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2JUSTIFICATION OF THE RELIABILITY OF EXPERIMENTAL RESEARCH
RESULTS
Rakhmonov I.U.1, Jalilova D.A.2, Usnatdinova R. S.3
'Rakhmonov Ikromjon Usmonovich - DSc, Professor, 2Jalilova Dinara Anvarovna - PhD, head teacher, TASHKENT STATE TECHNICAL UNIVERSITY,
TASHKENT, REPUBLIC OF UZBEKISTAN 3Usnatdinova Raushan Sadatbaevna - Assistant,
KARAKALPAK STATE UNIVERSITY, NUKUS, REPUBLIC OF KARAKALPAKSTAN
Abstract: in the process of conducting scientific research, understanding the accuracy and precision of research results is a crucial factor for continuing future work. The reliability of the obtained experimental values can be assessed through methods such as constructing histograms, checking confidence intervals, verifying according to the normal distribution law, using the least squares method, error propagation, and other similar approaches. Keywords: experimental research, mathematical processing, arithmetic mean mathematical variance, standard deviation, histogram, confidence interval, normal distribution law, voltage, and active power range.
UDC 621.311.12
At the core of every study, it is essential to obtain the results of experimental research conducted by the researcher and to assess their reliability in order to draw conclusions based on these results. The mathematical processing of the obtained results enables an assessment of the reliability of the conducted experiment. Thus, it is not sufficient for the researcher to merely conduct the experiment; they must also verify the results, identify relationships between values, and examine whether these results align with established principles based on mathematical processing. The processing of experimental research results is carried out through several methods. The results of experimental research can be evaluated by applying methods such as constructing histograms, checking confidence intervals, verifying with the normal distribution law, using the least squares method, error propagation, and other similar techniques [1, 2, 7].
In this scientific work, the experimental research results were evaluated through constructing histograms, checking confidence intervals, and verifying according to the normal distribution law. The sequence for processing experimental research results is carried out as follows: for nnn measurements, the arithmetic mean, median, mathematical variance, and sample standard deviation of the measured values are determined [3, 5].
When measuring experimental results, it is important to determine the value of the confidence interval for a given number of measurements. The confidence interval is necessary to establish the approximate evaluation boundaries of experimental research results. It ensures that the result of the experimental research lies within a specified interval with a certain level of confidence or confidence level [4, 6]. In this case, the confidence interval is expressed as follows:
U-£<U <U+£ (1)
P-£<P<P + £ (2)
The coverage accuracy e\varepsilone is determined by the formula.
£ = ^ (3)
An experimental study was conducted on the results of scientific research carried out at the "WBM ROMITEX DIROMM" spinning factory, focusing on data collected over a 3-day period, equivalent to 72 hours. The experimental research results were processed using the above expressions, yielding the following outcomes. The mathematical expectations (mean values) of the experimental results are as follows:
tfo'rt = 377,14 V Port = 2730,2 kVt
The medians of the experimental results are as follows:
Mev = 378 V Mep = 2735,5 kVt
The variances of the experimental results are as follows:
Du = 15,219 V2 Dp = 585,2622 kVt2
The standard deviations of the experimental results are as follows:
5u = 3,9012 V 5p = 24,1922 A
The coefficients of variation for the experimental results are as follows:
UU = 1,034 V UP= 0,886 V
To assess the reliability of the coefficient of variation, the median is used:
_ Vu^Q.S + ivu/l00)2 ,
m-u = ; (4)
^p*Vo.5 + (up/100)2 m»=-+jn-;
If 3mv<V or 3mv-V<0, the result is considered reliable, and the number of data points provided for statistical averages is deemed sufficient:
Based on the voltage value Based on the current value:
3mU = 1,4955; Ou = 3mU - Vu = - 3,9492 < 0
3mP = 1,5235; Op = 3mP - 7P = - 4,0225 < 0
As a result of measurements taken during the experiment, the graphs shown in Figure 4.8 were constructed.
These graphs use the values obtained during the measurement of network parameters.
a) b)
Fig 1. The variation of experimental research results according to the normal distribution law is as follows: a) based on the change in voltage value; b) based on the change in active power value.
The analysis of the histograms constructed for voltage and active power in Figure 1 shows that the experimental results follow the normal distribution law, specifically taking the form of a Newton-Gauss distribution. This indicates the reliability of the experimental research results.
Another method for evaluating experimental results is to check the confidence interval, whose randomness depends on a number of unaccounted factors that influence its value. The confidence interval guarantees that a random variable lies within a specified range with a certain level of confidence or confidence level [3, 5].
0,14
0,12 0,1
0,08 0,06 0,04 0,02 0
-0,02?" -0,04
0,14 0,12 0,1 0,08 0,06 0,04 0,02 0
-0,02 -0,04
m
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lOlOlOlOlOlOlO,.
<M <M <M cm CM CM <M
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<M <M <M <M <M <
a) b)
Fig. 2. Variation of the confidence interval for the experimental research results: a) based on the change in voltage value;
b) based on the change in active power value.
The analysis of the confidence intervals for voltage and active power shown in Figure 2 indicates that the experimental results adhere to the boundaries of the confidence interval. This confirms the reliability of the experimental research results.
In conclusion, it can be stated that when the results of the conducted experimental research are tested against the normal distribution law and confidence intervals, the adherence of experimental values to these principles confirms the authenticity and validity of the obtained values.
References
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