ИСПОЛЬЗОВАНИЕ ЭКСПЕРТНЫХ СИСТЕМ ДЛЯ ПОВЫШЕНИЯ НАДЕЖНОСТИ СИСТЕМ РАДИОСВЯЗИ

The problem of estimating the number of summands of random variables for a total normal distribution law or a sample average with a normal distribution is investigated. The Central limit theorem allows us to solve many complex applied problems using the developed mathematical apparatus of the normal probability distribution. Otherwise, we would have to operate with convolutions of distributions that are explicitly calculated in rare cases. The purpose of this paper is to theoretically estimate the number of terms of the Central limit theorem necessary for the sum or sample average to have a normal probability distribution law. The article proves two theorems and two consequences of them. The method of characteristic functions is used to prove theorems. The first theorem States the conditions under which the average sample of independent terms will have a normal distribution law with a given accuracy. The corollary of the first theorem determines the normal distribution for the sum of independent random variables under the conditions of theorem 1. The second theorem defines the normal distribution conditions for the average sample of independent random variables whose mathematical expectations fall in the same interval, and whose variances also fall in the same interval. The corollary of the second theorem determines the normal distribution for the sum of independent random variables under the conditions of theorem 2. According to the formula relations proved in theorem 1, a table of the required number of terms in the Central limit theorem is calculated to ensure the specified accuracy of approximation of the distribution of the values of the sample average to the normal distribution law. A graph of this dependence is constructed. The dependence is well approximated by a polynomial of the sixth degree. The relations and proved theorems obtained in the article are simple, from the point of view of calculations, and allow controlling the testing process for evaluating students ' knowledge. They make it possible to determine the number of experts when making collective decisions in the economy and organizational management systems, to conduct optimal selective quality control of products, to carry out the necessary number of observations and reasonable diagnostics in medicine.

The article deals with matters concerned with the problem of determining the statistical characteristics of variable parameters (the variation range and distribution law) in analyzing the uncertainty and sensitivity of calculation results to uncertainty in input data. A comparative analysis of modern approaches to uncertainty in input data is presented. The need to develop an alternative method for estimating the uncertainty of model parameters used in thermal–hydraulic computer codes, in particular, in the closing correlations of the loop thermal hydraulics block, is shown. Such a method shall feature the minimal degree of subjectivism and must be based on objective quantitative assessment criteria. The method includes three sequential stages: selecting experimental data satisfying the specified criteria, identifying the key closing correlation using a sensitivity analysis, and carrying out case calculations followed by statistical processing of the results. By using the method, one can estimate the uncertainty range of a variable parameter and establish its distribution law in the above-mentioned range provided that the experimental information is sufficiently representative. Practical application of the method is demonstrated taking as an example the problem of estimating the uncertainty of a parameter appearing in the model describing transition to post-burnout heat transfer that is used in the thermal–hydraulic computer code KORSAR. The performed study revealed the need to narrow the previously established uncertainty range of this parameter and to replace the uniform distribution law in the above-mentioned range by the Gaussian distribution law. The proposed method can be applied to different thermal–hydraulic computer codes. In some cases, application of the method can make it possible to achieve a smaller degree of conservatism in the expert estimates of uncertainties pertinent to the model parameters used in computer codes.

A survey of evaluation techniques used for expert systems in telecommunications

Summation of random errors having normal, uniform, and arcsine distribution laws

Modern livestock development trends in the agricultural production structure include the use of feed mixers and distribution equipment. However, a stream of malfunctions and failures is reported for mixer-feeders due to factors that are specific to agricultural enterprises in Ukraine, which reduce the operational reliability of feed mixers and distributors. The study aims to evaluate the quantitative indicators of the in-service reliability of mixer-feeders and develop methods to improve them. The reliability test plan [NMT] was used, which implies a certain number of research objects (N), objects undergoing repair in case of performance loss (M), and tests terminated when the operating time (T) is reached. Initial information was collected and processed, and empirical data on the time between failures of KUHN PROFILE 12.2 DS and PROFILE 14.2 DS mixer-feeders in Ukraine were analysed. The analysis established that the faulty condition of mixers-feeders in the initial operation period is caused by the second complexity group failures. Failures related to the loss of the grinding and mixing mechanism, which limits the average time between failures of the feed mixture and distribution equipment, were identified among the second complexity malfunction group. A statistical analysis of the mixer-feeder failure occurrence was carried out. The failure probability of the grinding-mixing mechanism of the feed mixer was determined to be within the normal distribution law. The main parameters of the given theoretical distribution law were determined by calculation results. The calculations determined that the average time between failures is 3152.0 motor-hours; the standard deviation is 902.6 motor-hours; and the coefficient of variation is 0.40. An average time between failures of the study objects was proved to be consistent with the normal distribution law following Kolmogorov’s agreement criterion. Calculations determined that the average reliability index value, according to the normal distribution law, is within the confidence intervals: 1964.2 motor-hours – lower confidence limit; 4339.8 motor-hours – upper confidence limit. The obtained results may be used to improve the mixer-feeder operational reliability

The paper analyzes the homogeneity of the stochastic structure of the samples of oil flax fibres of the Ukrainian and Polish selections. The distribution laws of fibres as mixtures of the normal and logarithmically normal distribution laws are identified. The general probability distribution law of fibre lengths of oil flax of the Ukrainian selection is a mixture of four logarithmically normal laws of distribution, and the general probability distribution law of fibre lengths of oil flax of the Polish selection is a mixture of a normal distribution law and three logarithmically normal laws of distribution. The parameters of the relevant components of the common distribution laws are found as a result of solving the problem of nonlinear optimization using the method of generalized lowering gradient that is implemented in Excel tabular processor. The adequacy of the built nonlinear models of the distribution laws is proved by estimating the value of the determination index. The comparative analysis of distribution laws of general totalities, from which the oil flax fibre samples of the Ukrainian and Polish selections are obtained, is conducted by the Kolmogorov-Smirnov statistical criterion. This criterion allows us to test and reject the hypothesis about belonging of two independent samples to the same general totality. The analysis of the general distribution laws shows that the oil flax fibres of the Ukrainian selection have a more pronounced tendency to stratification by a fibre length. Such a fibre is easily divided into factions. The oil flax fibres of the Polish selection have a larger part of short and extra-long fibres. Thus, it is clear that raw materials of the Ukrainian selection are more suitable for the production of non-woven materials of different target purposes, and the Polish selection - for the production of ropes, cords, etc. The obtained results can be used by specialists at processing enterprises for a reasonable choice of raw materials, optimization of processing modes and improving ready-made product quality.

The change of load of the transformer substation TS 10 / 0,4 kV in the mode of maximum and minimum load is measured.It is noted that the process is nonstationary at the daily interval.Hourly intervals of time are highlighted on the daily graph of electrical load, the study of the law of distribution is conducted, and the normal law of distribution is confirmed by Pearson's criterion.The stationarity test was performed on parametric tests, namely the verification of the Fisher's Fisher's constant variance and the mathematical expectation of the Student's t-test and the correlation function.The values of numerical characteristics were obtained at the stationary areas and a probabilistic mathematical model of the TS 10 / 0.4 kV load was constructed.

Warning and prevention of natural emergencies is based on the analysis and forecasting of threats of emergency situations in the state. At the same time, the forecasting of natural emergencies should be aimed at regulating natural safety in the country, assessing the threats of emergencies and their prevention. Prevention of natural emergencies of various natures, minimization of their consequences is a component of creating safe conditions for the individual and society as a whole, an integral part of the state policy of national security of the country. Ensuring safety in emergency situations requires reliable functioning of the emergency response system adequate to the level and nature of threats. The effectiveness of planning and implementing measures to prevent natural emergencies is determined by the quality of forecasting the threats of their occurrence Since the processes of occurrence of natural emergencies are of a random nature, knowledge of the law of distribution of the random variable “number of emergencies” in the state on the basis of statistical data acquires importance. The article presents the results of checking the compliance of statistical data on natural emergencies in the state with the normal distribution law. Based on the processing and analysis of monitoring data for natural emergencies, a hypothesis was put forward about the normal law of distribution of the random variable the «number of natural emergencies» in the state in accordance with the available information. Pearson’s goodness-of-fit test was chosen to test the proposed hypotheses. An assessment was made in accordance with the chosen criterion of the hypothesis about the agreement of the sample distribution with the law of normal distribution. Asa result of the research, it was found that the hypothesis put forward does not contradict the statistical data of monitoring natural emergencies over a certain period of time. The parameters of the established distribution law were evaluated.

Expert systems in telecommunications

The increased accessibility of data that computers provide has caused a range of expert and information-retrieval systems to be designed in all areas of knowledge, including corrosion knowledge. In that light, an analysis is made of corrosion information and what is needed in the process industry. It is shown that expert systems should be business- related, i.e. both the information storage and the retrieval method should be brought in close relation with the business of the users of the system. A new bussiness-related corrosion expert system provides expert knowledge about specific plants and equipment, has superior accessibility and can stay, as a dynamic system, comfortably ahead of the state-of-the-art.

The limit measurement errors in the geodesy are determining for the normal distribution law, But the errors, exceeding the limits are throw aside and accidental errors are obey the cut law. Cut laws are not study enough. The article is leading the results of calculate the probabilities hit accidental measurements errors for intervals σ, 2σ, 2,5σ, 3σ for cut normal and cut logical distribution laws. The analysis was accomplished.The probabilities of the cut normal and normal laws is different immaterial. 0,043 - maximum of the different. The normal law replace to the cut normal law is not recommending. Probabilities of the cut law may to use, when it is allowing to avoid the repetition of the field measurements.

The article presents research on the evaluation and selection of the sprayers for surface application of liquid mineral fertilizers to the soil based on the criterion of minimizing the power to disperse a unit of their volume and the quality of their distribution over the underlying surface. The expediency of using a combined hydro-pneumatic-mechanical sprayer has been established, which combines simplicity and reliability of the technological process execution inherent in the pneumatic method of dispersion, low power costs for this process (no more than 4 kW/t), as well as the possibility of using compressed air for pneumatic-mechanical spraying. The prospects of using rotating petal and plate-type sprayers for surface application of liquid mineral fertilizers, ensuring uneven distribution not exceeding 8%, expressed by the variation coefficient, have been substantiated. It has been determined that, regardless of the type of the atomizer, at a given speed (1700 min –1 ), the zone of stable distribution of the sprayed liquid (spray pattern width) is determined by the value of 2.2 m. The obtained characteristics of the quality of the distribution of the working fluid in the spray pattern allow concluding that as the pressure in the system increases, the flow rate of the working fluid increases, but the pattern of its deposition on the collecting surface follows the law of normal distribution. It has been established that the diameter of the sprayer and the pressure in the system exert the maximum influence on the quality indicator of the distribution of the working fluid, while the values of these factors are at a minimum level. Since the values of the coefficients for X 1 (the normalized value of the liquid pressure in the system) and X 2 (the normalized value of the nozzle hole diameter) are negative, their increase leads to a decrease in the uneven distribution of the working liquid on the underlying surface. In this case, the minimum value of unevenness – 3.6% – is achieved when the values of all factors are at the maximum level.

Computational Fluid Dynamics (CFD) methods have been developed into effective fluid simulation means to be used on the hydraulic design in the field of nuclear reactor. However, it is difficult to generate suitable mesh and select turbulence model for simulation because of the complex geometry structure and flow behavior in the pressure vessel. Based on CFX software, a hydraulic computation model of typical pressurized water reactor is established and the flow distribution at core inlet is analyzed. The simplified geometry model consists cold legs, downcomer, lower plenum, secondary support component, core support plate, and lower core plate. The computation model is divided into three parts for mesh generation, including the part of inlet and downcomer, the part of lower plenum and core inlet section, and the part of core. In order to reach the independence of grid several methods of mesh generation which contains different mesh density at local key parties are investigated to screen out the suitable mesh scheme. The k-ε, k-ω, and SST k-ω turbulence model are respectively used for simulation and the sensitivity of turbulence model at different locations of flow field is analyzed. The results show that the mass flow rate of the near wall flow field, computed by using k-ω turbulence model, is consistent with SST k-ω model, while the mass flow rate of central flow field computed by using k-ε turbulence agrees with SST k-ω model. The result computed by using k-ε turbulence model shows relatively uniform flow distribution at core inlet, which is more consistent with the measured data with the average difference of 3.1%. By using the k-ε model, the probability distribution of the difference between the calculated results and the experimental values follows the law of Normal distribution. The final coolant flow distribution at each orifice is evaluated, and the maximum normalized flow flux is found at center orifice while the flow rate at the edge of core is relatively lower.

The study of the reliability of the engine as a whole can be represented as a study of the probabilistic characteristics of its reliability according to the given probabilistic characteristics of the reliability of individual engine elements, that is, systems and mechanisms. The article substantiates that the method of similarity and dimensional theory allows us to establish patterns of change in the wear rate tgα depending on the adjustment of the engine parameters, and numerous experiments are required, which makes it little practical in determining the resource and predicting the operation of tractor engines. A more practically acceptable method for determining the residual life of automotive engines is the method of mathematical statistics and probability theory, and, in particular, the law of normal distribution. However, to determine the resource of engines, using this law, it is also necessary to conduct a large amount of testing. Thus, at the current stage of scientific and technological progress in automotive engineering, it is necessary to find other methods that are most practically acceptable and contribute in a short time, without a large amount of testing, to determine the resource of machines with maximum durability, which will be developed in subsequent works of the authors of the article.


 
 Introduction. A relatively new form of transformation of the territory in the current urban development, the renovation of quarters, requires close scientific study and methodological justification. Renovated neighborhoods, as well as projects for the construction of new houses, have individual features and characteristics. The authors hypothesize that, despite the variety of characteristics of renovated neighborhoods and projects for the construction of new houses, traditional in-line construction with the allocation of characteristic stages is possible.
 
 Materials and methods. To study the actual duration of the stages of creating objects under the renovation program (which is necessary to identify objects of similar duration), a special database was formed in the Scientific and Project Center “City Development”. As of 15.05.2021, 313 objects involved in the renovation program are included in this special database. A thorough verification of the specified database was performed. As a result, 122 objects with a spread of construction duration values from 11 months to 43.2 months are stored in the verified database. In addition, the materials of the information system for ensuring urban planning activities (ISOGD) of Moscow were used. The initial materials allowed us to identify a number of characteristic stages in the renovation program for each object.
 
 Results. To analyze the design duration of construction, the set of objects is divided into 2 parts: commissioning in 2021 and commissioning in subsequent years. For each part, histograms of the distribution of the duration of construction of houses during renovation are constructed and it is proved that the law of normal distribution is observed. A schematic model of renovation processes with multiple process durations is presented. The overall duration of the design (project stage) can take 1 year, construction — 2 years, and the combined stages: preparation of documents, relocation and demolition, will approximately take 1 year. This four-year wave cycle is then repeated the required number of times. The calendar plan of renovation for three wave objects with the allocation of the leading stream is presented. The ratio of flow processes during renovation is most clearly reflected in the constructed cyclogram of a multi-rhythmic object flow modified for renovation conditions. Combined schedules of renovation of in-line construction are constructed.
 
 Conclusions. Despite the considerable variety of renovated neighborhoods and projects for the construction of new houses, the authors of the article prove that traditional in-line construction with the allocation of characteristic stages is possible. For large contracting organizations, it is realistic to form a multi-rhythmic object flow with the allocation of the construction stage as the leading flow and calculate the renovation cyclogram.