DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Using wavelet analysisto obtain characteristics of accelerograms

Vestnik MGSU 7/2013
  • Mkrtychev Oleg Vartanovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, head, Scientific Laboratory of Reliability and Seismic Resistance of Structures, Professor, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Reshetov Andrey Aleksandrovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Technical Sciences, engineer, Research Laboratory “Reliability and Earthquake Engineering”, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 59-67

Application of accelerograms to the analysis of structures, exposed to seismic loads, and generation of synthetic accelerograms may only be implemented if their varied characteristics are available. The wavelet analysis may serve as a method for identification of the above characteristics. The wavelet analysis is an effective tool for identification of versatile regularities of signals. Wavelets can be used to detect inflection points, extremes, etc. Also, wavelets can be used to filter signals.The authors discuss particular theoretical principles of the wavelet analysis and the multiresolution analysis. The authors present formulas designated for the practical application. The authors implemented a wavelet transform in respect of a specific accelerogram.The recording of the horizontal component (N00E) of the Spitak earthquake (Armenia, 1988) was exposed to the analysis as an accelerogram. An accelerogram was considered as a non-stationary random process in the course of its decomposition into the envelope and the non-stationary part. This non-stationary random process was presented as a multiplication envelope of a stationary random process. Parameters of exposure of a construction site to the seismic impact can be used to synthesize accelerograms.

DOI: 10.22227/1997-0935.2013.7.59-67

References
  1. Blater K. Veyvlet-analiz. Osnovy teorii [Wavelet Analysis. Foundations of the Theory]. Moscow, Tekhnosfera Publ., 2007, 280 p.
  2. Percival D.B., Walden A.T. Wavelet Methods for Time Series Analysis. Cambridge University Press, 2000, 622 p.
  3. Dobeshi I. Desyat’ lektsiy po veyvletam [Ten Lectures on Wavelets]. Izhevsk, NITs «Regulyarnaya i khaoticheskaya dinamika» publ., 2001, 454 p.
  4. Addison P.S. The Illustrated Wavelet Transform Handbook. Institute of Physics, 2002, 358 p.
  5. Goswami J.C., Chan A.K., Fundamentals of Wavelets: Theory, Algorithms and Applications. John Wiley & Sons, Inc., 1999, 359 p.
  6. Chui C.K. Wavelets: A Mathematical Tool for Signal Analysis, SIAM. Philadelphia, 1997, 228 p.
  7. Mkrtychev O.V., Reshetov A.A. Primenenie veyvlet-preobrazovaniy pri analize akselerogramm [Application of Wavelet Transformations to the Analysis of Accelerograms]. International Journal for Computational Civil and Structural Engineering. 2011, vol. 7, no. 3, pp. 118—126.
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  10. Bakalov V.P. Tsifrovoe modelirovanie sluchaynykh protsessov [Digital Modeling of Random Processes]. Moscow, MAI Publ., 2002, 88 p.

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COMPUTATION OF CONVOLUTION OF FUNCTIONS WITHIN THE HAAR BASIS

Vestnik MGSU 8/2012
  • Mozgaleva Marina Leonidovna - Moscow State University of Civil Engineering (MSUCE) Candidate of Technical Sciences, Associated Professor, Department of Computer Science and Applied Mathematics +7 (499) 183-59-94, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Akimov Pavel Alekseevich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Corresponding Member of the Russian Academy of Architecture and Construction Science, Professor, Department of Computer Science and Applied Mathematics +7 (499) 183-59-94, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 98 - 103

The Wavelet analysis, that replaces the conventional Fourier analysis, is an exciting new
problem-solving tool employed by mathematicians, scientists and engineers. Recent decades have
witnessed intensive research in the theory of wavelets and their applications. Wavelets are mathematical
functions that divide the data into different frequency components, and examine each
component with a resolution adjusted to its scale. Therefore, the solution to the boundary problem
of structural mechanics within multilevel wavelet-based methods has local and global components.
The researcher may assess the infl uence of various factors. High-quality design models and reasonable
design changes can be made.
The Haar wavelet, known since 1910, is the simplest possible wavelet. Corresponding
computational algorithms are quite fast and effective. The problem of computing the convolution
of functions in the Haar basis, considered in this paper, arises, in particular, within the waveletbased
discrete-continual boundary element method of structural analysis. The authors present
their concept of convolution of functions within the Haar basis (one-dimensional case), share
their useful ideas concerning Haar functions, and derive a relevant convolution formula of Haar
functions.

DOI: 10.22227/1997-0935.2012.8.98 - 103

References
  1. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Diskretnye i diskretno-kontinual’nye realizatsii metoda granichnykh integral’nykh uravneniy [Discrete and Discrete-continual Versions of the Boundary Integral Equation Method]. Moscow, MSUCE, 2011, 368 p.
  2. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Diskretno-kontinual’nye metody rascheta sooruzheniy [Discrete-continual Methods of Structural Analysis]. Moscow, Arhitektura-S Publ., 2010, 336 p.
  3. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Chislennye i analiticheskie metody rascheta stroitel’nykh konstruktsiy [Numerical and Analytical Methods of Structural Analysis]. Moscow, ASV Publ., 2009, 336 p.
  4. Zakharova T.V., Shestakov O.V. Veyvlet-analiz i ego prilozheniya [Wavelet-analysis and Its Applications]. Moscow, Infra-M Publ., 2012, 158 p.
  5. Kech V., Teodoresku P. Vvedenie v teoriyu obobshchennykh funktsiy s prilozheniyami v tekhnike [Introduction into the Theory of Generalized Functions and Their Engineering Applications]. Moscow, Mir Publ., 1978, 518 p.

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