PCA and neural networks-based soft sensing

Journal of Experimental & Theoretical Artificial Intelligence Vol. 23, No. 1, March 2011, 127–136

PCA and neural networks-based soft sensing strategy with application in sodium aluminate solution Wei Wanga*, Wen Yub, Lijie Zhaoc and Tianyou Chaia a

Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang 110004, Liaoning Province, China; bDepartamento de Control Automatico, CINVESTAV-IPN, Mexico D.F., Mexico; cInformation Engineering School, Shenyang Institute Of Chemical Technology, Shenyang 110142, Liaoning Province, China

Downloaded By: [Wang, Wei] At: 02:32 19 February 2011

(Received 15 December 2008; final version received 10 April 2009) Component concentration of sodium aluminate solution is an important quality index for alumina production. In this article, we propose a new on-line soft sensing strategy for measuring component concentration of sodium aluminate solution. With this method, on-line control can be realised in aluminate production plants. Several advance techniques are used, such as principal component analysis (PCA), neural modelling and the least square algorithm. Industry experiments are conducted in the alumina production process and the results show the effectiveness of this method. Keywords: principal component analysis; neural modelling; soft sensing; sodium aluminate solution

1. Introduction Sodium aluminate solution is used almost in all sections in the alumina production process, and the measurement of component concentration for sodium aluminate solution plays a significant role in alumina production. The main quality indexes of sodium aluminate solution are caustic hydroxide and alumina. At present, its analysis mainly depends on manual timed sampling and titration in a chemical laboratory. The manual titration could be very accurate if all the procedures are performed with much care and by experienced analysts. Its main drawbacks are the long sampling interval, complicated procedure, necessary dilution before the titration, heavy reliance on operator’s experience, and the results of titration do not contribute to guiding production on time. Therefore, the real-time measurement for the component concentration of sodium aluminate solution is an important problem. Many methods have been explored to solve the above problem, for example photometric (Danchik and Oliver 1970), thermometric (Van Dalen and Ward 1973), potentiometric (Kowalski and Kubiak 1982) and micro-titration (Tan, Zhang, and Xiao 1999) method. However, most of them are based on traditional acid–base titration principles with different end-point detection technique and the measurements are off-line.

*Corresponding author. Email: [email protected] ISSN 0952–813X print/ISSN 1362–3079 online ß 2011 Taylor & Francis DOI: 10.1080/0952813X.2010.506296 http://www.informaworld.com


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Though several on-line devices are developed (Ferenc, Otto, and Bela 1982), there is difficulty in directly applying them in China for the low precision caused by the obvious character change of bauxites at home and abroad. With the advances in computer technology and instrumentation techniques, large amount of data from chemical processes is collected and computational intelligence methods are widely used for data processing and concentration measurement. For instance, bilinear interpolation and the least mean squares technique have been used to calculate a look-up table to evaluate the measurand of a sensor pair (Flammini, Marioli, and Taroni 1999). Mechanism analysis with the physical parameters of liquids such as conductivity, ultrasonic velocity, permittivity and so on has been used for concentration sensor (Henning, Daur, and Haceptmann 2000; Wei and Shida 2002). A reconstruction algorithm based on the natural cubic spline interpolation and artificial neural network approach is developed to estimate the concentration of NaCl and sucrose (Wei and Shida 2006). According to the physicochemical characters of sodium aluminate solution, a soft sensing strategy by measuring the temperatures and conductivities of the solution is proposed for estimating the component concentration. Through plenty of experiments, it has been proven that a certain proportion of sodium aluminate solution exists in a linear relation between its temperature and conductivity. A mechanism model is used to calculate the component concentration of sodium aluminate solution. A compensation model based on PCA and neural networks is used to compensate for the unknown modelling dynamics not included in the mechanistic model. Industrial application and experiment results demonstrate that the proposed soft sensing strategy can predict component concentration of sodium aluminate solution accurately.

2. Process description Alumina production aims to convert bauxite to alumina. The Bayer alumina production techniques is shown in Figure 1. It consists of original ore pulp batching, high-pressure digestion, seed decomposition, evaporation, roasting and so on. In the procedure of original ore pulp batching, sodium aluminate solution is mixed with bauxite and lime into original ore pulp, which plays an important role in alumina production. The quality of the original ore pulp processing directly affects the indexes of high-pressure digestion and the other subsequent procedures. Therefore, on-line measurement of component concentration in sodium aluminate solution becomes a very important task in the original ore pulp batching procedure, and it is required for close-loop control and operation optimisation of the addition amount of sodium aluminate solution.

3. Soft sensing for the component concentration of sodium aluminate solution 3.1. Soft sensing strategy According to the physical and chemical characters of sodium aluminate solution, the conductivity is a nonlinear function of temperature, caustic hydroxide and alumina (Browne and Finn 1977), which is formulated as d ¼ f ðT, cK , cA Þ,

ð1Þ

Journal of Experimental & Theoretical Artificial Intelligence

Ore crushing

Original ore pulp batching

Sodium aluminate solutions

Bauxite Lime

129

cK , c A

Titrimetric analysis

Sampling

Pump Artificial laboratory analysis

High-pressure digestion Sodium aluminate solutions

NaOH solution

Seed decomposition Causticisation


Al( OH )3 Separation and washing

Washings Alumina

Al (OH )3 Roasting

Mother liquid

Evaporation

Circulating mother liquid

Figure 1. The flowchart of Bayer alumina production.

where f () is a nonlinear function, d is the conductivity of sodium aluminate solution, T is temperature, cK is the concentration of caustic hydroxide and cA is the concentration of alumina. If the changes of temperatures and conductivities are observed, the concentration changes of sodium aluminate solution can be known. Some experiments are designed to measure the temperature and conductivity from different component concentration of sodium aluminate solution for their relationships. Experiment results with conductivity, temperature, caustic hydroxide and alumina content are shown in Figure 2. A conclusion is derived that conductivity is a function of temperature, caustic hydroxide and alumina content of sodium aluminate solution. In general, conductivity increases with temperature and caustic hydroxide content and decreases with alumina content if the other parameters are held constant. For a certain proportion of sodium aluminate solution, the temperature and conductivity have such a relation which is similar to a straight line (Browne and Finn 1981). It can be described by formula as follows: d ¼ kðcK , cA ÞT þ bðcK , cA Þ,

ð2Þ

where k is the slope, b is the intercept of the straight line and k and b are nonlinear function of cK and cA. A hybrid on-line soft sensing strategy is proposed, as shown in Figure 3. The proposed method is composed of a mechanism model and a neural network error compensation model. y is the artificial laboratory value, yˆm is the value of mechanism calculate model, e ¼ y yˆ m is the error between them and eˆ is the output of neural network compensation model. The output of this hybrid intelligent soft sensing model can be described as follows. y^ ¼ y^m þ e^

ð3Þ

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W. Wang et al. 800 700

d(ms/cm)

600 500

cK =208.8, cA =95.86 cK =208.8, cA =124.1 cK =251.2, cA =95.86 cK =251.2, cA =124.1

400 300

cK =200.0, cA =110 cK =260.8, cA =110 cK =230.0, cA =90 cK =230.0, cA =130 cK =230.0, cA =110

200 100 40

50

60

70 T(°C)

80

90

100

Chemical analysis

Data sampling and preprocessing

The device of measuring

The process of alumina production


Figure 2. Temperature vs. conductivity curves for a certain sodium aluminate solution.

Artificial laboratory value

Mechanism model of sodium aluminate solution

PCA-NN based error compensation model

.

yˆ m

yˆ

+ +

yˆ m y

eˆ –

–

+e

+

Figure 3. Structure of the soft sensing strategy.

3.2. Mechanism model According to formula (2), least squares linear regression of k against cA at each value of cK and b against cA at each value of cK yield equation of the form @k cA þ k0 k¼ ð4Þ @cA cK @b c A þ b0 b¼ ð5Þ @cA cK with a high degree of correlation. This yielded coefficients at each level of cK. It was found that regression of these coefficients against cK give the best fit when a quadratic least squares regression was used. This yielded equations of the form @k ¼ K1 cK 2 þ K2 cK þ K3 @cA

ð6Þ


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k0 ¼ K4 cK 2 þ K5 cK þ K6

ð7Þ

@b ¼ B1 cK 2 þ B2 cK þ B3 @cA

ð8Þ

b0 ¼ B4 cK 2 þ B5 cK þ B6

ð9Þ

Then on substitution of (6), (7) into (4), and (8), (9) into (5) yields k ¼ ðK1 cK 2 þ K2 cK þ K3 ÞcA þ ðK4 cK 2 þ K5 cK þ K6 Þ

ð10Þ

b ¼ ðB1 cK 2 þ B2 cK þ B3 ÞcA þ ðB4 cK 2 þ B5 cK þ B6 Þ

ð11Þ

From (10) and (11), cA is calculated by the formula


cA ¼

ðk bÞ ½ðK4 B4 Þc2K þ ðK5 B5 ÞcK þ ðK6 B6 Þ ðK1 B1 Þc2K þ ðK2 B2 ÞcK þ ðK3 B3 Þ

ð12Þ

and a univariate equation of higher degree for cK is as follows: ðB1 K4 K1 B4 Þc4K þ ðB1 K5 þ B2 K4 K1 B5 K2 B4 Þc3K þ ½ðbK1 K1 B6 K2 B5 K3 B4 Þ ðkB1 B1 K6 B2 K5 B3 K4 Þc2K þ ½ðbK2 K2 B6 K3 B5 Þ ðkB2 B2 K6 B3 K5 ÞcK þ ðbK3 K3 B6 kB3 B3 K6 Þ ¼ 0 ð13Þ Simplifying (12) and (13), we get cA ¼

ðk bÞ ðn4 c2K þ n5 cK þ n6 Þ n1 c2K þ n2 cK þ n3

ð14Þ

c4K þ m1 c3K þ ðm2 k þ m3 b þ m4 Þc2K þ ðm5 k þ m6 b þ m7 ÞcK þ ðm8 k þ m9 b þ m10 Þ ¼ 0 ð15Þ The undetermined coefficients mi (i ¼ 1, . . . , 10), nj ( j ¼ 1, . . . , 6) are identified by the training data cK, cA, k, b. cK can be calculated from formula (15), cA will be known when cK is substituted into formula (14).

3.3. Error compensation model based on PCA and neural networks As errors exist in the mechanistic model, a compensation model is needed. The input data has linear relationship, so PCA is used to remove collinearity. While deriving statistics, PCA technique is used for simplifying a dataset, by reducing multi-dimensional datasets to lower dimensions for analysis. It is a standard data reduction technique which extracts data, removes redundant information, high lights hidden features and visualises the main relationships that exist between observations. Unlike other linear transform methods, PCA does not have a fixed set of basis vectors. Its basis vectors depend on the dataset, and it has the additional advantage of indicating what is similar and different about the various models created. It has been widely used in data compression and feature extraction. The PCA finds the direction in space along which the variance of the data is the largest. This direction is called the first principal component. The second principal

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t1 t2

ecK

PCA

tm

ecA

yˆmcK yˆ mcA


Figure 4. The structure of error compensation model based on PCA and NN.

component is the direction in space orthogonal to the first principal component, which describes maximum variance not covered by the first principal component, and so on. The data matrix is decomposed by the PCA into a product of a loading matrix PT and of a sore matrix T and a matrix containing the residuals E (Liu, Yi, and Yang 2007, Ho and Wu 2009): X ¼ TPT þ E

ð16Þ

where T ¼ [t1, t2, . . . , tm] are score vectors and P ¼ [ p1, p2, . . . , pm] are loading vectors. Back propagation neural networks are analogous to the computational models of the brain. The modelling based on neural network is one of the identification techniques to determine a model of a system according to the observed inputs and outputs signals to the system. Identification is necessary when there is no sufficient information about the system for it to be accurately modelled by mathematical modelling approaches. It is believed that with sufficient hidden neurons and using some special training or learning algorithm based on the known input and output data set for adjusting or training the strengths of the connections and the biases to the neurons until a stopping criterion is met, a neural network can approximate arbitrary mapping or function (Antony, Zhou, and Wang 2006; Gonzaga, Meleiro, Kiang, and Filho 2009), so neural networks are chosen to compensate the unknown mechanism model errors. Combining with the advantages of PCA and neural network, an error compensation model based on PCA and neural network is proposed, as shown in Figure 4. The PCA inputs are heating, cooling, mixing temperatures T1, T2, T3 and conductivities d1, d2, d3. PCA is used as a data pretreatment tool, and it compresses the independent variables into fewer principal components which are used as input variables for the neural network. The neural network inputs are PCs from PCA and the mechanism calculation values yˆ mcK, yˆ mcA, and the neural network outputs are the errors from the mechanism calculation values and real laboratory analysis values. The predicted results of neural network are used to compensate the errors of mechanism model. 4. Industrial experiment According to the proposed soft sensing strategy, a measurement device is developed, as shown in Figure 5. First, sodium aluminate solution enters into the sampling device, dealt with heating, cooling and mixing. Then conductivity analysers measure the temperatures and conductivities, and transmit them to the PLC controller. At last, the data is

133


ycK ycA Temperature, conductivity Signal of instruction

PLC controller

Temperature, conductivity Conductivity analyser

Signal of instructions

Computer for calculating concentration


Sampling device

Inlet of solution

Outlet of solution

Figure 5. The measurement device of sodium aluminate solution.

Table 1. Stylebook data of the process for alumina production. Variables

1 Group

2 Group

3 Group

...

449 Group

450 Group

T1( C) d1(ms/cm) T2( C) d2(ms/cm)

89.30 566.88 73.20 455.08

87.65 594.84 75.52 504.38

91.17 553.05 72.83 421.95

... ... ... ...

88.94 549.06 72.03 398.91

91.42 584.61 66.03 417.66

transmitted to the computer which is used to implement the proposed strategy and calculate the component concentration of sodium aluminate solution. The measurement device is installed in the industry field, and median average filter method is used to deal with the collected data. Partial of the 450 groups of sampled data are listed in Table 1, among them 250 groups are used for training and 200 groups are used for predicting. The parameters in formula (15) which identified by the training data are as follows: c4K 459:34c3K þ 3:01bc2K þ 84:09kc2K þ 23840365:11cK 111533:18b 3912127:71k 2691569213:10 ¼ 0

ð17Þ

Imaginary roots are excluded, and the range of real roots is 190–260. If there are two roots satisfying this condition, retain the one closer to the last calculated value. The parameters in formula (14) are as follows: cA ¼

ðk bÞ ð0:18022c2K 60:643cK þ 5074:9Þ 0:0027749c2K 1:1637cK þ 121:4

ð18Þ

PCA is used to extract the score vectors from the inputs of temperatures and conductivities. Based on cross-validation, three factors t1, t2, t3 are sufficient for extracting

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Caustic hydroxide

240 230 220 210 200 Measured

PCR

NN

100 Data

120

Mechanism

Mechanism+PCA-NN

190 0

20

40

60

80

140

160

180

200

160

180

200

Figure 6. The predicted results of caustic hydroxide. 130 Measured

PCR

NN

Mechanism

Mechanism+PCA-NN

120 Alumina


125 115 110 105 100 95 90 0

20

40

60

80

100 Data

120

140

Figure 7. The predicted results of aluminate.

the relevant information. Including the mechanism calculation value yˆmcK and yˆ mcA, there are five inputs for the neural network. The mechanism model errors are used as the outputs for training the neural network and 11 hidden layer nodes are selected. Finally, the well-trained network is used to predict. Compare the proposed method with other methods, the measured values and predicted values, as shown in Figures 6 and 7. From the comparison of the curves, PCR method has poor accuracy, and it cannot follow the trend of concentration changes. NN is better than PCR and has good approximation capability. Mechanism model reflects the internal relation and good effect is achieved by using the error compensation model based on PCA and neural network. The accuracy of the proposed method is relatively high and fulfils the industrial requirements in alumina production. The prediction accuracy of these methods are shown in Table 2. Among them there is MSE defined as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X ð19Þ ^ yðkÞÞT ðyðkÞ ^ yðkÞÞ ðyðkÞ MSE ¼ t N k¼1


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Table 2. MSE of different methods.

Method

PCR

Neural network

Mechanism

Mechanism and PCA-NN

MSEcK MSEcA

9.00 10.29

7.43 5.52

5.24 8.25

2.35 3.41


5. Conclusion For the alumina production process, a hybrid soft sensing strategy is proposed for measuring the component concentration of sodium aluminate solution. The soft-sensing strategy is composed of a mechanism model and an error compensation model based on PCA and neural network. It provides a new on-line approach to measure the component concentration in the process of alumina production. The industrial experiment results indicate that the prediction accuracy of this method is relatively high and fulfils the industrial requirements, and it is shown that the proposed soft-sensing strategy has a high potential of being used to realise an effective control of the whole process in the alumina production.

Acknowledgements This work is supported by the Chinese National Hi-Tech Development Program (No. 2006AA040307); The 111plant of Ministry of Education of China (B08015); Research Foundation of Ministry of Education of China (No. 308007) and Research Foundation of Education Department of Liaoning Province (05L346).

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PCA and neural networks-based soft sensing

PCA and neural networks-based soft sensing

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