of missile motion in accordance with the complete mathematical model for a big quantity of randomly realized sets of tolerances, each of them is characterized by a specific transient process.

The necessity for the research has emerged in connection with the fact that existing diagnostic methods did not allow identify variants of tolerance combinations, whereby the oscillations with frequencies, amplitudes and durations exceeding the design values, occur in the respective transient processes. The process of critical variants manual study is labor intensive and ineffective. Not only is the information on the spectral content, but also the spectral components temporal localization is of interest herewith. Thus, the classic Fourier processing, with only frequency representation of a signaldoes not allow solve this problem.

A new methodology is described, allowing automation of the frequency and time domain analysis process of a large quantity of nonstationary signals. This methodology is based on the implementation of wavelet and wavelet package transformations of one-dimensional signals to obtain their frequency and time presentations, and subsequent analysis with pre-set parameters. The paper presents an example of the developed methodology implementation to reveal the variants of tolerances combination, located on the stability boundary, where oscillations’ with frequency, amplitude and duration higher than the preset values present in the respective transient processes. The main results of the developed technique implementation for stabilization algorithm parameters adjustment are presented.


statistical modeling, data processing, motion modeling, transient, time-frequency analysis, wavelet analysis, Daubechies wavelets, stabilization algorithm


  1. Plavnik G.G., Loshkarev A.N., Tochilova O.L. Trudy sektsii 22 imeni akademika V.N. Chelomeya XXXVIII Akademicheskikh chteniy po kosmonavtike, Reutov, JSC MIC NPO Mashinostroyenia, 2014, iss. 2, pp. 57–64.

  2. Besekerskiy V.A., Popov E.P. Teoriya sistem avtomaticheskogo regulirovaniya (The theory of automatic control systems), Saint Petersburg, Professiya, 2003, 752 p.

  3. Tochilova O.L. Trudy sektsii 22 imeni akademika V.N. Chelomeya XXXVIII Akademicheskikh chteniy po kosmonavtike, Reutov, JSC MIC NPO Mashinostroyenia, 2015, iss. 3, pp. 202–217.

  4. Astafyeva N.M. Uspekhi fizicheskikh nauk, 1996, vol. 166, no. 11, pp. 1145–1170.

  5. Yakovlev A.N. Vvedenie v veivlet-preobrazovaniya (Introduction to wavelet transformations), Novosibirsk, NSTU, 2003, 104 p.

  6. Petukhov A.P. Vvedenie v teoriyu bazisov vspleskov (Introduction to the theory of wavelet bases], Saint Petersburg, SPbGTU, 1999, 132 p.

  7. Smolentsev N.K. Osnovy teorii veivletov. Veivlety v MATLAB (Fundamentals of wavelet theory. Wavelets in MATLAB), Moscow, DMK, 2008, 448 p.

  8. Dobeshi I. Desyat’ lektsii po veivletam (Ten lectures on wavelets), Izhevsk, 2001, NIC Regulyarnaya i khaoticheskaya dinamika, 464 p.

  9. Dremin I.M., Ivanov O.V., Nechitaylo V.A. Uspekhi fizicheskikh nauk, 2001, vol. 171, no. 5, pp. 465–501.


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