The article deals with an actual task of developing engineering methods for predicting the durability of modern long-life machines should be based on the methodology for determining the degree of fatigue damage to materials and structural elements. In the development of such a methodology, the work proposes to use modern optical and computer tools that allow analyzing the parameters of the deformed surface of metal structure samples and, on this basis, to estimate the residual resource of the metal structure. The purpose of the article was to substantiate a methodical approach for determining the limit state of damage using photometric analysis of the topography of the micro-deformed surface of cyclically loaded metal structure samples. To analyze the fatigue damage characteristics of metals and alloys, an experimental information system was developed based on the method of coherent optical scanning of the deformed surface of metal structure samples with a resolution of 0.2 μm/px. The obtained specklograms of the photodiode matrix, corresponding to the two-dimensional image of the micro-deformed surface of the sample in shades of gray 0-255, were computer analyzed. This made it possible to construct diagrams of the kinetics of the process of accumulation of the amplitude of the deformation microrelief of the surface of the laboratory samples for the studied steels St 45 and St 20. It is shown that the kinetics of speckle brightness obtained in the work by the correlation method, which corresponds to the evolution of the accumulation of fatigue damage on the surface of the studied structural steel samples, is characterized by a nonlinear function, which is consistent with the results of deformation microrelief studies obtained by other methods. The proposed methodology for analyzing the discrete distribution of specklogram brightness can be used to predict the onset of the limit state of a metal structure before failure due to fatigue

The object of research is the processes of error correction transformation of information in automated systems. The research is aimed at reducing the complexity of decoding cyclic codes by combining modern mathematical models and practical tools. The main prerequisite for the complication of computations in deterministic linear error-correcting codes is the use of the algebraic representation as the main mathematical apparatus for these types of codes. Despite the universalism of the algebraic approach, its main drawback is the impossibility of taking into account the characteristic features of all subclasses of linear codes. In particular, the cyclic property is not taken into account at all for cyclic codes. Taking this property into account, one can go to a fundamentally different mathematical representation of cyclic codes – the theory of linear automata in Galois fields (linear finite-state machine). For the automaton representation of cyclic codes, it is proved that the problem of syndromic decoding of these codes in the general case is an NP-complete problem. However, if to use the proposed hierarchical approach to problems of complexity, then on its basis it is possible to carry out a more accurate analysis of the growth of computational complexity. Correction of single errors during one time interval (one iteration) of decoding has a linear decoding complexity on the length of the codeword, and error correction during m iterations of permutations of codeword bits has a polynomial complexity. According to three subclasses of cyclic codes, depending on the complexity of their decoding: easy decoding (linear complexity), iteratively decoded (polynomial complexity), complicate decoding (exponential complexity). Practical ways to reduce the complexity of computations are considered: alternate use of probabilistic and deterministic linear codes, simplification of software and hardware implementation by increasing the decoding time, use of interleaving. A method of interleaving is proposed, which makes it possible to simultaneously generate the burst errors and replace them with single errors. The mathematical apparatus of linear automata allows solving together the indicated problems of error correction coding.