CONTROL ENGINEERING LABORATORY Infotech Oulu and Department of Process
Engineering
Modelling of Pulp Characteristics in Kraft Cooking
Sakari Murtovaara Kauko Leiviskä
Esko Juuso Raimo Sutinen
Report A No 9, December 1999
University of Oulu Infotech Oulu and Department of Process Engineering Control Engineering Laboratory Report A No 9, December 1999
Modelling of Pulp Characteristics in Kraft Cooking
Sakari Murtovaara1, Kauko Leiviskä1, Esko Juuso1 and Raimo Sutinen2
1) Control Engineering Laboratory, Infotech Oulu and Department of Process Engineering,
University of Oulu Linnanmaa, FIN-90570 Oulu, Finland
2) ABB Industry Oy, Systems Group
Tyrnäväntie 14
FIN-90400 Oulu. Finland
Abstract This paper discusses a Kappa-number estimator using different modelling approaches in continuous cooking. Alkaline, total dissolved solids and lignin content are measured on-line from several circulations in a continuous digester. ABB’s Cooking Liquor Analyser (CLA 2000) and an on-line Kappa-number measurement were used in this research. With these measurements it is possible to estimate the blow-line Kappa-number long before the end of the cook and to gain a better understanding on the dependence of the Kappa-number on these variables. The developed models will be used in cooking control to reduce the Kappa-number variation. Artificial neural networks, fuzzy logic, partial least squares method and linguistic equations are used in building a model to map input-output relationships of the measurements. Keywords: Kraft pulping, digester control, neural networks, fuzzy logic, linguistic equations
and liquor analysis. ISBN 951-42-5480-5 University of Oulu ISSN 1238-9390 Infotech Oulu and Department of Process Engineering Control Engineering Laboratory PL 4300 FIN-90014 University of Oulu
1
1. INTRODUCTION
The pulp digester is one of the major unit operations in the pulp mill and its proper control is very important to the pulp production. The cooking should be made to the best quality at minimum cost. Computer control has been applied to continuous digesters since the beginning of 70's. Chip quality variations, measurement problems and long process delays make the control difficult. The main problem is that the desired control variable, the Kappa-number, can not be measured while the cooking progresses. Instead of it various indirect measurements have to be used. A description of the digester control system is given in Sutinen et. al. (1990). In the continuous digester (Fig. 1), pulp is cooked with chemicals (cooking liquor) in a high temperature (about 150 - 170 °C, depending on the wood species and grade requirements). While the cooking progresses inside the digester, some wood components start to dissolve into the cooking liquor. Usually alkali (alkali components of the liquor) is analysed by measuring the conductivity of the liquor sample, solid contents (dry solids) by measuring the refractive index and dissolved lignin by measuring the UV-absorbency of the liquor sample (Haataja et al., 1997).
Liquor toevaporators
Liquorcirculation
Chips andcooking liquor
Pulp to washingWashliquor
Figure 1. Continuous digester. With these measurements it is possible to estimate the development of the Kappa-number long before the end of the cook. The digester process is far from linear and simple input-output system. With these basics in mind a tool for analysing the measurements has to be able to deal with non-linear modelling and multivariable inputs. Different approaches can be used for mathematical modelling of the cooking result (Haataja et al., 1997, Lemmetti et al., 1998, Murtovaara et al., 1998a, b): fuzzy logic (FL), partial least squares method (MRL), artificial neural networks (ANN) and linguistic equations (LE).
2
Partial least squares method is a multivariate regression method suitable for studying the variation in large numbers of highly correlated process variables and relating them to a set of output variables. Neural networks represent non-linear behaviour. The most common ANN architecture is a feedforward network that performs input-output mappings. Backpropagation or Levenberg-Marquardt algorithm is used for learning. Different approaches and development methods can be combined through the linguistic equation framework. The framework provides a unified method for developing and tuning adaptive (fuzzy) expert systems.
3
2. MEASUREMENTS
Measurements that are traditionally used in the Kraft cooking process are temperatures and sometimes alkali measurements (based on liquor conductivity or an automated titrator). The liquor-to-wood ratio of the process is estimated from the chips feed and its moisture content. The final cooking result (Kappa-number) is achieved from the blow line after the digester by using laboratory analysis or an automatic device. So, with existing measurements long delays make it difficult to use feedback or feedforward control to change process conditions for stabilising the Kappa-number. The main control variables are temperatures and alkali concentrations of the digester. By measuring the liquor concentrations from the quench circulation of the impregnation vessel, the transfer circulation after the impregnation vessel, the trim circulation and extracting black liquor flow(s) the Kappa-number can be estimated in different stages of the Kraft cooking process. With a good Kappa-number estimate, control actions can be done before the pulp will reach the blow line of the digester (Haataja et al., 1997). CLA 2000 is an advanced measurement device developed for analysing the chemical pulping process (Sutinen, 1996). It utilises a continuous sampling technique that means also, in practice, a continuous measurement if the analyser is applied to one sampling point. CLA 2000 enables the analysis of alkali concentration and concentrations of total dissolved solids and dissolved lignin during individual batches in a batch digester house or from several cooking circulations in a continuous digester. Measurements are carried out in the actual process concentration and no dilution is needed. Alkali is measured based on conductivity and in the CLA2000 system the temperature compensation is improved as compared with conventional methods (Sutinen, 1996). This is crucial in the digester conditions. Total solids measurement is based on the refractive index and dissolved lignin is measured using UV-absorption at process concentrations. Measurements have shown high accuracy and reliability. In some cases the accuracy exceeds the existing laboratory analysis. The reliability is increased because the measurement system does not have any moving parts that always increase the risk of additional maintenance in demanding conditions as in the digester house (Haataja et al., 1997).
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3. DATA PRE-PROCESSING
A detailed mathematical model is based on a thorough understanding of the nature and behaviour of the actual process. It makes this approach laborious, costly and time consuming, and first of all this knowledge should be available. In many cases the process is too complicated and not completely understood. In these cases it is practical to use a different approach where available process measurements provide the necessary information. CLA 2000 analyser provides that kind of information during the cook, which can be used in modelling. Before the modelling the data has to be pre-processed in some way. From the data the suitable area are selected for modelling and then filtered by wavelet toolbox. First the data has to go through very carefully and draw different plots from data. After that we select data from time range when process has been stabile. In this case the data is selected from same production level. Then usual parameters (average, minimum, maximum, range and standard deviation of data) for the data has been calculated to make sure that there is no error in data. If there is some mismatch in data they have to be corrected or removed from data. The correlation analysis of the data has to done that we can select right variables for modelling. Usually variables, which have a correlation over 0.6 have been selected for the model, but in this case it wasn't possible. If two selected variables have good a correlation to the output variable and also to each other then the other variable can be dropped away model. For the selected variables it is useful to build up a regression model. If this gives good result for correlation and variables it means that selected variables are good for the modelling.
3.1 Data filtering with Matlab Wavelet's Wavelets are a very efficient tool for analysing, compressing, encoding and de-noising signals and data. In this study, the data is analysed and de-noised by using wavelets tools. This is done with Daubechies wavelets (Daubechies, 1992, Misiti, et al.,1996, Strang and Nguyen, 1996). These wavelets have no explicit expression except for db1, which is the Haar wavelet. However, the square modulus of the transfer function of h is explicit and fairy simple. Let where denotes the binomial coefficients. Then: where:
P y C ykN k
k
N k( ) ,= − +=
− 10
1
CkN k− +1
m PN
0
2 2 2
2 2( ) cos sinω
ω ω= � �
���
��
�
��
��
m h ekik
k
N0 0
2 112
( )ω ω= −=
−
(2)
(3)
(1)
5
The support length of ψ and ф (the smoothing function, Mallat and Zhong, 1992) is 2N-1. The number of vanishing moments ψ of is N. Most dbN, are not symmetrical. For some, the asymmetry is pronounced. The regularity increases with the order. When N becomes very large, ψ and ф belong to CµN, since µ is approximately equal to 0.2. This asymptotic value is too pessimistic for a small order of N. Note that the functions are more regular at certain points than at others. The analysis is orthogonal (Misiti, et al., 1996).
Ψ(x) = d ф(x)/dx (4) With db2 the data (Fig. 2) can be filtered better than with median filter, because db2 gives more stable results from data. With a median filter, some oscillations are left. Together db2 and de-noising with thresholds give better accuracy for modelling.
Median vs. db2 filter
16.8
17
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0
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Time
Extr
RI
Orginal db2 Median
Figure 2. Data filtering with db2 vs. median filter.
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4. MODELLING
Different approaches can be used for mathematical modelling of the Kappa-numbers. In this case, we compare linguistic equations and neural networks as tools to convert analyser measurements to Kappa-number prediction. The most important thing in modelling is the quality of data. Too noisy and insufficient data yields poor results and generalisation.
4.1 Modelling with neural networks
A neural network consists of a big amount of simple parallel processing units connected with each other. Each connection between the units has its weight parameter that describes the strength of the connection. The weights are tuned; i.e. the neural network is learning the certain application. Neural networks can represent non-linear behaviour. The most common neural network architecture is a feedforward network that performs input-output mappings. Backpropagation or Levenberg-Marquardt algorithm is used for learning. This method belongs to the group of supervised learning methods and it requires training examples as data sets. Each set or example consists of values for inputs and the desired output. The data set is presented to the network and the weights of network connections are modified to minimise the difference between the desired response and the calculated response. Neural networks are data intensive; i.e. they need a considerable amount of data to get reliable results. They are more or less black boxes and a great care should be taken in defining the reliable operating area of the neural network model. Care should also be taken in designing and testing networks. Separate data sets for training and testing should be used and the generalisation capability of the network should be considered ahead of good correlation in training. Neural networks were tested in Kappa-number prediction already in early stages (Haataja et al., 1997). The results were encouraging. Tested networks were quite small in the sense of number of parameters. There was a good conformity between the measured and estimated Kappa-numbers. Partly surprisingly it was also found out that CLA 2000 measurements from the transfer circulation predicted the final Kappa-number reasonably well.
4.2 Modelling with linguistic equations Different approaches and development methods can be combined through the Linguistic Equation Framework (Juuso and Leiviskä, 1995). The framework provides a unified method for developing and tuning adaptive (fuzzy) expert systems. The original framework has been extended to fuzzy equations and varying fuzzy partitions (Babuska and Juuso, 1995). Actually, the knowledge base and the database are separated in the systems, and therefore, also the tools for them can be separated as well.
7
In the linguistic approach, the fuzzy rules are replaced by linguistic equations (Juuso, 1996)
,01
, ==
j
m
jji XA (5)
where Xj is a linguistic level for the variable j. Levels Xj are calculated by membership definitions from measurements of the corresponding variable j. All variables are handled in the same way, i.e. there is no difference between input and output variables. Rule-based deduction can be replaced by matrix operations by using integers instead of linguistic labels. Varying fuzzy partitions can be handled with real-valued locations of membership function (Juuso, 1999a). Interaction matrix Aij describes the direction of interaction between variables. Large linguistic models can be presented as matrix equation AX = 0 (Juuso, 1996). For example in Kappa model variables are ExtrRI (refractive index), ExtrJK (conductivity), TExtr (temperature in extraction circulation) and Kappa-number (output) from an on-line device. The model can be presented with one interaction matrix. The interaction matrix (A) of the model is [-2 1 -6 -6]. This means, when ExtrRI decreases (-2), ExtrJK increases (1) and TExtr decreases (-6) then Kappa-number will increase (-6) (output variable is moved on the right side of the equation.
[ ] 0
)()()()(
6612
4
3
2
1
1,1
4
1
=
�
����
�
�
−
−−−=+=
numberKappaXTExtrXExtrJKXExtrRIX
BXA jjj
(6)
This model corresponds to a fuzzy model where different partitions are used for different variables. Linguistic levels Xj (Xj is value between -2 and 2) are calculated with the aid of membership definitions (Fig. 3). The membership definitions are developed from the training data set for each variable. They consist of two polynomial functions, one for the linguistic values [-2,0] and the other for the linguistic values [0,2]. The polynomial functions are overlapping at the linguistic value zero. The polynomial functions are developed from the training data by fitting a second order polynomial against the data points. The polynomial must be selected so that the membership definition is always monotonously increasing when the linguistic value moves from –2 to +2. The polynomial regression models are obtained by solving a set of equations (Juuso, 1999b). For example, the measured value for ExtrRI is 17.2, then by using membership definitions we get the linguistic value from figure 3 (-1.5). The linguistic values for other inputs are -1 (ExtrJK) and 1 (TExtr). Vector X is [ -1.5 -1 1 X4]T, where X4 is the linguistic value of the Kappa-number. When we have interaction matrix [-2 1 -6 -6], we can solve the linguistic value of Kappa-number. This interaction matrix is equivalent with normalised vector [-0.228 0.114 -0.684 -0.684].
X4 = -A4\([A1 A2 A3]*[X1 X2 X3]T) X4 = -(-6)\([-2 1 -6]*[-1.5 -1 1]T) = -0.667
8
Then we look again figure 3 and see that at the linguistic value of Kappa-number (-0.667) we get the model output 29.4.
-2 -1 0 1 217
17.2
17.4
17.6
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18ExtrRI
-2 -1 0 1 22.1
2.15
2.2
2.25
2.3
2.35ExtrJK
-2 -1 0 1 2165
166
167
168
169TExtr
-2 -1 0 1 228
29
30
31
32
33KappaBF
Figure 3. Membership definitions. In tuning of the LE model the strength of interactions in the matrix A are modified and/or the membership definitions of the output variable are modified. The strengths of interactions can be integer numbers or real numbers. The tuning of the membership definitions is based on constrained polynomial regression (Juuso, 1998). Because of monotonously increasing polynomial membership definitions, fuzzy systems can be generated on any partition level. Interaction matrix can be determined from expert knowledge or directly from data. If the interaction matrix is determined from data, relations are first defined. Linguistic levels are calculated for all samples. After this the interaction coefficient for one of the variables are set -1. Other interaction coefficients can be calculated with the least squares method by using the relation matrix. The last column of the relation matrix (the last variable) is selected as the output and its interaction is set to -1 (=A4). Thus systems can be presented with following equation (A5 is the bias term) A1X1 + A2X2 + A3X3 + A4X4 + A5 = 0 ⇔ X4 = A1X1 + A2X2 + A3X3 + A5 (7) This expression can be presented with following equation
y = xb (8) The interaction coefficients (regression vector b = y\x, left division of y into x) are calculated using the least squares method.
9
5. RESULTS AND DISCUSSION
CLA 2000 analyser measured cooking liquor from the extraction and transfer circulation. The modelling was based on the extraction flow measurements (conductivity (JK) and refractive index (RI)), temperature in extraction circulation, and the measurement of Kappa-number from an on-line device. The first data was collected between February and May in 1997. The data (1263 measurements) was collected from the different time periods, when the production rate has been around 900 tons a day. Some corrections to the data has been done. If successive measurements deviated more than twice the standard deviation, they have been replaced by the mean values of two earlier and two following measurements. Statistical properties of data are shown in Table 1 and the correlation matrix is in Table 2. The correlation between Kappa and ExtrRI (-0.32), and between Kappa and ExtrJK (0.016) are not good. But in the earlier research has shown that it is still reasonable to use measurements from extraction circulation (RI, JK and TE) in the modelling, because they describe better the state of the process. Before the modelling the regression analysis was made for the selected variables. It gave acceptable result for the modelling (Table 3). Then data was divided into training (600 measurements) and testing data (600 measurements). Also histograms for input data were drawn (Fig. 4 and 5). Table 1. Statistical parameters.
ExtrRI ExtrJK TExtr KappaStd. 0.25 0.04 0.51 1.55Average 17.51 2.23 167.49 29.68Range 1.51 0.24 3.2 9.9Minimum 16.70 2.12 165.4 25.7Maximum 18.21 2.36 168.6 35.6 Table2. Correlation matrix.
A/W-R L/W-R TTop ExtrRI ExtrJK Hfact FExtrLow FExtrUp FExtrTOT TExtr KappaA/W-R 1L/W-R 0.539 1.000TTop 0.603 0.510 1.000ExtrRI -0.066 -0.008 0.041 1.000ExtrJK 0.088 0.193 -0.172 -0.016 1.000Hfact 0.292 0.251 0.517 0.021 -0.235 1.000FExtrLow -0.093 0.165 -0.115 0.065 0.029 0.043 1.000FExtrUp 0.411 0.361 0.486 -0.164 0.102 0.239 -0.213 1.000FExtrTOT 0.268 0.297 0.332 -0.145 0.114 0.258 0.123 0.943 1.000TExtr 0.465 0.395 0.679 0.247 -0.256 0.415 -0.027 0.220 0.215 1.000Kappa -0.337 -0.335 -0.458 -0.318 0.064 -0.240 0.208 -0.046 0.016 -0.590 1.000 Table 3. Regression analysis. Regression StatisticsMultiple R 0.62095627R Square 0.385586689Adjusted R S 0.384121474Standard Erro 1.213191448Observations 1262
ANOVAdf SS MS F Significance F
Regression 3 1161.985579 387.3285263 263.160561 1.5395E-132Residual 1258 1851.566529 1.471833489Total 1261 3013.552108
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95,0%Upper 95,0%Intercept 342.5756544 12.2292005 28.01292321 1.369E-134 318.5837628 366.5675 318.5838 366.5675ExtrRI -1.038027089 0.132347049 -7.843220509 9.3158E-15 -1.297672522 -0.778382 -1.297673 -0.778382ExtrJK -2.922897733 0.798094996 -3.662343141 0.0002603 -4.48864266 -1.357153 -4.488643 -1.357153TExtr -1.720643867 0.071703632 -23.99660672 4.446E-105 -1.861315841 -1.579972 -1.861316 -1.579972
10
ExtrRI
0
50
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250
17 17.25 17.5 17.75 18 18.250 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
frequencycumulative
Figure 4. Histogram of variable ExtrRI for the training data.
TExtr
0
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250
165.5 166 166.5 167 167.5 168 168.5 1690 %
10 %
20 %
30 %
40 %
50 %
60 %
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frequencycumulative
Figure 5. Histogram of variable TExtr for the training data. Another data set was collected during one week period where the production rate was about 1170 tons a day. There were 320 suitable measurements, and their statistical parameters are shown in Table 4. This data was used in testing ANN and LE (Chapter 4.2) and the first data
11
was for training. Data analysis was made also for these measurements. Figures 6 and 7 present histograms of Kappa-number and ExtrRI for the test data. Table 4. Statistical parameters.
ExtrRI ExtrJK TExtr Kappa ProductionStd. 0.2316 0.0209 0.449 0.885 14Average 17.390 2.225 166.93 30.33 1171Range 0.87 0.16 2.3 4.5 52Minimum 17.01 2.15 165.9 28.0 1148Maximum 17.89 2.32 168.3 32.5 1199
ExtrRI
0
10
20
30
40
50
60
70
80
90
100
17.1 17.3 17.4 17.5 17.6 17.7 17.8 17.90 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
frequencycumulative
Figure 6. Histogram of variable ExtrRI for the test data.
Kappa
0
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80
28 28.5 29 29.5 30 30.5 31 31.5 32 32.5 330 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
frequencycumulative
Figure 7. Histogram of variable Kappa-number for the test data.
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5.1 Early testing of LE models A multimodel approach has been developed for combining several specialised submodels (Juuso, 1996). Output of each linguistic equation model is a vector of singleton values. Singleton values of each output variable are aggregated by weighted average. Working point variables define the weights of the submodels. The calculation of the weights can be a very complex system, e.g. the web break indicator (Juuso et al. 1998), or a simple fuzzification procedure. For linguistic equation modelling, the data was filtered to suit FuzzEqu toolbox ( Juuso, 1998) implemented in Matlab®. The input variables were extraction refractive index (ExtRI), extraction conductivity (ExtJK) and temperature (TExtr). Membership definitions were generated from training data in two ways: for a single model (general) the whole data set was used; for the multi-area model approach the data was divided into low (low area), normal (normal area) and high Kappa-number area (high area). Linguistic equations were generated separately for each Kappa-number area. Membership definitions (Fig. 8) for the output variable were tuned for each submodel. This way each area model works properly in a wide Kappa-number range. Tuning is based on solving linear equation system for coefficients of the second order polynomials in the least squares sense (Juuso, 1999b)
-2 -1 0 1 217
17.2
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18ExtrRI
-2 -1 0 1 22.1
2.15
2.2
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2.35ExtrJK
-2 -1 0 1 2165
166
167
168
169TExtr
-2 -1 0 1 228
29
30
31
32
33KappaBF
Figure 8. Membership definitions for the general model. In this application, there are three submodels and each submodel is presented by one equation. The resulting Kappa-number is a weighed average of the results of two submodels. The weights are calculated from linguistic levels obtained from the general model. In the training, each area model was tested as a single model. The general model with [-2 1 -3 -4] interaction matrix worked quite well, but the accuracy was a little bit poor in the middle of the Kappa-number area. The normal and the high area models operated very well generally. Performance of the low area model was quite poor because of very limited training data. The functioning of the high area model with [-2 1 -3 -5] interaction matrix was not so good at the lower level as functioning of the normal area model. In the multimodel case, we can take into
13
account the benefits of the different area models, but additional data is still needed especially for the low area model. The correlation of the normal area model was 0.743 for training data. For the general model it was 0.741. The normal model with [-2 1 -6 -6] interaction matrix improved the correlation although some data points were outside the operating area of the model (Fig. 9).
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pa
Estimated KappaKappa On-line
Figure 9. Kappa-number estimation by the general model for training data. In the testing, the normal area model with [-2 1 -3 -4] interaction matrix works well, but the difference to the general model was very small. The accuracy of the high area model was not on an appropriate level for wider use. The performance of the low area model was poor. Figure 10 shows an estimate obtained by the normal area model from extracting circulation measurements in continuous digester. Performance of the normal area model was generally very good when considering the amount of the training data is taken into account. In the testing, the correlation was 0.65 and 0.647 for the normal and general model, respectively. The correlation was about the same as for the general model. The largest errors were again in the cases, which were outside the operating area.
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pa
Kappa On-lineEstimated Kappa
Figure 10. Kappa-number estimation by the general model in a continuous digester (test data).
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The research has proven that fuzzy logic and linguistic equations are suitable for Kappa-number modelling. The results are more than promising. For the whole range, the multimodel approach is not yet able to improve results, because of limitations of the high and the low area models.
5.2 Comparing LE and Neural Network models The training data (1200 measurements, first data) was selected from different time periods where production rate was 900 tons/day. In LE methods the membership definitions (Fig. 11) and interaction matrix were re-tuned. For the testing, data (320 measurements, second data) was from a single time period when the production rate was 1170 tons/day. Root mean square error (RMS) and correlation factor describe the performance of each model. ANN model was based on a feedforward network. For training Levenberg-Marquardt algorithm was used. In a model there were two hidden layers and each layer consisted of four neurons. ANN model reached 0.72 correlation in training and 0.63 in testing. RMS for model was 0.94 in training and 0.96 in testing. Figures 12 and 13 show the estimated Kappa-number and the measured on-line Kappa-number.
-2 -1 0 1 217
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ExtrRI
Linguistic Level -2 -1 0 1 2
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ExtrJK
Linguistic Level
-2 -1 0 1 2165
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TExtr
Linguistic Level -2 -1 0 1 2
26
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34
KappaBF
Linguistic Level
Figure 11. Membership definitions for LE-model. The result of the ANN model is quite well as such, but usually after a little while the model performance is decreasing, because in the Kraft cooking process conditions are changing. In process operation, the ANN model has to be adapted to work properly for a longer period, i.e. it has to be re-trained. ANN models are suitable for processes, in which the process conditions are very stable and there is a lot of data available for training.
15
Kappa prediction with LE-model and FFNET-model
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Orginal LE FFNET
Figure 12. Kappa prediction with training data.
Kappa prediction with LE-model and FFNET-model
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3:30 11:30 19:30 3:30 11:30 19:30 3:30
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Orginal LE FFNET
Figure 13. Kappa prediction with testing data. LE models were done with FuzzEqu Toolbox. The best results were achieved in training with [-2 1 -6 -6] interaction matrix. In training, the correlation was 0.76 and RMS 0.89. For testing, the correlation was 0.72 and RMS 1.06. Figures 12 and 13 show the estimated Kappa-number and on-line Kappa-number.
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The functioning of the LE model is very promising. The LE model (Fig. 14) works better than the ANN model and it is more suitable for Kappa-number estimation than the ANN model (Fig. 15), because it is not that sensitive for changes in the process conditions. All LE models were simulated in Matlab’s Simulink®-environment (Fig. 16). In the future, the model adaptation has to be taken into account. Since only five parameters are needed for each variable, the LE system can be adapted to various operating conditions (Juuso, 1999a).
1717.2
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17.818
2.1
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2.431
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ExtrRI
Kappa prediction in temperature 166
ExtrJK
Kappa
Figure 14. The LE model output surface for Kappa-number at temperature 166 °C. The quality of the data is the most important thing in modelling. Always the data has to be filtered in some way and process delays should be compensated for. Measurements have to be reliable. Therefore, the analyser or the measurement equipment has to be calibrated and regularly maintained. If the calibration is forgotten when changes have been done to the analyser, measurements can be at the different level than before.
17
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2.427
28
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Kappa prediction in temperature 166
ExtrJK
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Figure 15. The ANN model output surface for Kappa-number at temperature 166 °C.
Figure 16. Simulink testing environment.
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6. CONCLUSIONS
This paper compares neural networks and linguistic equations in modelling the Kappa-number in continuous digesters. In training, both methods seem to learn the process behaviour in a similar manner. Differences come out in using the models in process environment. Neural network models are suitable for processes where process conditions are very stable and there is a lot of data available. The LE model works better and it is more suitable for the prediction of the Kappa-number, because it is not so sensitive for changes in process conditions. Linguistic equations offer also tools for modelling the system in several operating points and thus developing adaptive models. Since only five parameters are needed for each variable, the LE system can be adapted to various operating conditions. The possibilities to use Kappa-number prediction in continuous digester control are different in each control system and process. Analyser measurements can be utilised in selective alkali dosage and residual alkali control as well as in solids profile control when the process makes it possible. The quality of the data is the most important thing in modelling. Data has to be filtered always in some way, and the measurements have to be reliable. Therefore, the analyser or the measurement equipment has to be calibrated and regularly maintained.
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