An analytical approach to the study of Markov processes is proposed. Using an algorithm for selective search of input–output operators and simple analytical procedures, time probability functions are obtained for real and complex conjugate eigenvalues of the transition intensity matrix. Estimates of the time of onset of the stationary regime are given. Examples of the analysis of homogeneous and heterogeneous Markov processes with piecewise constant transition intensities, non-Markov processes with pseudo-states generated by Erlang flows, as well as substantiation of requirements for the intensity of restoration (efficiency of the repair body) in a technical system are considered. The main results are illustrated by probability estimation in a rigorous analytical form.

An approach to adjusting the parameters of adaptive control in a sliding mode with super-twisting, used for nonlinear systems with parametric uncertainty, is presented. The approach is based on Jaya algorithm, which ensures the efficiency and stability of the control system in changing conditions. Taking into account the complexity of the model description and the presence of uncertainty, as well as fine-tuning the parameters of the regulator in sliding mode with supercooling are essential to ensure optimal system performance. The influence of various system parameters on its behavior and stability is studied using the Jaya algorithm, which ensures the achievement of an optimal mode of operation. The results of numerical simulation show that adaptive control of a nonlinear system in a sliding mode with super-twisting, optimized using the Jaya algorithm, provides higher system performance and resistance to interference, compared with traditional approaches. The effectiveness of the proposed approach is confirmed by the example of an inverted pendulum model on a trolley.

The problem of automating the analysis of handwritten documents is solved. It is shown that artificial neural networks capable of recognizing images after training on the original data set are used to solve such problems. At the same time, the quality of recognizing new images largely depends on the stage of pre-processing of digitized handwritten documents. A particular preprocessing problem is considered - removing cell lines from an image of a notebook sheet. Four methods of image filtering are analyzed using the OpenCV library of the Python language. A neural network of convolutional architecture is trained to recognize handwritten characters. The work of the trained neural network on documents preprocessed by different algorithms is demonstrated.

A self-routing analog-to-digital converter based on a single-layer neural network consisting of basic measuring neurons is considered. For the main measuring neuron, a control system is presented that implements self-routing of signals in a neural network using the “echolocation” method when forming an individual meter of the required bit depth. A method is proposed to reduce the hardware costs of implementing a control system by using a local fragmented control device, the elements of which are distributed among neurons and can be combined to control the operation of an analog-to-digital converter. Functional schemes of a local fragmentary control device with separation of counters used in “echolocation” have been developed, on the basis of which models have been built in the Quartus environment, using the latter to estimate hardware costs measured in the number of LUT logic blocks and registers used. The compilation of the project for a programmable logic integrated circuit showed a 20-25% reduction in hardware costs (depending on the parameters of the neural network), compared with using a control device without separating counters. It should be noted that the local fragmented management device makes it easier to scale the network and increase its fault tolerance.

The features of the use of sacrificial layers in the manufacture of multilayer Al–Ni foil, characterized by the effect of self-expanding high-temperature synthesis, are considered. In order to avoid peeling during the foil production, there must be good adhesion between the substrate and the foil. On the other hand, to produce the final product, the foil must be peeled off the surface of the substrate, which implies a low degree of adhesion. It is possible to resolve this technological contradiction by using sacrificial layers, that is, films of material that are applied to the substrate before forming the foil, and then dissolved or etched off, thereby destroying the physical bond between the foil and the substrate. For this reason, it is particularly relevant to study the use of various materials as sacrificial layers in the manufacture of multilayer foils with the effect of self-expanding high-temperature synthesis. A variant of the layout of a magnetron sputtering system is proposed, which makes it possible to use six magnetrons in a single technological cycle for the formation of a multilayer Al–Ni structure. The thickness of the obtained foil is determined using electron microscopy. It is shown that the use of a polyvinyl alcohol film with a thickness of 30 microns as a sacrificial layer makes it possible to peel off multilayer Al–Ni foil without mechanical damage and loss of the ability to react with self-expanding high-temperature synthesis.

A method is proposed that involves adaptive change of laser power depending on the size of the forest area under study for early detection of forest fires. The proposed method is optimized in relation to finding such a power-distance dependence that minimizes the detectable concentration of the sought substance — the combustion product. Taking into account the limitation of the energy resource allocated for such monitoring, a functional dependence of the optimal power of the probing radiation on the distance to the object is obtained, at which the threshold for recording the concentration of combustion products reaches the lowest value.

A macro- and microstructural analysis of the axle box bearings of freight wagons has been carried out. An increase in the hardness of the material of the rollers that have been in use in relation to the hardness of the new roller has been established. It is found that in light and dark areas, there is a softening of the rollers and a significant decrease in the standard hard-ness of hardened bearing steel SHKh15SG. This leads to the creation of zones of residual stresses at the interfaces of the original martensitic and transformed troostomartensitic structures, which can ultimately cause the appearance of microcracks in the rollers and, as a consequence, cause a decrease in the service life of the axle box bearings of freight cars in operation.

In the conditions of shortage of engineering personnel, intelligent design and modeling platforms are designed to solve automation problems in the field of material production. Transformation of the technological business model of small enterprises during the transition to digital production is aimed at creating science-intensive products with improved consumer qualities and increasing the flexibility of the management system. The activities of small enterprises at the PDM/ MES level include tasks to ensure technological sovereignty, which is an integral part of the import substitution policy. CAD/CAE/CAM platforms are part of the enterprise’s information field, providing its filling with design and technological documentation. The digital format for executing projects and tasks at the stage of production preparation allows reducing product release times. The design practices in CAD/CAE/CAM applications of projects carried out at small instrument-making enterprises are shown.

The laser ablation method has significant advantages in processing workpieces from hard materials, since it ensures the removal of material without wear of the forming tool and load on the workpiece. A method for processing tungsten carbide using laser ablation of nanosecond pulse duration is described. The results of the analysis of the tungsten carbide surface morphology after exposure to short laser pulses are presented. The roughness of the processed surface is studied using the contact profilometry method. The effect of laser exposure parameters (pulse repetition rate, pulse duration) on the geometric parameters (ablation depth and roughness) of the surface of tungsten carbide workpieces is studied. It is found that with an increase in energy density, pulse duration and an increase in the overlap coefficient of laser pulses, the roughness of the processed surface increases. The tangential laser processing strategy is shown to provide the best surface quality.

A method for diagnosing the technical condition of electrical insulators installed on overhead power transmission lines is considered. The purpose of the study is to develop tools for assessing the operability of electrical equipment, which will improve the reliability of power supply and the safety of operation of overhead power transmission lines. An approach to the diagnosis of insulators based on mathematical modeling of their electrical and physical characteristics is proposed. The use of such models makes it possible to predict changes in insulation parameters under the influence of various factors, including climatic conditions, aging of materials and operational loads. The results demonstrate the prospects of using mathematical modeling in the tasks of diagnostics and preventive maintenance of high-voltage line equipment. The mathematical models take into account the mechanical and electrical effects on insulators, such as mechanical loads, temperature, humidity, and pollution levels. In particular, material state equations, fracture criteria, and damage accumulation models are used to assess the current condition and predict future failures. The use of machine learning methods makes it possible to automate the process of classifying the condition of equipment and predict the probability of its failure. The practical application of these approaches can significantly reduce the risks of emergencies and optimize equipment maintenance.