The paper tackles the problem of performing mutual testing in complex systems. It is assumed that units of complex systems can execute tests on each other. Tests among system units are part of system diagnosis that can be carried out both before and during system operation. The paper considers the case when tests are executed during system operation. Modelling and simulating mutual tests will allow evaluation of the efficiency of using joint testing in the system. In the paper, the models that use Petri Nets were considered. These models were used for simulating the execution of tests among system units. Two methods for performing such simulations were evaluated and compared. Recommendations for choosing a more appropriate way were made. Simulation results have revealed minor model deficiencies and possible implementation of mutual testing in complex systems. Improvement of the model was suggested and assessed. A recommendation for increasing the efficiency of system diagnosis based on joint testing was made.

The paper reveals the problem of the lack of standard non-destructive diagnostic methods for high-power microwave devices aimed at regeneration. The issue is understudied and requires further research. The conducted analysis of state of the art on the subject area exhibited that image processing was used to specify the examined object's target characteristics in a wide range of research. Having summarized the considered image comparison methods on the subject area of this work, the authors formulated several requirements for the selected image analysis method based on the automated non-destructive diagnosis of resonator units for high-power magnetrons. The primary requirement is using non-iterative algorithms; the second condition is a chosen method of image analysis, and the third option is the number of pixels for a processed image. It must significantly exceed the number of descriptors required for making a decision. Guided by the analysis results and based on the results of previous studies conducted by the authors, the algorithm for identifying a defect in the resonator unit of a microwave device based on the image of the frequency-azimuthal distribution for the probing field phase difference expressed by the Zernike moments is proposed. MATLAB R14a was used as a modeling environment. The descriptor vector was restricted to the Zernike moments, including the 7th order. The work is interdisciplinary and written at the intersection of technical diagnostics, microwave engineering, and digital image processing.

This manuscript presents the economic research results based on their input-output characteristics and functional description with inductive modeling methods and tools. There are a wide plethora of methods to be used for solving this type of problem, including various neural network models, linear and nonlinear regressions, reference vectors’ methods, fuzzy models, etc. The main disadvantage of these methods is that the obtained models cannot always interpret and obtain a model of optimal complexity. Unlike the mentioned methods and tools, the group method of data handling (GMDH) allows building models directly from a data sample without the attraction of additional a priori information. This algorithm admits finding internal dependencies in the data and determining optimal model complexity. There is a broad range of iterative GMDH algorithms that have been developed and studied. Oversampling algorithms are applicable for solving the structural identification problems for a limited number of arguments. Iteration algorithms are suitable for solving tasks with many arguments, but they do not guarantee proper structure development. Multi-row GMDH iteration algorithms are the most popular ones. However, they have several sufficient defects, such as informative argument loss or non-informative argument inclusion, as well as a polynomial degree of exponential growth. In this context, the applicability of the GMDH-based iterative and combined architectures for solving the model's interrelation problems between a volume of capital investments and GDP by activity types in the transport branch is considered. The determination coefficient is utilized for the estimation of the obtained models based on a complicated evaluation procedure. The Kolmogorov-Smirnov criterion estimates the model’s adequacy. The F-criterion Fisher assesses the significance of polynomial models. The demonstrated results proved that the combined iterative and combinatorial algorithms turned out to be the most effective solution for all evaluation criteria.