ABOUT MULTISCALE MODELING WITH THE USE OF HAAR DISCRETE WAVELETS FOR TARGETED DATA EXTRACTION IN PROBLEMS OF STRUCTURAL MECHANICS
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Abstract
The distinctive paper is devoted to multiscale modelling of functions with the use of Haar discrete wavelets. Numerical implementation is realized with the use of “Fortran” programming language (“Intel Visual Fortran” software). Particularly several sample functions are under consideration. Three basic parts of corresponding algorithm include full wave reconstruction (implementing the entire Hilbert space of the wave); extraction of wave components constructed solely by wavelet functions; isolation and visualization of the final wavelet layer. Modeling wave behavior from multiple perspectives enables the extraction of highly valuable information, which can reveal defects in mechanical or structural systems. The Haar discrete wavelet, due to its basis and step-like wavelet functions, is particularly suitable for numerical implementation (programming, computation), featuring straightforward algorithms.
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References
Olivier R., Vetterli M. Wavelets and signal processing. // IEEE signal processing magazine, 1991, Volume 8, No. 4, pp. 14-38.
Coifman R.R., Meyer Y., Wickerhauser V.M. Wavelet analysis and signal pro-cessing. // In Wavelets and their applica-tions, 1992.
Mallat S. A wavelet tour of signal pro-cessing. Elsevier, 1999, 620 pages.
Körner T.W. Fourier analysis. Cambridge university press, 2022, 606 pages.
Grafakos L. Classical fourier analysis. Volume 2. New York, Springer, 2008, 492 pages.
Norman L. Compaq Visual Fortran: A guide to creating windows applications. Elsevier, 2002, 462 pages.
Chen C.F., Hsiao C.H. Haar wavelet method for solving lumped and distributed-parameter systems. // IEE Proceedings-Control Theory and Applications, Volume 144, No. 1, 1997, pp. 87-94.
Burrus C.S. Introduction to wavelets and wavelet transforms: a primer. Pearson, 1997, 288 pages.
Mohamed A.R., Baleanu D. Haar wavelets scheme for solving the unsteady gas-flow in 4-D. // Thermal Science, Volume 24, No. 2, Part B, 2020, pp. 1357-1367.
Jin-Sheng G., Jiang W.-S. The Haar wave-lets operational matrix of integration. // In-ternational Journal of Systems Science, Volume 27, No. 7, 1996, pp. 623-628.
Lepik Ü. Numerical solution of differential equations using Haar wavelets. // Mathe-matics and computers in simulation, Vol-ume 68, No. 2, 2005, pp. 127-143.
Xinhua X., Xiao F., Wang S. Enhanced chiller sensor fault detection, diagnosis and estimation using wavelet analysis and prin-cipal component analysis methods. // Ap-plied Thermal Engineering, Volume 28, No. 2-3, 2008, pp, 226-237.
Abubakar U. et al. Induction motor fault detection based on multi-sensory control and wavelet analysis. // IET Electric Power Applications, Volume 14, No. 11, 2020, pp. 2051-2061.
Shen Y.-L., Wai R.-J. Wavelet-Analysis-Based Singular-Value-Decomposition Al-gorithm for Weak Arc Fault Detection via Current Amplitude Normalization. // IEEE Access, Volume 9, 2021, pp. 71535-71552.
Hani M., Kim H. Damage detection in concrete by Fourier and wavelet analyses. // Journal of Engineering Mechanics, Volume 129, No. 5, 2003, pp. 571-577.
Kim H., Hani M. Damage detection of structures by wavelet analysis. // Engineer-ing structures, Volume 26, No. 3, 2004, pp. 347-362.
Lepik Ü., Helle H. Haar wavelets. Springer Science & Business Media, 2014, 207 pag-es.
Aslami M., Akimov P.A. Wavelet-based finite element method for multilevel local plate analysis. // Thin-Walled Structures, Volume 98, 2016, pp. 392-402.
Mohammed O.A., Abed N.Y., Ganu S. Modeling and characterization of induction motor internal faults using finite-element and discrete wavelet transforms. // IEEE Transactions on Magnetics, Volume 42, No. 10, 2006, pp. 3434-3436.
Oruç Ö., Fatih B., Alaattin E. Numerical solutions of regularized long wave equation by Haar wavelet method. // Mediterranean Journal of Mathematics, Volume 13, No. 5, 2016, pp. 3235-3253.
Kim K. et al. Application of Haar wavelet discretization method for free vibration analysis of inversely coupled composite laminated shells. // International Journal of Mechanical Sciences, Volume 204, 2021, pp. 106549.