Research Article Fault Diagnosis Method on Polyvinyl Chloride Polymerization Process ... · 2018-12-08 · Research Article Fault Diagnosis Method on Polyvinyl Chloride Polymerization

Research ArticleFault Diagnosis Method on Polyvinyl Chloride PolymerizationProcess Based on Dynamic Kernel Principal Component andFisher Discriminant Analysis Method

Shu-zhi Gao1 Xiao-feng Wu1 Gui-cheng Wang1 Jie-sheng Wang2 and Zi-qing Chai3

1College of Information and Engineering Shenyang University of Chemical Technology Shenyang 110142 China2National Financial Security and System Equipment Engineering Research Center University of Science amp Technology LiaoningAnshan 114044 China3Beijing Institute of Technology School of Software Beijing 100081 China

Correspondence should be addressed to Jie-sheng Wang wang jiesheng126com

Received 8 July 2016 Accepted 29 September 2016

Academic Editor Yaguo Lei

Copyright copy 2016 Shu-zhi Gao et al 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

In view of the fact that the production process of Polyvinyl chloride (PVC) polymerization has more fault types and its type iscomplex a fault diagnosis algorithm based on the hybrid Dynamic Kernel Principal Component Analysis-Fisher DiscriminantAnalysis (DKPCA-FDA) method is proposed in this paper Kernel principal component analysis and Dynamic Kernel PrincipalComponent Analysis are used for fault diagnosis of Polyvinyl chloride (PVC) polymerization process while Fisher DiscriminantAnalysis (FDA) method was adopted to make failure data for further separation The simulation results show that the DynamicKernel Principal Component Analyses to fault diagnosis of Polyvinyl chloride (PVC) polymerization process have better diagnosticaccuracy the Fisher Discriminant Analysis (FDA) can further realize the fault isolation and the actual fault in the process ofPolyvinyl chloride (PVC) polymerization production can be monitored by Dynamic Kernel Principal Component Analysis

1 Introduction

In todayrsquos chemical industry the polymer production hasoccupied a very important position Polyvinyl chloride(PVC) is an important organic synthetic material and it isalso the chemical product which has a variety of uses PVCresin is a kind of chemical products the failure mechanismof the production process is complex and there are seriousdynamic and nonlinear problems in the production processthen there is an urgent need to improve the system reliabilityand safety production in order to avoid generating faultsystem otherwise it will lead to economic losses and evenaccidents Therefore the fault study in production of PVCresin has been an important issue research for experts [1 2]At present the principal component analysis is widely appliedin chemical process fault diagnosis Due to the large numberof pieces of data in PVC resin production process has seriousnonlinear [3] and strong coupling and dynamic problems[4 5] the rate of false positives and nonresponse rates of the

process by using conventional principal component analysis(PCA) are too high So in order tomake the PCAused inmorefields both the domestic and foreign scholars respectivelyconducted a series of improvements for example the kernelprincipal component analysis (KPCA) and dynamic principalcomponent analysis [6] (DPCA) In 1995 in view of themulti-sensor related timing measurements a sensor fault detectionbased on the dynamic principal component analysis (DPCA)method is proposed by Ku et al [7] simulation experimentsshow that this method can effectively detect and identify thefault sensors DPCAmethod was applied to the oil state over-haul model by Makis et al the simulation results show thatDPCA can accurately detect the fault of 119891 dynamic process[8] On the nonlinear problem there are mainly the methodsof neural network and principal component analysis andtargeting the problems caused by nonlinear data processingKramer proposed nonlinear principal component analysismethods based on the association of the neural networkThesimulation results show that it can effectively changemultiple

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 7263285 8 pageshttpdxdoiorg10115520167263285

2 Mathematical Problems in Engineering

P-12

VSP-PX19FV-PX05

VSP-PX13

FV-PX02

FV-PX01

VSP-PX37

VSP-PX01

VSP-PX08

VSP-PX04

VSP-PX03 VENT

VSP-PX23

VSP-PX12

VSP-PX10

VSP-PX09

VSP-PX21

VSP-PX36 VSP-PX16

VSP-PX25

VSP-PX22

VSP-PX26

VSP-PX33

FV-PX03

Cooling water

AIR

TIP109

Seal water

Dispersant initiatorfeed TIC

WA01FICP105

TIP107

Modifiers

Injected water

Terminator

VSP-PX15VSP-PX14

TICP101

PICP102

TIP110

FICP104

TICWA01

P-90

FICP102

FICP101

P-96

P-98

VCM feed

Rinse water

Remove the TK-IE

Remove SE-IF

Painted walls agent

High pressure wash water

Steam

P-101

Figure 1 Polymerizer process diagram

variables into a few independent variables [9] Because theautoassociative neural network is difficult to be trained DongandMcAvoy proposed a nonlinear PCAmethodbased on ele-ment curves andneural network [10] the results show that thenonlinear function can be expressed as a sum of the single-variable functions In dealing with nonlinear problems theintroduction of kernel functions (KPCA)method is proposedby Jong-Min et al [11] The results show that this methodcan be carried out for the nonlinear process fault diagnosisResults show that in the monitoring process of chemicalprocess the improved principal component analysis methodis better than the traditional principal component analysis

After analyzing the characteristics of the data for theproduction of PVC resin there are serious nonlinear anddynamic data and this article adopts the method of acompound Dynamic Kernel Principal Component Analysis(DKPCA) using the nonlinear and dynamic process andafter studying it there is the defect of the traditional principalcomponent At the same time this paper also included thefisher discriminantmethod for further classification of failure

data to ensure that one quickly finds out the cause of theproblem then for further processing

2 PVC Polymerization Introduction

Taking a unit of the production process of PVC resin as theresearch object polymerization process is shown in Figure 1

Themonomer initiator dispersion agent and othermate-rials are fed into the polymerization reactor from inlets Aftera series of reactions the polymers are ultimately generatedIn the polymerization process the heat is ceaselessly releasedso that the temperature in the polymerization reactor iscontinuously increased which will make the reaction moresevere and causing material flow imbalances so as to affectthe product quality So the mixing system is added inthe polymerization reactor and the cooling water is timelyinjected in the jacket and the damper in order to balance thetemperature in the polymerization reactor After the reactionjoin the terminators then the polymerization reaction will beterminated

Mathematical Problems in Engineering 3

From PVC polymerization process there are many indi-cators affecting the quality of product and any one variableover its boundaries it will lead the quality of the product to beout of control Therefore perform the real-time monitoringof quality index in the process of polymerization and thenensure the product quality changed can be diagnosed timelyand accurately After a comprehensive comparative study weultimately selected 10 variables identified as the object ofstudy these 10 variables are as follows the temperaturewithinthe reactor the reactor pressure stirring currents injectioninto the water flow seal water flow jacket water flow waterflow baffles cooling water inlet temperature outlet tempera-ture of the water jacket and the water outlet temperature ofthe baffle Monitor the 10 variables respectively and ensurethe stable operation of the polymerization system

3 Basic Principle of KPCA and DKPCA

31 Basic Principle of KPCA PCA is based on data toestablish the system statistical model and detect anomaliesand failures based on the multivariate statistical techniquesFirst take some normal conditions data set 119883119899times119898 (119899 is thenumber of sampling points 119898 is the number of variables)to build a statistical model PCA is made to process datavector which projected onto the main element vector spaceand residual space Matrix 119883 can be expressed as the sum of119899 vector cross products namely119883 = 119879119875119879 = 11990511199011198791 + 11990521199011198792 + sdot sdot sdot + 119905119899119901119879119899 (1)

where 119879 = [1199051 1199052 119905119899] is called scoring matrix and 119875 =[1199011 1199012 119901119899] is called the loadingmatrix Each score vectorand load vectors are orthogonal and the load vector length is1namely

119901119879119894 119901119895 = 0 119894 = 1198951 119894 = 119895 (2)

Equation (1) is carried out with the right multiplication with119901119894 to obtain 119905119894 = 119883119901119894It can be seen that each score vector is equal to the data

matrix projection on its load vector the size of 119905119894 determinesthe cover degree of the data matrix projection on the loadvectors the load vector related by maximum score vectorrepresents the maximum change in the direction of the data119883 and it is defined as the first principal component andso on determine the second main element the third mainelement and the nth main element The data 119883 changes aremainly embodied in the first several principal componentsthe projection data in the next few load vectors will be smalland it ismainly caused by noise expressedwithmatrix119864 andthen type (1) can be changed for the following form119883 = 119879119875119879 = 11990511199011198791 + 11990521199011198792 + sdot sdot sdot + 119905119896119901119879119896 + 119864 (119896 ≪ 119899) (3)

Generally adopt the principle of cumulative contributionrate and determine the number of PCA 119896 is the number ofselected principal components119864 is the errormatrix ignoring119864 usually can serve the purpose of clearing the measurement

noise equivalent to changing 119899 dimensional data into 119896dimensional PCA and 119899 minus 119896 dimensional residual space 119864it serves dimension reduction purposes After the principalnumber is determined the PCA statistical model is set upthrough the two subspaces Commonly the Hotelling 1198792 and119876 statistic (the squared prediction error SPE) are used whichare calculated by the following equation

119876 = 119890119894119890119879119894 = 119883119894 (119868 minus 119875119896119875119879119896 )119883119879119894 (4)

The statistic index of control limits is calculated as follows119876119871 = 119886 (119887 + 119888119911119886)119889 (5)

where

119886 = 119899sum119894=119896+1

120582119894119887 = 1 + [1205792ℎ0 (ℎ0 minus 1)]1198862 119888 = (119888119886radic21205792ℎ0)119886 119889 = 1ℎ 1205792 = 119899sum119894=119896+1

1205822119894 1205793 = 119899sum119894=119896+1

1205823119894 ℎ0 = (1 minus 21198861205793)(312057922)

(6)

119888119886 is the critical value of normal distribution in the testlevel and 120582119894 is the eigenvalue of matrix eigenvalues of originaldata119883 1198792 statistic is defined as1198792119894 = 119905119894120582minus1119905119879119894 = 119883119894119875119896120582minus1119901119879119896119883119894119879 (7)1198792 statistic index of the control limit calculations iscalculated as follows1198792119896119898120572 = 119896 (119899 minus 1)119899 minus 119896 119865119896119899minus1120572 (8)

where 120572 is the significance level of test 119899 is the data samplingfrequency and 119898 is a variable number 119896 is the number ofthe principal components and 119865120572(119896 119899 minus 119896) is the distributedcritical value in accordance to the level of test 120572 and thedegrees of freedom (119896 119899 minus 119896)

When statistics are within the scope of the control limitthen the system is in a trouble-free state if the statisticsare beyond the control limit then there is a fault in thesystem The basic idea of KPCA is through nonlinear map120601 and make the input spaces 1198831 1198832 119883119899 isin 119877119872 onto thefeature space 119865 120601 119877119872 rarr 119865 and then calculate principalcomponent on the new feature space


In the feature space119865 covariancematrix can be calculatedas follows

119862119865 = 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879 (9)

By determining the characteristics of the vector 119862119865 wecan get the principal component of 119865 and the feature vector119862119865 is directly related to the input space of PCA

120582119881 = 119862119865119881 = ( 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879)119881= 1119873 119873sum119894=1

⟨120601 (119909119894) 119881⟩ 120601 (119909119894) (10)

where ⟨119909 119910⟩ is representative dot product of 119909 and 119910 andthen it can be inferred that in any condition of 120582 = 0 allsolutions of 119881 can be determined by 120601(1199091) 120601(119909119899) So120582119881 = 119862119865119881 is equivalent to120582 ⟨120601 (119909119896) 119881⟩ = ⟨120601 (119909119896) 119862119865119881⟩ 119896 = 1 119899 (11)

There is a coefficient of 119886119894 (119894 = 1 119873) where 119881 =sum119873119894=1 119886119894120601(119909119894)Therefore combinedwith the type it can be obtained that

120582 119873sum119894=1

119886119894 ⟨120601 (119909119896) 120601 (119909119894)⟩= 1119873 ⟨120601 (119909119896) 119873sum

119894=1

120601 (119909119895)⟩⟨120601 (119909119895) 120601 (119909119894)⟩ (12)

At the same time 119873 times 119873 matrix is defined 119870 isin 119877119873times119873and [119870]119894119895 = 119870119894119895 = ⟨120601 (119909119894) 120601 (119909119895)⟩ (13)

Therefore (12) can be simplified as120582119873119886 = 119870119886 119886 = [1198861 119886119873]119879 (14)

In the application of KPCA first you have to get themeancentered on high dimensional space It can be done by usingthe following formula instead of nuclear matrix119870 = 119870 minus 119868119873119870 minus 119870119868119873 + 119868119873119870119868119873 (15)

where each element of 119868119873 is equal to 1119873 and 119864 isin 119877119873times119873Therefore the principal 119905 of vector 119909 can be acquired

through 120601(119909) mapping to the characteristic vector 119881119896 of 119865where

119905119896 = ⟨119881119896 120601 (119909)⟩ = 119873sum119894=1

119886119896119894 ⟨120601 (119909119894) 120601 (119883)⟩= 119873sum119894=1

119886119896119894 119896 (119909119894 119883) 119896 = 1 119901 (16)

We found that KPCA is by introducing 119896(119909 119910) =⟨120601(119909) 120601(119910)⟩ kernel function avoiding dot product of thenonlinear mapping and calculating the feature space Thechoice of kernel function is completely determine by 120601 andfeature space 119865 The most commonly used kernel function isradial basis kernel function

119896 (119909 119910) = exp(minus1003817100381710038171003817119909 minus 11991010038171003817100381710038172120590 ) (17)

The kernel function used in this paper is radial basiskernel function

4 The Principle of Dynamic Kernel PrincipalComponent Analysis

The traditional PCAmethod to the diagnosis result of systemprocess data with dynamic properties and the nonlinear char-acteristics is not very ideal so for such a dynamic nonlinearsystem one should study a new method this method mustbe able to capture the dynamic and nonlinear characteristicsof the data at the same time This is the following DynamicKernel Principal Component Analysis (DKPCA) method

The fault detection principle of Dynamic Kernel Prin-cipal Component Analysis is as follows analyze the systemdynamic characteristics at first the time-series data of thesystem at normal state were analyzed and kernel principalcomponent analysis mode of the system under the normalstate is constructed Then a new system data is mapped tothe kernel principal component model and respectively byprincipal component scores and the residuals to determinethe state of the system

DKPCA fault diagnosis method is that each of theobservation variables is expanded by119867 observations in frontthe augmentedmatrix containing the first 119878 time observationsis constructed [12] and augmented matrix is as follows

119883 (119878) = ((

119883119879119905 119883119879119905minus1 sdot sdot sdot 119883119879119905minus119904119883119879119905minus1 119883119879119905minus2 sdot sdot sdot 119883119879119905minus119878minus1 d119883119879119905minus119878minus119899 119883119879119905+119878minus119899minus1 sdot sdot sdot 119883119879119905minus119899

))

(18)

After the augmented matrix by extending the timesequence the kernel principal component analysis is used forfault detection DKPCA flow chart is shown in Figure 2

5 The Fault Classification Research Based onFisher Discriminant Method

The FDArsquos basic idea is to maximize the dispersion betweenclasses at the same time to minimize the dispersion in classthrough the optimization objective function to determine theoptimal FDA vector FDA and the vector can represent thedirection of the different fault class optimal separation [13ndash15]

maxV =0

V119879119878119887VV119879119878119908V (19)


Graced matrix structure

Nonlinear transformation is completedby the kernel function

Eigenvalues and eigenvectors

Determine the number of principals

Dynamic kernel principal obtained

Normal Fault

Training Test

Yes No

Normalize the data X

Get data X normal stateOnline data collection Xnew

Strike Xnew dynamic kernel principal

Calculation of online test data T2

new and SPEnew

T2

new lt T2

a

SPEnew lt SPE

calculated separatelyT

2 and SPE control limit are

Determine the size of the delay S

Figure 2 Dynamic flow chart of kernel principal component analysis

where 119878119887 is the discrete degree matrix between classes 119878119908 isthe discrete degree matrix in class and V is the FDA featurevector [16]

To further classify the fault the FDA method is adoptedfor further classification to the failure data detected byDKPCA to ensure that one finds out the cause of the problemquickly which provides the theoretical basis to make failurecountermeasures

6 The Simulation Example Results

First of all the characteristics of the polymerization processwere analyzed this analysis found that there are 10 processvariables affecting the polymerization product quality indi-cators 50 sets of data under normal polymerization processare collected and used as the training sample matrix 11988350times10and 200 groups of observed data online are used as testdata Every one minute sampling occurs one time in the51st group failure 1 was introduced and it is mainly thatbecause of the rise of temperature the temperature of thenormal production of PVC resin is 565plusmn05 as temperaturescontinue to rise leading to transformation of resin In the125th group failure 2 was introduced and the stirring electriccurrent is increased by 15

According to the above process T2 and SPE are usedfor fault monitoring of PVC polymerization process by usingthe traditional principal component analysis kernel principalcomponent analysis and the Dynamic Kernel PrincipalComponent Analysis

(1) The traditional principal component analysis wasadopted 200 groups of data are to be collected the

Table 1 Diagnostic results

Diagnostic methods PCA KPCA DKPCAFalse alarm rate 17 8 1

sampling interval is 1min and the fault detectionresults are as shown in Figure 3

(2) The kernel principal component analysis wasadopted 200 groups of data are to be collected thesampling interval is 1min and the fault detectionresults are as shown in Figure 4

(3) The Dynamic Kernel Principal Component Analysiswas adopted 200 groups of data are to be collectedthe sampling interval is 1min and the fault detectionresults are as shown in Figure 5

In order to more clearly identify which kind of diagnosismethods is more effective the false positive rates are com-pared The lower the false positive rate the more appropriatethis method to be applied in the polymerization kettle faultdiagnosis system Diagnostic results are as Table 1

It can be clearly seen from the simulation results thatthere are many cases exceeding the control limits and thefalse positive rate is quite serious for the traditional principalcomponent analysis method and the kernel principal com-ponent analysis method before the 50 sampled points whichwill lead to the incorrect judgment of the operators But inthe fault detection of Dynamic Kernel Principal ComponentAnalysis there are only two false alarms and the introductionof fault phase obvious beyond control limit thus improvesthe efficiency of fault diagnosis


PCA fault diagnosis

0

20

40

60

80

100

120

140

160

180T

2co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(a)

PCA fault diagnosis

0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 400 80 100 120 140 160 180 20060Batch number(b)

Figure 3 Principal component analysis of fault detection results

KPCA fault diagnosis

20 40 60 80 100 120 140 160 180 2000Batch number

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

(a)


0

20

40

60

80

100

120

140SP

E co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(b)

Figure 4 Kernel principal component analysis of fault detection results

DKPCA fault diagnosis

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(a)


0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(b)

Figure 5 Dynamic Kernel Principal Component Analysis of fault detection results


084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)

Figure 6 Fault classification results of FDA

In order to further find out the cause of the problem weneed to make further classification of failure data to ensurerapid recovery production and now we will extract 100groups detected by DKPCA There are two types of failuresrespectively one is resin transformation due to temperatureand pressure and the other failure is caused by the stirringelectric current in order to make better separation of twotypes of failure we use the method of judging the FDA andthe results are shown in Figure 6

By the graph we can see clearly that lowast represents thefailure caused by temperature and pressure and I representsthe failure caused by stirring electric current increased faultseparation accuracy reached 97 and it can be used to isolatetwo faults in the polymerization process

7 Conclusions

Based on the traditional principal component analysis andkernel principal component analysis the data of dynamicprinciple were introduced introducing Dynamic KernelPrincipal Component Analysis method which is used forfault detection to the dynamic and nonlinear strong polymer-izing process At the same time there are further references tothe FDAmethods for fault isolation Simulation results showthat themethod can real timemonitor the change of variablesin the polymerization process the fault of the polymerizationprocess is more sensitive to reduce the probability of falsealarm and can quickly find out the cause of the problemResults indicate that this method can be applied to thefault handling of polymerization at the same time and forthe general nonlinear dynamic chemical process also it hascertain applicability

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

This work is partially supported by the Project by NationalNatural Science Foundation of China (Grant no 21576127)

the Program for Liaoning Excellent Talents in University(Grant no LR2014008) the Project by Liaoning ProvincialNatural Science Foundation of China (Grant no 2014020177)the Program for Research Special Foundation of University ofScience and Technology of Liaoning (Grant no 2015TD04)and the Opening Project of National Financial Security andSystem Equipment Engineering Research Center (Grant noUSTLKFGJ201502)

References

[1] S Z Gao XW Gao J SWang and P C Fei ldquoRough set-neuralnetwork fault diagnosis of polymerization based on improvedattribute reduction algorithm of discernibility matrixrdquo Journalof Chemical Industry and Engineering vol 62 no 3 pp 759ndash7652011

[2] Y H Gao and Z Yang ldquoAn application of PCA for monitoringand diagnosing fault in a chemical polymeric processrdquo Journalof Southern Yangtze University vol 4 no 4 pp 352ndash356 2005

[3] G W Dou and A L Liu ldquoFault detection based on kernelprincipal component analysisrdquo Chinese Journal of ScientificInstrument vol 30 no 6 pp 443ndash447 2009

[4] H Song H Zhang and X Wang ldquoMultiple faults diagnosisapproach for nonlinear systemrdquo Journal of Beijing University ofAeronautics and Astronautics vol 31 no 11 pp 1198ndash1203 2005

[5] S-H Jiang W-H Gui C-H Yang and Z-H Tang ldquoMethodbased on kernel principal component analysis and supportvector machine and its applicationrdquo Journal of Central SouthUniversity (Science andTechnology) vol 40 no 5 pp 1323ndash13282009

[6] L Li J N Zhu and H B Shi ldquoFault detection of chemical pro-cess based on multiscale dynamic kernel principal componentanalysis control and instruments in chemical industryrdquoControland Instruments in Chemical Industry vol 35 no 4 pp 23ndash262008

[7] W Ku R H Storer and C Georgakis ldquoDisturbance detec-tion and isolation by dynamic principal component analysisrdquoChemometrics and Intelligent Laboratory Systems vol 30 no 1pp 179ndash196 1995

[8] VMakis JWu and Y Gao ldquoAn application of DPCA to oil datafor CBM modelingrdquo European Journal of Operational Researchvol 174 no 1 pp 112ndash123 2006

[9] M A Kramer ldquoNonlinear principal component analysis usingautoassociative neural networksrdquo AIChE Journal vol 37 no 2pp 233ndash243 1991

[10] D Dong and T J McAvoy ldquoNonlinear principal componentanalysismdashbased on principal curves and neural networksrdquoComputers amp Chemical Engineering vol 20 no 1 pp 65ndash781996

[11] L Jong-Min C K Yoo S W Choi et al ldquoNonlinearProeessmonitoring using kemel Prineipal component analysisrdquoChemieal Engineering Seienee vol 59 2004

[12] H T Shi J C Liu X D Ding and S Tan ldquoFault detection basedon hybrid dynamic principal component analysisrdquo ControlEngineering of China vol 19 no 1 pp 148ndash150 2012

[13] Z Q Bian and X G Zhang Pattern Recognition TsinghuaUniversity Press Beijing China 1999

[14] H H Xin Process Monitoring based on Fisher DisciminantAnalysis China University of Petroleum (East China) 2011


[15] N Lv Process Monitoring based on Fisher Disciminant AnalysisHarbin University of Science and Technology 2009

[16] L H Chiang E L Russell and R D Braatz Fault Detection andDiagnosis in Industrial Systems Advanced Textbooks in Controland Signal Processing Springer London UK 2001

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P-12

VSP-PX19FV-PX05

VSP-PX13

FV-PX02

FV-PX01

VSP-PX37

VSP-PX01

VSP-PX08

VSP-PX04

VSP-PX03 VENT

VSP-PX23

VSP-PX12

VSP-PX10

VSP-PX09

VSP-PX21

VSP-PX36 VSP-PX16

VSP-PX25

VSP-PX22

VSP-PX26

VSP-PX33

FV-PX03

Cooling water

AIR

TIP109

Seal water

Dispersant initiatorfeed TIC

WA01FICP105

TIP107

Modifiers

Injected water

Terminator

VSP-PX15VSP-PX14

TICP101

PICP102

TIP110

FICP104

TICWA01

P-90

FICP102

FICP101

P-96

P-98

VCM feed

Rinse water

Remove the TK-IE

Remove SE-IF

Painted walls agent

High pressure wash water

Steam

P-101

Figure 1 Polymerizer process diagram

variables into a few independent variables [9] Because theautoassociative neural network is difficult to be trained DongandMcAvoy proposed a nonlinear PCAmethodbased on ele-ment curves andneural network [10] the results show that thenonlinear function can be expressed as a sum of the single-variable functions In dealing with nonlinear problems theintroduction of kernel functions (KPCA)method is proposedby Jong-Min et al [11] The results show that this methodcan be carried out for the nonlinear process fault diagnosisResults show that in the monitoring process of chemicalprocess the improved principal component analysis methodis better than the traditional principal component analysis

After analyzing the characteristics of the data for theproduction of PVC resin there are serious nonlinear anddynamic data and this article adopts the method of acompound Dynamic Kernel Principal Component Analysis(DKPCA) using the nonlinear and dynamic process andafter studying it there is the defect of the traditional principalcomponent At the same time this paper also included thefisher discriminantmethod for further classification of failure

data to ensure that one quickly finds out the cause of theproblem then for further processing

2 PVC Polymerization Introduction

Taking a unit of the production process of PVC resin as theresearch object polymerization process is shown in Figure 1

Themonomer initiator dispersion agent and othermate-rials are fed into the polymerization reactor from inlets Aftera series of reactions the polymers are ultimately generatedIn the polymerization process the heat is ceaselessly releasedso that the temperature in the polymerization reactor iscontinuously increased which will make the reaction moresevere and causing material flow imbalances so as to affectthe product quality So the mixing system is added inthe polymerization reactor and the cooling water is timelyinjected in the jacket and the damper in order to balance thetemperature in the polymerization reactor After the reactionjoin the terminators then the polymerization reaction will beterminated






119901119879119894 119901119895 = 0 119894 = 1198951 119894 = 119895 (2)





119876 = 119890119894119890119879119894 = 119883119894 (119868 minus 119875119896119875119879119896 )119883119879119894 (4)


where

119886 = 119899sum119894=119896+1


1205822119894 1205793 = 119899sum119894=119896+1

1205823119894 ℎ0 = (1 minus 21198861205793)(312057922)

(6)






119862119865 = 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879 (9)


120582119881 = 119862119865119881 = ( 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879)119881= 1119873 119873sum119894=1

⟨120601 (119909119894) 119881⟩ 120601 (119909119894) (10)



120582 119873sum119894=1

119886119894 ⟨120601 (119909119896) 120601 (119909119894)⟩= 1119873 ⟨120601 (119909119896) 119873sum

119894=1

120601 (119909119895)⟩⟨120601 (119909119895) 120601 (119909119894)⟩ (12)






119905119896 = ⟨119881119896 120601 (119909)⟩ = 119873sum119894=1

119886119896119894 ⟨120601 (119909119894) 120601 (119883)⟩= 119873sum119894=1

119886119896119894 119896 (119909119894 119883) 119896 = 1 119901 (16)


119896 (119909 119910) = exp(minus1003817100381710038171003817119909 minus 11991010038171003817100381710038172120590 ) (17)






119883 (119878) = ((


))

(18)




maxV =0

V119879119878119887VV119879119878119908V (19)







Normal Fault

Training Test

Yes No





new and SPEnew

T2

new lt T2

a

SPEnew lt SPE



















PCA fault diagnosis

0

20

40

60

80

100

120

140

160

180T

2co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(a)

PCA fault diagnosis

0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 400 80 100 120 140 160 180 20060Batch number(b)



20 40 60 80 100 120 140 160 180 2000Batch number

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

(a)


0

20

40

60

80

100

120

140SP

E co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(b)



0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(a)


0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(b)



084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)




7 Conclusions


Competing Interests


Acknowledgments



References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119901119879119894 119901119895 = 0 119894 = 1198951 119894 = 119895 (2)





119876 = 119890119894119890119879119894 = 119883119894 (119868 minus 119875119896119875119879119896 )119883119879119894 (4)


where

119886 = 119899sum119894=119896+1


1205822119894 1205793 = 119899sum119894=119896+1

1205823119894 ℎ0 = (1 minus 21198861205793)(312057922)

(6)






119862119865 = 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879 (9)


120582119881 = 119862119865119881 = ( 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879)119881= 1119873 119873sum119894=1

⟨120601 (119909119894) 119881⟩ 120601 (119909119894) (10)



120582 119873sum119894=1

119886119894 ⟨120601 (119909119896) 120601 (119909119894)⟩= 1119873 ⟨120601 (119909119896) 119873sum

119894=1

120601 (119909119895)⟩⟨120601 (119909119895) 120601 (119909119894)⟩ (12)






119905119896 = ⟨119881119896 120601 (119909)⟩ = 119873sum119894=1

119886119896119894 ⟨120601 (119909119894) 120601 (119883)⟩= 119873sum119894=1

119886119896119894 119896 (119909119894 119883) 119896 = 1 119901 (16)


119896 (119909 119910) = exp(minus1003817100381710038171003817119909 minus 11991010038171003817100381710038172120590 ) (17)






119883 (119878) = ((


))

(18)




maxV =0

V119879119878119887VV119879119878119908V (19)







Normal Fault

Training Test

Yes No





new and SPEnew

T2

new lt T2

a

SPEnew lt SPE



















PCA fault diagnosis

0

20

40

60

80

100

120

140

160

180T

2co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(a)

PCA fault diagnosis

0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 400 80 100 120 140 160 180 20060Batch number(b)



20 40 60 80 100 120 140 160 180 2000Batch number

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

(a)


0

20

40

60

80

100

120

140SP

E co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(b)



0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(a)


0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(b)



084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)




7 Conclusions


Competing Interests


Acknowledgments



References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119862119865 = 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879 (9)


120582119881 = 119862119865119881 = ( 1119873 119873sum119894=1

120601 (119909119894) 120601 (119909119894)119879)119881= 1119873 119873sum119894=1

⟨120601 (119909119894) 119881⟩ 120601 (119909119894) (10)



120582 119873sum119894=1

119886119894 ⟨120601 (119909119896) 120601 (119909119894)⟩= 1119873 ⟨120601 (119909119896) 119873sum

119894=1

120601 (119909119895)⟩⟨120601 (119909119895) 120601 (119909119894)⟩ (12)






119905119896 = ⟨119881119896 120601 (119909)⟩ = 119873sum119894=1

119886119896119894 ⟨120601 (119909119894) 120601 (119883)⟩= 119873sum119894=1

119886119896119894 119896 (119909119894 119883) 119896 = 1 119901 (16)


119896 (119909 119910) = exp(minus1003817100381710038171003817119909 minus 11991010038171003817100381710038172120590 ) (17)






119883 (119878) = ((


))

(18)




maxV =0

V119879119878119887VV119879119878119908V (19)







Normal Fault

Training Test

Yes No





new and SPEnew

T2

new lt T2

a

SPEnew lt SPE



















PCA fault diagnosis

0

20

40

60

80

100

120

140

160

180T

2co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(a)

PCA fault diagnosis

0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 400 80 100 120 140 160 180 20060Batch number(b)



20 40 60 80 100 120 140 160 180 2000Batch number

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

(a)


0

20

40

60

80

100

120

140SP

E co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(b)



0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(a)


0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(b)



084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)




7 Conclusions


Competing Interests


Acknowledgments



References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















Normal Fault

Training Test

Yes No





new and SPEnew

T2

new lt T2

a

SPEnew lt SPE



















PCA fault diagnosis

0

20

40

60

80

100

120

140

160

180T

2co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(a)

PCA fault diagnosis

0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 400 80 100 120 140 160 180 20060Batch number(b)



20 40 60 80 100 120 140 160 180 2000Batch number

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

(a)


0

20

40

60

80

100

120

140SP

E co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(b)



0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(a)


0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(b)



084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)




7 Conclusions


Competing Interests


Acknowledgments



References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










PCA fault diagnosis

0

20

40

60

80

100

120

140

160

180T

2co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(a)

PCA fault diagnosis

0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 400 80 100 120 140 160 180 20060Batch number(b)



20 40 60 80 100 120 140 160 180 2000Batch number

0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

(a)


0

20

40

60

80

100

120

140SP

E co

ntro

l lim

its

20 40 60 80 100 120 140 160 180 2000Batch number(b)



0

20

40

60

80

100

120

140

160

180

T2

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(a)


0

20

40

60

80

100

120

140

SPE

cont

rol l

imits

20 40 60 80 100 120 140 160 180 2000Batch number(b)



084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)




7 Conclusions


Competing Interests


Acknowledgments



References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










084083

082081

Pressure (kPa) 5657

5859

140

150

160

170

180

190

Elec

tric

curr

ent (

A)

Temperature (∘ C)




7 Conclusions


Competing Interests


Acknowledgments



References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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