1School of Materials Science and Engineering Anhui University of Science and Technology Huainan 232001 China2Panji Coal Preparation Plant Huaihe Energy (Group) Co Ltd Huainan 232082 China3School of Resources and Environmental Engineering Shandong University of Technology Zibo 255049 China
Correspondence should be addressed to Jinbo Zhu pgb2austeducn
Received 14 October 2020 Revised 6 January 2021 Accepted 12 January 2021 Published 21 January 2021
Academic Editor Radek Matusu
Copyright copy 2021 Zaisheng Zhu et al)is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
)is paper proposes a fuzzy comprehensive evaluation of ultrafine powders namely yield and quality value-based featureselection )ree indicators reflecting product yield and quality were selected to construct a simple and practical fuzzy com-prehensive evaluation protocol )e weight set of the indices and the fuzzy evaluation set were calculated based on the analytichierarchy process (AHP) method)e fuzzy comprehensive evaluation value was worked out as the only comprehensive index forthe evaluation of product )e best ultrafine comminution condition will be established through the comparison of the fuzzycomprehensive evaluation values Single-factor experiments and orthogonal experiments of the main influencing factors ofultrafine comminution were conducted It was concluded that the importance of each factor is sequentially the concentrationspecific surface area (SSA) of the media and percentage of critical speed (PCS) Moreover the concentration and SSA of the mediawere equally important Ultrafine comminution by ball mill had the best overall performance under the PCS of 85 the SSA of themedia of 024m2kg and the concentration of 75
1 Introduction
Grinding has been utilized in manufacturing fine and ultrafinepowders for the development of new materials and for im-proving product quality [1 2] )e grinding technology cansignificantly affect the particle characteristics [3] but not asingle-objective process [4] It is difficult to pulverize theparticles directly to required particle size which generallyincludes pulverization and classification or prepulverizationand ultrafine pulverization [5] )e grinding optimization hasbeen studied in the fields of cement production chemicalindustry metallurgical fine grinding mineral grinding andother industries [6 7] It can be seen that the proportion of thegrinding cost is a large part [8 9] )erefore the study ongrinding optimization is valuable and significant so as to makethe equipment have a better grinding response
In order to solve the problem of multiobjective opti-mization many scholars have established comprehensive
evaluation criteria or methods such as power coefficientmeasurement method constraint method and failure modeand effect analysis (FMEA) method [10 11] )e optimi-zation of the mineral ultrafine grinding process is a mul-tiobjective optimization problem [4 12] In many cases theunit of measurement of each index is different )erefore itis difficult to objectively evaluate whether the optimizedmultiobjective problem is good or not
Fuzzy set theory introduced by Zadeh [13] resembleshuman reasoning in its use of approximate information anduncertainty to generate decisions It was specificallydesigned to provide formalized tools for dealing with theimprecision intrinsic to many problems [14] )e fuzzycomprehensive evaluation method has been well applied inmany fields [15 16] however it is less involved in the field ofmineral crushing In this study the fuzzy comprehensiveevaluation system which is based on the analytic hierarchyprocess was introduced into the field of ultrafine grinding
HindawiJournal of Control Science and EngineeringVolume 2021 Article ID 6642402 7 pageshttpsdoiorg10115520216642402
comprehensive indicators were used to optimize the ultra-fine grinding process of mineral powders)e study aimed atoptimizing the three main factors (the mass of powderssmaller than 10 μm the fractal dimension of particle sizedistribution and d97) affecting the ultrafine grinding ofmineral powders
2 Materials and Methods
21Materials Potassium feldspar powders were used in thisstudy which were collected in Jiangsu Province )e d97 ofsample was 6368 μm and the particle size of smaller than10 μm was about 3532 which was measured by a laserparticle size analyzer (Model BT-9300H) Sodium poly-acrylate dispersant was purchased from the ChengxinChemical Material Supply Station in Zhejiang Province
22 Experiments )e samples were ground in a steel tankball mill using the wet ultrafine pulverization method by theball grinder with the rated power of 1000W and the criticalspeed of 85 rpm)e ceramic tank with the inner diameter of250mm the inner height of 275mm and the volume of135 L were used Two kinds of steel balls with the sizes of12mm and 17mm were used in this experiment Refer toprevious research experiments [17] the mass of ore powderswas fixed at 366 kg at a slurryrsquos mass concentration of 55and the amount of dispersant was of 02 of the mineralpowder weight )e specific surface area of the grindingmedia that consists of 66 kg of 12mm steel balls and 28 kg of17mm steel balls was 020m2kg )e operational per-centage of critical speed was 95 )e relevant data of theproduct ultrafine pulverized after 3 h were analyzed Asingle-factor experiment was designed to analyze the maininfluence factors of the ball mill (rotation rate SSA of themedia and concentration) in turn and then the orthogonalexperiments were designed to find the optimal processconditions
23 Calculation of the Weight Based on AHP )ree indi-cators reflecting product quantity and quality were selectedto construct a simple and practical fuzzy comprehensiveevaluation scheme for ultrafine powders )e mass ofpowders smaller than 10 μm (mminus10) was used to measure theyield )e fractal dimension of particle size distribution(PSD) and d97 were chosen to measure the quality of theproduction
)e analytic hierarchy process established by Saaty [18]is a decision-making method combined qualitatively andquantitatively [19 20] )e function f(x y) indicates howimportant the indicator x is compared to the indicator y thefunction f(y x) indicates how important the indicator y iscompared to the indicator x )e values of f(x y) and f(y x)can be defined according to subjective judgment If x is asimportant as y f(x y) 1 if x is especially more importantthan y f(x y) 9 and so on f(x y) isin [1 9] f(y x) isin [19 1]
)ree indicators were compared pairwise and the de-scription matrix of importance is given as follows
Equal Evident Between equal and evident
Equal Equal
Equal
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (1)
)is description matrix is converted into a judgmentmatrix
A aij1113872 11138733times3
1 5 4
02 1 1
025 1 1
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (2)
)e judgment matrix is usually not a consistent matrixand the consistency ratio should be calculated )e firsteigenvalue of A can be calculated according to the followingequation
λ1 1n
1113944
n
i1
1113936nj1aijwj
wi
(3)
where λ1 3006)e consistency index CI of A can be calculated
according to the following equation
CI minus1
n minus 11113944
n
i2λi
λ1 minus n
n minus 1 n 3 (4)
where CI 0003)e consistency ratio CR can be calculated according to
CR CIRI
(5)
If CRle 01 it can be acceptable When potential conflictemerges in evaluation [21] the CR is unacceptable and thedecision-maker is encouraged to repeat the pairwise com-parisons or some approaches should be adopted to processhighly conflicting data [22 23]
From the relevant chart [24 25] the index RI of the 3-dimensional judgment matrix is 058
CR 0003058
0005lt 01 (6)
)erefore the judgment matrix A is reliable andconsistent
According to the AHP theory the weight vector iscalculated using the power method sum method rootmethod and the characteristic roots method among whichthe sum method is the simplest In the case where thejudgment matrix is consistent each calculation method canobtain an accurate solution)e summethod was selected tocalculate the weight vector in this study )e weight of eachindicator is obtained through related calculation formulas)e weight ofmminus10 (w1) is 069 the weight of D (w2) is 0149and the weight of d97 (w3) is 0161 so the weight vector canbe represented as W (069 0149 0161)T
24 Comprehensive Evaluation )e degree of membershipμ1 of index mminus10 value was calculated by membershipfunction f(mminus10) degree of membership μ2 of index D value
2 Journal of Control Science and Engineering
calculated by membership function f(D) and degree ofmembership μ3 of index d97 value calculated by membershipfunction f(d97) respectively )e membership functionsf(mminus10) f(D) and f(d97) are constructed in Section 311 )eweight of mminus10 (w1) the weight of D (w2) and the weight ofd97 (w3) was calculated according to the AHP theory
)e construction process of the fuzzy comprehensiveevaluation is shown in Figure 1
3 Results and Discussion
31 Application of Comprehensive Evaluation
311 Evaluation Set and Membership Functions )e initialexperiment conditions were set first )e ore powder slurrywas prepared at 55 solid concentration by mass SSA of thegrinding media was 020m2kg )e additive amount ofdispersant was 02 of mineral powder )e PCS of the tankwas 95 )e result shows that mminus10 2656 kg D 2225According to PSD curve calculation it can be calculated thatd97 2536 μm )erefore the evaluation set U (mminus10 Dd97) (2656 2225 2536)
In the raw material mminus10 was 1293 kg And the totalmass of the raw material was 366 kg so the value range ofthe mass mminus10 isin [1293 366] From geometric knowledge[26] the range of D isin [1 3]
Ideally when all raw mineral powders are pulverized tominus10 μm d100 was 10 μm and d97 was less than 10 μm In this
study d97 could be approximated as d100 and thusd97 asymp10 μm In the worst case there were no fresh minus10 μmpowders formed in the product so the upper limit of d97 was6368 μm )erefore d97 isin [10 6368]
)e kinetic equation [27] which has been revised byAliavden [28] used to describe the grinding process ofmaterials is obtained as the following equation
y(t) y0 exp minusktn
( 1113857 (7)
where y0 is the initial sieve residue of groundmaterials with acertain particle size k is the grinding rate constant and n isthe time index and determined by the property of groundmaterial and its grinding conditions
)e comminution kinetics equation is as follows
y+10(t) 8476eminus064t066
(8)
With the propelling of the ultrafine pulverization thedifficulty became greater )e second-degree parabolicmembership function which corresponded to pulverizationkinetic curve [29] was selected Because the indicator mminus10was a benefit-type indicator the larger the value the betterthe product While D and d97 were the cost-type indicatorsthe smaller the value the better the product )erefore themembership functions used for the three indicators weredifferent )e following formulas (equation (6)) are themembership functions of the indicators mminus10 D and d97
f mminus10 1293 366 2( 1113857
0 mminus10 le 1293
mminus 10 minus 12932367
1113874 11138752 1293ltmminus10 lt 366
1 mminus10 ge 366
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
f(D 1 3 2)
1 Dle 1
3 minus D
21113874 1113875
2 1lt Dlt 3
0 Dge 3
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
f d97 10 6368 2( 1113857
1 d97 le 10
6368 minus d97( 1113857
53681113888 1113889
2 10ltd97 lt 6368
0 d97 ge 6368
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(9)
312 Fuzzification and Comprehensive Evaluation )evalues of indicators were changed into membership degreesndash μ μ isin [0 1] Take one indicator of them mminus10 as an
example In the product mminus10 2656 kg and1293lt 2656lt 366 so the membership degree of mminus10could be obtained by equation (6)
Journal of Control Science and Engineering 3
μ1 f(2656 1293 366 2) (2656 minus 1293)
23671113888 1113889
2
0332
(10)
In turn the membership degrees μ2 and μ3 of D and d97could be calculated as 015 and 051 respectively )e fuzzyevaluation set of each indicator is U (0332 015 051)
Z U1times3W3times1 (11)
According to equation (7) the multi-indicator fuzzycomprehensive evaluation value Z can be calculated from thefuzzy evaluation set U and weight set of each indicator Wwhere U (0332 015 051) and W (069 0149 0161)Ttherefore Z 0334
32 Effect of Factors on the Ultrafine Powders )e single-factor experiment was designed to find the influence ofsingle factor )en the orthogonal experiments were fol-lowed to analyze the best process conditions Taguchi L9 (34)orthogonal arrays were generated by the IBM SPSS Statistics250
321 Effect of PCS on the Ultrafine Powders )e best pa-rameters of PCS were explored under the conditions wherethe operational concentration was 55 and SSA of themediawas 024m2kg )e results are shown in Table 1
When the experimental PCS was set to 85 the effect ofultrafine pulverization of mineral powders was best With a
gradual increase in the PCS the fuzzy comprehensiveevaluation value of the experiment results increased rapidlyAfter the curve reached the highest point it gradually de-creased but the decrease of Z value was not as rapid asbefore When the PCS exceeded 100 the fuzzy compre-hensive evaluation value of the results also dropped rapidly
With the increase of the PCS the movement of balls waschanged from the principal tumbling form to the combi-native impacting form and the tumbling form )e con-tinuous increase of the PCS could cause the media to adhereto the wall and the force on the particles would reduceChanges of PCS changed the force distribution (impactforce shear force frictional force etc) [30] between mediaand powders )e synthetic effect of several forces accordingto a certain distribution ratio made the possibility of particlerefinement increase thus the effect was better
322 Effect of SSA of the Media on the Ultrafine Powders)e best parameters of SSA of the media were exploredunder the conditions where the operational concentrationwas 55 and the PCS was 85 )e different SSAs of themedia were achieved by adjusting the ratio of the two dif-ferent-sized media )e results are shown in Table 2
When the SSA of the media was 022m2kg ultrafinepulverization of mineral powders performs best Small SSAof the media would greatly reduce the number of pointcontact among the balls and the chance of the contact ofslurry with grinding balls would be dramatically reduced[31] During the movement of the media although the
Index
Membershipfunction
Degree ofmembership
Weight
Comprehensive evaluation index
mndash10 D
Z
AHP AHP AHP
f (mndash10) f (D) f (d97)
d97
μ1 μ2 μ3
w1 w2 w3
Figure 1 Flow chart of fuzzy comprehensive evaluation
4 Journal of Control Science and Engineering
impact force of a single ball on the material was increasedthe frictional force and shear force were greatly reduced)eSSA of the media continued to increase and the fuzzycomprehensive evaluation value of the product did notdecrease greatly which indicates that the impact force wasnot the main force )e friction force and shear force werethe main forces in the pulverization process In the late stageof ultrafine pulverization the particles became round andthe edges and corners basically disappeared
323 Effect of Concentration on the Ultrafine Powders)e optimal concentration was explored under the condi-tions where the operational PCS was 85 and SSA of themedia was 022m2kg )e results are shown in Table 3
When the concentration was 65 the ultrafine pul-verization of mineral powders works best When the con-centration was low the PSD of product was narrowhowever the yield of product was low In reverse the PSD ofproduct was extremely wide although the yield of producthad advantages there were many large particles in theproduct which affected the total quality If the concentrationwas low there were more opportunities for the occurrence ofcontact between the balls and the particles but the contactbetween the particles was insufficient When the concen-tration was too high the liquidity of the slurry reducedsharply and the motion of balls and particles wereobstructed leaving some large particles uncrushedAccording to ldquoBed comminutionrdquo [32] when there weremore particles there were more ldquoparticle-particle contactrdquosmaller particles would definitely be produced under thesame pulverization condition )erefore an appropriateincrease in the concentration would increase the fuzzycomprehensive evaluation value of the product
324 Optimization Parameters As shown in Table 4 thefuzzy comprehensive evaluation values of products werecalculated Due to the change in the concentration the rangeof mminus10 changed )us mminus10 isin [1293 549]
)e sequence of the factors influencing the productfeature was listed by polar value analysis With the indicatorm-10 as the appraising indicator maximum differences (R) ofeach factor were calculated orderly R (concentration)
0994 R (PCS) 0227 R (SSA of the media) 0330 thefactors were ranked in order of importance and concen-trationgt SSA of the mediagtPCS With the indicator D asthe appraising indicator R (concentration) 0181 R(PCS) 0130 R (SSA of the media) 0163 and concen-trationgt SSA of the mediagtPCS With the indicator d97 asthe appraising indicator R (concentration) 17817 R(PCS) 6343 R (SSA of the media) 5233 andconcentrationgt PCSgt SSA of the media Obviously thesignificance ordering of the factors was contradictory whenchoosing different appraising indicators With the indicatorZ as the appraising indicator R (concentration) 0054 R(PCS) 0039 and R (SSA of the media) 0053 Concen-trationgt SSA of the mediagt PCS moreover the concen-tration and SSA of the media were equally important
Using the fuzzy comprehensive evaluation value as anindicator combined with polar value analysis the optimalprocess conditions were obtained )e optimal PCS shouldbe at 85 the optimal SSA of the media should be at024m2kg and the optimal concentration should be at 75
Under the optimal conditions a verification experimentwas conducted to analyze the relevant parameters of theproduct and the results are shown as followsmminus10 3415 kg D 2483 and d97 4796 μm Based on themembership function used in the orthogonal experimentsthe membership degrees of each indicator were calculated
Table 1 Variation of product feature at different speeds
Table 2 Variation of product features at different SSAs of the media
Product feature mminus10 (kg) D (-) d97 (μm) Z (-)SSA of the media (m2kg)020 2190 2262 3307 0172022 2501 2257 2865 0269024 2433 2158 2557 0267026 2410 2201 2941 0243
Journal of Control Science and Engineering 5
μ1 0256 μ2 0067 and μ3 0086 Finally the maximumfuzzy comprehensive evaluation value under the optimalprocess parameters was obtained Z 0200 )erefore theoptimal operational factors obtained by polar value analysiswere correct
4 Conclusions
(1) )ree indicators reflecting quantity and quality havebeen selected and a comprehensive index has beenconstructed using a fuzzy comprehensive evaluationmethod based on hierarchical analysis and this hasbeen used to successfully find the optimal commi-nution operating conditions
(2) )e effect of different indicators on the ultrafinepowders was analyzed with the AHP )e weight setof three indicators ofmminus10 D and d97 wasW (0690149 0161)T
(3) )e significance ordering of the factors of ultrafinepulverization was concentration SSA of the mediaand PCS Moreover the concentration and SSA ofthe media were equally important
(4) When the optimal operating conditions were at thePCS of 85 the SSA of the media of 024m2kg andthe concentration of 75 the comprehensive per-formance of the product was the best and Z 0200
Data Availability
)e partial data used to support the findings of this study areincluded within the article and other partial data areavailable from the first author upon request
Additional Points
(1) )e significance of three indicators of the ultrafinepowders is analyzed by the analytic hierarchy process
method (2) According to the three indicators the fuzzycomprehensive evaluation based on analytic hierarchyprocess is used to obtain the comprehensive indicator (3))e three main factors influencing ultrafine comminutionconcentration specific surface area of the media and per-centage of critical speed are significantly ranked by theorthogonal test )e optimal operating conditions have beenobtained subsequently
Conflicts of Interest
)e authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
)e authors gratefully acknowledge the financial supportsprovided by the National Natural Science Foundation ofChina (51374015) Natural Science Foundation of AnhuiProvince (2008085QE272) China Postdoctoral ScienceFoundation (2020M671837 2019M662134) and AnhuiProvincial Excellent Talent Project (gxyqZD2020019) )eauthors would like to extend their special thanks to ProfZhenfu Luo
References
[1] S Qu Y Gong Y Yang M Cai H Xie and H ZhangldquoGrinding characteristics and removal mechanism of 25D-needled CfSiC compositesrdquo Ceramics International vol 45no 17 pp 21608ndash21617 2019
[2] B Oksuzoglu andM Uccedilurum ldquoAn experimental study on theultra-fine grinding of gypsum ore in a dry ball millrdquo PowderTechnology vol 291 pp 186ndash192 2016
[3] S Liu Q Li and J Song ldquoStudy on the grinding kinetics ofcopper tailing powderrdquo Powder Technology vol 330pp 105ndash113 2018
[4] H Choi W Lee J Lee H Chung andW S Choi ldquoUltra-finegrinding of inorganic powders by stirred ball mill effect of
Table 3 Variation of product feature at different concentrations
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
Journal of Control Science and Engineering 7
comprehensive indicators were used to optimize the ultra-fine grinding process of mineral powders)e study aimed atoptimizing the three main factors (the mass of powderssmaller than 10 μm the fractal dimension of particle sizedistribution and d97) affecting the ultrafine grinding ofmineral powders
2 Materials and Methods
21Materials Potassium feldspar powders were used in thisstudy which were collected in Jiangsu Province )e d97 ofsample was 6368 μm and the particle size of smaller than10 μm was about 3532 which was measured by a laserparticle size analyzer (Model BT-9300H) Sodium poly-acrylate dispersant was purchased from the ChengxinChemical Material Supply Station in Zhejiang Province
22 Experiments )e samples were ground in a steel tankball mill using the wet ultrafine pulverization method by theball grinder with the rated power of 1000W and the criticalspeed of 85 rpm)e ceramic tank with the inner diameter of250mm the inner height of 275mm and the volume of135 L were used Two kinds of steel balls with the sizes of12mm and 17mm were used in this experiment Refer toprevious research experiments [17] the mass of ore powderswas fixed at 366 kg at a slurryrsquos mass concentration of 55and the amount of dispersant was of 02 of the mineralpowder weight )e specific surface area of the grindingmedia that consists of 66 kg of 12mm steel balls and 28 kg of17mm steel balls was 020m2kg )e operational per-centage of critical speed was 95 )e relevant data of theproduct ultrafine pulverized after 3 h were analyzed Asingle-factor experiment was designed to analyze the maininfluence factors of the ball mill (rotation rate SSA of themedia and concentration) in turn and then the orthogonalexperiments were designed to find the optimal processconditions
23 Calculation of the Weight Based on AHP )ree indi-cators reflecting product quantity and quality were selectedto construct a simple and practical fuzzy comprehensiveevaluation scheme for ultrafine powders )e mass ofpowders smaller than 10 μm (mminus10) was used to measure theyield )e fractal dimension of particle size distribution(PSD) and d97 were chosen to measure the quality of theproduction
)e analytic hierarchy process established by Saaty [18]is a decision-making method combined qualitatively andquantitatively [19 20] )e function f(x y) indicates howimportant the indicator x is compared to the indicator y thefunction f(y x) indicates how important the indicator y iscompared to the indicator x )e values of f(x y) and f(y x)can be defined according to subjective judgment If x is asimportant as y f(x y) 1 if x is especially more importantthan y f(x y) 9 and so on f(x y) isin [1 9] f(y x) isin [19 1]
)ree indicators were compared pairwise and the de-scription matrix of importance is given as follows
Equal Evident Between equal and evident
Equal Equal
Equal
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (1)
)is description matrix is converted into a judgmentmatrix
A aij1113872 11138733times3
1 5 4
02 1 1
025 1 1
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (2)
)e judgment matrix is usually not a consistent matrixand the consistency ratio should be calculated )e firsteigenvalue of A can be calculated according to the followingequation
λ1 1n
1113944
n
i1
1113936nj1aijwj
wi
(3)
where λ1 3006)e consistency index CI of A can be calculated
according to the following equation
CI minus1
n minus 11113944
n
i2λi
λ1 minus n
n minus 1 n 3 (4)
where CI 0003)e consistency ratio CR can be calculated according to
CR CIRI
(5)
If CRle 01 it can be acceptable When potential conflictemerges in evaluation [21] the CR is unacceptable and thedecision-maker is encouraged to repeat the pairwise com-parisons or some approaches should be adopted to processhighly conflicting data [22 23]
From the relevant chart [24 25] the index RI of the 3-dimensional judgment matrix is 058
CR 0003058
0005lt 01 (6)
)erefore the judgment matrix A is reliable andconsistent
According to the AHP theory the weight vector iscalculated using the power method sum method rootmethod and the characteristic roots method among whichthe sum method is the simplest In the case where thejudgment matrix is consistent each calculation method canobtain an accurate solution)e summethod was selected tocalculate the weight vector in this study )e weight of eachindicator is obtained through related calculation formulas)e weight ofmminus10 (w1) is 069 the weight of D (w2) is 0149and the weight of d97 (w3) is 0161 so the weight vector canbe represented as W (069 0149 0161)T
24 Comprehensive Evaluation )e degree of membershipμ1 of index mminus10 value was calculated by membershipfunction f(mminus10) degree of membership μ2 of index D value
2 Journal of Control Science and Engineering
calculated by membership function f(D) and degree ofmembership μ3 of index d97 value calculated by membershipfunction f(d97) respectively )e membership functionsf(mminus10) f(D) and f(d97) are constructed in Section 311 )eweight of mminus10 (w1) the weight of D (w2) and the weight ofd97 (w3) was calculated according to the AHP theory
)e construction process of the fuzzy comprehensiveevaluation is shown in Figure 1
3 Results and Discussion
31 Application of Comprehensive Evaluation
311 Evaluation Set and Membership Functions )e initialexperiment conditions were set first )e ore powder slurrywas prepared at 55 solid concentration by mass SSA of thegrinding media was 020m2kg )e additive amount ofdispersant was 02 of mineral powder )e PCS of the tankwas 95 )e result shows that mminus10 2656 kg D 2225According to PSD curve calculation it can be calculated thatd97 2536 μm )erefore the evaluation set U (mminus10 Dd97) (2656 2225 2536)
In the raw material mminus10 was 1293 kg And the totalmass of the raw material was 366 kg so the value range ofthe mass mminus10 isin [1293 366] From geometric knowledge[26] the range of D isin [1 3]
Ideally when all raw mineral powders are pulverized tominus10 μm d100 was 10 μm and d97 was less than 10 μm In this
study d97 could be approximated as d100 and thusd97 asymp10 μm In the worst case there were no fresh minus10 μmpowders formed in the product so the upper limit of d97 was6368 μm )erefore d97 isin [10 6368]
)e kinetic equation [27] which has been revised byAliavden [28] used to describe the grinding process ofmaterials is obtained as the following equation
y(t) y0 exp minusktn
( 1113857 (7)
where y0 is the initial sieve residue of groundmaterials with acertain particle size k is the grinding rate constant and n isthe time index and determined by the property of groundmaterial and its grinding conditions
)e comminution kinetics equation is as follows
y+10(t) 8476eminus064t066
(8)
With the propelling of the ultrafine pulverization thedifficulty became greater )e second-degree parabolicmembership function which corresponded to pulverizationkinetic curve [29] was selected Because the indicator mminus10was a benefit-type indicator the larger the value the betterthe product While D and d97 were the cost-type indicatorsthe smaller the value the better the product )erefore themembership functions used for the three indicators weredifferent )e following formulas (equation (6)) are themembership functions of the indicators mminus10 D and d97
f mminus10 1293 366 2( 1113857
0 mminus10 le 1293
mminus 10 minus 12932367
1113874 11138752 1293ltmminus10 lt 366
1 mminus10 ge 366
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
f(D 1 3 2)
1 Dle 1
3 minus D
21113874 1113875
2 1lt Dlt 3
0 Dge 3
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
f d97 10 6368 2( 1113857
1 d97 le 10
6368 minus d97( 1113857
53681113888 1113889
2 10ltd97 lt 6368
0 d97 ge 6368
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(9)
312 Fuzzification and Comprehensive Evaluation )evalues of indicators were changed into membership degreesndash μ μ isin [0 1] Take one indicator of them mminus10 as an
example In the product mminus10 2656 kg and1293lt 2656lt 366 so the membership degree of mminus10could be obtained by equation (6)
Journal of Control Science and Engineering 3
μ1 f(2656 1293 366 2) (2656 minus 1293)
23671113888 1113889
2
0332
(10)
In turn the membership degrees μ2 and μ3 of D and d97could be calculated as 015 and 051 respectively )e fuzzyevaluation set of each indicator is U (0332 015 051)
Z U1times3W3times1 (11)
According to equation (7) the multi-indicator fuzzycomprehensive evaluation value Z can be calculated from thefuzzy evaluation set U and weight set of each indicator Wwhere U (0332 015 051) and W (069 0149 0161)Ttherefore Z 0334
32 Effect of Factors on the Ultrafine Powders )e single-factor experiment was designed to find the influence ofsingle factor )en the orthogonal experiments were fol-lowed to analyze the best process conditions Taguchi L9 (34)orthogonal arrays were generated by the IBM SPSS Statistics250
321 Effect of PCS on the Ultrafine Powders )e best pa-rameters of PCS were explored under the conditions wherethe operational concentration was 55 and SSA of themediawas 024m2kg )e results are shown in Table 1
When the experimental PCS was set to 85 the effect ofultrafine pulverization of mineral powders was best With a
gradual increase in the PCS the fuzzy comprehensiveevaluation value of the experiment results increased rapidlyAfter the curve reached the highest point it gradually de-creased but the decrease of Z value was not as rapid asbefore When the PCS exceeded 100 the fuzzy compre-hensive evaluation value of the results also dropped rapidly
With the increase of the PCS the movement of balls waschanged from the principal tumbling form to the combi-native impacting form and the tumbling form )e con-tinuous increase of the PCS could cause the media to adhereto the wall and the force on the particles would reduceChanges of PCS changed the force distribution (impactforce shear force frictional force etc) [30] between mediaand powders )e synthetic effect of several forces accordingto a certain distribution ratio made the possibility of particlerefinement increase thus the effect was better
322 Effect of SSA of the Media on the Ultrafine Powders)e best parameters of SSA of the media were exploredunder the conditions where the operational concentrationwas 55 and the PCS was 85 )e different SSAs of themedia were achieved by adjusting the ratio of the two dif-ferent-sized media )e results are shown in Table 2
When the SSA of the media was 022m2kg ultrafinepulverization of mineral powders performs best Small SSAof the media would greatly reduce the number of pointcontact among the balls and the chance of the contact ofslurry with grinding balls would be dramatically reduced[31] During the movement of the media although the
Index
Membershipfunction
Degree ofmembership
Weight
Comprehensive evaluation index
mndash10 D
Z
AHP AHP AHP
f (mndash10) f (D) f (d97)
d97
μ1 μ2 μ3
w1 w2 w3
Figure 1 Flow chart of fuzzy comprehensive evaluation
4 Journal of Control Science and Engineering
impact force of a single ball on the material was increasedthe frictional force and shear force were greatly reduced)eSSA of the media continued to increase and the fuzzycomprehensive evaluation value of the product did notdecrease greatly which indicates that the impact force wasnot the main force )e friction force and shear force werethe main forces in the pulverization process In the late stageof ultrafine pulverization the particles became round andthe edges and corners basically disappeared
323 Effect of Concentration on the Ultrafine Powders)e optimal concentration was explored under the condi-tions where the operational PCS was 85 and SSA of themedia was 022m2kg )e results are shown in Table 3
When the concentration was 65 the ultrafine pul-verization of mineral powders works best When the con-centration was low the PSD of product was narrowhowever the yield of product was low In reverse the PSD ofproduct was extremely wide although the yield of producthad advantages there were many large particles in theproduct which affected the total quality If the concentrationwas low there were more opportunities for the occurrence ofcontact between the balls and the particles but the contactbetween the particles was insufficient When the concen-tration was too high the liquidity of the slurry reducedsharply and the motion of balls and particles wereobstructed leaving some large particles uncrushedAccording to ldquoBed comminutionrdquo [32] when there weremore particles there were more ldquoparticle-particle contactrdquosmaller particles would definitely be produced under thesame pulverization condition )erefore an appropriateincrease in the concentration would increase the fuzzycomprehensive evaluation value of the product
324 Optimization Parameters As shown in Table 4 thefuzzy comprehensive evaluation values of products werecalculated Due to the change in the concentration the rangeof mminus10 changed )us mminus10 isin [1293 549]
)e sequence of the factors influencing the productfeature was listed by polar value analysis With the indicatorm-10 as the appraising indicator maximum differences (R) ofeach factor were calculated orderly R (concentration)
0994 R (PCS) 0227 R (SSA of the media) 0330 thefactors were ranked in order of importance and concen-trationgt SSA of the mediagtPCS With the indicator D asthe appraising indicator R (concentration) 0181 R(PCS) 0130 R (SSA of the media) 0163 and concen-trationgt SSA of the mediagtPCS With the indicator d97 asthe appraising indicator R (concentration) 17817 R(PCS) 6343 R (SSA of the media) 5233 andconcentrationgt PCSgt SSA of the media Obviously thesignificance ordering of the factors was contradictory whenchoosing different appraising indicators With the indicatorZ as the appraising indicator R (concentration) 0054 R(PCS) 0039 and R (SSA of the media) 0053 Concen-trationgt SSA of the mediagt PCS moreover the concen-tration and SSA of the media were equally important
Using the fuzzy comprehensive evaluation value as anindicator combined with polar value analysis the optimalprocess conditions were obtained )e optimal PCS shouldbe at 85 the optimal SSA of the media should be at024m2kg and the optimal concentration should be at 75
Under the optimal conditions a verification experimentwas conducted to analyze the relevant parameters of theproduct and the results are shown as followsmminus10 3415 kg D 2483 and d97 4796 μm Based on themembership function used in the orthogonal experimentsthe membership degrees of each indicator were calculated
Table 1 Variation of product feature at different speeds
Table 2 Variation of product features at different SSAs of the media
Product feature mminus10 (kg) D (-) d97 (μm) Z (-)SSA of the media (m2kg)020 2190 2262 3307 0172022 2501 2257 2865 0269024 2433 2158 2557 0267026 2410 2201 2941 0243
Journal of Control Science and Engineering 5
μ1 0256 μ2 0067 and μ3 0086 Finally the maximumfuzzy comprehensive evaluation value under the optimalprocess parameters was obtained Z 0200 )erefore theoptimal operational factors obtained by polar value analysiswere correct
4 Conclusions
(1) )ree indicators reflecting quantity and quality havebeen selected and a comprehensive index has beenconstructed using a fuzzy comprehensive evaluationmethod based on hierarchical analysis and this hasbeen used to successfully find the optimal commi-nution operating conditions
(2) )e effect of different indicators on the ultrafinepowders was analyzed with the AHP )e weight setof three indicators ofmminus10 D and d97 wasW (0690149 0161)T
(3) )e significance ordering of the factors of ultrafinepulverization was concentration SSA of the mediaand PCS Moreover the concentration and SSA ofthe media were equally important
(4) When the optimal operating conditions were at thePCS of 85 the SSA of the media of 024m2kg andthe concentration of 75 the comprehensive per-formance of the product was the best and Z 0200
Data Availability
)e partial data used to support the findings of this study areincluded within the article and other partial data areavailable from the first author upon request
Additional Points
(1) )e significance of three indicators of the ultrafinepowders is analyzed by the analytic hierarchy process
method (2) According to the three indicators the fuzzycomprehensive evaluation based on analytic hierarchyprocess is used to obtain the comprehensive indicator (3))e three main factors influencing ultrafine comminutionconcentration specific surface area of the media and per-centage of critical speed are significantly ranked by theorthogonal test )e optimal operating conditions have beenobtained subsequently
Conflicts of Interest
)e authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
)e authors gratefully acknowledge the financial supportsprovided by the National Natural Science Foundation ofChina (51374015) Natural Science Foundation of AnhuiProvince (2008085QE272) China Postdoctoral ScienceFoundation (2020M671837 2019M662134) and AnhuiProvincial Excellent Talent Project (gxyqZD2020019) )eauthors would like to extend their special thanks to ProfZhenfu Luo
References
[1] S Qu Y Gong Y Yang M Cai H Xie and H ZhangldquoGrinding characteristics and removal mechanism of 25D-needled CfSiC compositesrdquo Ceramics International vol 45no 17 pp 21608ndash21617 2019
[2] B Oksuzoglu andM Uccedilurum ldquoAn experimental study on theultra-fine grinding of gypsum ore in a dry ball millrdquo PowderTechnology vol 291 pp 186ndash192 2016
[3] S Liu Q Li and J Song ldquoStudy on the grinding kinetics ofcopper tailing powderrdquo Powder Technology vol 330pp 105ndash113 2018
[4] H Choi W Lee J Lee H Chung andW S Choi ldquoUltra-finegrinding of inorganic powders by stirred ball mill effect of
Table 3 Variation of product feature at different concentrations
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
Journal of Control Science and Engineering 7
calculated by membership function f(D) and degree ofmembership μ3 of index d97 value calculated by membershipfunction f(d97) respectively )e membership functionsf(mminus10) f(D) and f(d97) are constructed in Section 311 )eweight of mminus10 (w1) the weight of D (w2) and the weight ofd97 (w3) was calculated according to the AHP theory
)e construction process of the fuzzy comprehensiveevaluation is shown in Figure 1
3 Results and Discussion
31 Application of Comprehensive Evaluation
311 Evaluation Set and Membership Functions )e initialexperiment conditions were set first )e ore powder slurrywas prepared at 55 solid concentration by mass SSA of thegrinding media was 020m2kg )e additive amount ofdispersant was 02 of mineral powder )e PCS of the tankwas 95 )e result shows that mminus10 2656 kg D 2225According to PSD curve calculation it can be calculated thatd97 2536 μm )erefore the evaluation set U (mminus10 Dd97) (2656 2225 2536)
In the raw material mminus10 was 1293 kg And the totalmass of the raw material was 366 kg so the value range ofthe mass mminus10 isin [1293 366] From geometric knowledge[26] the range of D isin [1 3]
Ideally when all raw mineral powders are pulverized tominus10 μm d100 was 10 μm and d97 was less than 10 μm In this
study d97 could be approximated as d100 and thusd97 asymp10 μm In the worst case there were no fresh minus10 μmpowders formed in the product so the upper limit of d97 was6368 μm )erefore d97 isin [10 6368]
)e kinetic equation [27] which has been revised byAliavden [28] used to describe the grinding process ofmaterials is obtained as the following equation
y(t) y0 exp minusktn
( 1113857 (7)
where y0 is the initial sieve residue of groundmaterials with acertain particle size k is the grinding rate constant and n isthe time index and determined by the property of groundmaterial and its grinding conditions
)e comminution kinetics equation is as follows
y+10(t) 8476eminus064t066
(8)
With the propelling of the ultrafine pulverization thedifficulty became greater )e second-degree parabolicmembership function which corresponded to pulverizationkinetic curve [29] was selected Because the indicator mminus10was a benefit-type indicator the larger the value the betterthe product While D and d97 were the cost-type indicatorsthe smaller the value the better the product )erefore themembership functions used for the three indicators weredifferent )e following formulas (equation (6)) are themembership functions of the indicators mminus10 D and d97
f mminus10 1293 366 2( 1113857
0 mminus10 le 1293
mminus 10 minus 12932367
1113874 11138752 1293ltmminus10 lt 366
1 mminus10 ge 366
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
f(D 1 3 2)
1 Dle 1
3 minus D
21113874 1113875
2 1lt Dlt 3
0 Dge 3
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
f d97 10 6368 2( 1113857
1 d97 le 10
6368 minus d97( 1113857
53681113888 1113889
2 10ltd97 lt 6368
0 d97 ge 6368
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(9)
312 Fuzzification and Comprehensive Evaluation )evalues of indicators were changed into membership degreesndash μ μ isin [0 1] Take one indicator of them mminus10 as an
example In the product mminus10 2656 kg and1293lt 2656lt 366 so the membership degree of mminus10could be obtained by equation (6)
Journal of Control Science and Engineering 3
μ1 f(2656 1293 366 2) (2656 minus 1293)
23671113888 1113889
2
0332
(10)
In turn the membership degrees μ2 and μ3 of D and d97could be calculated as 015 and 051 respectively )e fuzzyevaluation set of each indicator is U (0332 015 051)
Z U1times3W3times1 (11)
According to equation (7) the multi-indicator fuzzycomprehensive evaluation value Z can be calculated from thefuzzy evaluation set U and weight set of each indicator Wwhere U (0332 015 051) and W (069 0149 0161)Ttherefore Z 0334
32 Effect of Factors on the Ultrafine Powders )e single-factor experiment was designed to find the influence ofsingle factor )en the orthogonal experiments were fol-lowed to analyze the best process conditions Taguchi L9 (34)orthogonal arrays were generated by the IBM SPSS Statistics250
321 Effect of PCS on the Ultrafine Powders )e best pa-rameters of PCS were explored under the conditions wherethe operational concentration was 55 and SSA of themediawas 024m2kg )e results are shown in Table 1
When the experimental PCS was set to 85 the effect ofultrafine pulverization of mineral powders was best With a
gradual increase in the PCS the fuzzy comprehensiveevaluation value of the experiment results increased rapidlyAfter the curve reached the highest point it gradually de-creased but the decrease of Z value was not as rapid asbefore When the PCS exceeded 100 the fuzzy compre-hensive evaluation value of the results also dropped rapidly
With the increase of the PCS the movement of balls waschanged from the principal tumbling form to the combi-native impacting form and the tumbling form )e con-tinuous increase of the PCS could cause the media to adhereto the wall and the force on the particles would reduceChanges of PCS changed the force distribution (impactforce shear force frictional force etc) [30] between mediaand powders )e synthetic effect of several forces accordingto a certain distribution ratio made the possibility of particlerefinement increase thus the effect was better
322 Effect of SSA of the Media on the Ultrafine Powders)e best parameters of SSA of the media were exploredunder the conditions where the operational concentrationwas 55 and the PCS was 85 )e different SSAs of themedia were achieved by adjusting the ratio of the two dif-ferent-sized media )e results are shown in Table 2
When the SSA of the media was 022m2kg ultrafinepulverization of mineral powders performs best Small SSAof the media would greatly reduce the number of pointcontact among the balls and the chance of the contact ofslurry with grinding balls would be dramatically reduced[31] During the movement of the media although the
Index
Membershipfunction
Degree ofmembership
Weight
Comprehensive evaluation index
mndash10 D
Z
AHP AHP AHP
f (mndash10) f (D) f (d97)
d97
μ1 μ2 μ3
w1 w2 w3
Figure 1 Flow chart of fuzzy comprehensive evaluation
4 Journal of Control Science and Engineering
impact force of a single ball on the material was increasedthe frictional force and shear force were greatly reduced)eSSA of the media continued to increase and the fuzzycomprehensive evaluation value of the product did notdecrease greatly which indicates that the impact force wasnot the main force )e friction force and shear force werethe main forces in the pulverization process In the late stageof ultrafine pulverization the particles became round andthe edges and corners basically disappeared
323 Effect of Concentration on the Ultrafine Powders)e optimal concentration was explored under the condi-tions where the operational PCS was 85 and SSA of themedia was 022m2kg )e results are shown in Table 3
When the concentration was 65 the ultrafine pul-verization of mineral powders works best When the con-centration was low the PSD of product was narrowhowever the yield of product was low In reverse the PSD ofproduct was extremely wide although the yield of producthad advantages there were many large particles in theproduct which affected the total quality If the concentrationwas low there were more opportunities for the occurrence ofcontact between the balls and the particles but the contactbetween the particles was insufficient When the concen-tration was too high the liquidity of the slurry reducedsharply and the motion of balls and particles wereobstructed leaving some large particles uncrushedAccording to ldquoBed comminutionrdquo [32] when there weremore particles there were more ldquoparticle-particle contactrdquosmaller particles would definitely be produced under thesame pulverization condition )erefore an appropriateincrease in the concentration would increase the fuzzycomprehensive evaluation value of the product
324 Optimization Parameters As shown in Table 4 thefuzzy comprehensive evaluation values of products werecalculated Due to the change in the concentration the rangeof mminus10 changed )us mminus10 isin [1293 549]
)e sequence of the factors influencing the productfeature was listed by polar value analysis With the indicatorm-10 as the appraising indicator maximum differences (R) ofeach factor were calculated orderly R (concentration)
0994 R (PCS) 0227 R (SSA of the media) 0330 thefactors were ranked in order of importance and concen-trationgt SSA of the mediagtPCS With the indicator D asthe appraising indicator R (concentration) 0181 R(PCS) 0130 R (SSA of the media) 0163 and concen-trationgt SSA of the mediagtPCS With the indicator d97 asthe appraising indicator R (concentration) 17817 R(PCS) 6343 R (SSA of the media) 5233 andconcentrationgt PCSgt SSA of the media Obviously thesignificance ordering of the factors was contradictory whenchoosing different appraising indicators With the indicatorZ as the appraising indicator R (concentration) 0054 R(PCS) 0039 and R (SSA of the media) 0053 Concen-trationgt SSA of the mediagt PCS moreover the concen-tration and SSA of the media were equally important
Using the fuzzy comprehensive evaluation value as anindicator combined with polar value analysis the optimalprocess conditions were obtained )e optimal PCS shouldbe at 85 the optimal SSA of the media should be at024m2kg and the optimal concentration should be at 75
Under the optimal conditions a verification experimentwas conducted to analyze the relevant parameters of theproduct and the results are shown as followsmminus10 3415 kg D 2483 and d97 4796 μm Based on themembership function used in the orthogonal experimentsthe membership degrees of each indicator were calculated
Table 1 Variation of product feature at different speeds
Table 2 Variation of product features at different SSAs of the media
Product feature mminus10 (kg) D (-) d97 (μm) Z (-)SSA of the media (m2kg)020 2190 2262 3307 0172022 2501 2257 2865 0269024 2433 2158 2557 0267026 2410 2201 2941 0243
Journal of Control Science and Engineering 5
μ1 0256 μ2 0067 and μ3 0086 Finally the maximumfuzzy comprehensive evaluation value under the optimalprocess parameters was obtained Z 0200 )erefore theoptimal operational factors obtained by polar value analysiswere correct
4 Conclusions
(1) )ree indicators reflecting quantity and quality havebeen selected and a comprehensive index has beenconstructed using a fuzzy comprehensive evaluationmethod based on hierarchical analysis and this hasbeen used to successfully find the optimal commi-nution operating conditions
(2) )e effect of different indicators on the ultrafinepowders was analyzed with the AHP )e weight setof three indicators ofmminus10 D and d97 wasW (0690149 0161)T
(3) )e significance ordering of the factors of ultrafinepulverization was concentration SSA of the mediaand PCS Moreover the concentration and SSA ofthe media were equally important
(4) When the optimal operating conditions were at thePCS of 85 the SSA of the media of 024m2kg andthe concentration of 75 the comprehensive per-formance of the product was the best and Z 0200
Data Availability
)e partial data used to support the findings of this study areincluded within the article and other partial data areavailable from the first author upon request
Additional Points
(1) )e significance of three indicators of the ultrafinepowders is analyzed by the analytic hierarchy process
method (2) According to the three indicators the fuzzycomprehensive evaluation based on analytic hierarchyprocess is used to obtain the comprehensive indicator (3))e three main factors influencing ultrafine comminutionconcentration specific surface area of the media and per-centage of critical speed are significantly ranked by theorthogonal test )e optimal operating conditions have beenobtained subsequently
Conflicts of Interest
)e authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
)e authors gratefully acknowledge the financial supportsprovided by the National Natural Science Foundation ofChina (51374015) Natural Science Foundation of AnhuiProvince (2008085QE272) China Postdoctoral ScienceFoundation (2020M671837 2019M662134) and AnhuiProvincial Excellent Talent Project (gxyqZD2020019) )eauthors would like to extend their special thanks to ProfZhenfu Luo
References
[1] S Qu Y Gong Y Yang M Cai H Xie and H ZhangldquoGrinding characteristics and removal mechanism of 25D-needled CfSiC compositesrdquo Ceramics International vol 45no 17 pp 21608ndash21617 2019
[2] B Oksuzoglu andM Uccedilurum ldquoAn experimental study on theultra-fine grinding of gypsum ore in a dry ball millrdquo PowderTechnology vol 291 pp 186ndash192 2016
[3] S Liu Q Li and J Song ldquoStudy on the grinding kinetics ofcopper tailing powderrdquo Powder Technology vol 330pp 105ndash113 2018
[4] H Choi W Lee J Lee H Chung andW S Choi ldquoUltra-finegrinding of inorganic powders by stirred ball mill effect of
Table 3 Variation of product feature at different concentrations
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
Journal of Control Science and Engineering 7
μ1 f(2656 1293 366 2) (2656 minus 1293)
23671113888 1113889
2
0332
(10)
In turn the membership degrees μ2 and μ3 of D and d97could be calculated as 015 and 051 respectively )e fuzzyevaluation set of each indicator is U (0332 015 051)
Z U1times3W3times1 (11)
According to equation (7) the multi-indicator fuzzycomprehensive evaluation value Z can be calculated from thefuzzy evaluation set U and weight set of each indicator Wwhere U (0332 015 051) and W (069 0149 0161)Ttherefore Z 0334
32 Effect of Factors on the Ultrafine Powders )e single-factor experiment was designed to find the influence ofsingle factor )en the orthogonal experiments were fol-lowed to analyze the best process conditions Taguchi L9 (34)orthogonal arrays were generated by the IBM SPSS Statistics250
321 Effect of PCS on the Ultrafine Powders )e best pa-rameters of PCS were explored under the conditions wherethe operational concentration was 55 and SSA of themediawas 024m2kg )e results are shown in Table 1
When the experimental PCS was set to 85 the effect ofultrafine pulverization of mineral powders was best With a
gradual increase in the PCS the fuzzy comprehensiveevaluation value of the experiment results increased rapidlyAfter the curve reached the highest point it gradually de-creased but the decrease of Z value was not as rapid asbefore When the PCS exceeded 100 the fuzzy compre-hensive evaluation value of the results also dropped rapidly
With the increase of the PCS the movement of balls waschanged from the principal tumbling form to the combi-native impacting form and the tumbling form )e con-tinuous increase of the PCS could cause the media to adhereto the wall and the force on the particles would reduceChanges of PCS changed the force distribution (impactforce shear force frictional force etc) [30] between mediaand powders )e synthetic effect of several forces accordingto a certain distribution ratio made the possibility of particlerefinement increase thus the effect was better
322 Effect of SSA of the Media on the Ultrafine Powders)e best parameters of SSA of the media were exploredunder the conditions where the operational concentrationwas 55 and the PCS was 85 )e different SSAs of themedia were achieved by adjusting the ratio of the two dif-ferent-sized media )e results are shown in Table 2
When the SSA of the media was 022m2kg ultrafinepulverization of mineral powders performs best Small SSAof the media would greatly reduce the number of pointcontact among the balls and the chance of the contact ofslurry with grinding balls would be dramatically reduced[31] During the movement of the media although the
Index
Membershipfunction
Degree ofmembership
Weight
Comprehensive evaluation index
mndash10 D
Z
AHP AHP AHP
f (mndash10) f (D) f (d97)
d97
μ1 μ2 μ3
w1 w2 w3
Figure 1 Flow chart of fuzzy comprehensive evaluation
4 Journal of Control Science and Engineering
impact force of a single ball on the material was increasedthe frictional force and shear force were greatly reduced)eSSA of the media continued to increase and the fuzzycomprehensive evaluation value of the product did notdecrease greatly which indicates that the impact force wasnot the main force )e friction force and shear force werethe main forces in the pulverization process In the late stageof ultrafine pulverization the particles became round andthe edges and corners basically disappeared
323 Effect of Concentration on the Ultrafine Powders)e optimal concentration was explored under the condi-tions where the operational PCS was 85 and SSA of themedia was 022m2kg )e results are shown in Table 3
When the concentration was 65 the ultrafine pul-verization of mineral powders works best When the con-centration was low the PSD of product was narrowhowever the yield of product was low In reverse the PSD ofproduct was extremely wide although the yield of producthad advantages there were many large particles in theproduct which affected the total quality If the concentrationwas low there were more opportunities for the occurrence ofcontact between the balls and the particles but the contactbetween the particles was insufficient When the concen-tration was too high the liquidity of the slurry reducedsharply and the motion of balls and particles wereobstructed leaving some large particles uncrushedAccording to ldquoBed comminutionrdquo [32] when there weremore particles there were more ldquoparticle-particle contactrdquosmaller particles would definitely be produced under thesame pulverization condition )erefore an appropriateincrease in the concentration would increase the fuzzycomprehensive evaluation value of the product
324 Optimization Parameters As shown in Table 4 thefuzzy comprehensive evaluation values of products werecalculated Due to the change in the concentration the rangeof mminus10 changed )us mminus10 isin [1293 549]
)e sequence of the factors influencing the productfeature was listed by polar value analysis With the indicatorm-10 as the appraising indicator maximum differences (R) ofeach factor were calculated orderly R (concentration)
0994 R (PCS) 0227 R (SSA of the media) 0330 thefactors were ranked in order of importance and concen-trationgt SSA of the mediagtPCS With the indicator D asthe appraising indicator R (concentration) 0181 R(PCS) 0130 R (SSA of the media) 0163 and concen-trationgt SSA of the mediagtPCS With the indicator d97 asthe appraising indicator R (concentration) 17817 R(PCS) 6343 R (SSA of the media) 5233 andconcentrationgt PCSgt SSA of the media Obviously thesignificance ordering of the factors was contradictory whenchoosing different appraising indicators With the indicatorZ as the appraising indicator R (concentration) 0054 R(PCS) 0039 and R (SSA of the media) 0053 Concen-trationgt SSA of the mediagt PCS moreover the concen-tration and SSA of the media were equally important
Using the fuzzy comprehensive evaluation value as anindicator combined with polar value analysis the optimalprocess conditions were obtained )e optimal PCS shouldbe at 85 the optimal SSA of the media should be at024m2kg and the optimal concentration should be at 75
Under the optimal conditions a verification experimentwas conducted to analyze the relevant parameters of theproduct and the results are shown as followsmminus10 3415 kg D 2483 and d97 4796 μm Based on themembership function used in the orthogonal experimentsthe membership degrees of each indicator were calculated
Table 1 Variation of product feature at different speeds
Table 2 Variation of product features at different SSAs of the media
Product feature mminus10 (kg) D (-) d97 (μm) Z (-)SSA of the media (m2kg)020 2190 2262 3307 0172022 2501 2257 2865 0269024 2433 2158 2557 0267026 2410 2201 2941 0243
Journal of Control Science and Engineering 5
μ1 0256 μ2 0067 and μ3 0086 Finally the maximumfuzzy comprehensive evaluation value under the optimalprocess parameters was obtained Z 0200 )erefore theoptimal operational factors obtained by polar value analysiswere correct
4 Conclusions
(1) )ree indicators reflecting quantity and quality havebeen selected and a comprehensive index has beenconstructed using a fuzzy comprehensive evaluationmethod based on hierarchical analysis and this hasbeen used to successfully find the optimal commi-nution operating conditions
(2) )e effect of different indicators on the ultrafinepowders was analyzed with the AHP )e weight setof three indicators ofmminus10 D and d97 wasW (0690149 0161)T
(3) )e significance ordering of the factors of ultrafinepulverization was concentration SSA of the mediaand PCS Moreover the concentration and SSA ofthe media were equally important
(4) When the optimal operating conditions were at thePCS of 85 the SSA of the media of 024m2kg andthe concentration of 75 the comprehensive per-formance of the product was the best and Z 0200
Data Availability
)e partial data used to support the findings of this study areincluded within the article and other partial data areavailable from the first author upon request
Additional Points
(1) )e significance of three indicators of the ultrafinepowders is analyzed by the analytic hierarchy process
method (2) According to the three indicators the fuzzycomprehensive evaluation based on analytic hierarchyprocess is used to obtain the comprehensive indicator (3))e three main factors influencing ultrafine comminutionconcentration specific surface area of the media and per-centage of critical speed are significantly ranked by theorthogonal test )e optimal operating conditions have beenobtained subsequently
Conflicts of Interest
)e authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
)e authors gratefully acknowledge the financial supportsprovided by the National Natural Science Foundation ofChina (51374015) Natural Science Foundation of AnhuiProvince (2008085QE272) China Postdoctoral ScienceFoundation (2020M671837 2019M662134) and AnhuiProvincial Excellent Talent Project (gxyqZD2020019) )eauthors would like to extend their special thanks to ProfZhenfu Luo
References
[1] S Qu Y Gong Y Yang M Cai H Xie and H ZhangldquoGrinding characteristics and removal mechanism of 25D-needled CfSiC compositesrdquo Ceramics International vol 45no 17 pp 21608ndash21617 2019
[2] B Oksuzoglu andM Uccedilurum ldquoAn experimental study on theultra-fine grinding of gypsum ore in a dry ball millrdquo PowderTechnology vol 291 pp 186ndash192 2016
[3] S Liu Q Li and J Song ldquoStudy on the grinding kinetics ofcopper tailing powderrdquo Powder Technology vol 330pp 105ndash113 2018
[4] H Choi W Lee J Lee H Chung andW S Choi ldquoUltra-finegrinding of inorganic powders by stirred ball mill effect of
Table 3 Variation of product feature at different concentrations
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
Journal of Control Science and Engineering 7
impact force of a single ball on the material was increasedthe frictional force and shear force were greatly reduced)eSSA of the media continued to increase and the fuzzycomprehensive evaluation value of the product did notdecrease greatly which indicates that the impact force wasnot the main force )e friction force and shear force werethe main forces in the pulverization process In the late stageof ultrafine pulverization the particles became round andthe edges and corners basically disappeared
323 Effect of Concentration on the Ultrafine Powders)e optimal concentration was explored under the condi-tions where the operational PCS was 85 and SSA of themedia was 022m2kg )e results are shown in Table 3
When the concentration was 65 the ultrafine pul-verization of mineral powders works best When the con-centration was low the PSD of product was narrowhowever the yield of product was low In reverse the PSD ofproduct was extremely wide although the yield of producthad advantages there were many large particles in theproduct which affected the total quality If the concentrationwas low there were more opportunities for the occurrence ofcontact between the balls and the particles but the contactbetween the particles was insufficient When the concen-tration was too high the liquidity of the slurry reducedsharply and the motion of balls and particles wereobstructed leaving some large particles uncrushedAccording to ldquoBed comminutionrdquo [32] when there weremore particles there were more ldquoparticle-particle contactrdquosmaller particles would definitely be produced under thesame pulverization condition )erefore an appropriateincrease in the concentration would increase the fuzzycomprehensive evaluation value of the product
324 Optimization Parameters As shown in Table 4 thefuzzy comprehensive evaluation values of products werecalculated Due to the change in the concentration the rangeof mminus10 changed )us mminus10 isin [1293 549]
)e sequence of the factors influencing the productfeature was listed by polar value analysis With the indicatorm-10 as the appraising indicator maximum differences (R) ofeach factor were calculated orderly R (concentration)
0994 R (PCS) 0227 R (SSA of the media) 0330 thefactors were ranked in order of importance and concen-trationgt SSA of the mediagtPCS With the indicator D asthe appraising indicator R (concentration) 0181 R(PCS) 0130 R (SSA of the media) 0163 and concen-trationgt SSA of the mediagtPCS With the indicator d97 asthe appraising indicator R (concentration) 17817 R(PCS) 6343 R (SSA of the media) 5233 andconcentrationgt PCSgt SSA of the media Obviously thesignificance ordering of the factors was contradictory whenchoosing different appraising indicators With the indicatorZ as the appraising indicator R (concentration) 0054 R(PCS) 0039 and R (SSA of the media) 0053 Concen-trationgt SSA of the mediagt PCS moreover the concen-tration and SSA of the media were equally important
Using the fuzzy comprehensive evaluation value as anindicator combined with polar value analysis the optimalprocess conditions were obtained )e optimal PCS shouldbe at 85 the optimal SSA of the media should be at024m2kg and the optimal concentration should be at 75
Under the optimal conditions a verification experimentwas conducted to analyze the relevant parameters of theproduct and the results are shown as followsmminus10 3415 kg D 2483 and d97 4796 μm Based on themembership function used in the orthogonal experimentsthe membership degrees of each indicator were calculated
Table 1 Variation of product feature at different speeds
Table 2 Variation of product features at different SSAs of the media
Product feature mminus10 (kg) D (-) d97 (μm) Z (-)SSA of the media (m2kg)020 2190 2262 3307 0172022 2501 2257 2865 0269024 2433 2158 2557 0267026 2410 2201 2941 0243
Journal of Control Science and Engineering 5
μ1 0256 μ2 0067 and μ3 0086 Finally the maximumfuzzy comprehensive evaluation value under the optimalprocess parameters was obtained Z 0200 )erefore theoptimal operational factors obtained by polar value analysiswere correct
4 Conclusions
(1) )ree indicators reflecting quantity and quality havebeen selected and a comprehensive index has beenconstructed using a fuzzy comprehensive evaluationmethod based on hierarchical analysis and this hasbeen used to successfully find the optimal commi-nution operating conditions
(2) )e effect of different indicators on the ultrafinepowders was analyzed with the AHP )e weight setof three indicators ofmminus10 D and d97 wasW (0690149 0161)T
(3) )e significance ordering of the factors of ultrafinepulverization was concentration SSA of the mediaand PCS Moreover the concentration and SSA ofthe media were equally important
(4) When the optimal operating conditions were at thePCS of 85 the SSA of the media of 024m2kg andthe concentration of 75 the comprehensive per-formance of the product was the best and Z 0200
Data Availability
)e partial data used to support the findings of this study areincluded within the article and other partial data areavailable from the first author upon request
Additional Points
(1) )e significance of three indicators of the ultrafinepowders is analyzed by the analytic hierarchy process
method (2) According to the three indicators the fuzzycomprehensive evaluation based on analytic hierarchyprocess is used to obtain the comprehensive indicator (3))e three main factors influencing ultrafine comminutionconcentration specific surface area of the media and per-centage of critical speed are significantly ranked by theorthogonal test )e optimal operating conditions have beenobtained subsequently
Conflicts of Interest
)e authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
)e authors gratefully acknowledge the financial supportsprovided by the National Natural Science Foundation ofChina (51374015) Natural Science Foundation of AnhuiProvince (2008085QE272) China Postdoctoral ScienceFoundation (2020M671837 2019M662134) and AnhuiProvincial Excellent Talent Project (gxyqZD2020019) )eauthors would like to extend their special thanks to ProfZhenfu Luo
References
[1] S Qu Y Gong Y Yang M Cai H Xie and H ZhangldquoGrinding characteristics and removal mechanism of 25D-needled CfSiC compositesrdquo Ceramics International vol 45no 17 pp 21608ndash21617 2019
[2] B Oksuzoglu andM Uccedilurum ldquoAn experimental study on theultra-fine grinding of gypsum ore in a dry ball millrdquo PowderTechnology vol 291 pp 186ndash192 2016
[3] S Liu Q Li and J Song ldquoStudy on the grinding kinetics ofcopper tailing powderrdquo Powder Technology vol 330pp 105ndash113 2018
[4] H Choi W Lee J Lee H Chung andW S Choi ldquoUltra-finegrinding of inorganic powders by stirred ball mill effect of
Table 3 Variation of product feature at different concentrations
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
Journal of Control Science and Engineering 7
μ1 0256 μ2 0067 and μ3 0086 Finally the maximumfuzzy comprehensive evaluation value under the optimalprocess parameters was obtained Z 0200 )erefore theoptimal operational factors obtained by polar value analysiswere correct
4 Conclusions
(1) )ree indicators reflecting quantity and quality havebeen selected and a comprehensive index has beenconstructed using a fuzzy comprehensive evaluationmethod based on hierarchical analysis and this hasbeen used to successfully find the optimal commi-nution operating conditions
(2) )e effect of different indicators on the ultrafinepowders was analyzed with the AHP )e weight setof three indicators ofmminus10 D and d97 wasW (0690149 0161)T
(3) )e significance ordering of the factors of ultrafinepulverization was concentration SSA of the mediaand PCS Moreover the concentration and SSA ofthe media were equally important
(4) When the optimal operating conditions were at thePCS of 85 the SSA of the media of 024m2kg andthe concentration of 75 the comprehensive per-formance of the product was the best and Z 0200
Data Availability
)e partial data used to support the findings of this study areincluded within the article and other partial data areavailable from the first author upon request
Additional Points
(1) )e significance of three indicators of the ultrafinepowders is analyzed by the analytic hierarchy process
method (2) According to the three indicators the fuzzycomprehensive evaluation based on analytic hierarchyprocess is used to obtain the comprehensive indicator (3))e three main factors influencing ultrafine comminutionconcentration specific surface area of the media and per-centage of critical speed are significantly ranked by theorthogonal test )e optimal operating conditions have beenobtained subsequently
Conflicts of Interest
)e authors declare that there are no conflicts of interestregarding the publication of this article
Acknowledgments
)e authors gratefully acknowledge the financial supportsprovided by the National Natural Science Foundation ofChina (51374015) Natural Science Foundation of AnhuiProvince (2008085QE272) China Postdoctoral ScienceFoundation (2020M671837 2019M662134) and AnhuiProvincial Excellent Talent Project (gxyqZD2020019) )eauthors would like to extend their special thanks to ProfZhenfu Luo
References
[1] S Qu Y Gong Y Yang M Cai H Xie and H ZhangldquoGrinding characteristics and removal mechanism of 25D-needled CfSiC compositesrdquo Ceramics International vol 45no 17 pp 21608ndash21617 2019
[2] B Oksuzoglu andM Uccedilurum ldquoAn experimental study on theultra-fine grinding of gypsum ore in a dry ball millrdquo PowderTechnology vol 291 pp 186ndash192 2016
[3] S Liu Q Li and J Song ldquoStudy on the grinding kinetics ofcopper tailing powderrdquo Powder Technology vol 330pp 105ndash113 2018
[4] H Choi W Lee J Lee H Chung andW S Choi ldquoUltra-finegrinding of inorganic powders by stirred ball mill effect of
Table 3 Variation of product feature at different concentrations
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
Journal of Control Science and Engineering 7
process parameters on the particle size distribution of groundproducts and grinding energy efficiencyrdquo Metals and Mate-rials International vol 13 no 4 pp 353ndash358 2007
[5] G Guosheng Powder Engineering Tsinghua University PressBeijing China 2010
[6] D W Chen X L Ge Q Shi and Y Tian ldquoStudy on the non-linear ultra-fine grinding kinetics of calcium carbonate instirred millrdquoMaterials Research Innovations vol 19 no sup5pp S5-S999ndashS5-1003 2015
[7] S Nkwanyana and B Loveday ldquoAddition of pebbles to a ball-mill to improve grinding efficiencyrdquo Minerals Engineeringvol 103-104 pp 72ndash77 2017
[8] W Xie Y He Y Yang et al ldquoExperimental investigation ofbreakage and energy consumption characteristics of mixturesof different components in vertical spindle pulverizerrdquo Fuelvol 190 pp 208ndash220 2017
[9] J Duan Q Lu Z Zhao et al ldquoGrinding behaviors ofcomponents in heterogeneous breakage of coals of differentash contents in a ball-and-race millrdquo Minerals vol 10 no 3p 230 2020
[10] M Ehrgott Multicriteria Optimization Springer BerlinChina 2005
[11] D Wu and Y Tang ldquoAn improved failure mode and effectsanalysis method based on uncertainty measure in the evidencetheoryrdquo Quality and Reliability Engineering Internationalvol 36 no 5 pp 1786ndash1807 2020
[12] J Zhao D Wang X Wang S Liao and H Lin ldquoUltrafinegrinding of fly ash with grinding aids impact on particlecharacteristics of ultrafine fly ash and properties of blendedcement containing ultrafine fly ashrdquo Construction andBuilding Materials vol 78 pp 250ndash259 2015
[13] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965
[14] G Zheng N Zhu Z Tian Y Chen and B Sun ldquoApplicationof a trapezoidal fuzzy AHP method for work safety evaluationand early warning rating of hot and humid environmentsrdquoSafety Science vol 50 no 2 pp 228ndash239 2012
[15] Y Zhang R Wang P Huang X Wang and S Wang ldquoRiskevaluation of large-scale seawater desalination projects basedon an integrated fuzzy comprehensive evaluation and analytichierarchy process methodrdquo Desalination vol 478 p 1142862020
[16] T Guo S Tang J Sun et al ldquoA coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extractionin the enhanced geothermal system based on analytic hier-archy process and fuzzy comprehensive evaluationrdquo AppliedEnergy vol 258 p 113981 2020
[17] Z Zhu ldquoUltra-fine grinding potassium shale processingtechnology with balling millrdquo in School of Chemical Engi-neering and TechnologyChina University of Mining andTechnology Xuzhou China 2012
[18] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977
[19] R R Tan K B Aviso A P Huelgas andM A B PromentillaldquoFuzzy AHP approach to selection problems in process en-gineering involving quantitative and qualitative aspectsrdquoProcess Safety and Environmental Protection vol 92 no 5pp 467ndash475 2014
[20] S K Mangla P Kumar and M K Barua ldquoRisk analysis ingreen supply chain using fuzzy AHP approach a case studyrdquoResources Conservation and Recycling vol 104 pp 375ndash3902015
[21] D Wu Z Liu and Y Tang ldquoA new classification methodbased on the negation of a basic probability assignment in theevidence theoryrdquo Engineering Applications of Artificial In-telligence vol 96 p 103985 2020
[22] M Jing and Y Tang ldquoA new base basic probability assignmentapproach for conflict data fusion in the evidence theoryrdquoApplied Intelligence vol 51 pp 1ndash13 2020
[23] Y Chen Y Tang and Y Lei ldquoAn improved data fusionmethod based on weighted belief entropy considering thenegation of basic probability assignmentrdquo Journal of Math-ematics vol 2020 Article ID 1594967 1 page 2020
[24] T L Sattye Analytic Hierarchy Process McGraw-Hill NYUSA 1980
[25] R E Breaz O Bologa and S G Racz ldquoSelecting industrialrobots for milling applications using AHPrdquo Procedia Com-puter Science vol 122 pp 346ndash353 2017
[26] K Falconer Zeng Wenqu Fractal Geometry MathematicalFoundations and Applications Posts amp Telecom Press BeijingChina 2007
[27] S F Shinkorenko ldquoNew equations for the kinetics of crushingand their use for calculating the output of ball millsrdquo SovietMining Science vol 13 no 4 pp 382ndash388 1977
[28] S Liu Q Li G Xie L Li and H Xiao ldquoEffect of grinding timeon the particle characteristics of glass powderrdquo PowderTechnology vol 295 pp 133ndash141 2016
[29] O Celep and E Y Yazici ldquoUltra fine grinding of silver planttailings of refractory ore using vertical stirred media millrdquoTransactions of Nonferrous Metals Society of China vol 23no 11 pp 3412ndash3420 2013
[30] D Fan Research on the Media Movement Form and Pa-rameters of Ball Mill Zhejiang University of TechnologyHangzhou China 2010
[31] L Chang W Wang and H Ru ldquoEffect of ball milling pa-rameters on the preparing ultrafine WC powdersrdquo Journal ofMinerals Metallurgy andMaterials vol 18 pp 207ndash212 2019
[32] M Khanal W Schubert and J Tomas ldquoDiscrete elementmethod simulation of bed comminutionrdquo Minerals Engi-neering vol 20 no 2 pp 179ndash187 2007
