In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.

The article considers the synthesis methods of an automatic invariant system of the pitch angle stabilization of an unmanned aerial vehicle that is based on the concept of inverse dynamics problems. The methods and results of simulation mathematical results of synthesized stabilization loop with using the Simulink of program MATLAB. The results of a comparative analysis of the dynamic characteristics of the contour of angular stabilization of an unmanned aerial vehicle by pitch angle with a PID-controller and a synthesized robust controller are presented.

In this paper, the influence of various types of distortion of an image on its quality while reducing its sizes, is investigated. To assess the image quality, it is proposed to use the method of comparison with the standard using a previously developed measure based on the proximity of the values of the parameters of the Weibull distribution, which describes the gradient field of the image. The well-known TID2013 image database was used as the material, which includes 3000 images distorted by 24 types of distorting algorithms with five levels. Each image of the base was reduced by 2, 4 and 8 times by the two most common methods and compared with the original image-original. The calculations were performed for five types of distortions implemented in the database. To make a decision on the acceptability of the applied quality measure, the calculated measure values were compared with the subjective quality ratings provided along with the documentation on the TID2013 database. The comparison was carried out using Spearman’s correlation coefficient. It is shown that the average values of correlations for all images at three types of distortions are very high, while for the other two they are unacceptably low. An attempt has been made to explain this situation by the properties of distorting algorithms that change the structural properties of the image to varying degrees.

The possibility of comparing images of the same scene, but with different resolutions, is demonstrated.

The possibility of an accurate estimation of the pipe wall thickness measured directly from the reconstructed image of the pipe, reconstructed from only a few X-ray projections made in a limited viewing angle, is discussed. Since the effects of radiation scattering and X-ray beam hardening distort up to 50 % of the primary radiation, ignoring these effects leads to blurred images, strong artifacts, and inaccurate sizing. A computerized technique has been developed that takes into account the contribution of scattered radiation and the hardening of the X-ray beam. Iterative Bayesian reconstruction techniques are then used to reconstruct the pipe image using the volumetric and surface-oriented representation of the pipe. Using these methods, the error in estimating the pipe wall thickness can be increased to 300 microns.

Nowadays, when designing and operating electric power systems, special attention is paid to predicting emergency situations and minimizing losses in case they occur. The most common method of overvoltage investigations is the use of simulation models in specialized application packages, which imposes additional qualification requirements on the electrical engineer.

The authors propose modeling technologies and a software tool for modeling and research of overvoltages that occur in 6–10 kV distribution networks at single-phase ground faults, including the method of visual design of the distribution network through the use of information technology and automated generation of mathematical model for its further study to analyze overvoltages.

When creating cellular structures, one of the tasks is to study the flows of liquids in the cavities of structures in order to obtain data on the velocities, pressures, and features of the current lines. The properties of cellular structures depend on the geometry of the cavities and their relative position.

The article describes the sequence of stages of modeling fluid flow in the cavities of cellular structures and the results of variant calculations for various types of such structures.