1. Introduction—Collected Data
Belt conveyors are not only a more cost-effective alternative to wheeled transport [
1,
2,
3,
4,
5,
6,
7], but they are also more environmentally friendly due to their use of electric motors for propulsion and bulk material handling [
8,
9,
10]. Additionally, when operating on downhill slopes, they can serve as energy generators [
11,
12], contributing to energy recovery and efficiency improvements.
Beyond their primary function in material transport, belt conveyors present innovative opportunities for energy management. They can serve as a form of dry energy storage, similar to pumped-storage power plants [
13], by utilizing gravitational energy. Additionally, they can help mitigate renewable energy curtailment by enabling the seasonal transfer of surplus energy from summer to winter. This can be achieved by integrating conveyors with bucket-wheel excavators that remove overburden and expose lignite seams near power plants, effectively creating coal storage reserves [
14]. In some cases, conveyors can be powered directly by solar panels, providing both a renewable energy source and protection for transported materials against adverse weather conditions [
15].
This study explores the impact of varying conveyor loads on energy consumption, analyzing extensive operational data collected from a Polish lignite mine over four years. The findings aim to enhance the efficiency of belt conveyor systems and identify potential strategies for reducing energy consumption in large-scale mining operations.
Energy and Economic Efficiency of Belt Conveyors
The energy and economic efficiency of belt conveyors, both in standard applications and specialized scenarios like those mentioned earlier, depend largely on the energy required to transport a unit of mass over a distance of 1 km. A unit energy consumption indicator (ZE) was introduced in previous studies [
16,
17,
18,
19,
20,
21] to facilitate accurate comparisons between different conveyor systems, providing a standardized metric for evaluating conveyor performance. This indicator also enables the optimal selection of conveyors for specific transport tasks, including open pit optimization [
22,
23,
24,
25] and the selection of belt conveyors for underground operations [
26].
Extensive research, including both laboratory and industrial studies, has been conducted to analyze the primary sources of conveyor motion resistance. Findings indicate that indentation rolling resistance [
27,
28,
29,
30,
31] contributes to over 60% of total motion resistance (
Figure 1). Researchers have also sought to systematically assess the energy efficiency of belt conveyors [
21], and explore methods for reducing energy consumption.
Key areas of investigation include:
Reduction of idler resistance [
32,
33,
34,
35],
The development of energy-saving belt conveyors and conveyor belts [
36,
37,
38,
39],
Adjustments to belt speed to improve trough loading efficiency [
8,
37,
40,
41,
42],
Optimization of chute design to minimize energy losses [
43,
44,
45,
46,
47].
A methodology for comparing the energy consumption of belt conveyors has been presented in previous studies [
16]. These studies have demonstrated that variations in monthly energy consumption are statistically significant, making direct comparisons between different conveyors challenging. Even when operating under nearly identical conditions, fluctuations in transported mass and monthly energy usage resulted in considerable differences.
This study focuses on two twin conveyors operating in parallel coal transport lines. Despite their nearly identical construction and function—both transferring coal from the same pit to the same power plant during similar periods—they exhibited negligible small differences in length (
Table 1) and, more importantly, in the total mass of coal transported and the total time of their operation (
Table 2). This difference was found to directly influence their average capacity and, consequently, the degree to which their theoretical capacity was utilized (
Table 3).
The width and speed of the belts were identical for both conveyors, ensuring that variations in energy consumption were not due to structural differences or external weather conditions. Instead, discrepancies in energy use were solely attributed to differences in transferred coal mass and achieved monthly performance levels.
Because these conveyors operated in parallel, direct comparison was complicated by significant monthly and overall differences in transported coal mass and operating time. Consequently, their actual average efficiency—measured as the ratio of transported mass to operating time—varied monthly. Additionally, Conveyor A’s data were incomplete, missing 12 months of measurements.
Direct energy consumption values were not used to ensure a fair and reliable comparison. Instead, the unit energy consumption (ZE) index was analyzed, allowing for a standardized evaluation of conveyor efficiency across varying operational conditions.
2. Method of Comparison of Energy Consumption by Twin Conveyors
The energy consumption of two twin belt conveyors (A and B) operating in a lignite mine in Poland was compared over a four-year period, from January 2014 to December 2017. Both conveyors transported lignite from the mine to the power plant and had nearly identical specifications, including belt type and length, leading to their classification as “twins.” Despite operating under similar conditions, differences in energy consumption were observed. The aim of this comparison was to determine whether the monthly variability in load impacted energy consumption.
The method of comparison focused on calculating the unit energy consumption (ZE) index required to transport 1 Mg of coal over a 1 km distance (Wh/Mg/km), which provided a consistent basis for comparison.
One important observation from the data was the differences in the coefficient of variation (CV) for various parameters. The CV for energy consumption was 13.1% for Conveyor A and 21.6% for Conveyor B, which was somewhat lower than the CV for mass transported (17.0% for A and 25.15% for B). This suggests that energy consumption was more stable compared with the variability in mass transported and operational hours. In contrast, capacity (measured in Mg/h) and the energy consumption (ZE) index per unit mass and distance showed much less fluctuation, with CVs of 6.19% and 6.30%, respectively, for both conveyors. This made these indices more reliable for comparison.
When analyzing the energy consumption indices, it was found that the unit energy consumption on Conveyor A averaged 288.57 Wh/Mg/km, while Conveyor B averaged 303.58 Wh/Mg/km, indicating a 5.23% higher energy consumption on Conveyor B. This difference was statistically significant. Despite these global differences, the monthly variation in unit energy consumption (ZE) index was considerable, ranging from 254.7 Wh/Mg/km to 344.6 Wh/Mg/km for Conveyor B and from 256.87 Wh/Mg/km to 336.35 Wh/Mg/km for Conveyor A.
To further explore these differences, statistical tests were conducted on the monthly data, revealing a negative correlation between the capacity of the conveyors and the energy consumption indicators (ZE). This suggests that higher capacity led to lower energy consumption, a relationship that was consistent across both conveyors. It was hypothesized that the variation in energy consumption could be influenced by operational factors such as monthly load fluctuations.
Ultimately, this analysis highlighted the fact that despite the conveyors’ similar design, significant and persistent differences in energy consumption remained. Further investigation is needed to explore the underlying factors contributing to these differences, particularly those associated with operational (load variability) and weather conditions (temperature).
3. Results and Discussion
3.1. Comparison of the Average Monthly Capacities of the Tested Conveyors
During the analyzed period, the average capacity of Conveyor A was 2381.99 Mg/h, with an energy consumption index (ZE
A) of 286.45 Wh/Mg/km. Conveyor B had an average capacity of 2309.47 Mg/h, with a slightly higher energy consumption index (ZE
B) of 300.69 Wh/Mg/km (
Table 3). This means Conveyor B consumed 14.24 Wh/Mg/km more energy per transported unit than Conveyor A. Although the relative difference of 4.97% was not substantial, it was statistically significant and was caused by a 1.13% increase in average conveyor capacity.
Interestingly, an inverse relationship was observed between capacity and energy efficiency. Despite being less loaded, Conveyor B had a lower average monthly capacity (72.51 Mg/h, or 3.04%, compared with Conveyor A). This suggests that higher unit energy consumption is associated with lower capacity utilization. A strong negative correlation was identified between ZE and conveyor capacity (R2 = −0.84 and −0.85 for Conveyors A and B, respectively). A 35% relative increase in capacity (from 2000 up to 2700 Mg/h) led to a 26% reduction in ZE (from 340 down to 250 Wh/Mg/km), equating to a 90 Wh/Mg/km decrease. Proper load distribution could reduce unit energy consumption by up to 30%.
A statistical comparison of two independent sample distributions was conducted to verify the significance of these differences. The results, illustrated in
Figure 2, show the histograms of monthly average capacities for both conveyors. The modal value for Conveyor A (~2400 Mg/h) is slightly higher than that for Conveyor B (~2300 Mg/h), indicating a small but measurable shift in performance.
A more detailed view of the density distributions (
Figure 3) confirms this shift. The peak value for Conveyor A is approximately 135 Mg/h higher than that for Conveyor B, which is almost twice the difference observed in the mean values (72.51 Mg/h). Additionally, the efficiency distribution of Conveyor A shows slight left-hand asymmetry, while Conveyor B exhibits a right-hand asymmetry, suggesting different operational characteristics.
3.2. Statistical Analysis of Conveyor Capacities
Table 1 presents key descriptive statistics for the analyzed datasets of monthly capacities. Notably, Conveyor A consistently exhibited higher values across various measures of central tendency (mean, median), with differences ranging from 3% to 4%. The median showed the most significant difference (−4.36%), while the harmonic mean differed the least (−3.1%).
In terms of dispersion, Conveyor A displayed more significant variability, with a higher standard deviation (146.62 Mg/h vs. 142.20 Mg/h) and variance. Conveyor B’s variance was 5.94% lower, and its standard error was 16.01% lower, indicating slightly more consistent performance (
Table 4).
The key observations are as follows:
While statistically significant, the observed differences in capacities between the two conveyors do not appear to be solely due to construction differences. Instead, variations in load distribution, seasonal effects, and potential external factors likely contributed to the discrepancies. These factors warrant further exploration, particularly concerning their impact on energy consumption trends.
A separate study is needed to investigate atmospheric and seasonal influences on belt conveyor efficiency, as these may also explain the observed variability in capacity utilization.
Statistical Significance of Differences in Monthly Average Capacities
The differences observed visually (
Figure 1 and
Figure 2) and identified through various descriptive statistics (
Table 1) may appear significant but could still be coincidental. A series of tests was conducted to formally verify their statistical significance. Given that the differences affect not only central tendency measures but also positional statistics and density distribution traces (
Figure 2), they are unlikely to occur by chance. However, a rigorous statistical approach is required.
To compare the means of the two conveyors, 95% confidence intervals were determined, as follows:
Additionally, a 95% confidence interval was calculated for the differences in the unit energy consumption (ZE) index, assuming equal variances:
Since this interval does not contain zero, we conclude that the difference in means is statistically significant at the 95% confidence level.
A Student’s t-test was performed to compare the means of the two samples. The null hypothesis (H0) assumed equal means, while the alternative hypothesis (H1) suggested a difference. Assuming equal variances, we obtain the following:
t-statistic: 2.31884
p-value: 0.02289
Since the p-value is less than 0.05, we reject the null hypothesis, confirming a statistically significant difference between the mean capacities of Conveyors A and B.
Before performing the t-test, an F-test was conducted to check whether the two samples had equal variances. The standard deviations were as follows:
Conveyor A: 146.622 [118.92; 191.26]
Conveyor B: 142.201 [118.38; 178.18]
Variance ratio: 1.0632
95% confidence interval for variance ratio: [0.57575; 2.0211]
The F statistic was 1.06315 with a p-value of 0.83486. As the p-value exceeds 0.05, we do not reject the null hypothesis, confirming no statistically significant difference in standard deviations.
A Mann–Whitney test was conducted to compare the medians, as follows:
Median capacities:
- -
Conveyor A: 2390.6
- -
Conveyor B: 2286.37
Mean ranks:
- -
Conveyor A: 49.6111
- -
Conveyor B: 37.1667
W-statistic: 608
p-value: 0.02092
Since the p-value is less than 0.05, we reject the null hypothesis and confirm a statistically significant difference between the medians at the 95% confidence level.
The Kolmogorov–Smirnov (K-S) test was used to compare the distributions of both samples, as follows:
DN Statistic: 0.3819
K-S Statistic: 1.7323
p-value: 0.00049
Since the p-value is below 0.05, we conclude that there is a statistically significant difference between the two distributions at a 95% confidence level.
Figure 4 compares box-and-whisker plots, scatter plots, and confidence intervals for the mean and median monthly capacities of both conveyors. The intervals do not overlap, reinforcing the statistical significance of the differences.
Figure 5 displays cumulative empirical distribution functions, showing that the distribution shift is most pronounced in the central region, with smaller variations at the tails.
The statistical tests confirm that the A and B conveyors’ observed differences in monthly average capacities are significant. These differences primarily impact the variation of the unit energy consumption (ZE) index. The next chapter will explore the relationship between capacity and energy efficiency in greater detail through regression analysis.
3.3. Regression of the Unit Energy Consumption Indicator ZE Against the Average Capacity of the Conveyor
The impact of the monthly average capacity on the specific energy consumption index of the conveyor can be observed in the matrix graph (
Figure 5), where all data points are plotted, differentiating between Conveyors A and B. The points are mixed and aligned along a negatively inclined diagonal, confirming a strong negative correlation (−0.84 and −0.85 for conveyors A and B, respectively).
The graphs (
Figure 6 and
Figure 7) presents 84 complete data pairs (36 for Conveyor A and 48 for Conveyor B). More blue points (Conveyor A) are located in the lower part of the graph, while red points (Conveyor B) dominate the upper part. This indicates differences in the average specific energy consumption for Conveyor A (288.6 Wh/Mg/km) and Conveyor B (303.6 Wh/Mg/km), primarily due to differences in their monthly average capacities—2370.6 Mg/h for A and 2296.9 Mg/h for B.
A simple regression test was performed to analyze the relationship between the dependent variable (unit energy consumption indicator ZE) and the independent variable (average efficiency Q) for Conveyors A and B separately and together.
For Conveyor A, the best-fit model was a hyperbolic function (inverse linear for Y,
Figure 8), expressed as the following Equation (1):
The estimation analysis, including ANOVA, yielded the following results:
Correlation coefficient: 0.854862
R-squared: 73.0789%
R-squared (df corrected): 72.2871%
Standard error of estimation: 0.0000796077
Mean absolute error: 0.0000882741
Durbin–Watson statistic: 0.909369 (p = 0.00001)
Residual autocorrelation lag 1: 0.335697
Since the
p-value in the ANOVA table (
Table 5) is below 0.05, a statistically significant relationship exists between the indicator ZEA and capacity QA at a 95% confidence level.
The R2 statistic shows that the model explains 73.1% of the variability in the energy consumption index of Conveyor A. The correlation coefficient (0.854862) indicates a moderately strong relationship between the variables. The residuals’ standard deviation is 0.0001115. The mean absolute error (MAE) is 0.000079608, and the Durbin–Watson statistic suggests some serial correlation due to potential seasonal variations in the data.
For Conveyor B, multiple models were tested (logistic S curve, double hyperbolic, hyperbolic for the logarithm), but differences in correlation coefficients and R
2 values were minimal. The best correlation coefficient was 0.8616, while the hyperbolic model’s correlation was slightly lower at 0.8603, making it the most comparable model, (
Figure 9). The Equation (2) is as follows:
The estimation analysis, including ANOVA, yielded the following:
Correlation coefficient: 0.86031
R-squared: 74.012%
Standard error of estimation: 0.00010734
Mean absolute error: 0.000089
Durbin–Watson statistic: 0.58731 (p = 0.0000)
Residual autocorrelation lag 1: 0.66312
Since the
p-value in ANOVA (
Table 6) is below 0.05, a statistically significant relationship exists between indicator ZE
B and Q
B at a 95% confidence level.
When analyzing data from both conveyors together, the hyperbolic model ranked third after logarithmic and square root hyperbolic models. The minor differences in correlation coefficient (0.0001 lower) and R
2 index (0.07 lower) made the hyperbolic model suitable for comparative purposes. The Equation (3) is as follows:
The combined regression analysis resulted in the following:
Correlation coefficient: 0.86312
R-squared: 74.498%
Standard error of estimation: 0.00011448
Mean absolute error: 0.000088274
Durbin–Watson statistic: 1.0102 (p = 0.0000)
Residual autocorrelation Lag 1: 0.46853
The model explains 74.498% of the unit energy consumption indicators variability for both conveyors.
The selected regression curves for Conveyors A and B, and combined data were plotted on a standard graph (
Figure 10). The regression curves run almost parallel, with minor differences in energy consumption indices. The difference for 2000 Mg/h is 9.9 Wh/Mg/km, reducing to 4.3 Wh/Mg/km at 2700 Mg/h, a decrease from 3% to 1.7%.
The hyperbolic model fits well, with point dispersion (forecast vs. observed) being mostly uniform, except for a few outliers (
Figure 11). However, a variance of up to 30 Wh/Mg/km suggests that factors other than capacity influence energy consumption.
The scatter of results around the diagonal in the graph of observed and predicted values (
Figure 12) and especially seasonal temperature variations appear to contribute significantly, with negative residuals in winter–spring and positive ones in summer–autumn (
Figure 13). Future analysis will explore the influence of atmospheric conditions.
4. Conclusions
This study demonstrates that variations in conveyor energy consumption primarily result from differences in load distribution. A statistically significant disparity was observed between the average capacities of Conveyors A and B, with Conveyor A operating at 2381.99 Mg/h and Conveyor B at 2309.47 Mg/h—an absolute difference of 72.51 Mg/h (3.04%).
A strong negative correlation was identified between ZE and conveyor capacity (R2 = −0.84 and −0.85 for Conveyors A and B, respectively). A 35% relative increase in capacity (from 2000 up to 2700 Mg/h) led to a 26% reduction in ZE (from 340 down to 250 Wh/Mg/km), equating to a 90 Wh/Mg/km decrease. Proper load distribution could potentially reduce unit energy consumption by up to 30%.
Optimizing conveyor utilization—such as alternating higher load levels between conveyor lines—can yield substantial energy savings. For instance, instead of running both lines at 30% capacity daily, increasing one line’s load to 60% while idling the other could further reduce energy consumption by as much as 150 Wh/Mg/km. These optimizations require no additional infrastructure investment, making them a cost-effective strategy for improving efficiency.
The Bełchatów power plant receives 30–40 million Mg of coal annually, transported over conveyor lines spanning several dozen kilometers. For 10 million Mg/year over 10 km, this equates to potential energy savings of 9 GWh (or 15 GWh at 60%). Scaling up to actual conditions—four times the coal volume and double the conveyor length—yields estimated savings of 72 GWh (or 120 GWh). Including overburden removal, these estimates could increase further (by multiplication by overburden to coal ratio + 1), emphasizing the potential of improved load management through centralized control in surface mines.
An additional opportunity lies in synchronizing conveyor operations with the daily solar cycle for overburden removal and coal extraction. Excess renewable energy, particularly from PV sources, often results in low or negative electricity prices and RES curtailments. Dynamic load control allows conveyor utilization to maximize this opportunity during peak solar production. A recent study in
Energies explored this approach, demonstrating its feasibility in developing the Złoczew lignite deposit [
14].
Future research will investigate additional energy-saving measures, such as energy-saving conveyor belts, and evaluate the benefits of load optimization and technological improvements. Further studies will also assess the impact of environmental factors, particularly temperature, on energy consumption variability, as preliminary findings suggest that up to 75% of ZE fluctuations stem from load variations.
Identifying the primary drivers of conveyor energy consumption under long-term industrial conditions enhances predictive accuracy and highlights significant opportunities for efficiency improvements. These findings provide practical guidelines for reducing operational costs and improving the sustainability of belt conveyor systems in lignite mining operations.
Author Contributions
Conceptualization, L.J. and M.B.; methodology, L.J.; software, L.J.; validation, M.B., L.J. and Z.K.; formal analysis, M.B.; investigation, Z.K.; resources, L.J. and M.B.; data curation, Z.K.; writing—original draft preparation, L.J.; writing—review and editing, M.B.; visualization, L.J.; supervision, M.B.; project administration, M.B.; funding acquisition, M.B. and L.J. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Data Availability Statement
The data presented in this study are available on request from the corresponding author.
Acknowledgments
The authors would like to thank the mine management, for providing detailed data on the energy consumption of the analyzed conveyors.
Conflicts of Interest
Author Zbigniew Konieczka was employed by the PGE Polska Grupa Energetyczna S.A. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Figure 1.
Shares of different components in the total motion resistance of a belt conveyor [
9].
Figure 1.
Shares of different components in the total motion resistance of a belt conveyor [
9].
Figure 2.
Comparison of the histograms of monthly average capacities (Q) for Conveyors A and B.
Figure 2.
Comparison of the histograms of monthly average capacities (Q) for Conveyors A and B.
Figure 3.
Density traces of monthly average capacities (Q) for Conveyors A and B.
Figure 3.
Density traces of monthly average capacities (Q) for Conveyors A and B.
Figure 4.
Graphical analysis of dispersion and confidence intervals of capacities Q for Conveyors A and B.
Figure 4.
Graphical analysis of dispersion and confidence intervals of capacities Q for Conveyors A and B.
Figure 5.
Chart of two cumulative empirical distributions for the monthly averages of capacity Q for Conveyors A and B.
Figure 5.
Chart of two cumulative empirical distributions for the monthly averages of capacity Q for Conveyors A and B.
Figure 6.
Matrix diagram showing the impact of monthly average capacity Q on the specific unit energy consumption indicator ZE for conveyors A and B.
Figure 6.
Matrix diagram showing the impact of monthly average capacity Q on the specific unit energy consumption indicator ZE for conveyors A and B.
Figure 7.
Scatter plot of average capacities Q and energy consumption indicators ZE for each month, with calculated averages (denoted by “X”) for Conveyors A (blue diamonds) and B (red circle).
Figure 7.
Scatter plot of average capacities Q and energy consumption indicators ZE for each month, with calculated averages (denoted by “X”) for Conveyors A (blue diamonds) and B (red circle).
Figure 8.
A simple regression of ZE for Conveyor A against average capacity Q over the analyzed months. Green color—2-sided 95% confidence intervals for the mean at given capacity Q. Yellow color—two sided prediction limits for new observations at the 95% level of confidence.
Figure 8.
A simple regression of ZE for Conveyor A against average capacity Q over the analyzed months. Green color—2-sided 95% confidence intervals for the mean at given capacity Q. Yellow color—two sided prediction limits for new observations at the 95% level of confidence.
Figure 9.
A simple regression of ZE for Conveyor B against average capacity Q.
Figure 9.
A simple regression of ZE for Conveyor B against average capacity Q.
Figure 10.
A simple regression of ZE for Conveyors A and B against average capacity Q.
Figure 10.
A simple regression of ZE for Conveyors A and B against average capacity Q.
Figure 11.
Comparison of regression models for Conveyors A (blue line), B (red line), and combined data (dashed line).
Figure 11.
Comparison of regression models for Conveyors A (blue line), B (red line), and combined data (dashed line).
Figure 12.
Comparison of predicted and observed values.
Figure 12.
Comparison of predicted and observed values.
Figure 13.
Distribution of residuals over analyzed months for Conveyors A and B. The numbers at the points indicate the months of the year for which the data was collected.
Figure 13.
Distribution of residuals over analyzed months for Conveyors A and B. The numbers at the points indicate the months of the year for which the data was collected.
Table 1.
Technical data of Conveyors A and B.
Table 1.
Technical data of Conveyors A and B.
Conveyor Construction Data | A | B |
---|
Length in m | 1012.6 | 1018.5 |
Belt speed in m/s | 5.24 | 5.24 |
Theoretical mass capacity in Mg/h | 6400 | 6400 |
Theoretical volume capacity Mg/h | 8000 | 8000 |
Number of pulleys in a set | 3 | 3 |
Idler length in mm | 670 | 670 |
Idler diameter in mm | 191 | 191 |
Idler set spacing in m | 1.24 | 1.24 |
Trough angle | 45 | 45 |
Belt type | St3150 | St3150 |
Belt width in mm | 1800 | 1800 |
Coal bulk density in Mg/m3 | 0.8 | 0.8 |
Table 2.
Collected operational data (January 2014–December 2017).
Table 2.
Collected operational data (January 2014–December 2017).
Collected Operating Data | A | B |
---|
Number of monthly measurements | 36 * | 48 |
Total mass transferred in Mg | 42,096,610 | 46,540,032 |
Total operating time in hours | 17,672.9 | 20,151.84 |
Total energy consumption in MWh | 12,058.42 | 13,994.02 |
Average monthly operating time in hours | 490.91 | 419.83 |
Standard deviation | 60.98 | 91.28 |
Coefficient of variation in % | 12.42% | 21.74% |
Minimum | 352.1 | 198.6 |
Maximum | 629.4 | 584.7 |
Range of change | 277.3 | 386.1 |
The average amount of mass transferred in Mg | 1,169,350 | 969,584 |
Standard deviation | 198,752 | 243,846 |
Coefficient of variation | 17.00% | 25.15% |
Minimum | 760,503 | 424,723 |
Maximum | 1,695,160 | 1,574,020 |
Range of change | 934,657 | 1,149,297 |
Average energy consumption in MWh | 334.956 | 291.542 |
Standard deviation | 43.88 | 62.97 |
Coefficient of variation | 13.10% | 21.60% |
Minimum | 212.0 | 140.7 |
Maximum | 441.6 | 406.5 |
Range of change | 229.6 | 265.8 |
Table 3.
Calculated performance and ZE indicators.
Table 3.
Calculated performance and ZE indicators.
Calculated Capacities and ZE Indicators | A | B |
---|
Average efficiency for total values in Mg/h | 2381.99 | 2309.47 |
The degree to which the theoretical capacity was utilized in % | 37.22% | 36.09% |
Unit indicator ZE for total energy consumption in Wh/Mg/km | 286.45 | 300.69 |
Average monthly efficiency Q in Mg/h | 2370.56 | 2296.89 |
Standard deviation | 146.622 | 142.201 |
Coefficient of variation | 6.19% | 6.19% |
Minimum | 2119.17 | 2045.89 |
Maximum | 2693.29 | 2692.01 |
Range of change | 574.12 | 646.12 |
ZE indicator in Wh/Mg/km | 288.57 | 303.58 |
Standard deviation | 18.18 | 19.12 |
Coefficient of variation | 6.30% | 6.30% |
Minimum | 256.87 | 254.7 |
Maximum | 336.35 | 344.57 |
Range of change | 79.48 | 89.87 |
Table 4.
Basic statistics for monthly average capacities (Q) of Conveyors A and B.
Table 4.
Basic statistics for monthly average capacities (Q) of Conveyors A and B.
Descriptive Statistics | Conveyor A | Conveyor B | Absolute Difference | Relative Difference (%) |
---|
No. of measurements | 36 | 48 | 12 | 33.33 |
Mean in Mg/h | 2370.56 | 2296.89 | −73.67 | −3.11 |
Median in Mg/h | 2390.60 | 2286.37 | −104.23 | −4.36 |
Geometric mean in Mg/h | 2366.14 | 2292.63 | −73.51 | −3.11 |
Harmonic mean in Mg/h | 2361.69 | 2288.42 | −73.27 | −3.10 |
Standard deviation in Mg/h | 146.62 | 142.20 | −4.42 | −3.02 |
Coefficient of variation | 6.19% | 6.19% | 0.10 | 0.10 |
Standard error in Mg/h | 24.437 | 20.525 | −3.912 | −16.01 |
Variance in Mg2/h2 | 21,498.1 | 20,221.2 | −1276.9 | −5.94 |
Minimum capacity in Mg/h | 2119.17 | 2045.89 | −73.28 | −3.46 |
Maximum capacity in Mg/h | 2693.29 | 2692.01 | −1.28 | −0.05 |
Range in Mg/h | 574.12 | 646.12 | 72.00 | 12.54 |
Lower quartile (Q1) in Mg/h | 2307.98 | 2200.30 | −107.68 | −4.67 |
Upper quartile (Q3) in Mg/h | 2445.07 | 2409.83 | −35.24 | −1.44 |
Interquartile range in Mg/h | 137.10 | 209.53 | 72.44 | 52.84 |
Skewness | 0.0178 | 0.4232 | 0.4053 | 2273.16 |
Kurtosis | −0.0170 | 0.0559 | 0.0729 | −427.76 |
Table 5.
Coefficients and variance analysis for selected regression model for Conveyor A (Df—degrees of freedom).
Table 5.
Coefficients and variance analysis for selected regression model for Conveyor A (Df—degrees of freedom).
| Least Squares Method | Standard | Statistics | Value |
---|
Parameter | Estimate | Error | T | p |
Offset | 0.0005512 | 0.00030525 | 1.8057 | 0.0798 |
Slope | 0.000001235 | 1.2853 × 10−7 | 9.6070 | 0.0000 |
Variance Analysis |
Source | Sum of squares | Df | Medium squares | F-statist. | Value p |
Model | 0.0000011472 | 1 | 0.0000011472 | 92.30 | 0.0000 |
The Rest | 4.22607 × 10−7 | 34 | 1.24296 × 10−8 | | |
Together (Corr.) | 0.00000157 | 35 | | | |
Table 6.
Coefficients and variance analysis for selected regression model for Conveyor B (Df—degrees of freedom).
Table 6.
Coefficients and variance analysis for selected regression model for Conveyor B (Df—degrees of freedom).
| Least Squares Method | Standard | Statistics | Value |
---|
Parameter | Estimate | Error | T | p |
Offset | 0.00041227 | 0.00025337 | 1.6277 | 0.1105 |
Slope | 0.0000012602 | 1.10102 × 10−7 | 11.446 | 0.0000 |
Variance Analysis |
Source | Sum of squares | Df | Medium squares | F-statist. | Value p |
Model | 0.0000015094 | 1 | 0.0000015094 | 131.01 | 0.0000 |
The rest | 5.29975 × 10−7 | 46 | 1.15212 × 10−8 | | |
Together (corr.) | 0.000002039 | 47 | | | |
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