Digital Spectral Analysis by means of the Method of Averag Modified Periodograms Using Binary-Sign Stochastic Quantization of Signals

The method of averaging modified periodograms is one of the main methods for estimating the power spectral density (PSD). The aim of this work was the development of mathematical and algorithmic support, which can increase the computational efficiency of signals digital spectral analysis by this method.The solution to this problem is based on the use of binary-sign stochastic quantization for converting the analyzed signal into a digital code. A special feature of this quantization is the use of a randomizing uniformly distributed auxiliary signal as a stochastic continuous quantization threshold (threshold function). Taking into account the theory of discrete-event modeling the result of binary-sign quantization is interpreted as a chronological sequence of instantaneous events in which its values change. In accordance with this we have a set of time samples that uniquely determine the result of binary-sign quantization in discrete-time form. Discrete-event modeling made it possible to discretize the process of calculating PSD estimates. As a result, the calculation of PSD estimates was reduced to discrete processing of the cosine and sine Fourier transforms for window functions. These Fourier transforms are calculated analytically based on the applied window functions. The obtained mathematical equations for calculating the PSD estimates practically do not require multiplication operations. The main operations of these equations are addition and subtraction. As a consequence, the time spent on digital spectral analysis of signals is reduced.Numerical experiments have shown that the developed mathematical and algorithmic support allows us to calculate the PSD estimates by the method of averaging modified periodograms with a high frequency resolution and accuracy even for a sufficiently low signal-to-noise ratio. This result is especially important for spectral analysis of broadband signals.The developed software module is a problem-oriented component that can be used as part of metrologically significant software for the operational analysis of complex signals.

Averaging technique in the problem of satellite attitude stabilization in indirect position in the orbital reference frame with the use of Lorentz torque

A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging differential equations is developed. Using the original construction of the unsteady Lyapunov function, we obtain sufficient conditions for the asymptotic stability of the programmed satellite motion mode in the form of constructive inequalities with respect to the control parameters.

Research of Soil Intrusion Depth of Crude Oil upon Emergency Spills of Oil Products

The task regarding determination of optimum temperature upon which the oil products soil intrusion depth reaches minimum is formulated and solved. It is noted that increase of temperature enhance vaporization of liquid hydrocarbons from one side which leads to decrease of intrusion depth and from another side increase speed of intrusion into soil which increase the intrusion depth. As a result the mean depth of intrusion calculated using method of averaging these factors effects has a minimum in some value of temperature. It is shown that this minimum is proportional to logarithm of time interval passed after spill event.

Formation of technological schemes during working off steeply inclined layers

Purpose. Creation of technological schemes ofdevelopment of steeply inclined layers in the conditions of the formation of edges of deep iron ore pits during the development of deep steeply dipping deposits in order to determine the width of the working platform. The research of the methodology consists in the development of new technological schemes and the use of existing schemes for the development of benches in the conditions of steeply dipping deposits. The next step is determining the width of the working platform, depending on the layout of the main equipment and the sequence of working off the bench. At the same time, the selected equipment allows to determine the parameters of the working platform of bench. For selecting the equipment, four options of equipment were distinguished according to the averaged parameters of modern mining machines, i.e. the method of averaging indicators was used. Findings. New technological schemes have been developed, as well as existing technological schemes have been used to substantiate the width of the working platform during the formation of steeply inclined layers on the deep edges of pits during the development of deep iron ore deposits. A technique was created that allows you to preliminarily determine the width of the working platform using a nomogram that takes into account the height of the bench, one of the options of equipment that can be used in the development of the bench and the scheme of development. The originality. Graphic dependencies were established for determining the width of the steeply inclined layer. These dependencies will be used during the development of the pit edge. Based on the obtained dependencies, taking into account the formation of technological schemes, it is possible to determine in advance what the width of the bench. Also, the complex mechanization (options 1-4) and the scheme with different heights of the bench are used, which allows to determine the most promising schemes of development, and in the future the rate of change in the level of areas of the steeply inclined layer. Practical implications. The possibility was established by a graphical method to determine the optimal width of the working platform or layer on a separate horizon or within a block, using complex mechanization. The results allow to prepare data (mining flowsheet bench (s), a width platform (layer) by selecting the equipment suitable to work on the bench with the corresponding parameters) for further design of the staged development of steeply inclined layers of deep open pits.

Method of Averaging the Effective Thermal Conductivity Based on Thermal Response Tests of Borehole Heat Exchangers

This work concerns borehole heat exchangers and their testing using apparatus for thermal response tests. In the theoretical part of the article, an equation was derived from the known equation of heat flow, on which the interpretation of the thermal response test was based. The practical part presents the results of several measurements taken in the AGH Laboratory of Geoenergetics. They were aimed at examining the potential heat exchange capacity between the heat carrier and rock mass. Measurement results in the form of graphs are shown in relation to the examined, briefly described wells. Result analysis made it possible to draw conclusions regarding the interpretation of the thermal response test. The method of averaging the measurement results was subjected to further study. The measuring apparatus recorded data at a frequency of one second, however such accuracy was too large to be analyzed efficiently. Therefore, an average of every 1 min, every 10 min, and every 60 min was proposed. The conclusions stemming from the differences in the values of effective thermal conductivity in the borehole heat exchanger, resulting from different data averaging, were described. In the case of three borehole heat exchangers, ground properties were identical. The effective thermal conductivity λeff was shown to depend on various borehole heat exchanger (BHE) designs, heat carrier flow geometry, and grout parameters. It is important to consider the position of the pipes relative to each other. As shown in the charts, the best (the highest) effective thermal conductivity λeff occurred in BHE-1 with a coaxial construction. At the same time, this value was closest to the theoretical value of thermal conductivity of rocks λ, determined on the basis of literature. The standard deviation and the coefficient of variation confirmed that the effective thermal conductivity λeff, calculated for different time intervals, showed little variation in value. The values of effective thermal conductivity λeff for each time interval for the same borehole exchanger were similar in value. The lowest values of effective thermal conductivity λeff most often appeared for analysis with averaging every 60 min, and the highest—for analysis with averaging every 1 min. For safety reasons, when designing (number of BHEs), safer values should be taken for analysis, i.e., lower, averaging every 60 min.