Research of Entropy Estimates of Diagnostic Characteristics of Technological Systems Based on Probability Distributions

Abstract

In the study, a combination of theoretical fundamentals and practical experiments is carried out to substantiate a universal information-based approach to the diagnosis of technological systems. At the outset of the study, the authors invoke the fundamental concepts of Shannon entropy as a measure of uncertainty, explaining its role in the quantitative assessment of the informational richness of diagnostic signals. The central premise is that traditional statistical metrics — such as the mean or variance — do not always allow for a comprehensive description of complex structural changes in materials, especially under conditions of magneto-resonant processing. It is for this reason that an approach was developed enabling the comparison of different probabilistic models on a single informational scale. The methodology is presented in detail, involving the construction of a unified, normalized parameter space: all distributions are aligned according to common characteristics of mean value and dispersion, ensuring an impartial comparison. Using five materials — steel, copper, duralumin, textolite, and acrylic glass — as examples, the authors model spectral responses to broadband vibrational excitation in a constant magnetic field. For each sample, amplitude-frequency characteristics are obtained, which make it possible to identify the unique “spectral fingerprints” of the materials. The high degree of order in the steel response, manifested by a pronounced resonance peak, contrasts with the nearly uniform spectrum of the dielectrics, indicating different interaction mechanisms between broadband vibrations and the magnetic field in these materials. The results demonstrate that spectral entropy is a sensitive indicator of structural changes: a decrease in its value correlates with an increase in material ordering, whereas an elevated entropy indicates an even distribution of energy across frequencies. Based on these findings, practical recommendations are formulated for selecting optimal statistical models for different classes of materials: for example, for ferromagnetic metals it is advisable to use distributions with heavier tails, while for non-metallic materials models with maximal informational uncertainty are preferred. The proposed approach opens new prospects for information-oriented diagnostics and non-destructive testing, contributing to enhanced reliability and efficiency of technological processes in mechanical engineering and materials science.