26 Statistical Analysis of Measuring Errors the Pollution of the Atmospheric Bottom Layer by Exhaust Gas Iryna Darmorost1, Petro Stakhiv2, Mykola Shynkaryk3, Vasylyna Melnyk4 1,3,4. Department of Computer Science, Ternopil National Economic University, UKRAINE, Ternopil, 8 Chekhova str., email: imadiudia@gmail.com1 2. Lodz University of Technology, POLAND, Lodz, 116 Stefana Żeromskiego str., email: spg@polynet.lviv.ua Abstract: The statistical analysis of the errors of minutes. In this work it is proposed to investigate the measurements pollution in the bottom-layer of the statistical characteristics of random error, in order to confirm atmosphere with exhaust gases of vehicles has been carried the effectiveness of the selected averaging interval. out. The method of performing statistical analysis is proposed. On this basis, the most optimal time averaging II. STATEMENT OF THE PROBLEM interval for the instantaneous concentrations of harmful The traffic intensity is one of the most important factors substances is established. contributing to the pollution of the bottom-layer of the Keywords: traffic intensity, harmful emissions, nitrogen atmosphere by harmful emissions, but the concentration of air dioxide, correlation coefficient, random error, averaging in a chemical compound such as nitrogen dioxide varies interval. depending on the characteristics of the medium in which the measurements are carried out. I. INTRODUCTION Based on preliminary studies, it was found that the traffic The progress of human society is inseparable from the intensity and the known concentrations of harmful substances history of transport development. With the expansion of states, in the atmosphere in certain time bands correlate. The research the construction of cities, with the resettlement of people in was based on the assumption that the random error is normally increasingly large territories, the growth of trade rates of distributed with zero mathematical expectation, and as a result development of transport has steadily increased. The rapid of averaging, is compensated for this error. pace of growth in the level motorization of the population And on this basis the idea was based on the choice of leads to inevitable negative changes in the environment. averaging interval. Pollution of the atmosphere by harmful emissions of vehicles It has been established that in order to compensate for the causes irreparable harm to the health of the population. It is casual component related to the influence of other factors on known that during the day, people consume about 15-25 kg of pollution of the city's territory, such as ventilation, it is air, 2.5-5 kg of water, 2.5 kg of food. When inhaled, the advisable to choose the range of averaging instantaneous chemical elements are absorbed by the body most intensively. values of the concentration harmful emissions and the traffic Thus, lead, which comes with air, is absorbed by blood by intensity of the transport units close to the interval of 20 60%, if it comes with water, it is absorbed by 10%, with food minutes. Such an interval is used in standard measuring - by 5%. Therefore, when polluting the environment, techniques Sanitary and Epidemiological Services. atmospheric air is the main supplier of toxic substances in the In order to confirm or refute the justified averaging interval, human body [1]. it is proposed to investigate the statistical characteristics of the The exhaust gases of cars contain more than 200 compounds random error. and components, many of which are very toxic. As is known, the correlation coefficient between the two The environment contains carbon monoxide (CO), nitrogen variables is given by Eq.1: (NO), sulfur dioxide (SO2), aldehydes, soot (C), lead (Pb), and m others [2]. One of the most harmful substances, the concentration of which exceeds any allowable norms is ∑ ( x − x )( y − y ) i i nitrogen dioxide, the chemical formula of which – NO 2 . rxy = i =1 , (1) m m There is a clear linear dependence between the traffic intensity and the concentration of harmful substances in the ∑ (x − x) ∑ ( y − y) i =1 i 2 i =1 i 2 atmosphere. However, measuring the value of NO 2 , with the use of modern means of measurement, occurs almost where x, y − average sample from each sample   x = x1 ...x m ; y = y1 ... y m accordingly, rxy ∈ [− 1,1]. instantaneously, and in this connection, the problem of averaging the obtained indicators. In the paper [3], experimental studies were performed and the correlation It is worth mentioning that the values   coefficients were calculated for different time averaging x = x1 ...x m ; y = y1 ... y m , are calculated for different time intervals: for 5, 10, 20 and 30 minutes. The correlation coefficient is the most optimal at the averaging interval in 20 averaging intervals of instantaneous values of traffic intensity and concentration of harmful substances, respectively. ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 27 Thus, for different time averaging intervals of instantaneous values, we calculate the correlation coefficient between the traffic intensity and the concentration of nitrogen dioxide and carry out a statistical analysis of the errors measurements of contamination the bottom-layer of the atmosphere by exhaust gases of vehicles. II. METHOD OF RESEARCHING Statistical analysis of the measurement errors the bottom- layer of atmosphere on the example of the established correlation between the traffic intensity and the concentration of nitrogen dioxide (NO 2 ) was conducted. To obtain experimental data, measurements of the concentration of nitrogen dioxide in the air at the crossroads of streets in city Ternopil Chekhova - Za Rudkoiu was conducted. Average air temperature was 0 ° C, humidity - 70%. Obtaining a sample of data was done using gas analyzer SPEC Sensors, DSG – NO2- 968-037, accuracy - ±15%, at a range of operating temperatures from -20 ºС to +40 ºС. The traffic intensity was evaluated using a set webcam every minute. Fig.2. Coefficients of correlation for different time averaging Concentration value NO 2 received every second. intervals. As you can see from Figure 2, we get a curve that has an extremum at the point with averaging of 20 minutes. For statistical analysis, the averaging intervals of 1, 5, 10, 20 and 30 minutes were selected. The method of conducting the analysis includes the following steps: 1. Averaging of the concentrations of nitrogen dioxide in the bottom-layer of atmosphere at intervals of 1, 5, 10, 20, 30 minutes, in a time interval of 1 hour. For each interval averaging according to the value of the interval. For each of the intervals, 60, 12, 6, 3, and 2 averaging values were obtained, respectively. 2. On each averaging interval, net error and average value were selected. The calculation of the values of a random error occurs according to the following equations: ei = a mid − z m , (2) Fig.1. Interval of averaging concentration of NO 2 in 20 minutes. where ei - random errors at different time intervals, amid Using eq. (1), the correlation coefficients were calculated on time averaging intervals of 5, 10, 20, and 30 minutes. Figure 1 - averaging the concentration of nitrogen dioxide in shows a graph of the averaging interval of nitrogen dioxide different time ranges, z m - value measurement of concentration in 20 minutes [3]. nitrogen dioxide per second, m=1..n . Figure 2 shows the generalized results of the correlation coefficients at different time intervals. 3. At all averaging intervals after calculations using eq. (2), the sum of random errors was obtained by the equations: N S i = ∑ ei , (3) i =1 where S i - amount of error values at different time averaging intervals. III. ANALYSIS OF RECEIVED RESULTS The results of the research are shown in Figures 3-7. Statistical analysis of measurement errors, according to the ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 28 research method, was conducted for different time intervals, in particular: 1, 5, 10, 20 and 30 minutes. Figure 3 shows the value of random errors in the averaging 0,1 interval of 1 minute. 0,1 0,05 0,05 0 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 Error value 0 -0,05 Error value 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 -0,1 -0,05 -0,15 -0,1 -0,2 -0,15 Seconds Seconds Fig. 3. The value of random errors in the time range of 1 minute in Fig. 5. The value of random errors in the time range of 1 minute in the averaging interval in 1 minute. the averaging interval in 10 minutes. Figure 4 shows the value of random errors in the averaging Figure 6 shows the value of random errors in the averaging interval in 5 minutes. interval in 20 minutes. 0,15 0,05 0,1 0 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 0,05 Error value -0,05 Error value 0 -0,1 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 -0,05 -0,15 -0,1 Seconds -0,2 Seconds Fig. 4. The value of random errors in the time range of 1 minute in Fig. 6. The value of random errors in the time range of 1 minute in the averaging interval of 5 minutes. the averaging interval in 20 minutes. Figure 5 shows the values of random errors in the averaging Figure 7 shows the value of random errors in the averaging interval of 10 minutes. interval in 30 minutes. ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 29 0,1 0,05 0 1 4 7 1013161922252831343740434649525558 Error value -0,05 -0,1 -0,15 -0,2 Seconds Fig. 7. The value of random errors in the time range of 1 minute in Fig. 8. Measured values of nitrogen dioxide in the averaging interval the averaging interval in 30 minutes. in 1 hour. On the basis of the proposed error, using the eq. (3) the IV. ACKNOWLEDGMENT general errors are calculated. This research was supported by National Grant of Ministry On the interval in 1 minute S1 = −7,015 , it means that the of Education and Science of Ukraine “Mathematical tools and interval error is not normally distributed, but includes trend software for control air pollution from vehicles” (0116U005507). values, on 5 minutes S 5 = 13,148 , which is also not the V. CONCLUSION optimum value, in 10 minutes - S10 = 2,94 , on 20 minutes A statistical analysis of random errors was carried out at - S 20 = 2,808 , on 30 minutes - S 5 = 3,0056 . different intervals of averaging - at 1, 5, 10, 20 and 30 minutes. Apparently, as a result of the calculations performed by the Thus, the averaging interval of instantaneous values of the proposed methodology, it has been found that in subsequent concentration of nitrogen dioxide in bottom-layer of studies, as averaging interval of , it is necessary to use the atmosphere was formed, which will be used in further studies averaging interval in the range of 10 to 20 minutes. to construct models of the dependence the concentration of The vast majority of sources [4] use an interval of averaging harmful emissions between the traffic intensity . The value of of 1 hour. The averaging graph for 1 hour is depicted in Figure the averaging interval will be in the range of 10 to 20 minutes. 8. For the visualization, a sample of data was obtained from the measurement of nitrogen dioxide concentration values at REFERENCES Street Jana Pawla II in Lodz, Poland. On the ordinates axis, the [1] V. Stukanov, “Effect of motor transport on the state of the averaged values are deferred value of nitrogen dioxide (NO 2 ) , environment of the large industrial cities”, Vestnik VSU, along the abscissa axis - hours of day. Series: Chemistry, Biology, Pharmacy, no.1,pp.168-175, The conducted studies have shown that such averaging 2012 (In Ukrainian). gives distortion of results due to the use of an incorrect and [2] V.Garin, “Industrial ecology”, Moscow-Marshrut,328 p., ineffective averaging interval of the measured values of 2005 (In Russian). nitrogen dioxide, which can not be neglected by the action of [3] M.Dyvak, I.Darmorost, R.Shevchuk, V.Manzhula and random factors such as ventilation of the environment, that is, N.Kasatkina., “Correlation analysis traffic intensity of the gusts of wind, vertical and horizontal streams, turbulence, and motor vehicles and the air pollution by their harmful so on. emissions”, Proceedings of XIVth International Conference on Modern Problem of Radio Engineering, Telecommunications and Computer Science (TCSET), Lviv-Slavske, 2018, pp.855-858. [4] Wojewódzki Inspektorat Ochrony Środowiska w Łodzi [Online]. Available: http://www.wios.lodz.pl/. Accessed on: April, 22, 2018. ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic