Research ArticleModeling for the Calcination Process of IndustryRotary Kiln Using ANFIS Coupled with a Novel HybridClustering Algorithm
Yongchang Cai12
1School of Electronics and Information Engineering Shunde Polytechnic Foshan 528300 China2Technical University of Dresden 01062 Dresden Germany
Correspondence should be addressed to Yongchang Cai herocych163com
Received 4 December 2016 Accepted 12 February 2017 Published 2 March 2017
Academic Editor Tarek Ahmed-Ali
Copyright copy 2017 Yongchang Cai This 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
Rotary kiln is important equipment in heavy industries and its calcination process is the key impact to the product quality Dueto the difficulty in obtaining the accurate algebraic model of the calcination process an intelligent modeling method based onANFIS and clustering algorithms is studied In the model ANFIS is employed as the core structure and aiming to improve bothits performance in reduced computation and accuracy a novel hybrid clustering algorithm is proposed by combining FCM andSubtractive methods A quasi-random data set is then hired to test the new hybrid clustering algorithm and results indicate itssuperiority to FCM and Subtractive methods Further a set of data from the successful control activity of sophisticated workersin manufacturing field is used to train the model and the model demonstrates its advantages in both fast convergence and moreaccuracy approaching
1 Introduction
Calcination process is omnipresent in heavy industriesworldwide such as chemical industry steel manufactory andmetallurgical industryThis process is significantly importantfor the final product quality because the calcination is wherethe product changed its form physically or chemically undercertain temperature for a certain span of time Featuringnonlinearity long time delay multivariables and their seri-ous coupling and a lot of control theories and modelingmethodologies for rotary kiln have been studied in the pastfew decades [1ndash3]
Some researchers built up the algebraic models of rotarykiln by analyzing the gas flow granularmaterial flow and heattransfer The approaches they used were mainly based uponaerodynamics and mechanical structure [4ndash7] However fora specific production kiln it is usually difficult to obtainthe necessary parameters for the adequately accurate modelwhich is a bottleneck for them to be generalized in widerapplications
In the past decade many researches have been carried outon the rotary kiln control based on intelligent and predictiontechniques For instance expert system was proposed tocontrol the kiln which improved the production outcome[7 8] Soft modeling methods based on neural networksupport vector machines and subspace method were used topredict the output index the calcination temperature and tailtemperature of the kiln respectively [9ndash11] However thereare still many problems among those studies such as bulkycomputation and excessive restrictions and also researcheson themodeling for the calcination process of the kiln whichis the core factor for the product quality are rarely reported
ANFIS (Adaptive Network-based Fuzzy Inference Sys-tem) as a model identification method has drawn muchattention in different application fields recently [12ndash14] Com-pared with conventional techniques it has the advantagesof mapping all the inputs to the corresponding outputsbased only on the available data and incorporating linguisticknowledge for problem solving and strong generalizationcapability
HindawiMathematical Problems in EngineeringVolume 2017 Article ID 1067351 8 pageshttpsdoiorg10115520171067351
2 Mathematical Problems in Engineering
Inner pot
Drying part
Calciner
Air flowEntry
Head temperature Drying
rotary speed
ExitCalcination rotary speed
Calcination temperature
Inspection tower
Air flow
19 m 18 m
25 m
Figure 1 Schematic diagram of the rotary kiln
In order to improve the computation efficiency andidentifying ability of ANFIS clustering algorithm is utilizedto partition the data into clusters and generate appropriatenumber of fuzzy rules Amongmany clusters fuzzy C-meansClustering Method (FCM) [15] and Subtractive ClusteringMethod (Subclust) [16] are widely adopted But each of themhas its drawback Subclust only yields the approximations forthe actual cluster centers whereas for FCM the number ofclusters has to be decided empirically and the algorithm issensitive to randomly initiated membership grade It meansthere is no enough guarantee to find the actual centersfor the clusters by applying each of the two clusteringmethods Overcoming these problems is significant becausetiny deviation of the clustering centers leads to apparentdifference in the identifiedmodel when the training data havehigh dimension and they are not so explicitly distinguished
In this paper ANFIS is employed as the core structure forthe calcination control model with the input and output vari-ables selected by analyzing the calcination reaction and theexperience of sophisticated workers As a premise procedureto modeling a hybrid clustering algorithm combing FCMand Subclust is put forwards which gets over the weaknessesof FCMand Subclust and leads tomore accuracy of the clustercenters
The rest of this paper starts with an introduction to theindustrial rotary kiln and its calcination process in Section 2In Section 3 FCM and Subclust methods are introduced andthen a novel hybrid clustering way of combining these twoclustering algorithms is proposed and illustrated in detailSection 4 presents ANFIS concisely which is adopted as a coremodeling structure for the calcination process of the kiln inthe next section In Section 5 modeling is conducted withthemethod of ANFIS coupled with the new hybrid clusteringalgorithm and the implementation results are discussed
2 The Rotary Kiln and Calcination Process
The rotary kiln to be studied in this paper is composed oftwo cylinders calciner and drying part which are connectedby an inspection tower It is actually gigantic equipment with
Exit
Inner pot
Calciner
Figure 2 Schematic diagram of the inner pot
length of 37 meters and a diameter of 25 meters as seen inFigure 1 The kiln is installed with a slope of around 5∘ and itrotates around its axis The drying part has similar length asthe calciner acting as a preheater for the inner material [17]
The material going through the kiln is lithopone aninorganic compound used as a white pigment It is first fedinto the elevated cold end the right side of the drying partand as the kiln rotates it moves along the declining inner beddue to gravity towards the exit which is at the left side ofcalciner During the long inner rolling the material is firstpreheated in drying part where the temperature is 150∘Csim200∘C and then goes into the calciner which includes aninner pot as shown in Figure 2 The temperature around thepot is relatively higher ranging between 600∘C and 800∘Cunderwhich the lithopone changes its decoloration capability(DC)
At the hot end (head) of the kiln the left side of thecalciner diesel or petrol is sprayed and burned to generate theheat for the whole calcining and drying process A thermalsensor is arranged there and the head temperature is normallymaintained at about 1200∘C to assure the heat is enough andstable As a blower and an exhauster are working at the hotend and cold end respectively the air flows from the hot endto cold end facing up to thematerial fluid conveying the heat
Mathematical Problems in Engineering 3
through the kiln and at the same time taking away the watersteam from the material
Since there is no effective way to detect the output index(DC) directly which has to be measured offline and normallycomes out 2 hours later after the lithopone comes out of theexit the control largely depends on the experienced workerwho empirically adjusts the calcination rotary speed accord-ing to the calcination temperature In general the workerincreases the rotary speed if the temperature is high and viceversa to ensure the material inside is heated properly
3 Data Clustering Algorithm
Data clustering is the prerequisite for training the ANFISmodel and it decides the number of fuzzy rules in the modelThere have been different clustering techniques proposed inother literatures [15ndash18] among which FCM and Subclust arehighly regarded and widely adopted
In FCM however the group number has to be given as apremise and iterative process is time consuming Randomlyinitialized belongingness matrix leads to uncertainty of theresult as well Also as for Subclust since taking data pointsas candidates it does not always perform well for finding theoptimal centers when the actual centers are not among thedata points For these drawbacks the author is inspired to finda new clustering technique aiming at improving not only theaccuracy of the result but also the reduced bulk of calculation
31 FCM Algorithm Consider a set of 119899 data points 1199091 1199092 119909119899 in a 119901-dimensional space that is 119909119894 (119894 = 1 119899) isa vector of 119901 coordinates Given the cluster number119898 FCMstarts by initializing a membership grade 119898 times 119899matrix119872 inrandomaccording to (1) indicating the belongingness of eachdata point to the initial centers
0 le 120583119894119895 le 1 forall1 le 119894 le 119898 1 le 119895 le 119899
119898
sum119894=1
120583119894119895 = 1 forall119895 = 1 119899(1)
where120583119894119895 (1 le 119894 le 119898 1 le 119895 le 119899) is the degree ofmembershipof 119895th data point to 119894th cluster center
Then new centers are attained and119872 is upgraded by thefollowing equations respectively
where sdot is the Euclidean distanceThis procedure is carried out repeatedly until the cost
function 119869 is below a certain tolerance value or no more
improvement between the consecutive iterations is noticed119869 is defined by
119869 =119898
sum119894=1
119869119894 =119898
sum119894=1
119899
sum119895=1
12058311989811989411989510038171003817100381710038171003817119909119894119895 minus 119909
lowast119894
100381710038171003817100381710038172
(4)
and 119869119894 is cost function for each cluster center 119894 = 1 119898
32 Subclust Algorithm For the same collection of 119899 datapoints Subclust begins with calculating the density value 119863for each point by the following formula
where1198631119894 is the density value of 119894th data point at the 1st roundof calculation and 119903119886 is a positive constant representing aneighborhood radius After all the data points are computedthen the point with the highest density value is chosen as thefirst cluster center 119909lowast1 and its density value is referred to as119863
lowast1
Afterwards the calculation goes into the 2nd round and eachpointrsquos density value is revised by
1198632119894 = 1198631119894 minus 119863lowast1 119890minus119909119894minus119909
lowast1 2(1199031198872)
2
119894 = 1 119899 (6)
where 1198632119894 is the density value of 119894th data point at the 2ndround of calculation and 119903119887 is also a positive constant defininga neighborhood which has measurable reduction in densityvalueThen the second point with the highest value is attainedand if it satisfies some kind of criteria then it is selected asthe 2nd cluster center This process repeats until the highestdensity value is less than a certain threshold In general atthe 119896th round of calculation the equation for computing thedensity value is
119863119896119894 = 119863119896minus1119894 minus 119863lowast119896minus1119890
33 A New Hybrid Clustering Algorithm Combining FCMand Subclust A feasible hybrid way is to use the Subclustto obtain the implicit number of clusters and then employFCM to find their exact centers [19] But the improvement israther limited and needs to be further developed This paperproposes a new way of their combinations which greatlyenhance both the computation efficiency and accuracy andit is illustrated in this section
Considering the above set of data points first Subclust isadopted to attain 119898 group centers 119909lowast1 119909
lowast119898 and then we
use Gaussian function to define a distance grade119898times119899matrix119872119889 as follows
where 120583119895119894 represents the relationship between the distance of119895th data point and 119894th cluster center and 120575 is the standarddeviation According to (8) the data point close to a clustercenter has a bigger distance grade value 120575 is a key parameterthat largely affects the distance grade value A recommended
4 Mathematical Problems in Engineering
choice is letting 120575 = (01sim1)times119903119886 Further ahead we normalizeeach column of119872119889 to be the initial membership gradematrix1198720
1205831198941198950 =120583119895119894
sum119898119896=1 120583119895
119896
119894 = 1 119898 119895 = 1 119899 (9)
and 1205831198941198950 is initial belongingness of 119895th data point to 119894th clustercenter
The next part of the hybrid clustering algorithm is ini-tializing FCM with1198720 Since1198720 reflects the actual distancebetween each point and cluster center that is the initial cen-ters are already close to the actual centers therefore the bulkof computation time in FCM definitely decreases substan-tially The holistic procedure of the new clustering algorithmuses the following steps
Step 1 Normalize the data set 1199091 1199092 119909119899 in a 119901-dimen-sion space
Step 2 Find the first cluster center 119909lowast1 and 119863lowast1 with (5) being
used in the computational process
Step 3 Revise each pointrsquos density value with (6) and findother cluster centers by using the following criteria suppos-ing (119896 minus 1)th (119896 ge 2) cluster center has been obtained
(1) If 119863lowast119896 lt 120576119863lowast1 and 120576 is a threshold for rejecting a pointas a cluster center go to Step 4
(2) If119863lowast119896 gt 120576119863lowast1 and 120576 specifies an accepting threshold for
a new cluster center accept119863lowast119896 as a new cluster centerand repeat Step 3
(3) If 120576119863lowast1 lt 119863lowast119896 lt 120576119863lowast1 accept it as a new cluster centerif it satisfies
119889min119903119886
+119863lowast119896119863lowast1
ge 1 (10)
and 119889min represents the shortest distance between 119909lowast119896and all the previous centers otherwise reject it andchoose the point with the next highest density valueand retest according to the above three criteria
Step 4 Based on the 119898 cluster centers 119909lowast1 119909lowast119898 found
from the previous steps calculate the distance grade matrix119872119889 with (8) and then the initial membership grade matrix1198720 with (9)
Step 5 Start FCM by letting119872 = 1198720
Step 6 Upgrade the cluster centers using (2)
Step 7 Calculate the cost function according to (4) End theclustering process if 119869 is below a certain tolerance value or theimprovement over the previous iteration is less than a certainthreshold
Step 8 Upgrade the belongingness matrix119872 with (3)
4 Adaptive Network-Based InferenceSystem (ANFIS)
ANFIS is produced by Jang [20] and is based on a multilayerfeedforward network structure It has 5 layers with two kindsof nodes square ones with parameters to be identified andcircle ones with none The directional links between nodesindicate the flow direction of signals
Consider the system has 119901 inputs 1199101 1199102 119910119901 and oneoutput 119911 and suppose each input has two fuzzy sets as seen inFigure 3Thenodes of the same layers have the same functionas described below
The 1st layer is composed of square nodes with the nodefunction 120583119860119894119895(119910119894) (119894 = 1 119901 119895 = 1 2) where 119910119894 is the inputto node 119894 and 119860 119894119895 is a linguistic label representing a fuzzy set120583119860119894119895(119910119894) is usually chosen among bell-shaped functions andits parameters are referred to as premise parameters
Every node in the 2nd layer is a circle node with thelabel prod which multiplies all the incoming signals from theprevious layer and sends the product out
and 119878119894 is the input set of 119894th node from 1st layer 120596119894 representsthe firing strength for 119894th rule
The third layer has the same number of circle nodes asthe second layer Each node labeled119873 calculates the ratio ofits input firing strength to the sum of firing strengths in theprevious layer
120596119894 =120596119894
sum119898119895=1 120596119894 (12)
Each node of 4th layer is a square node generating eachrulersquos output
and 119886119894119895 119887119894 (119894 = 1 119898 119895 = 1 119901) are the set ofparameters in this layer and are referred to as consequentparameters
In the fifth layer there is only one circle node with thelabel sum simply adding all the incoming signals together andproducing the overall output 119911
119911 =119898
sum119894=1
120596119894119891119894 (14)
The parameters of the network are identified by anotherhybrid learning procedure forwards and backwards passand the least squares estimate (LSE) formulas and gradientdescent method are employed respectively in each passMore details can be found in [20] and applications of ANFIScan be found in [21 22]
5 Implementation and Results
Having introduced the hybrid clustering algorithm andANFIS and their mathematical foundations this section
Mathematical Problems in Engineering 5
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
z
Forward pass
Backward pass
y1
yp
A11
A12
An1
An2
120596m
1205961
1205962
1205961
1205962
120596m
120596m
fm
sum
1205961f1
1205962f2
prod
prod
prod
prod
prod
prod
Figure 3 ANFIS architecture
Table 1 Value of related parameters of the three clustering algo-rithms
turns back to study the modeling for the calcination processof industrial kiln First a benchmark group of data is citedto test the three clustering techniques presented in Section 3and the implementation for modeling is studied afterwards
51 Comparison among Different Clustering Algorithms Aquasi-random two-dimensional data set is used as a bench-mark problem to test the performance of the three clusteringalgorithms The quasi-random data set is cited from MatlabToolbox and it includes 140 two-dimension chaotic datapoints Assuming there are 3 cluster centers to be foundthe three algorithms are implemented individually and theirperformances are tested Table 1 lists the value of relatedparameters in the implementation of the three algorithms
Figure 4 shows the cluster centers attained by the threemethods and it is noticed that the results of FCM and hybridalgorithm are more close to the actual centers Actually theroot mean square error (RMSE) of Subclust turns out to be
147956 which is the highest one Figure 5 shows the changeof cost function over time of FCM and hybrid algorithm andit is evident that the convergence speed of hybrid algorithmprevails over FCM greatly Table 2 compares the iterationnumber and RMSE between FCM and hybrid algorithmwhich also indicates the superior performance of the hybridalgorithm to FCM
52 Calcination Process Modeling The first question to besolved is the determination of the input and output variablesfor the control model The method undertaken in this paperis to rely on the experience of the sophisticated workers andthe analysis on the calcination mechanism inside the kiln Inpractice the worker regulates the calcination rotary speed 119877(Hz) according to the calcination temperature T (∘C) as seenin Figure 1 which provides important information that 119877 canbe the only output and119879 should be one of the input variables
A further study at the inside calcination processmanifeststhat the material changes its property to meet the qualityrequirement that is DC mainly when it is going through theinner pot because the temperature there is much higher thanother parts inside the kiln This process normally takes 15 to20 minutes depending on the rotary speed 119877 Consequentlythe calcination temperature 119879 and rotary speed 119877 in theprevious time phase should also be considered into theinput variables of the model which matches the time-delayproperty of the calcination process After testing differentcombinations of 119879 and 119877 in their previous time phases a setof inputs is chosen as below
119884 = [119879 (119896) 119879 (119896 minus 1) 119879 (119896 minus 2) 119879 (119896 minus 3) 119877 (119896 minus 1) 119877 (119896 minus 2) 119877 (119896 minus 3)] (15)
where 119896 is the time index and the time interval between thetwo successive time indexes is 5 minutes
The model for the calcination process is then built upby adopting ANFIS coupled with the novel hybrid clustering
algorithm proposed in Section 3 A group of 600 consecutivedata points coming from successful control of sophisticatedworkers are chosen to train and test themodel among which400 are used as training data and 200 are used as checking
6 Mathematical Problems in Engineering
10
02
04
06
08
1
0 05(a)
10
02
04
06
08
1
0 05(b)
10
02
04
06
08
1
0 05(c)
10
02
04
06
08
1
0 05(d)
Figure 4 Cluster centers from different algorithms on the quasi-random data (a)The quasi-random data (b) Cluster centers from Subclust(c) Cluster centers from FCM (d) Cluster centers from hybrid algorithm
2
(a)(b)
4 6 8 10 12 1410
12
14
16
18
20
22
(a) FCM(b) Hybrid
Figure 5 Plots of cost function of FCM and hybrid algorithm
data In the clustering stage related parameters are selectedas 119903119886 = 03081 119903119887 = 125 times 119903119886 120576 = 015 120576 = 05 120575 = 05
Table 2 Clustering performance of FCM and hybrid algorithm
Performance FCM Hybrid SubclustIteration times 7 2RMSE 143025 137007
and 119908 = 2 which yields 11 rules for ANFIS Figure 6 showsthe outputs of the model after a training of 250 epochs andit is noticed that the model works satisfactorily on both thetraining data and checking data
A further comparison is made between ANFIS with FCMclustering and ANFIS with the new hybrid algorithm Alonger training as 300 epochs is applied for ANFIS this timeDuring the process the cost function on clustering phase andchecking data error for ANFIS are checked respectively asseen in Figures 7 and 8 It can be seen that both the costfunction and checking data error in the method of ANFISwith the new hybrid algorithm are smaller at each epoch andconverge more quickly Detailed performance for these twomethods is listed in Table 3
Mathematical Problems in Engineering 7
0 50 100 150 200 250 300 350 4000
10
20
30
Modelrsquos outputOriginal output
(a)
0 50 100 150 2000
10
20
30
Modelrsquos outputOriginal output
(b)
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
In order to improve the computation efficiency andidentifying ability of ANFIS clustering algorithm is utilizedto partition the data into clusters and generate appropriatenumber of fuzzy rules Amongmany clusters fuzzy C-meansClustering Method (FCM) [15] and Subtractive ClusteringMethod (Subclust) [16] are widely adopted But each of themhas its drawback Subclust only yields the approximations forthe actual cluster centers whereas for FCM the number ofclusters has to be decided empirically and the algorithm issensitive to randomly initiated membership grade It meansthere is no enough guarantee to find the actual centersfor the clusters by applying each of the two clusteringmethods Overcoming these problems is significant becausetiny deviation of the clustering centers leads to apparentdifference in the identifiedmodel when the training data havehigh dimension and they are not so explicitly distinguished
In this paper ANFIS is employed as the core structure forthe calcination control model with the input and output vari-ables selected by analyzing the calcination reaction and theexperience of sophisticated workers As a premise procedureto modeling a hybrid clustering algorithm combing FCMand Subclust is put forwards which gets over the weaknessesof FCMand Subclust and leads tomore accuracy of the clustercenters
The rest of this paper starts with an introduction to theindustrial rotary kiln and its calcination process in Section 2In Section 3 FCM and Subclust methods are introduced andthen a novel hybrid clustering way of combining these twoclustering algorithms is proposed and illustrated in detailSection 4 presents ANFIS concisely which is adopted as a coremodeling structure for the calcination process of the kiln inthe next section In Section 5 modeling is conducted withthemethod of ANFIS coupled with the new hybrid clusteringalgorithm and the implementation results are discussed
2 The Rotary Kiln and Calcination Process
The rotary kiln to be studied in this paper is composed oftwo cylinders calciner and drying part which are connectedby an inspection tower It is actually gigantic equipment with
Exit
Inner pot
Calciner
Figure 2 Schematic diagram of the inner pot
length of 37 meters and a diameter of 25 meters as seen inFigure 1 The kiln is installed with a slope of around 5∘ and itrotates around its axis The drying part has similar length asthe calciner acting as a preheater for the inner material [17]
The material going through the kiln is lithopone aninorganic compound used as a white pigment It is first fedinto the elevated cold end the right side of the drying partand as the kiln rotates it moves along the declining inner beddue to gravity towards the exit which is at the left side ofcalciner During the long inner rolling the material is firstpreheated in drying part where the temperature is 150∘Csim200∘C and then goes into the calciner which includes aninner pot as shown in Figure 2 The temperature around thepot is relatively higher ranging between 600∘C and 800∘Cunderwhich the lithopone changes its decoloration capability(DC)
At the hot end (head) of the kiln the left side of thecalciner diesel or petrol is sprayed and burned to generate theheat for the whole calcining and drying process A thermalsensor is arranged there and the head temperature is normallymaintained at about 1200∘C to assure the heat is enough andstable As a blower and an exhauster are working at the hotend and cold end respectively the air flows from the hot endto cold end facing up to thematerial fluid conveying the heat
Mathematical Problems in Engineering 3
through the kiln and at the same time taking away the watersteam from the material
Since there is no effective way to detect the output index(DC) directly which has to be measured offline and normallycomes out 2 hours later after the lithopone comes out of theexit the control largely depends on the experienced workerwho empirically adjusts the calcination rotary speed accord-ing to the calcination temperature In general the workerincreases the rotary speed if the temperature is high and viceversa to ensure the material inside is heated properly
3 Data Clustering Algorithm
Data clustering is the prerequisite for training the ANFISmodel and it decides the number of fuzzy rules in the modelThere have been different clustering techniques proposed inother literatures [15ndash18] among which FCM and Subclust arehighly regarded and widely adopted
In FCM however the group number has to be given as apremise and iterative process is time consuming Randomlyinitialized belongingness matrix leads to uncertainty of theresult as well Also as for Subclust since taking data pointsas candidates it does not always perform well for finding theoptimal centers when the actual centers are not among thedata points For these drawbacks the author is inspired to finda new clustering technique aiming at improving not only theaccuracy of the result but also the reduced bulk of calculation
31 FCM Algorithm Consider a set of 119899 data points 1199091 1199092 119909119899 in a 119901-dimensional space that is 119909119894 (119894 = 1 119899) isa vector of 119901 coordinates Given the cluster number119898 FCMstarts by initializing a membership grade 119898 times 119899matrix119872 inrandomaccording to (1) indicating the belongingness of eachdata point to the initial centers
0 le 120583119894119895 le 1 forall1 le 119894 le 119898 1 le 119895 le 119899
119898
sum119894=1
120583119894119895 = 1 forall119895 = 1 119899(1)
where120583119894119895 (1 le 119894 le 119898 1 le 119895 le 119899) is the degree ofmembershipof 119895th data point to 119894th cluster center
Then new centers are attained and119872 is upgraded by thefollowing equations respectively
where sdot is the Euclidean distanceThis procedure is carried out repeatedly until the cost
function 119869 is below a certain tolerance value or no more
improvement between the consecutive iterations is noticed119869 is defined by
119869 =119898
sum119894=1
119869119894 =119898
sum119894=1
119899
sum119895=1
12058311989811989411989510038171003817100381710038171003817119909119894119895 minus 119909
lowast119894
100381710038171003817100381710038172
(4)
and 119869119894 is cost function for each cluster center 119894 = 1 119898
32 Subclust Algorithm For the same collection of 119899 datapoints Subclust begins with calculating the density value 119863for each point by the following formula
where1198631119894 is the density value of 119894th data point at the 1st roundof calculation and 119903119886 is a positive constant representing aneighborhood radius After all the data points are computedthen the point with the highest density value is chosen as thefirst cluster center 119909lowast1 and its density value is referred to as119863
lowast1
Afterwards the calculation goes into the 2nd round and eachpointrsquos density value is revised by
1198632119894 = 1198631119894 minus 119863lowast1 119890minus119909119894minus119909
lowast1 2(1199031198872)
2
119894 = 1 119899 (6)
where 1198632119894 is the density value of 119894th data point at the 2ndround of calculation and 119903119887 is also a positive constant defininga neighborhood which has measurable reduction in densityvalueThen the second point with the highest value is attainedand if it satisfies some kind of criteria then it is selected asthe 2nd cluster center This process repeats until the highestdensity value is less than a certain threshold In general atthe 119896th round of calculation the equation for computing thedensity value is
119863119896119894 = 119863119896minus1119894 minus 119863lowast119896minus1119890
33 A New Hybrid Clustering Algorithm Combining FCMand Subclust A feasible hybrid way is to use the Subclustto obtain the implicit number of clusters and then employFCM to find their exact centers [19] But the improvement israther limited and needs to be further developed This paperproposes a new way of their combinations which greatlyenhance both the computation efficiency and accuracy andit is illustrated in this section
Considering the above set of data points first Subclust isadopted to attain 119898 group centers 119909lowast1 119909
lowast119898 and then we
use Gaussian function to define a distance grade119898times119899matrix119872119889 as follows
where 120583119895119894 represents the relationship between the distance of119895th data point and 119894th cluster center and 120575 is the standarddeviation According to (8) the data point close to a clustercenter has a bigger distance grade value 120575 is a key parameterthat largely affects the distance grade value A recommended
4 Mathematical Problems in Engineering
choice is letting 120575 = (01sim1)times119903119886 Further ahead we normalizeeach column of119872119889 to be the initial membership gradematrix1198720
1205831198941198950 =120583119895119894
sum119898119896=1 120583119895
119896
119894 = 1 119898 119895 = 1 119899 (9)
and 1205831198941198950 is initial belongingness of 119895th data point to 119894th clustercenter
The next part of the hybrid clustering algorithm is ini-tializing FCM with1198720 Since1198720 reflects the actual distancebetween each point and cluster center that is the initial cen-ters are already close to the actual centers therefore the bulkof computation time in FCM definitely decreases substan-tially The holistic procedure of the new clustering algorithmuses the following steps
Step 1 Normalize the data set 1199091 1199092 119909119899 in a 119901-dimen-sion space
Step 2 Find the first cluster center 119909lowast1 and 119863lowast1 with (5) being
used in the computational process
Step 3 Revise each pointrsquos density value with (6) and findother cluster centers by using the following criteria suppos-ing (119896 minus 1)th (119896 ge 2) cluster center has been obtained
(1) If 119863lowast119896 lt 120576119863lowast1 and 120576 is a threshold for rejecting a pointas a cluster center go to Step 4
(2) If119863lowast119896 gt 120576119863lowast1 and 120576 specifies an accepting threshold for
a new cluster center accept119863lowast119896 as a new cluster centerand repeat Step 3
(3) If 120576119863lowast1 lt 119863lowast119896 lt 120576119863lowast1 accept it as a new cluster centerif it satisfies
119889min119903119886
+119863lowast119896119863lowast1
ge 1 (10)
and 119889min represents the shortest distance between 119909lowast119896and all the previous centers otherwise reject it andchoose the point with the next highest density valueand retest according to the above three criteria
Step 4 Based on the 119898 cluster centers 119909lowast1 119909lowast119898 found
from the previous steps calculate the distance grade matrix119872119889 with (8) and then the initial membership grade matrix1198720 with (9)
Step 5 Start FCM by letting119872 = 1198720
Step 6 Upgrade the cluster centers using (2)
Step 7 Calculate the cost function according to (4) End theclustering process if 119869 is below a certain tolerance value or theimprovement over the previous iteration is less than a certainthreshold
Step 8 Upgrade the belongingness matrix119872 with (3)
4 Adaptive Network-Based InferenceSystem (ANFIS)
ANFIS is produced by Jang [20] and is based on a multilayerfeedforward network structure It has 5 layers with two kindsof nodes square ones with parameters to be identified andcircle ones with none The directional links between nodesindicate the flow direction of signals
Consider the system has 119901 inputs 1199101 1199102 119910119901 and oneoutput 119911 and suppose each input has two fuzzy sets as seen inFigure 3Thenodes of the same layers have the same functionas described below
The 1st layer is composed of square nodes with the nodefunction 120583119860119894119895(119910119894) (119894 = 1 119901 119895 = 1 2) where 119910119894 is the inputto node 119894 and 119860 119894119895 is a linguistic label representing a fuzzy set120583119860119894119895(119910119894) is usually chosen among bell-shaped functions andits parameters are referred to as premise parameters
Every node in the 2nd layer is a circle node with thelabel prod which multiplies all the incoming signals from theprevious layer and sends the product out
and 119878119894 is the input set of 119894th node from 1st layer 120596119894 representsthe firing strength for 119894th rule
The third layer has the same number of circle nodes asthe second layer Each node labeled119873 calculates the ratio ofits input firing strength to the sum of firing strengths in theprevious layer
120596119894 =120596119894
sum119898119895=1 120596119894 (12)
Each node of 4th layer is a square node generating eachrulersquos output
and 119886119894119895 119887119894 (119894 = 1 119898 119895 = 1 119901) are the set ofparameters in this layer and are referred to as consequentparameters
In the fifth layer there is only one circle node with thelabel sum simply adding all the incoming signals together andproducing the overall output 119911
119911 =119898
sum119894=1
120596119894119891119894 (14)
The parameters of the network are identified by anotherhybrid learning procedure forwards and backwards passand the least squares estimate (LSE) formulas and gradientdescent method are employed respectively in each passMore details can be found in [20] and applications of ANFIScan be found in [21 22]
5 Implementation and Results
Having introduced the hybrid clustering algorithm andANFIS and their mathematical foundations this section
Mathematical Problems in Engineering 5
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
z
Forward pass
Backward pass
y1
yp
A11
A12
An1
An2
120596m
1205961
1205962
1205961
1205962
120596m
120596m
fm
sum
1205961f1
1205962f2
prod
prod
prod
prod
prod
prod
Figure 3 ANFIS architecture
Table 1 Value of related parameters of the three clustering algo-rithms
turns back to study the modeling for the calcination processof industrial kiln First a benchmark group of data is citedto test the three clustering techniques presented in Section 3and the implementation for modeling is studied afterwards
51 Comparison among Different Clustering Algorithms Aquasi-random two-dimensional data set is used as a bench-mark problem to test the performance of the three clusteringalgorithms The quasi-random data set is cited from MatlabToolbox and it includes 140 two-dimension chaotic datapoints Assuming there are 3 cluster centers to be foundthe three algorithms are implemented individually and theirperformances are tested Table 1 lists the value of relatedparameters in the implementation of the three algorithms
Figure 4 shows the cluster centers attained by the threemethods and it is noticed that the results of FCM and hybridalgorithm are more close to the actual centers Actually theroot mean square error (RMSE) of Subclust turns out to be
147956 which is the highest one Figure 5 shows the changeof cost function over time of FCM and hybrid algorithm andit is evident that the convergence speed of hybrid algorithmprevails over FCM greatly Table 2 compares the iterationnumber and RMSE between FCM and hybrid algorithmwhich also indicates the superior performance of the hybridalgorithm to FCM
52 Calcination Process Modeling The first question to besolved is the determination of the input and output variablesfor the control model The method undertaken in this paperis to rely on the experience of the sophisticated workers andthe analysis on the calcination mechanism inside the kiln Inpractice the worker regulates the calcination rotary speed 119877(Hz) according to the calcination temperature T (∘C) as seenin Figure 1 which provides important information that 119877 canbe the only output and119879 should be one of the input variables
A further study at the inside calcination processmanifeststhat the material changes its property to meet the qualityrequirement that is DC mainly when it is going through theinner pot because the temperature there is much higher thanother parts inside the kiln This process normally takes 15 to20 minutes depending on the rotary speed 119877 Consequentlythe calcination temperature 119879 and rotary speed 119877 in theprevious time phase should also be considered into theinput variables of the model which matches the time-delayproperty of the calcination process After testing differentcombinations of 119879 and 119877 in their previous time phases a setof inputs is chosen as below
119884 = [119879 (119896) 119879 (119896 minus 1) 119879 (119896 minus 2) 119879 (119896 minus 3) 119877 (119896 minus 1) 119877 (119896 minus 2) 119877 (119896 minus 3)] (15)
where 119896 is the time index and the time interval between thetwo successive time indexes is 5 minutes
The model for the calcination process is then built upby adopting ANFIS coupled with the novel hybrid clustering
algorithm proposed in Section 3 A group of 600 consecutivedata points coming from successful control of sophisticatedworkers are chosen to train and test themodel among which400 are used as training data and 200 are used as checking
6 Mathematical Problems in Engineering
10
02
04
06
08
1
0 05(a)
10
02
04
06
08
1
0 05(b)
10
02
04
06
08
1
0 05(c)
10
02
04
06
08
1
0 05(d)
Figure 4 Cluster centers from different algorithms on the quasi-random data (a)The quasi-random data (b) Cluster centers from Subclust(c) Cluster centers from FCM (d) Cluster centers from hybrid algorithm
2
(a)(b)
4 6 8 10 12 1410
12
14
16
18
20
22
(a) FCM(b) Hybrid
Figure 5 Plots of cost function of FCM and hybrid algorithm
data In the clustering stage related parameters are selectedas 119903119886 = 03081 119903119887 = 125 times 119903119886 120576 = 015 120576 = 05 120575 = 05
Table 2 Clustering performance of FCM and hybrid algorithm
Performance FCM Hybrid SubclustIteration times 7 2RMSE 143025 137007
and 119908 = 2 which yields 11 rules for ANFIS Figure 6 showsthe outputs of the model after a training of 250 epochs andit is noticed that the model works satisfactorily on both thetraining data and checking data
A further comparison is made between ANFIS with FCMclustering and ANFIS with the new hybrid algorithm Alonger training as 300 epochs is applied for ANFIS this timeDuring the process the cost function on clustering phase andchecking data error for ANFIS are checked respectively asseen in Figures 7 and 8 It can be seen that both the costfunction and checking data error in the method of ANFISwith the new hybrid algorithm are smaller at each epoch andconverge more quickly Detailed performance for these twomethods is listed in Table 3
Mathematical Problems in Engineering 7
0 50 100 150 200 250 300 350 4000
10
20
30
Modelrsquos outputOriginal output
(a)
0 50 100 150 2000
10
20
30
Modelrsquos outputOriginal output
(b)
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
through the kiln and at the same time taking away the watersteam from the material
Since there is no effective way to detect the output index(DC) directly which has to be measured offline and normallycomes out 2 hours later after the lithopone comes out of theexit the control largely depends on the experienced workerwho empirically adjusts the calcination rotary speed accord-ing to the calcination temperature In general the workerincreases the rotary speed if the temperature is high and viceversa to ensure the material inside is heated properly
3 Data Clustering Algorithm
Data clustering is the prerequisite for training the ANFISmodel and it decides the number of fuzzy rules in the modelThere have been different clustering techniques proposed inother literatures [15ndash18] among which FCM and Subclust arehighly regarded and widely adopted
In FCM however the group number has to be given as apremise and iterative process is time consuming Randomlyinitialized belongingness matrix leads to uncertainty of theresult as well Also as for Subclust since taking data pointsas candidates it does not always perform well for finding theoptimal centers when the actual centers are not among thedata points For these drawbacks the author is inspired to finda new clustering technique aiming at improving not only theaccuracy of the result but also the reduced bulk of calculation
31 FCM Algorithm Consider a set of 119899 data points 1199091 1199092 119909119899 in a 119901-dimensional space that is 119909119894 (119894 = 1 119899) isa vector of 119901 coordinates Given the cluster number119898 FCMstarts by initializing a membership grade 119898 times 119899matrix119872 inrandomaccording to (1) indicating the belongingness of eachdata point to the initial centers
0 le 120583119894119895 le 1 forall1 le 119894 le 119898 1 le 119895 le 119899
119898
sum119894=1
120583119894119895 = 1 forall119895 = 1 119899(1)
where120583119894119895 (1 le 119894 le 119898 1 le 119895 le 119899) is the degree ofmembershipof 119895th data point to 119894th cluster center
Then new centers are attained and119872 is upgraded by thefollowing equations respectively
where sdot is the Euclidean distanceThis procedure is carried out repeatedly until the cost
function 119869 is below a certain tolerance value or no more
improvement between the consecutive iterations is noticed119869 is defined by
119869 =119898
sum119894=1
119869119894 =119898
sum119894=1
119899
sum119895=1
12058311989811989411989510038171003817100381710038171003817119909119894119895 minus 119909
lowast119894
100381710038171003817100381710038172
(4)
and 119869119894 is cost function for each cluster center 119894 = 1 119898
32 Subclust Algorithm For the same collection of 119899 datapoints Subclust begins with calculating the density value 119863for each point by the following formula
where1198631119894 is the density value of 119894th data point at the 1st roundof calculation and 119903119886 is a positive constant representing aneighborhood radius After all the data points are computedthen the point with the highest density value is chosen as thefirst cluster center 119909lowast1 and its density value is referred to as119863
lowast1
Afterwards the calculation goes into the 2nd round and eachpointrsquos density value is revised by
1198632119894 = 1198631119894 minus 119863lowast1 119890minus119909119894minus119909
lowast1 2(1199031198872)
2
119894 = 1 119899 (6)
where 1198632119894 is the density value of 119894th data point at the 2ndround of calculation and 119903119887 is also a positive constant defininga neighborhood which has measurable reduction in densityvalueThen the second point with the highest value is attainedand if it satisfies some kind of criteria then it is selected asthe 2nd cluster center This process repeats until the highestdensity value is less than a certain threshold In general atthe 119896th round of calculation the equation for computing thedensity value is
119863119896119894 = 119863119896minus1119894 minus 119863lowast119896minus1119890
33 A New Hybrid Clustering Algorithm Combining FCMand Subclust A feasible hybrid way is to use the Subclustto obtain the implicit number of clusters and then employFCM to find their exact centers [19] But the improvement israther limited and needs to be further developed This paperproposes a new way of their combinations which greatlyenhance both the computation efficiency and accuracy andit is illustrated in this section
Considering the above set of data points first Subclust isadopted to attain 119898 group centers 119909lowast1 119909
lowast119898 and then we
use Gaussian function to define a distance grade119898times119899matrix119872119889 as follows
where 120583119895119894 represents the relationship between the distance of119895th data point and 119894th cluster center and 120575 is the standarddeviation According to (8) the data point close to a clustercenter has a bigger distance grade value 120575 is a key parameterthat largely affects the distance grade value A recommended
4 Mathematical Problems in Engineering
choice is letting 120575 = (01sim1)times119903119886 Further ahead we normalizeeach column of119872119889 to be the initial membership gradematrix1198720
1205831198941198950 =120583119895119894
sum119898119896=1 120583119895
119896
119894 = 1 119898 119895 = 1 119899 (9)
and 1205831198941198950 is initial belongingness of 119895th data point to 119894th clustercenter
The next part of the hybrid clustering algorithm is ini-tializing FCM with1198720 Since1198720 reflects the actual distancebetween each point and cluster center that is the initial cen-ters are already close to the actual centers therefore the bulkof computation time in FCM definitely decreases substan-tially The holistic procedure of the new clustering algorithmuses the following steps
Step 1 Normalize the data set 1199091 1199092 119909119899 in a 119901-dimen-sion space
Step 2 Find the first cluster center 119909lowast1 and 119863lowast1 with (5) being
used in the computational process
Step 3 Revise each pointrsquos density value with (6) and findother cluster centers by using the following criteria suppos-ing (119896 minus 1)th (119896 ge 2) cluster center has been obtained
(1) If 119863lowast119896 lt 120576119863lowast1 and 120576 is a threshold for rejecting a pointas a cluster center go to Step 4
(2) If119863lowast119896 gt 120576119863lowast1 and 120576 specifies an accepting threshold for
a new cluster center accept119863lowast119896 as a new cluster centerand repeat Step 3
(3) If 120576119863lowast1 lt 119863lowast119896 lt 120576119863lowast1 accept it as a new cluster centerif it satisfies
119889min119903119886
+119863lowast119896119863lowast1
ge 1 (10)
and 119889min represents the shortest distance between 119909lowast119896and all the previous centers otherwise reject it andchoose the point with the next highest density valueand retest according to the above three criteria
Step 4 Based on the 119898 cluster centers 119909lowast1 119909lowast119898 found
from the previous steps calculate the distance grade matrix119872119889 with (8) and then the initial membership grade matrix1198720 with (9)
Step 5 Start FCM by letting119872 = 1198720
Step 6 Upgrade the cluster centers using (2)
Step 7 Calculate the cost function according to (4) End theclustering process if 119869 is below a certain tolerance value or theimprovement over the previous iteration is less than a certainthreshold
Step 8 Upgrade the belongingness matrix119872 with (3)
4 Adaptive Network-Based InferenceSystem (ANFIS)
ANFIS is produced by Jang [20] and is based on a multilayerfeedforward network structure It has 5 layers with two kindsof nodes square ones with parameters to be identified andcircle ones with none The directional links between nodesindicate the flow direction of signals
Consider the system has 119901 inputs 1199101 1199102 119910119901 and oneoutput 119911 and suppose each input has two fuzzy sets as seen inFigure 3Thenodes of the same layers have the same functionas described below
The 1st layer is composed of square nodes with the nodefunction 120583119860119894119895(119910119894) (119894 = 1 119901 119895 = 1 2) where 119910119894 is the inputto node 119894 and 119860 119894119895 is a linguistic label representing a fuzzy set120583119860119894119895(119910119894) is usually chosen among bell-shaped functions andits parameters are referred to as premise parameters
Every node in the 2nd layer is a circle node with thelabel prod which multiplies all the incoming signals from theprevious layer and sends the product out
and 119878119894 is the input set of 119894th node from 1st layer 120596119894 representsthe firing strength for 119894th rule
The third layer has the same number of circle nodes asthe second layer Each node labeled119873 calculates the ratio ofits input firing strength to the sum of firing strengths in theprevious layer
120596119894 =120596119894
sum119898119895=1 120596119894 (12)
Each node of 4th layer is a square node generating eachrulersquos output
and 119886119894119895 119887119894 (119894 = 1 119898 119895 = 1 119901) are the set ofparameters in this layer and are referred to as consequentparameters
In the fifth layer there is only one circle node with thelabel sum simply adding all the incoming signals together andproducing the overall output 119911
119911 =119898
sum119894=1
120596119894119891119894 (14)
The parameters of the network are identified by anotherhybrid learning procedure forwards and backwards passand the least squares estimate (LSE) formulas and gradientdescent method are employed respectively in each passMore details can be found in [20] and applications of ANFIScan be found in [21 22]
5 Implementation and Results
Having introduced the hybrid clustering algorithm andANFIS and their mathematical foundations this section
Mathematical Problems in Engineering 5
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
z
Forward pass
Backward pass
y1
yp
A11
A12
An1
An2
120596m
1205961
1205962
1205961
1205962
120596m
120596m
fm
sum
1205961f1
1205962f2
prod
prod
prod
prod
prod
prod
Figure 3 ANFIS architecture
Table 1 Value of related parameters of the three clustering algo-rithms
turns back to study the modeling for the calcination processof industrial kiln First a benchmark group of data is citedto test the three clustering techniques presented in Section 3and the implementation for modeling is studied afterwards
51 Comparison among Different Clustering Algorithms Aquasi-random two-dimensional data set is used as a bench-mark problem to test the performance of the three clusteringalgorithms The quasi-random data set is cited from MatlabToolbox and it includes 140 two-dimension chaotic datapoints Assuming there are 3 cluster centers to be foundthe three algorithms are implemented individually and theirperformances are tested Table 1 lists the value of relatedparameters in the implementation of the three algorithms
Figure 4 shows the cluster centers attained by the threemethods and it is noticed that the results of FCM and hybridalgorithm are more close to the actual centers Actually theroot mean square error (RMSE) of Subclust turns out to be
147956 which is the highest one Figure 5 shows the changeof cost function over time of FCM and hybrid algorithm andit is evident that the convergence speed of hybrid algorithmprevails over FCM greatly Table 2 compares the iterationnumber and RMSE between FCM and hybrid algorithmwhich also indicates the superior performance of the hybridalgorithm to FCM
52 Calcination Process Modeling The first question to besolved is the determination of the input and output variablesfor the control model The method undertaken in this paperis to rely on the experience of the sophisticated workers andthe analysis on the calcination mechanism inside the kiln Inpractice the worker regulates the calcination rotary speed 119877(Hz) according to the calcination temperature T (∘C) as seenin Figure 1 which provides important information that 119877 canbe the only output and119879 should be one of the input variables
A further study at the inside calcination processmanifeststhat the material changes its property to meet the qualityrequirement that is DC mainly when it is going through theinner pot because the temperature there is much higher thanother parts inside the kiln This process normally takes 15 to20 minutes depending on the rotary speed 119877 Consequentlythe calcination temperature 119879 and rotary speed 119877 in theprevious time phase should also be considered into theinput variables of the model which matches the time-delayproperty of the calcination process After testing differentcombinations of 119879 and 119877 in their previous time phases a setof inputs is chosen as below
119884 = [119879 (119896) 119879 (119896 minus 1) 119879 (119896 minus 2) 119879 (119896 minus 3) 119877 (119896 minus 1) 119877 (119896 minus 2) 119877 (119896 minus 3)] (15)
where 119896 is the time index and the time interval between thetwo successive time indexes is 5 minutes
The model for the calcination process is then built upby adopting ANFIS coupled with the novel hybrid clustering
algorithm proposed in Section 3 A group of 600 consecutivedata points coming from successful control of sophisticatedworkers are chosen to train and test themodel among which400 are used as training data and 200 are used as checking
6 Mathematical Problems in Engineering
10
02
04
06
08
1
0 05(a)
10
02
04
06
08
1
0 05(b)
10
02
04
06
08
1
0 05(c)
10
02
04
06
08
1
0 05(d)
Figure 4 Cluster centers from different algorithms on the quasi-random data (a)The quasi-random data (b) Cluster centers from Subclust(c) Cluster centers from FCM (d) Cluster centers from hybrid algorithm
2
(a)(b)
4 6 8 10 12 1410
12
14
16
18
20
22
(a) FCM(b) Hybrid
Figure 5 Plots of cost function of FCM and hybrid algorithm
data In the clustering stage related parameters are selectedas 119903119886 = 03081 119903119887 = 125 times 119903119886 120576 = 015 120576 = 05 120575 = 05
Table 2 Clustering performance of FCM and hybrid algorithm
Performance FCM Hybrid SubclustIteration times 7 2RMSE 143025 137007
and 119908 = 2 which yields 11 rules for ANFIS Figure 6 showsthe outputs of the model after a training of 250 epochs andit is noticed that the model works satisfactorily on both thetraining data and checking data
A further comparison is made between ANFIS with FCMclustering and ANFIS with the new hybrid algorithm Alonger training as 300 epochs is applied for ANFIS this timeDuring the process the cost function on clustering phase andchecking data error for ANFIS are checked respectively asseen in Figures 7 and 8 It can be seen that both the costfunction and checking data error in the method of ANFISwith the new hybrid algorithm are smaller at each epoch andconverge more quickly Detailed performance for these twomethods is listed in Table 3
Mathematical Problems in Engineering 7
0 50 100 150 200 250 300 350 4000
10
20
30
Modelrsquos outputOriginal output
(a)
0 50 100 150 2000
10
20
30
Modelrsquos outputOriginal output
(b)
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
choice is letting 120575 = (01sim1)times119903119886 Further ahead we normalizeeach column of119872119889 to be the initial membership gradematrix1198720
1205831198941198950 =120583119895119894
sum119898119896=1 120583119895
119896
119894 = 1 119898 119895 = 1 119899 (9)
and 1205831198941198950 is initial belongingness of 119895th data point to 119894th clustercenter
The next part of the hybrid clustering algorithm is ini-tializing FCM with1198720 Since1198720 reflects the actual distancebetween each point and cluster center that is the initial cen-ters are already close to the actual centers therefore the bulkof computation time in FCM definitely decreases substan-tially The holistic procedure of the new clustering algorithmuses the following steps
Step 1 Normalize the data set 1199091 1199092 119909119899 in a 119901-dimen-sion space
Step 2 Find the first cluster center 119909lowast1 and 119863lowast1 with (5) being
used in the computational process
Step 3 Revise each pointrsquos density value with (6) and findother cluster centers by using the following criteria suppos-ing (119896 minus 1)th (119896 ge 2) cluster center has been obtained
(1) If 119863lowast119896 lt 120576119863lowast1 and 120576 is a threshold for rejecting a pointas a cluster center go to Step 4
(2) If119863lowast119896 gt 120576119863lowast1 and 120576 specifies an accepting threshold for
a new cluster center accept119863lowast119896 as a new cluster centerand repeat Step 3
(3) If 120576119863lowast1 lt 119863lowast119896 lt 120576119863lowast1 accept it as a new cluster centerif it satisfies
119889min119903119886
+119863lowast119896119863lowast1
ge 1 (10)
and 119889min represents the shortest distance between 119909lowast119896and all the previous centers otherwise reject it andchoose the point with the next highest density valueand retest according to the above three criteria
Step 4 Based on the 119898 cluster centers 119909lowast1 119909lowast119898 found
from the previous steps calculate the distance grade matrix119872119889 with (8) and then the initial membership grade matrix1198720 with (9)
Step 5 Start FCM by letting119872 = 1198720
Step 6 Upgrade the cluster centers using (2)
Step 7 Calculate the cost function according to (4) End theclustering process if 119869 is below a certain tolerance value or theimprovement over the previous iteration is less than a certainthreshold
Step 8 Upgrade the belongingness matrix119872 with (3)
4 Adaptive Network-Based InferenceSystem (ANFIS)
ANFIS is produced by Jang [20] and is based on a multilayerfeedforward network structure It has 5 layers with two kindsof nodes square ones with parameters to be identified andcircle ones with none The directional links between nodesindicate the flow direction of signals
Consider the system has 119901 inputs 1199101 1199102 119910119901 and oneoutput 119911 and suppose each input has two fuzzy sets as seen inFigure 3Thenodes of the same layers have the same functionas described below
The 1st layer is composed of square nodes with the nodefunction 120583119860119894119895(119910119894) (119894 = 1 119901 119895 = 1 2) where 119910119894 is the inputto node 119894 and 119860 119894119895 is a linguistic label representing a fuzzy set120583119860119894119895(119910119894) is usually chosen among bell-shaped functions andits parameters are referred to as premise parameters
Every node in the 2nd layer is a circle node with thelabel prod which multiplies all the incoming signals from theprevious layer and sends the product out
and 119878119894 is the input set of 119894th node from 1st layer 120596119894 representsthe firing strength for 119894th rule
The third layer has the same number of circle nodes asthe second layer Each node labeled119873 calculates the ratio ofits input firing strength to the sum of firing strengths in theprevious layer
120596119894 =120596119894
sum119898119895=1 120596119894 (12)
Each node of 4th layer is a square node generating eachrulersquos output
and 119886119894119895 119887119894 (119894 = 1 119898 119895 = 1 119901) are the set ofparameters in this layer and are referred to as consequentparameters
In the fifth layer there is only one circle node with thelabel sum simply adding all the incoming signals together andproducing the overall output 119911
119911 =119898
sum119894=1
120596119894119891119894 (14)
The parameters of the network are identified by anotherhybrid learning procedure forwards and backwards passand the least squares estimate (LSE) formulas and gradientdescent method are employed respectively in each passMore details can be found in [20] and applications of ANFIScan be found in [21 22]
5 Implementation and Results
Having introduced the hybrid clustering algorithm andANFIS and their mathematical foundations this section
Mathematical Problems in Engineering 5
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
z
Forward pass
Backward pass
y1
yp
A11
A12
An1
An2
120596m
1205961
1205962
1205961
1205962
120596m
120596m
fm
sum
1205961f1
1205962f2
prod
prod
prod
prod
prod
prod
Figure 3 ANFIS architecture
Table 1 Value of related parameters of the three clustering algo-rithms
turns back to study the modeling for the calcination processof industrial kiln First a benchmark group of data is citedto test the three clustering techniques presented in Section 3and the implementation for modeling is studied afterwards
51 Comparison among Different Clustering Algorithms Aquasi-random two-dimensional data set is used as a bench-mark problem to test the performance of the three clusteringalgorithms The quasi-random data set is cited from MatlabToolbox and it includes 140 two-dimension chaotic datapoints Assuming there are 3 cluster centers to be foundthe three algorithms are implemented individually and theirperformances are tested Table 1 lists the value of relatedparameters in the implementation of the three algorithms
Figure 4 shows the cluster centers attained by the threemethods and it is noticed that the results of FCM and hybridalgorithm are more close to the actual centers Actually theroot mean square error (RMSE) of Subclust turns out to be
147956 which is the highest one Figure 5 shows the changeof cost function over time of FCM and hybrid algorithm andit is evident that the convergence speed of hybrid algorithmprevails over FCM greatly Table 2 compares the iterationnumber and RMSE between FCM and hybrid algorithmwhich also indicates the superior performance of the hybridalgorithm to FCM
52 Calcination Process Modeling The first question to besolved is the determination of the input and output variablesfor the control model The method undertaken in this paperis to rely on the experience of the sophisticated workers andthe analysis on the calcination mechanism inside the kiln Inpractice the worker regulates the calcination rotary speed 119877(Hz) according to the calcination temperature T (∘C) as seenin Figure 1 which provides important information that 119877 canbe the only output and119879 should be one of the input variables
A further study at the inside calcination processmanifeststhat the material changes its property to meet the qualityrequirement that is DC mainly when it is going through theinner pot because the temperature there is much higher thanother parts inside the kiln This process normally takes 15 to20 minutes depending on the rotary speed 119877 Consequentlythe calcination temperature 119879 and rotary speed 119877 in theprevious time phase should also be considered into theinput variables of the model which matches the time-delayproperty of the calcination process After testing differentcombinations of 119879 and 119877 in their previous time phases a setof inputs is chosen as below
119884 = [119879 (119896) 119879 (119896 minus 1) 119879 (119896 minus 2) 119879 (119896 minus 3) 119877 (119896 minus 1) 119877 (119896 minus 2) 119877 (119896 minus 3)] (15)
where 119896 is the time index and the time interval between thetwo successive time indexes is 5 minutes
The model for the calcination process is then built upby adopting ANFIS coupled with the novel hybrid clustering
algorithm proposed in Section 3 A group of 600 consecutivedata points coming from successful control of sophisticatedworkers are chosen to train and test themodel among which400 are used as training data and 200 are used as checking
6 Mathematical Problems in Engineering
10
02
04
06
08
1
0 05(a)
10
02
04
06
08
1
0 05(b)
10
02
04
06
08
1
0 05(c)
10
02
04
06
08
1
0 05(d)
Figure 4 Cluster centers from different algorithms on the quasi-random data (a)The quasi-random data (b) Cluster centers from Subclust(c) Cluster centers from FCM (d) Cluster centers from hybrid algorithm
2
(a)(b)
4 6 8 10 12 1410
12
14
16
18
20
22
(a) FCM(b) Hybrid
Figure 5 Plots of cost function of FCM and hybrid algorithm
data In the clustering stage related parameters are selectedas 119903119886 = 03081 119903119887 = 125 times 119903119886 120576 = 015 120576 = 05 120575 = 05
Table 2 Clustering performance of FCM and hybrid algorithm
Performance FCM Hybrid SubclustIteration times 7 2RMSE 143025 137007
and 119908 = 2 which yields 11 rules for ANFIS Figure 6 showsthe outputs of the model after a training of 250 epochs andit is noticed that the model works satisfactorily on both thetraining data and checking data
A further comparison is made between ANFIS with FCMclustering and ANFIS with the new hybrid algorithm Alonger training as 300 epochs is applied for ANFIS this timeDuring the process the cost function on clustering phase andchecking data error for ANFIS are checked respectively asseen in Figures 7 and 8 It can be seen that both the costfunction and checking data error in the method of ANFISwith the new hybrid algorithm are smaller at each epoch andconverge more quickly Detailed performance for these twomethods is listed in Table 3
Mathematical Problems in Engineering 7
0 50 100 150 200 250 300 350 4000
10
20
30
Modelrsquos outputOriginal output
(a)
0 50 100 150 2000
10
20
30
Modelrsquos outputOriginal output
(b)
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
turns back to study the modeling for the calcination processof industrial kiln First a benchmark group of data is citedto test the three clustering techniques presented in Section 3and the implementation for modeling is studied afterwards
51 Comparison among Different Clustering Algorithms Aquasi-random two-dimensional data set is used as a bench-mark problem to test the performance of the three clusteringalgorithms The quasi-random data set is cited from MatlabToolbox and it includes 140 two-dimension chaotic datapoints Assuming there are 3 cluster centers to be foundthe three algorithms are implemented individually and theirperformances are tested Table 1 lists the value of relatedparameters in the implementation of the three algorithms
Figure 4 shows the cluster centers attained by the threemethods and it is noticed that the results of FCM and hybridalgorithm are more close to the actual centers Actually theroot mean square error (RMSE) of Subclust turns out to be
147956 which is the highest one Figure 5 shows the changeof cost function over time of FCM and hybrid algorithm andit is evident that the convergence speed of hybrid algorithmprevails over FCM greatly Table 2 compares the iterationnumber and RMSE between FCM and hybrid algorithmwhich also indicates the superior performance of the hybridalgorithm to FCM
52 Calcination Process Modeling The first question to besolved is the determination of the input and output variablesfor the control model The method undertaken in this paperis to rely on the experience of the sophisticated workers andthe analysis on the calcination mechanism inside the kiln Inpractice the worker regulates the calcination rotary speed 119877(Hz) according to the calcination temperature T (∘C) as seenin Figure 1 which provides important information that 119877 canbe the only output and119879 should be one of the input variables
A further study at the inside calcination processmanifeststhat the material changes its property to meet the qualityrequirement that is DC mainly when it is going through theinner pot because the temperature there is much higher thanother parts inside the kiln This process normally takes 15 to20 minutes depending on the rotary speed 119877 Consequentlythe calcination temperature 119879 and rotary speed 119877 in theprevious time phase should also be considered into theinput variables of the model which matches the time-delayproperty of the calcination process After testing differentcombinations of 119879 and 119877 in their previous time phases a setof inputs is chosen as below
119884 = [119879 (119896) 119879 (119896 minus 1) 119879 (119896 minus 2) 119879 (119896 minus 3) 119877 (119896 minus 1) 119877 (119896 minus 2) 119877 (119896 minus 3)] (15)
where 119896 is the time index and the time interval between thetwo successive time indexes is 5 minutes
The model for the calcination process is then built upby adopting ANFIS coupled with the novel hybrid clustering
algorithm proposed in Section 3 A group of 600 consecutivedata points coming from successful control of sophisticatedworkers are chosen to train and test themodel among which400 are used as training data and 200 are used as checking
6 Mathematical Problems in Engineering
10
02
04
06
08
1
0 05(a)
10
02
04
06
08
1
0 05(b)
10
02
04
06
08
1
0 05(c)
10
02
04
06
08
1
0 05(d)
Figure 4 Cluster centers from different algorithms on the quasi-random data (a)The quasi-random data (b) Cluster centers from Subclust(c) Cluster centers from FCM (d) Cluster centers from hybrid algorithm
2
(a)(b)
4 6 8 10 12 1410
12
14
16
18
20
22
(a) FCM(b) Hybrid
Figure 5 Plots of cost function of FCM and hybrid algorithm
data In the clustering stage related parameters are selectedas 119903119886 = 03081 119903119887 = 125 times 119903119886 120576 = 015 120576 = 05 120575 = 05
Table 2 Clustering performance of FCM and hybrid algorithm
Performance FCM Hybrid SubclustIteration times 7 2RMSE 143025 137007
and 119908 = 2 which yields 11 rules for ANFIS Figure 6 showsthe outputs of the model after a training of 250 epochs andit is noticed that the model works satisfactorily on both thetraining data and checking data
A further comparison is made between ANFIS with FCMclustering and ANFIS with the new hybrid algorithm Alonger training as 300 epochs is applied for ANFIS this timeDuring the process the cost function on clustering phase andchecking data error for ANFIS are checked respectively asseen in Figures 7 and 8 It can be seen that both the costfunction and checking data error in the method of ANFISwith the new hybrid algorithm are smaller at each epoch andconverge more quickly Detailed performance for these twomethods is listed in Table 3
Mathematical Problems in Engineering 7
0 50 100 150 200 250 300 350 4000
10
20
30
Modelrsquos outputOriginal output
(a)
0 50 100 150 2000
10
20
30
Modelrsquos outputOriginal output
(b)
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
Figure 4 Cluster centers from different algorithms on the quasi-random data (a)The quasi-random data (b) Cluster centers from Subclust(c) Cluster centers from FCM (d) Cluster centers from hybrid algorithm
2
(a)(b)
4 6 8 10 12 1410
12
14
16
18
20
22
(a) FCM(b) Hybrid
Figure 5 Plots of cost function of FCM and hybrid algorithm
data In the clustering stage related parameters are selectedas 119903119886 = 03081 119903119887 = 125 times 119903119886 120576 = 015 120576 = 05 120575 = 05
Table 2 Clustering performance of FCM and hybrid algorithm
Performance FCM Hybrid SubclustIteration times 7 2RMSE 143025 137007
and 119908 = 2 which yields 11 rules for ANFIS Figure 6 showsthe outputs of the model after a training of 250 epochs andit is noticed that the model works satisfactorily on both thetraining data and checking data
A further comparison is made between ANFIS with FCMclustering and ANFIS with the new hybrid algorithm Alonger training as 300 epochs is applied for ANFIS this timeDuring the process the cost function on clustering phase andchecking data error for ANFIS are checked respectively asseen in Figures 7 and 8 It can be seen that both the costfunction and checking data error in the method of ANFISwith the new hybrid algorithm are smaller at each epoch andconverge more quickly Detailed performance for these twomethods is listed in Table 3
Mathematical Problems in Engineering 7
0 50 100 150 200 250 300 350 4000
10
20
30
Modelrsquos outputOriginal output
(a)
0 50 100 150 2000
10
20
30
Modelrsquos outputOriginal output
(b)
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
Figure 6 Plots of the modelrsquos output (a) Output on training data (b) Output on checking data
Table 3 Performance comparison between ANFIS with FCM and ANFIS with the new hybrid method
Performance ANFIS with FCM algorithm ANFIS with the new hybrid algorithmIterations of clustering 25 5Mean of training 03923 03262Mean of checking 04214 03943RMSE of training 00321 00279RMSE of checking 00467 00459
0 20 40 60 80 10006
08
1
12
14
16
18
2
22
(a)
(b)
(a) FCM(b) Hybrid
times104
Figure 7 Plots of cost function on clustering phase
6 Conclusion
A novel hybrid clustering algorithm combining FCM withSubtractive Clustering Method is proposed and is proved tobe more efficient with reduced computation and it leads tomore accuracy for the clustering result ANFIS is employedto establish the control model for the calcination processof industrial rotary kiln with a satisfactory outcome and itsets a role model for similar control situations in industrialfield Coupled with the new hybrid clustering algorithm theperformance of ANFIS improves greatly with reduced com-putation on clustering phase and approaches more accuracy
0 50 100 150 200 250 300
065
07
075
08
085
09
095
1
(a)
(b)
(a) ANFIS with FCM (b) ANFIS with hybrid
Figure 8 Error plots on checking data for ANFIS
to the original outputs Furthermore study can be focused onthe issue of determining the number of time phases and thetime interval in the input vector 119884 since it is mainly decidedempirically currently Also the effect from the drying part ofthe rotary kiln on modeling is neglected in this paper theroles of drying temperature and drying rotary speed on themodel are to be into consideration as well
Competing Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
8 Mathematical Problems in Engineering
Acknowledgments
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
This research is partially supported by National NaturalScience Foundation of China (61403264) partially supportedby Program of Cultivation for Outstanding Young Scholarsand ldquoThousand Hundred and Tenrdquo Teacher Cultivation Pro-gram of Guangdong Province (ZX03240302) and partiallysupported by Program of Building Brand Major of HighVocational Education of Guangdong Province
References
[1] M Jarvensivu E Juuso and O Ahava ldquoIntelligent control ofa rotary kiln fired with producer gas generated from biomassrdquoEngineering Applications of Artificial Intelligence vol 14 no 5pp 629ndash653 2001
[2] M Jarvensivu K Saari and S-L Jamsa-Jounela ldquoIntelligentcontrol system of an industrial lime kiln processrdquo ControlEngineering Practice vol 9 no 6 pp 589ndash606 2001
[3] N Q Dinh and N V Afzulpurkar ldquoNeuro-fuzzy MIMOnonlinear control for ceramic roller kilnrdquo Simulation ModellingPractice andTheory vol 15 no 10 pp 1239ndash1258 2007
[4] M Georgallis P Nowak M Salcudean and I S GartshoreldquoModelling the rotary lime kilnrdquo The Canadian Journal ofChemical Engineering vol 83 no 2 pp 212ndash223 2005
[5] Z Sogut Z Oktay and H Karakoc ldquoMathematical modeling ofheat recovery from a rotary kilnrdquo Applied Thermal Engineeringvol 30 no 8-9 pp 817ndash825 2010
[6] Y H Kim ldquoDevelopment of process model of a rotary kilnfor volatile organic compound recovery from coconut shellrdquoKorean Journal of Chemical Engineering vol 29 no 12 pp 1674ndash1679 2012
[7] Y Wang X-H Fan and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction (Part I) mathematical models of grate processrdquoJournal of Central South University of Technology vol 19 no 4pp 1092ndash1097 2012
[8] X-H Fan Y Wang and X-L Chen ldquoMathematical modelsand expert system for grate-kiln process of iron ore oxide pelletproduction Part II rotary kiln process controlrdquo Journal ofCentral South University of Technology vol 19 no 6 pp 1724ndash1727 2012
[9] Y Cai ldquoResearch on soft measurement modeling for industryrotary kiln based on flexible neural networkrdquo in Proceedingsof the International Conference on Computer Science and Elec-tronics Engineering (ICCSEE rsquo12) pp 343ndash346 IEEEHangzhouChina March 2012
[10] T Zhongda L Shujiang W Yanhong and W XiangdongldquoA multi-model fusion soft sensor modelling method andits application in rotary kiln calcination zone temperaturepredictionrdquo Transactions of the Institute of Measurement andControl vol 38 no 1 pp 110ndash124 2016
[11] L Zhang C Zhang Q Xu and C Wang ldquoModelling of limekiln using subspacemethod with new order selection criterionrdquoMathematical Problems in Engineering vol 2014 Article ID816831 11 pages 2014
[12] M Badoni A Singh and B Singh ldquoAdaptive neurofuzzyinference system least-mean-square-based control algorithmfor DSTATCOMrdquo IEEE Transactions on Industrial Informaticsvol 12 no 2 pp 483ndash492 2016
[13] P Garcıa C A Garcıa L M Fernandez F Llorens andF Jurado ldquoANFIS-Based control of a grid-connected hybridsystem integrating renewable energies hydrogen and batteriesrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp1107ndash1117 2014
[14] K S Ajil P KThapliyal M V Shukla P K Pal P C Joshi andR R Navalgund ldquoA new technique for temperature and humid-ity profile retrieval from infrared-sounder observations usingthe adaptive neuro-fuzzy inference systemrdquo IEEE Transactionson Geoscience and Remote Sensing vol 48 no 4 pp 1650ndash16592010
[15] J C Bezdek R Ehrlich and W Full ldquoFCM the fuzzy c-meansclustering algorithmrdquoComputers and Geosciences vol 10 no 2-3 pp 191ndash203 1984
[16] S L Chiu ldquoFuzzy model identification based on cluster estima-tionrdquo Journal of Intelligent and Fuzzy Systems vol 2 no 3 pp267ndash278 1994
[17] Q Du Analysis and research on process control for a lithoponecalcination rotary kiln [PhD thesis] South China University ofTechnology 2008
[18] A K Jain and R C Dubes Algorithms for clustering dataPrentice Hall Advanced Reference Series Prentice Hall IncEnglewood Cliffs NJ 1988
[19] Q Yang D Zhang and F Tian ldquoAn initialization methodfor fuzzy c-means algorithm using subtractive clusteringrdquo inProceedings of the 3rd International Conference on IntelligentNetworks and Intelligent Systems (ICINIS rsquo10) pp 393ndash396Shenyang China November 2010
[20] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993
[21] K Tan Y Ye Q Cao P Du and J Dong ldquoEstimation of arseniccontamination in reclaimed agricultural soils using reflectancespectroscopy andANFISmodelrdquo IEEE Journal of Selected Topicsin Applied Earth Observations and Remote Sensing vol 7 no 6pp 2540ndash2546 2014
[22] S A Khan M D Equbal and T Islam ldquoA comprehensivecomparative study of DGA based transformer fault diagnosisusing fuzzy logic and ANFIS modelsrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 22 no 1 pp 590ndash5962015
