Models based on regression analysis for predicting the operational efficiency of high-pressure roller crushers are considered. A systematized and structured production database is created and statistically analyzed. The consistency of the data is verified. The parameters with the greatest influence on the productivity are identified. The basic structure of the mathematical models is determined, and the limits on their applicability are assessed. Predictive mathematical models are developed. Their adequacy is verified, and their precision is established in assessing the productivity of mills at an enrichment plant where the mineral composition of the incoming ore varie

Fedorov, V. I.

Ivashchuk, O. A.

Ivashchuk, O. D.

Shtana, A. I.

DSpace at Belgorod State University

ISSN 1068-798X, Russian Engineering Research, 2020, Vol. 40, No. 11, pp. 970–972. © Allerton Press, Inc., 2020.Russian Text © The Author(s), 2020, published in STIN, 2020, No. 6, pp. 37–40.Predicting the Operational Efficiency of High-Pressure Roller CrushersO. A. Ivashchuka, *, O. D. Ivashchuka, **, V. I. Fedorova, ***, and A. I. Shtanaa, ****aBelgorod State University, Belgorod, 308015 Russia*e-mail: ivaschuk@bsu.edu.ru**e-mail: ivaschuk_o@bsu.edu.ru***e-mail: fedorov_v@bsu.edu.ru****e-mail: 1335477@bsu.edu.ruReceived January 24, 2020; revised January 24, 2020; accepted January 24, 2020Abstract—Models based on regression analysis for predicting the operational efficiency of high-pressureroller crushers are considered. A systematized and structured production database is created and statisticallyanalyzed. The consistency of the data is verified. The parameters with the greatest influence on the produc-tivity are identified. The basic structure of the mathematical models is determined, and the limits on theirapplicability are assessed. Predictive mathematical models are developed. Their adequacy is verified, andtheir precision is established in assessing the productivity of mills at an enrichment plant where the mineralcomposition of the incoming ore varies.Keywords: high-pressure roller crushers, iron ore, ore crushing, regression analysis, modeling, operationalefficiency, predictionDOI: 10.3103/S1068798X2011009XAs the global economy develops, there is growingdemand for all kinds of mineral resources, of whichthe most important is iron ore. By 2024, mineralextraction in Russia will have increased by 10–15%and demand for iron ore will rise from 331 to 380 mil-lion t (by 14.8%), according to the predictions in [1].Enrichment plants process iron ore and producedconcentrate with high iron content. The processingcosts depend greatly on the crushing of the minerals inspecial equipment.The principles for determining the operational effi-ciency of such equipment and identifying means ofincreasing the efficiency are well known. Besides tradi-tional methods—based on physicochemical models[2‒6] and standard methods of optimal process control[7–11]—smart data analysis may be employed [12–14].However, problems associated with predicting theoperational efficiency of crushing equipment are oftensuperficially discussed. If the assessment of the pro-ductivity fails to take account of the ore’s mineralcomposition, which is a key factor, the results are of nopractical value.In that context, we need to develop a reliablemethod of predicting the productivity of mills withdifferent composition and properties of the incomingore, on the basis of appropriate research. Satisfactoryanalysis of the relation between crusher performanceand the parameters of the incoming ore permits pre-diction of the output, which is extremely important ineconomic planning at enrichment enterprises, espe-cially on switching to different ore.We have developed models for predicting the oper-ational efficiency of mills at enrichment enterprises onthe basis of regression analysis. Specifically, we con-sider an enrichment enterprise in the Belgorod region,which is known as a world leader in iron production.The operational characteristics of the mills are col-lected for primary statistical analysis. A database cov-ering all the necessary parameters is created. Shift anddaily data in which even one of the necessary parame-ters is missing are disregarded.After verifying that the data are correct and consis-tent, we eliminate the shift characteristics and create adatabase solely of daily data. Then this database isdivided into four parts containing the general opera-tional characteristics of specific production sections.In each subdivision of the database, days on which themills operate for less than 24 h are disregarded.By assessing the pair correlations of the granulo-metric composition and all the ore-processing param-eters with the mill productivity Q, we are able to selectthe most significant characteristics. For each one, wedetermine the pair correlation coefficient with the fac-tors Q, Q0.5, Q1.2, Q2, Q3, and Q0.2.970PREDICTING THE OPERATIONAL EFFICIENCY 971Fig. 1. Mean daily values of the actual productivity andthe predicted Q curve for the aggregate data in mill sec-tions 1 and 2.0 30 60 90 120 150 180 210 240400440480520560600640Q, t/hDayThen, in order to derive an adequate regressionrelation, we eliminate possible multiple correlations.As a result, we select the following parameters: thecontent (by mass) of specific mineralogical types; theease of enrichment (W); and the content of the ≤0.045mm class in the concentrate ( . The mineralogicaltypes chosen are micaceous hematite–magnetite ,biotite–hematite (B), and magnetite (M)To assess the applicability of standard correlationanalysis and multiparametric regression analysis, weverify that the model parameters conform to a normaldistribution (by means of Statistica 6.0 software). Theassumption of a normal distribution is confirmed.In the next stage, in order to assess the relation betweenQ and the selected parameters, we analyze the depen-dences of , , , , 3, and 0.2 on the corre-sponding combination of characteristics, in the form Qi = wherei, j, k, l, m, and n may take the values 1, 0.5, 1.2, 2, 3,and 0.2; and Az are the regression coefficients.The best result for the first data subdivision is Q2 =, withdetermination coefficient R = 0.77.A dependence of this form is also satisfactory forthe second data subdivision. In that case, we may1)С( )FeQ 0.5Q 1.2Q 2Q Q Q( )+ + + + +10 1 2 3 4 1 5Fe ,kj m nA A M А B А W А C А( )+ + + + +22 2 2 3/20 1 2 3 4 1 5FeBA A M А А W А C АMRUSSIAN ENGINEERING RESEARCH  Vol. 40  No. 1combine the data in these two subdivisions and ana-lyze the resulting aggregate database. The samedependence is obtained, with R = 0.785.After analyzing models with different coefficients,we select a model with the minimum possible meandeviations and the maximum R)(= − + + − − −3/2 2 2 2 213280533 25Fe 877 58 15 600 .Q W C M BThe predicted and calculated Q values are in good Analogously, the regression formula for the thirdagreement for this model: the mean deviation ΔQme isno more than 0.25%. In Fig. 1, we show the meandaily values of the actual productivity and the pre-dicted Q curve.data subdivision is .We obtain the model( )3/23/2 3/20 1 2Q A A M А B= + + +3/2 3/2 3/23 4 1 5FeА W А C А+ +( )= − + + − + − 22 2 2 2 23 3 33 3 3 194386.8 68.6 Fe 1  81.9  30.3 6.0 1.3 .Q W B C МThe mean deviation ΔQ  is no more than 0.2%. In Fig. 2, we show the mean daily values of themeSince the operational system for these three sec-tions is the same, we may attempt to formulate a com-mon model. However, regression analysis shows thatthis is unsatisfactory.For the fourth data subdivision, the best result isQ1/5 = A0 + A1M1/5 + A2(B)1/5 + A3W2/3 +.The model takes the form−× +6  8 34 1 510 FeА C А()−−= − + × +− × − −24 3 3512 6 5 5115.91 0.91 10 Fe 1.2740.7 .02 10 0.274 0.169Q WC M Bactual productivity and the predicted Q curve for thefourth data subdivision. The mean discrepancy overthe period is no more than 0.35%.With model parameters close to the mean, theregression formulas correspond to the following confi-dence levels: with 0.95% probability, the actual pro-ductivity is within ±1% of the calculated value(around ±2% for the fourth subdivision). However, atthe boundaries of this interval, higher values are seen:±5, ±8, and ±15% for the three models describing allthe sections.As a result, the models are applicable when M =80.28–89.03, B = 4.77–9.93, W = 67.96–68.27, and = 72.33–88.63.1C1  2020972 IVASHCHUK et al.Fig. 2. Mean daily values of the actual productivity and thepredicted Q curve for the fourth mill section.0 20 40 60 80 100 120570600630660690720750780Q, t/hDayEstimates show that the compliance  with a nor-mal distribution is no more than 13.5 for all the regres-sion models, with a critical value of 31.CONCLUSIONS(1) We have developed mathematical models char-acterizing the causal relations between the mill pro-ductivity at an enrichment enterprise and the mineralcomposition of the incoming ore and verified theiradequacy and accuracy.(2) We have obtained predictive models of the millproductivity with R = 0.8 for the first and second sec-tions; R = 0.68 for the third section; and R = 0.7 for thefourth. This indicates that the models provide satisfac-tory predictions.(3) The proposed models permit effective assess-ment and prediction of the expected daily mill pro-ductivity, which may be used as the main parameter ineconomic planning of plant output.REFERENCES1. Strategiya razvitiya mineral’no-syr’evoi bazy RossiiskoiFederatsii do 2035 goda (utverzhdennaya Rasporyazhe-niem Pravitel’stva RF ot 22 dekabrya 2018 godano. 2914-r (The Strategy of Development of Mineral2 χRUSSIAN Resources of Russian Federation until 2035 Aproved bythe Resolution of RF Government No. 2914-r of De-cember 22, 2014), Moscow, 2014.2. Mining encyclopedia. http://www.mining-enc.ru/.3. Abramov, A.A., Pererabotka, obogashchenie i kompleks-noe ispol’zovanie tverdykh poleznykh iskopaemykh (Pro-cessing, Dressing, and Complex Use of Solid Fossils),Moscow: Gornaya Kniga, 2012.4. Sergo, E.E., Droblenie, izmel’chenie, i grokhochenie pole-znykh iskopaemykh (Crushing, Grinding, and Screeningof Minerals), Moscow: Nedra, 1985.5. Andreev, S.E., Zverevich, V.V., and Perov, V.A., Droble-nie, izmel’chenie, i grokhochenie poleznykh iskopaemykh(Crushing, Grinding, and Screening of Minerals), Mos-cow: Nedra, 1980.6. Avdokhin, V.M., Osnovy obogashcheniya poleznykh is-kopaemykh (Principles of Dressing of Minerals), Mos-cow: Gornaya Kniga, 2010.7. Morkun, V.S. and Lutsevich, I.A., Adaptivnye sistemyoptimal’nogo upravleniya tekhnologicheskimi protsessamigorno-obogatitel’nykh kombinatov (Adaptive Systems forOptimal Control of Technological Processes of Miningand Processing Plants), Moscow: Mineral, 2009.8. Tikhonov, O.N., Avtomatizatsiya proizvodstvennykhprotsessov na obogatitel’nykh fabrikakh (Automated In-dustrial Processes at Processing Plants), Moscow: Ne-dra, 1985.9. Kozin, V.Z., Trop, A.E., and Komarov, A.Ya., Avtoma-tizatsiya proizvodstvennykh protsessov na obogatitel’nykhfabrikakh; Uchebnoe posobie dlya vuzov (Automated In-dustrial Processes at Processing Plants: Manual forHigher Education Institutions), Moscow: Nedra, 1980.10. Protsuto, V.S., Avtomatizirovannye sistemy upravleniyatekhnologicheskimi protsessami obogatitel’nykh kombina-tov (Automated Control Systems of Technological Pro-cesses at the Processing Plants), Moscow: Nedra, 1987.11. Butkarev, A.P., Nekrasova, E.V., Mashir, N.G., andSiverin, Yu.V., Mathematical modeling of the produc-tion of iron ore pellets in the automated process controlsystem, Stal’, 1990, no. 3, pp. 15–21.12. Dyuk, V.A. and Samoilenko, A.P., Data Mining:Uchebnyi kurs (Data Mining: Study Course), St. Peters-burg: Piter, 2001.13. Williams, G., Data Mining with Rattle and R: The Art ofExcavating Data for Knowledge Discovery, New York:Springer-Verlag, 2011.14. Zaitseva, T.V., Vasina, N.V., Pusnaya, O.P., et al.,Computer-based solution tree software for implemen-tation of the problems of classification and forecasting,Nauchn. Ved. Belgorod. Gos. Univ., Ser.: Ekon., Inf.,2013, vol. 7 (150), no. 26-1, pp. 121–127.Translated by B. GilbertENGINEERING RESEARCH  Vol. 40  No. 11  2020

Predicting the operational efficiency of high-pressure roller crushers

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