Analysis of G -Transformation Modes for Building Neuro-like Parallel–Hierarchical Network Identification of Rail Surface Defects

Vaidas Lukoševičius (), Volodymyr Tverdomed (), Leonid Tymchenko, Natalia Kokriatska, Yurii Didenko, Mariia Demchenko and Olena Oliynyk
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Vaidas Lukoševičius: Department of Transport Engineering, Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentų Str. 56, 44249 Kaunas, Lithuania
Volodymyr Tverdomed: Kyiv Institute of Railway Transport, State University of Infrastructure and Technology, Kyrylivska Str. 9, 04071 Kyiv, Ukraine
Leonid Tymchenko: Kyiv Institute of Railway Transport, State University of Infrastructure and Technology, Kyrylivska Str. 9, 04071 Kyiv, Ukraine
Natalia Kokriatska: Kyiv Institute of Railway Transport, State University of Infrastructure and Technology, Kyrylivska Str. 9, 04071 Kyiv, Ukraine
Yurii Didenko: Kyiv Institute of Railway Transport, State University of Infrastructure and Technology, Kyrylivska Str. 9, 04071 Kyiv, Ukraine
Mariia Demchenko: Kyiv Institute of Railway Transport, State University of Infrastructure and Technology, Kyrylivska Str. 9, 04071 Kyiv, Ukraine
Olena Oliynyk: Kyiv Institute of Railway Transport, State University of Infrastructure and Technology, Kyrylivska Str. 9, 04071 Kyiv, Ukraine

Mathematics, 2025, vol. 13, issue 6, 1-14

Abstract: This work presents the construction of a transformation for the identification of surface defects on rails, starting with the selection of elements from the matrix and the creation of different matrices. It further elaborates on the recursive formulation of the transformation and demonstrates that, regardless of the elements’ uniqueness, the sum of the transformed matrix remains equal to the sum of the original matrix. This study also addresses the handling of matrices with repeated elements and proves that the G -transformation preserves information, ensuring the integrity of data without any loss or redundancy.

Keywords: transformations; parallel–hierarchical networks; parallelism; signal processing; neural networks; rail surface defects (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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