The Application of Back Propagation Neural Network of Multi-channel ...
Tamkang Journal of Science and Engineering, Vol. 5, No. 4, pp. 209-217 (2002)
209
The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor for Mixed Organic Vapours Ping Chang and Jeng-Shong Shih* Department of Chemistry National Taiwan Normal University Taipei, Taiwan 116, R.O.C. E-mail: [email protected]
Abstract A multi-channel piezoelectric quartz crystal sensor with a homemade computer interface was prepared and employed in the present study to detect mixture of organic molecules. Back propagation neural network (BPN) was used to distinguish the species in the mixture organic molecules and multivariate linear regression analysis (MLR) was used to compute the concentration of the species. A six-channel piezoelectric sensor detecting organic molecules in static system was investigated and discussed. Amine, carboxylic acid, alcohol and aromatic molecules can easily be distinguished by this system with back propagation neural network. Furthermore, the concentrations of the organic compounds were computed with an error of about 10% by multivariate linear regression analysis (MLR). Detection of organic mixture with amine, carboxylic acid, alcohol and aromatic molecules by this method also had good qualitative and quantitative results. In order to achieve better distinguishability, change of fault-tolerance in back propagation neural network was also investigated and discussed in this study. Key Words: Pizoelectric Crystal, Multichannel Sensor, Organic Vapours, Back Propagation Neural Network, Linear Regression Analysis
1. Introduction It is well known that the use of gas sensor array and pattern recognition analysis has the advantage in identifying odors, organic molecules and gases because of poor selectivity of a lot of other gas sensors [1-5]. The qualitative and quantitative analysis of a gas mixture with non-selective sensor elements is achievable with a combination of several different sensor elements in an array. Piezoelectric quartz crystals were very sensitive for the changes in mass [6-12]. By coating some special materials on the surface,
the frequency of the crystal can be decreased by adsorbing targets on the crystal's surface. The relationship derived for quartz crystals (AT-cut) vibrating in the thickness shear-mode is as follows [13,14]: ∆F = -2.3 × 10 6 · f2 · ∆m/A (1) ∆F Where is the frequency shift due to the coating, f (MHz) is the frequency of quartz crystal, ∆m (gram) is the mass of deposited coating and A (cm2 ) is the area coated. Principal component analysis (PCA), a well-known technology of statistics, is useful in selecting the classic independents of all
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materials [15]. We can easily differentiate different analytes by takeing a view of the profile discrimination with the responses of several channels in a plot. However, it is necessary to distinguish the different gases by sensor array without subjective judgment in many cases. Therefore, using of computer for the study is the best choosing. Can a computer smart as a human being? Artificial neural network (ANN) capacitates a computer the ability of learning and thinking. Chemical sensors were developed for an artificial nose in the past decade [16]. The application of ANN method proved to be particularly advantageous if the measured property is not connected exactly to the signal of the transducers of sensors. The optimum structure of neural network is determined by a trial and error method. Back propagation neural network (BPN) is the most popular technology of the chemical sensor array. The back propagation method is part of the parallel distributed processing system [17]. One-layer networks like Hopfield and Kohonen structure, and multi-layer systems like counter propagation and back propagation of errors, can be used for chemical applications. Backpropagation refers to the method for computing the gradient of the case-wise error function with respect to the weights for a feedforward network which is straightforward and elegant application of the chain rule of elementary calculus. By definition, backpropagation or backprop refers to a training method that uses backpropagation to compute the gradient. In other words, a backprop network is a feedforward network trained by backpropagation [18]. In this study, qualitative analysis of the analytes (mixture gas) was done by using PZ sensor array and BPN. Three layers network structure of BPN was established and three units of hidden layer were used. Furthermore, the concentration of each compound of the gases was computed by MLR.
2. Experimental 2.1 Crystal Coating Piezoelectric crystals used were AT-cut spherical quartz crystals, with a radius of 4.0 mm and a thickness of 0.18 mm with a basic
resonant frequency of 10 MHz and were provided with silver-plated metal electrodes on both sides (Taiwan Crystal Co.). The crystals were coated with the prepared solution via dropping method with a microsyringe. An aliquot of 2 mL of the prepared coating solution was dropped onto one side of the quartz crystals. After evaporation of the solvent, differently functioning PZ crystals were obtained. The coating materials selected with PCA were polyvinyl alcohol, fullerene, polystyrene, stearic acid, polyethylene adipate and polyvinyl pyrrolidene [8]. 2.2 Apparatus Figure 1 depicts the experimental setup of a piezoelectric quartz crystal detection system with an assembled computer interface. The multi- channel PZ sensor connected with an oscillator system was placed in a glass cell. Organic liquid was injected into the injecting port which incudes a heat plant. A home-made computer interface, including an oscillator, Altera programmable logic devices, a standard crystal and a programming peripheral interface (PPI 8255) was prepared for frequency to digital conversion. The Altera was designed with a 24 bits counter and 24 bits register to treat the 10 MHz frequency and no frequency mixing was used. Therefore, the true frequencies were obtained and hence the errors were reduced [15]. Data processing and signal acquisition were automatically performed on a microcomputer (PC/AT) with a program in Qbasic. The MLR is done with the commercial statistical software package SAS and the back propagation neural network (BPN) is a program written in Qbasic. Oscillation circuit and Ferquency counter
Sample
Injecting port
Flow controller
Heater Multi-channel sensor
Nitrogen
Figure 1. Experimental setup of detection system with an assembled computer interface
The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor for Mixed Organic Vapours
BPN program
Training process: Step 1. Design the structure of neural network and input parameters of the nertwork . Step 2. Get initial weights W and initial θ values from randomizing. Step 3. Input training data matrix X and output matrix T. Step 4. Compute the output vector of each neural units. (a) Compute the output vecter H of the hidden layer (2) net k = ∑ Wik X i − θ k Hk = f ( netk ) (3) (b) Compute the output vecter Y of the output layer net j = ∑ Wkj Hi − θ j Yj = f ( net j ) Step 5. Compute the distances d (a) Compute the distances d of the output layer δ j = ( Tj − Yj ) • f ' ( net j ) (b) Compute the distances d of the hidden layer δ k = ( ∑ δ jWkj ) • f ' ( net k )
(4) (5)
(6) (7)
j
Step 6. Compute the modification of W and θ ( η is the learning rate) (a) Compute the modification of W and θ of the output layer ∆Wkj = ηδ j H k ∆θ j = − ηδ j (b) Compute the modification of W and θ of the hidden layer ∆Wik = ηδ k X i ∆θ k = − ηδ k Step 7. Renew W and θ (a) Renew W and θ of the output layer Wkj = Wkj + ∆Wkj
θ j = θ j + ∆θ j
(b) Renew W and θ of the hidden layer Wik = Wik + ∆Wik
θ k = θ k + ∆θ k
(8) (9) (10) (11) (12) (13) (14) (15)
Step 8. Repeat step 3 to step7 until convergence. Testing process: Step 1. Input the parameters of the network. Step 2. Input the W and θ Step 3. Input an unknown data matrix X Step 4. Compute the output vector (a) Compute the output vector H of hidden layer net k = ∑ Wik X i − θ k Hk = f ( netk ) (b) Compute the output vecter Y of the output layer net j = ∑ Wkj Hi − θ j
Yj = f ( net j )
(16) (17)
(18) (19)
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3. Results And Discussion In this study, a 6-3-4 network structure was used as shown in Figure 2. The response of six coated (polyvinyl alcohol, fullerene, polystyrene, stearic acid, polyethylene adipate and polyvinyl pyrrolidene) PZ crystals was the input layer matrix of the network. First, pure organic gases such as toluene, butanol, butyl amine and acetic acid was analyzed by this system. 40 training examples and 20 testing examples were prepared for training and testing the network respectively. In the BPN network, the problem of classification had been solved. On the other words, using BPN network in PZ multichannel sensor can distinguish different organic gases, toluene, butanol, butyl amine and acetic acid, rapidly and accurately. Input Layer #6
Hidden Layer #3
Output Layer #4
Response of channel 1 Toluene
Response of channel 2
Butyl alcohol
Response of channel 3
Acetic acid
Response of channel 4
Butyl amine
Response of channel 5 Response of channel 6 Hz
Presence (+1) Presence(+1) (-1) Absence Absence (-1)
Figure 2. The structure of neural network adopted in this study
In the calculation of BPN, input data processing and output data reprocessing were done as in equation (20) and equation (21)
D New =
D Old − µ κ×σ
(20)
µ: mean of the data of the unit σ: standard deviation of the data of the unit k = 2.58 (99%) D New =
D Old − Min ( 0.8 − 0.2 ) + 0.2 Max − Min
(21)
Min: minimum of the data of the unit Max: maximum of the data of the unit In this network, each unit of the output layer stands for the presence (+1) or absence (-1) of the detected molecule. 0.9 as a target value of the presence and -0.9 as a target value of the unexpected answer were used for computing the back propagation of error algorithm. When the value of output is larger than 0.9 or smaller than -0.9, we define the analytes presence or absence. However, +0.8 bias
of the processing data was used for error algorithm. In this study, batch learning (change weights and threshold limits after all training samples were computed), 0.5 of learning rate, 0.1 of minimum learning rate and random initial weights and threshold limits were used. Table 1 depicts that overfiting does not occur in the training process of BPN because testing result has smaller error. NNs (Neural networks), like other flexible nonlinear estimation methods such as kernel regression and smoothing splines, can suffer from either underfitting or overfitting. A network that is not sufficiently complex can fail to detect fully the signal in a complicated data set, leading to underfitting. A network that is too complex may fit the noise, not just the signal, leading to overfitting. Overfitting is especially dangerous because it can easily lead to predictions that are far beyond the range of the training data with many of the common types of NNs. Overfitting can also produce wild predictions in multilayer perceptrons even with noise-free data18. Table 1. The error rate for BPN of organic molecules detection system
Learning cycles: 5000 Number of examples Training 40 Testing 20
Error rate/units 0.625 % 0%
Error rate /examples 7.5 % 0%
error-rate/units=(unitstotal - unitscorrect)/unitscorrect error-rate/examples=(examplestotal - examplescorrect)/ samplescorrect The linear relationship between the response and concentration is shown in Figure 3. Regression analysis usalysis. Although quite high sensitivity was was founded to compute the concentration of the organic molecule. Table 2 was obtained by linear regression an in the case of stearic acid , however, relatively quite low relative coefficient (R2 = 0.9626) was also observed in the case of stearic acid as shown in Table 2 which implied that stearic acid was not a good adsorbent for the analysis of butyl amine. Different experimental data set is used to test the regression equation as shown in Table 3. Quite good linear responses to toluene were found for all adsorbents which indicated that toluene in organic mixtures could be analyzed by multivariate linear regression analysis with these adsorbents on multi-channel quartz crystals.
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213
target value "zero" maybe dangerous for the predictions should be tested carefully. Table 5 shows the error rate (units) of various target values of training and testing. In the Table 5, both error rates of training and testing of target value "zero" are smaller than others. It indicates that learning fault-tolerance is helpful to distinguish organic molecule in gas mixture. In this case, BPN is confusing whether butyl alcohol was in the gas mixture or not, as edvent in Table 6. However, it could be easily to distinguish toluene, butyl amine and acetic acid. Table 3. Testing result of linear regression
Analytes Figure 3. The response of multichannel PZ sensor for toluene
Toluene
Table 2. Regression equations of linear regression analysis for organic gases
Regression Analytes channel
Regression equation
2
R
Toluene Polystyrene Y=6.9075X+1.25 0.9998 Butyl Polyvinyl Y=7.1517X+15.14 0.9992 alcohol pyrrolidene Acetic Polyvinyl Y=28.003X+33.35 0.9815 acid pyrrolidene Butyl Polystyrene Y=7.2733X+20.05 0.9917 amine *Stearic Y=10.386X+115.15 0.9626 acid
Butyl alcohol
*High sensitivity, but relatively low relative coefficient (R2)
Furthermore, The qualitative and quantitative analysis of a gas mixture was also investigated and discussed. Five types with different concentrations of gas mixture (40 examples for training and calibration, 20 examples for testing), as shown in Table 4, had been detected (three times of each sample) by PZ mulitichannel sensor. Like previous study, the same 6- 3-4 network structure was used as shown in Figure 2. Also, positive output as a target value of the presence and negative output as a target value of the unexpected answer was used for computing the back propagation of error algorithm. Figure 4 shows the relationship between the error rate and the number of training cycle. Choosing an appropriate target value in the error algorithm is very important. By comparing line A, B, C and D, it can be seen that ±0.9 is not an appropriate target value in this case. However,
Acetic acid
Butyl amine
Theoretic
Testing
conc.(mg/L) conc.(mg/L)
Error
8.65
9.23
6.7%
17.30
18.20
5.2%
25.95
30.80
18.7%
34.60
38.76
12.0%
43.25
47.59
10.0%
4.06
4.84
19.4%
8.11
9.59
18.2%
12.17
13.37
9.9%
16.22
17.70
9.12%
20.28
22.88
12.8%
2.10
2.41
14.9%
4.20
4.49
7.0%
6.29
6.1
-1.3%
8.39
7.59
-9.5%
10.49
8.92
-15.0%
1.48
1.65
11.5%
2.96
3.29
11.4%
4.43
4.94
11.5%
5.91
6.46
9.2%
7.39
8.11
9.7%
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Ping Chang and Jeng-Shong Shih
Sample
Toluene
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4
7.21 14.42 21.63 28.84 7.21 14.42 21.63 28.84 4.33 8.66 12.99 17.32 3.93 7.86 11.79 15.72 3.93 7.86 11.79 15.72
Butyl alcohol 0 0 0 0 0 0 0 0 4.06 8.12 12.18 16.24 3.69 7.38 11.07 14.76 3.69 7.38 11.07 14.76
Acetic acid 0 0 0 0 1.75 3.50 5.25 7.00 0 0 0 0 0.95 1.90 2.85 3.80 0 0 0 0
Butyl amine 1.23 2.46 3.69 4.29 0 0 0 0 0 0 0 0 0 0 0 0 0.67 1.34 2.01 2.68
Error Rate/units %
Table 4. Samples of gas mixtures (mg/L)
Training Cycles Figure 4. Error rate curves in training process, A: target value is ±0.9; B: target value is ±0.5; C: target value is ±0.2; D: target value is ±0. Table 5. The error rate/units of BPN of gas mixture
Training Training Training Training
Target value ±0.9 ±0.5 ±0.2 ±0
Error rate/units 0.75 0.15625 0.10625 0.05625
Testing Testing Testing Testing
Error rate/units 0.75 0.16249 0.15 0.0625
Number of examples of training: 40(160 output units) Number of examples of testing: 20(80 output units) Learning cycles: 8000
Table 6. Testing results of BPN of gas mixtures
Examples A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4
Theoretic output* [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, 1, -1] [1, 1, 1, -1] [1, 1, 1, -1] [1, 1, 1, -1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1]
*[ toluene, butyl alcohol, acetic acid, butyl amine ] ** Incorrect output
Output [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1**, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, -1**, 1, -1] [1, -1**, 1, -1] [1, -1**, 1, -1] [1, -1**, 1, -1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1]
Judgement toluene and butyl amine toluene and butyl amine toluene and butyl amine toluene and butyl amine toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene toluene and butyl alcohol toluene and butyl alcohol toluene and butyl alcohol toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene, butyl alcohol and butyl amine toluene, butyl alcohol and butyl amine toluene, butyl alcohol and butyl amine toluene, butyl alcohol and butyl amine
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Table 7. Regression equations of MLR of gas mixtures
Organic molecule Toluene Butyl alcohol Acetic acid Butyl amine
Regression equations Y=0.906+0.145X1+0.003X2-0.005X3-0.179X4+0.215X5-0.014X6 Y=1.630+0.638X1-0.274X2+0.017X3+0.055X4-0.271X5+0.03X6 Y=-0.238-0.052X1+0.026X2+0.001X3-0.003X4+0.008X5-0.007X6 Y=-0.47-0.091X1+0.031X2-0.004X3-0.018X4+0.017X5-0.000X6
R2 0.902 0.959 0.981 0.951
X1: The response of polystyrene X2: The response of polyvinyl alcohol X3: The response of stearic acid X4: The response of fullerene X5: The response of polyethylene adipate X6: The response of polyvinyl pyrrolidene Table 8. MLR Testing results of organic mixtures
Sample True 7.21
A1 (difference) (error ﹪) A2
14.42
A3
21.63
A4
28.4
B1
7.21
B2
14.42
B3
21.63
B4
28.84
C1
4.33
C2
8.66
C3
12.99
C4
17.32
Toluene Type1 6.26 -0.95 -13.1﹪ 11.73 -2.69 -18.7﹪ 15.39 -6.24 -26.3﹪ 22.47 -6.38 -22.1﹪ 7.62 0.41 5.7﹪ 14.55 0.13 0.9﹪ 20.70 -0.93 -4.3﹪ 28.63 -0.21 -0.7﹪ 3.84 -0.49 -11.3﹪ 7.45 -1.21 -13.9﹪ 10.30 -2.69 -20.7﹪ 14.24 -3.08 -17.8﹪
Type2 6.20 -1.01 -14.0﹪ 11.62 -2.80 -19.4﹪ 15.34 -6.29 -29.1﹪ 22.25 -6.59 -22.9﹪ 7.56 0.35 0.9﹪ 14.45 0.03 -0.2﹪ 20.00 -1.63 -7.5﹪ 28.43 0.41 -1.4﹪ 3.81 -0.52 -12﹪ 7.34 -1.32 -14.7﹪ 10.20 -2.79 -15.5﹪ 14.10 -3.22 -18.6﹪
Acetic acid True Type1 Type2 0
True 1.23
0
2.46
0
3.69
0
4.92
1.75
3.50
5.25
7.00
1.87 0.12 6.7﹪ 3.24 -0.26 -7.5﹪ 4.83 -0.42 -8.1﹪ 7.02 0.02 0.2﹪
1.90 0.15 8.6﹪ 3.30 -0.20 -5.8﹪ 4.92 -0.33 -6.3﹪ 7.13 0.13 -1.9﹪
0
0
0
0
0
0
0
0
0
0
0
0
Butyl amine Type1 Type2 1.34 1.35 0.11 0.12 9.5﹪ 8.7﹪ 2.23 2.24 -0.23 -0.22 -9.5﹪ -8.8﹪ 2.70 2.73 -0.99 -0.96 -26.0﹪ -26.8﹪ 3.80 3.84 -1.12 -1.08 -22.7﹪ 22.0﹪
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Ping Chang and Jeng-Shong Shih
Table 9. MLR Testing results of organic mixtures (continued from Table 8)
Sample D1
True 3.93
D2
7.86
D3
11.79
D4
15.72
E1
3.93
E2
7.86
E3
11.79
E4
15.72
Toluene Type1 6.46 2.53 64.4﹪ 9.87 2.01 25.5﹪ 14.28 2.49 21.1﹪ 20.62 4.90 31.1﹪ 4.71 0.78 19.9﹪ 7.16 -0.70 -8.9﹪ 12.44 0.65 5.5﹪ 16.37 0.65 4.1﹪
Type2 6.40 2.47 62.8﹪ 9.76 1.91 24.1﹪ 14.12 2.33 19.8﹪ 20.40 4.68 29.8﹪ 4.65 0.72 13.8﹪ 7.05 -0.82 -10.4﹪ 12.27 0.48 4.1﹪ 16.16 0.44 2.8﹪
True 0.95
1.90
2.85
3.80
Quantitative analysis for organic gas mixture, including toluene, butyl amine, acetic acid and butyl alcohol (interferent in this case), was calculated by multivariate linear regression analysis (MLR). Regression equations are shown in Table 7 and the testing results are shown in Table 8 and Table 9. MLR working-out of gas mixture with butyl alcohol was shown as Type 2 (butyl alcohol is an interferent). No obvious difference was observed between these two types. In other words, the system can work even the presence of interferent. In conclusion, various organic molecules, amine (butyl amine), carboxylic acid (acetic acid), alcohol (butyl alcohol) and aromatic molecule (toluene), can be distinguished clearly and determined by the six-channel (polyvinyl alcohol, fullerene, polystyrene, stearic acid, polyethylene adipate and polyvinyl pyrrolidene) piezoelectric detection system. A 6-3-4 back propagation neural network was used to recognize the organic molecules can be distinguished very clearly. The network also worked in gas mixture cases. Toluene, acetic acid and butyl amine were distinguished
Acetic acid Type1 Type2 1.10 1.14 0.15 0.19 19.5﹪ 15.4﹪ 1.72 1.79 -0.18 -0.11 -9.5﹪ 5.8﹪ 2.41 2.50 -0.45 -0.35 -15.6﹪ -12.4﹪ 3.20 3.32 -0.60 -0.14 -15.7﹪ -12.6﹪
True 0
Butyl amine Type1 Type2
0
0
0
0
0.67
0
1.34
0
2.01
0
2.68
0.64 -0.03 -3.1﹪ 1.2 -0.14 -10.4﹪ 1.58 -0.43 -21.3﹪ 2.03 -0.65 -24.3﹪
0.66 -0.06 -1.3﹪ 1.24 -1.10 -7.6﹪ 1.64 -0.37 -18.4﹪ 2.11 -0.57 -21.4﹪
from gas mixture with interferent, alcohol. With an error of about 5-20%, we suggest, the method can be used to detect the components of organic mixtures both qualitatively and quantitatively.
Acknowledgment The authors would like to thank the National Science Council of Republic of China in Taiwan for the financial support.
References [1] [2] [3] [4] [5] [6] [7]
Persaud, K.; Dodd, G. Nature 1982, 299, 352. Carey, W. P.; Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1986, 58, 149. Sundgren, H.; Lundstrom, I.; Winquist, F. Sensors and Actuators B 1990, 2, 115. Krebs, P.; Grisel, A. Sensors and Actuators B 1993, 13, 155. Wang, X.; Yee, S.; Carey, P. Sensors and Actuators B 1993, 13-14, 458. Lu, C. J.; Shih, J. S. Analytica Chimica Acta 1995, 306, 129. Sheng, H. J.; Shih, J. S. Analytica Chimica
The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor for Mixed Organic Vapours
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
Acta 1997, 350, 109. Jane, Y. S.; Shih, J. S. Analyst 1995, 120, 517. Chao, Y. C.; Shih, J. S. Analytica Chimica Acta 1998, 374, 39. Chiou, C. S.; Shih, J. S. Analytica Chimica Acta 1998, 360, 69. Chang, P.; Shih, J. S. Analytica Chimica Acta 1999, 380, 55. Chang, P.; Shih, J. S. Analytica Chimica Acta 1998, 360, 61. Sauerbrey, G. Z. Z. Phys. 1959, 155, 206. Sauerbrey, G. Z. Z. Phys. 1964, 178, 457. Chang, P.; Shih, J. S. Analytica Chimica Acta 2000, 403, 39. Taylor, M.; Lisboa, P. Techniques and Application of Neural Networks 1993, Ellis Horwood. Rumelhart, D. E.; McClelland, J. L. Parallel Distributed Processing; MIT Press, U.S.A. 1986. ftp://ftp.sas.com/pub/neural/FAQ.html
Manuscript Received: Sept. 11, 2002 and Accepted: Oct. 11, 2002
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The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor for Mixed Organic Vapours Ping Chang and Jeng-Shong Shih* Department of Chemistry National Taiwan Normal University Taipei, Taiwan 116, R.O.C. E-mail: [email protected]
Abstract A multi-channel piezoelectric quartz crystal sensor with a homemade computer interface was prepared and employed in the present study to detect mixture of organic molecules. Back propagation neural network (BPN) was used to distinguish the species in the mixture organic molecules and multivariate linear regression analysis (MLR) was used to compute the concentration of the species. A six-channel piezoelectric sensor detecting organic molecules in static system was investigated and discussed. Amine, carboxylic acid, alcohol and aromatic molecules can easily be distinguished by this system with back propagation neural network. Furthermore, the concentrations of the organic compounds were computed with an error of about 10% by multivariate linear regression analysis (MLR). Detection of organic mixture with amine, carboxylic acid, alcohol and aromatic molecules by this method also had good qualitative and quantitative results. In order to achieve better distinguishability, change of fault-tolerance in back propagation neural network was also investigated and discussed in this study. Key Words: Pizoelectric Crystal, Multichannel Sensor, Organic Vapours, Back Propagation Neural Network, Linear Regression Analysis
1. Introduction It is well known that the use of gas sensor array and pattern recognition analysis has the advantage in identifying odors, organic molecules and gases because of poor selectivity of a lot of other gas sensors [1-5]. The qualitative and quantitative analysis of a gas mixture with non-selective sensor elements is achievable with a combination of several different sensor elements in an array. Piezoelectric quartz crystals were very sensitive for the changes in mass [6-12]. By coating some special materials on the surface,
the frequency of the crystal can be decreased by adsorbing targets on the crystal's surface. The relationship derived for quartz crystals (AT-cut) vibrating in the thickness shear-mode is as follows [13,14]: ∆F = -2.3 × 10 6 · f2 · ∆m/A (1) ∆F Where is the frequency shift due to the coating, f (MHz) is the frequency of quartz crystal, ∆m (gram) is the mass of deposited coating and A (cm2 ) is the area coated. Principal component analysis (PCA), a well-known technology of statistics, is useful in selecting the classic independents of all
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materials [15]. We can easily differentiate different analytes by takeing a view of the profile discrimination with the responses of several channels in a plot. However, it is necessary to distinguish the different gases by sensor array without subjective judgment in many cases. Therefore, using of computer for the study is the best choosing. Can a computer smart as a human being? Artificial neural network (ANN) capacitates a computer the ability of learning and thinking. Chemical sensors were developed for an artificial nose in the past decade [16]. The application of ANN method proved to be particularly advantageous if the measured property is not connected exactly to the signal of the transducers of sensors. The optimum structure of neural network is determined by a trial and error method. Back propagation neural network (BPN) is the most popular technology of the chemical sensor array. The back propagation method is part of the parallel distributed processing system [17]. One-layer networks like Hopfield and Kohonen structure, and multi-layer systems like counter propagation and back propagation of errors, can be used for chemical applications. Backpropagation refers to the method for computing the gradient of the case-wise error function with respect to the weights for a feedforward network which is straightforward and elegant application of the chain rule of elementary calculus. By definition, backpropagation or backprop refers to a training method that uses backpropagation to compute the gradient. In other words, a backprop network is a feedforward network trained by backpropagation [18]. In this study, qualitative analysis of the analytes (mixture gas) was done by using PZ sensor array and BPN. Three layers network structure of BPN was established and three units of hidden layer were used. Furthermore, the concentration of each compound of the gases was computed by MLR.
2. Experimental 2.1 Crystal Coating Piezoelectric crystals used were AT-cut spherical quartz crystals, with a radius of 4.0 mm and a thickness of 0.18 mm with a basic
resonant frequency of 10 MHz and were provided with silver-plated metal electrodes on both sides (Taiwan Crystal Co.). The crystals were coated with the prepared solution via dropping method with a microsyringe. An aliquot of 2 mL of the prepared coating solution was dropped onto one side of the quartz crystals. After evaporation of the solvent, differently functioning PZ crystals were obtained. The coating materials selected with PCA were polyvinyl alcohol, fullerene, polystyrene, stearic acid, polyethylene adipate and polyvinyl pyrrolidene [8]. 2.2 Apparatus Figure 1 depicts the experimental setup of a piezoelectric quartz crystal detection system with an assembled computer interface. The multi- channel PZ sensor connected with an oscillator system was placed in a glass cell. Organic liquid was injected into the injecting port which incudes a heat plant. A home-made computer interface, including an oscillator, Altera programmable logic devices, a standard crystal and a programming peripheral interface (PPI 8255) was prepared for frequency to digital conversion. The Altera was designed with a 24 bits counter and 24 bits register to treat the 10 MHz frequency and no frequency mixing was used. Therefore, the true frequencies were obtained and hence the errors were reduced [15]. Data processing and signal acquisition were automatically performed on a microcomputer (PC/AT) with a program in Qbasic. The MLR is done with the commercial statistical software package SAS and the back propagation neural network (BPN) is a program written in Qbasic. Oscillation circuit and Ferquency counter
Sample
Injecting port
Flow controller
Heater Multi-channel sensor
Nitrogen
Figure 1. Experimental setup of detection system with an assembled computer interface
The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor for Mixed Organic Vapours
BPN program
Training process: Step 1. Design the structure of neural network and input parameters of the nertwork . Step 2. Get initial weights W and initial θ values from randomizing. Step 3. Input training data matrix X and output matrix T. Step 4. Compute the output vector of each neural units. (a) Compute the output vecter H of the hidden layer (2) net k = ∑ Wik X i − θ k Hk = f ( netk ) (3) (b) Compute the output vecter Y of the output layer net j = ∑ Wkj Hi − θ j Yj = f ( net j ) Step 5. Compute the distances d (a) Compute the distances d of the output layer δ j = ( Tj − Yj ) • f ' ( net j ) (b) Compute the distances d of the hidden layer δ k = ( ∑ δ jWkj ) • f ' ( net k )
(4) (5)
(6) (7)
j
Step 6. Compute the modification of W and θ ( η is the learning rate) (a) Compute the modification of W and θ of the output layer ∆Wkj = ηδ j H k ∆θ j = − ηδ j (b) Compute the modification of W and θ of the hidden layer ∆Wik = ηδ k X i ∆θ k = − ηδ k Step 7. Renew W and θ (a) Renew W and θ of the output layer Wkj = Wkj + ∆Wkj
θ j = θ j + ∆θ j
(b) Renew W and θ of the hidden layer Wik = Wik + ∆Wik
θ k = θ k + ∆θ k
(8) (9) (10) (11) (12) (13) (14) (15)
Step 8. Repeat step 3 to step7 until convergence. Testing process: Step 1. Input the parameters of the network. Step 2. Input the W and θ Step 3. Input an unknown data matrix X Step 4. Compute the output vector (a) Compute the output vector H of hidden layer net k = ∑ Wik X i − θ k Hk = f ( netk ) (b) Compute the output vecter Y of the output layer net j = ∑ Wkj Hi − θ j
Yj = f ( net j )
(16) (17)
(18) (19)
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3. Results And Discussion In this study, a 6-3-4 network structure was used as shown in Figure 2. The response of six coated (polyvinyl alcohol, fullerene, polystyrene, stearic acid, polyethylene adipate and polyvinyl pyrrolidene) PZ crystals was the input layer matrix of the network. First, pure organic gases such as toluene, butanol, butyl amine and acetic acid was analyzed by this system. 40 training examples and 20 testing examples were prepared for training and testing the network respectively. In the BPN network, the problem of classification had been solved. On the other words, using BPN network in PZ multichannel sensor can distinguish different organic gases, toluene, butanol, butyl amine and acetic acid, rapidly and accurately. Input Layer #6
Hidden Layer #3
Output Layer #4
Response of channel 1 Toluene
Response of channel 2
Butyl alcohol
Response of channel 3
Acetic acid
Response of channel 4
Butyl amine
Response of channel 5 Response of channel 6 Hz
Presence (+1) Presence(+1) (-1) Absence Absence (-1)
Figure 2. The structure of neural network adopted in this study
In the calculation of BPN, input data processing and output data reprocessing were done as in equation (20) and equation (21)
D New =
D Old − µ κ×σ
(20)
µ: mean of the data of the unit σ: standard deviation of the data of the unit k = 2.58 (99%) D New =
D Old − Min ( 0.8 − 0.2 ) + 0.2 Max − Min
(21)
Min: minimum of the data of the unit Max: maximum of the data of the unit In this network, each unit of the output layer stands for the presence (+1) or absence (-1) of the detected molecule. 0.9 as a target value of the presence and -0.9 as a target value of the unexpected answer were used for computing the back propagation of error algorithm. When the value of output is larger than 0.9 or smaller than -0.9, we define the analytes presence or absence. However, +0.8 bias
of the processing data was used for error algorithm. In this study, batch learning (change weights and threshold limits after all training samples were computed), 0.5 of learning rate, 0.1 of minimum learning rate and random initial weights and threshold limits were used. Table 1 depicts that overfiting does not occur in the training process of BPN because testing result has smaller error. NNs (Neural networks), like other flexible nonlinear estimation methods such as kernel regression and smoothing splines, can suffer from either underfitting or overfitting. A network that is not sufficiently complex can fail to detect fully the signal in a complicated data set, leading to underfitting. A network that is too complex may fit the noise, not just the signal, leading to overfitting. Overfitting is especially dangerous because it can easily lead to predictions that are far beyond the range of the training data with many of the common types of NNs. Overfitting can also produce wild predictions in multilayer perceptrons even with noise-free data18. Table 1. The error rate for BPN of organic molecules detection system
Learning cycles: 5000 Number of examples Training 40 Testing 20
Error rate/units 0.625 % 0%
Error rate /examples 7.5 % 0%
error-rate/units=(unitstotal - unitscorrect)/unitscorrect error-rate/examples=(examplestotal - examplescorrect)/ samplescorrect The linear relationship between the response and concentration is shown in Figure 3. Regression analysis usalysis. Although quite high sensitivity was was founded to compute the concentration of the organic molecule. Table 2 was obtained by linear regression an in the case of stearic acid , however, relatively quite low relative coefficient (R2 = 0.9626) was also observed in the case of stearic acid as shown in Table 2 which implied that stearic acid was not a good adsorbent for the analysis of butyl amine. Different experimental data set is used to test the regression equation as shown in Table 3. Quite good linear responses to toluene were found for all adsorbents which indicated that toluene in organic mixtures could be analyzed by multivariate linear regression analysis with these adsorbents on multi-channel quartz crystals.
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213
target value "zero" maybe dangerous for the predictions should be tested carefully. Table 5 shows the error rate (units) of various target values of training and testing. In the Table 5, both error rates of training and testing of target value "zero" are smaller than others. It indicates that learning fault-tolerance is helpful to distinguish organic molecule in gas mixture. In this case, BPN is confusing whether butyl alcohol was in the gas mixture or not, as edvent in Table 6. However, it could be easily to distinguish toluene, butyl amine and acetic acid. Table 3. Testing result of linear regression
Analytes Figure 3. The response of multichannel PZ sensor for toluene
Toluene
Table 2. Regression equations of linear regression analysis for organic gases
Regression Analytes channel
Regression equation
2
R
Toluene Polystyrene Y=6.9075X+1.25 0.9998 Butyl Polyvinyl Y=7.1517X+15.14 0.9992 alcohol pyrrolidene Acetic Polyvinyl Y=28.003X+33.35 0.9815 acid pyrrolidene Butyl Polystyrene Y=7.2733X+20.05 0.9917 amine *Stearic Y=10.386X+115.15 0.9626 acid
Butyl alcohol
*High sensitivity, but relatively low relative coefficient (R2)
Furthermore, The qualitative and quantitative analysis of a gas mixture was also investigated and discussed. Five types with different concentrations of gas mixture (40 examples for training and calibration, 20 examples for testing), as shown in Table 4, had been detected (three times of each sample) by PZ mulitichannel sensor. Like previous study, the same 6- 3-4 network structure was used as shown in Figure 2. Also, positive output as a target value of the presence and negative output as a target value of the unexpected answer was used for computing the back propagation of error algorithm. Figure 4 shows the relationship between the error rate and the number of training cycle. Choosing an appropriate target value in the error algorithm is very important. By comparing line A, B, C and D, it can be seen that ±0.9 is not an appropriate target value in this case. However,
Acetic acid
Butyl amine
Theoretic
Testing
conc.(mg/L) conc.(mg/L)
Error
8.65
9.23
6.7%
17.30
18.20
5.2%
25.95
30.80
18.7%
34.60
38.76
12.0%
43.25
47.59
10.0%
4.06
4.84
19.4%
8.11
9.59
18.2%
12.17
13.37
9.9%
16.22
17.70
9.12%
20.28
22.88
12.8%
2.10
2.41
14.9%
4.20
4.49
7.0%
6.29
6.1
-1.3%
8.39
7.59
-9.5%
10.49
8.92
-15.0%
1.48
1.65
11.5%
2.96
3.29
11.4%
4.43
4.94
11.5%
5.91
6.46
9.2%
7.39
8.11
9.7%
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Ping Chang and Jeng-Shong Shih
Sample
Toluene
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4
7.21 14.42 21.63 28.84 7.21 14.42 21.63 28.84 4.33 8.66 12.99 17.32 3.93 7.86 11.79 15.72 3.93 7.86 11.79 15.72
Butyl alcohol 0 0 0 0 0 0 0 0 4.06 8.12 12.18 16.24 3.69 7.38 11.07 14.76 3.69 7.38 11.07 14.76
Acetic acid 0 0 0 0 1.75 3.50 5.25 7.00 0 0 0 0 0.95 1.90 2.85 3.80 0 0 0 0
Butyl amine 1.23 2.46 3.69 4.29 0 0 0 0 0 0 0 0 0 0 0 0 0.67 1.34 2.01 2.68
Error Rate/units %
Table 4. Samples of gas mixtures (mg/L)
Training Cycles Figure 4. Error rate curves in training process, A: target value is ±0.9; B: target value is ±0.5; C: target value is ±0.2; D: target value is ±0. Table 5. The error rate/units of BPN of gas mixture
Training Training Training Training
Target value ±0.9 ±0.5 ±0.2 ±0
Error rate/units 0.75 0.15625 0.10625 0.05625
Testing Testing Testing Testing
Error rate/units 0.75 0.16249 0.15 0.0625
Number of examples of training: 40(160 output units) Number of examples of testing: 20(80 output units) Learning cycles: 8000
Table 6. Testing results of BPN of gas mixtures
Examples A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4
Theoretic output* [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, 1, -1] [1, 1, 1, -1] [1, 1, 1, -1] [1, 1, 1, -1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1]
*[ toluene, butyl alcohol, acetic acid, butyl amine ] ** Incorrect output
Output [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, -1, 1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1, 1, -1] [1, -1**, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, 1, -1, -1] [1, -1**, 1, -1] [1, -1**, 1, -1] [1, -1**, 1, -1] [1, -1**, 1, -1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1] [1, 1, -1, 1]
Judgement toluene and butyl amine toluene and butyl amine toluene and butyl amine toluene and butyl amine toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene toluene and butyl alcohol toluene and butyl alcohol toluene and butyl alcohol toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene and acetic acid toluene, butyl alcohol and butyl amine toluene, butyl alcohol and butyl amine toluene, butyl alcohol and butyl amine toluene, butyl alcohol and butyl amine
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215
Table 7. Regression equations of MLR of gas mixtures
Organic molecule Toluene Butyl alcohol Acetic acid Butyl amine
Regression equations Y=0.906+0.145X1+0.003X2-0.005X3-0.179X4+0.215X5-0.014X6 Y=1.630+0.638X1-0.274X2+0.017X3+0.055X4-0.271X5+0.03X6 Y=-0.238-0.052X1+0.026X2+0.001X3-0.003X4+0.008X5-0.007X6 Y=-0.47-0.091X1+0.031X2-0.004X3-0.018X4+0.017X5-0.000X6
R2 0.902 0.959 0.981 0.951
X1: The response of polystyrene X2: The response of polyvinyl alcohol X3: The response of stearic acid X4: The response of fullerene X5: The response of polyethylene adipate X6: The response of polyvinyl pyrrolidene Table 8. MLR Testing results of organic mixtures
Sample True 7.21
A1 (difference) (error ﹪) A2
14.42
A3
21.63
A4
28.4
B1
7.21
B2
14.42
B3
21.63
B4
28.84
C1
4.33
C2
8.66
C3
12.99
C4
17.32
Toluene Type1 6.26 -0.95 -13.1﹪ 11.73 -2.69 -18.7﹪ 15.39 -6.24 -26.3﹪ 22.47 -6.38 -22.1﹪ 7.62 0.41 5.7﹪ 14.55 0.13 0.9﹪ 20.70 -0.93 -4.3﹪ 28.63 -0.21 -0.7﹪ 3.84 -0.49 -11.3﹪ 7.45 -1.21 -13.9﹪ 10.30 -2.69 -20.7﹪ 14.24 -3.08 -17.8﹪
Type2 6.20 -1.01 -14.0﹪ 11.62 -2.80 -19.4﹪ 15.34 -6.29 -29.1﹪ 22.25 -6.59 -22.9﹪ 7.56 0.35 0.9﹪ 14.45 0.03 -0.2﹪ 20.00 -1.63 -7.5﹪ 28.43 0.41 -1.4﹪ 3.81 -0.52 -12﹪ 7.34 -1.32 -14.7﹪ 10.20 -2.79 -15.5﹪ 14.10 -3.22 -18.6﹪
Acetic acid True Type1 Type2 0
True 1.23
0
2.46
0
3.69
0
4.92
1.75
3.50
5.25
7.00
1.87 0.12 6.7﹪ 3.24 -0.26 -7.5﹪ 4.83 -0.42 -8.1﹪ 7.02 0.02 0.2﹪
1.90 0.15 8.6﹪ 3.30 -0.20 -5.8﹪ 4.92 -0.33 -6.3﹪ 7.13 0.13 -1.9﹪
0
0
0
0
0
0
0
0
0
0
0
0
Butyl amine Type1 Type2 1.34 1.35 0.11 0.12 9.5﹪ 8.7﹪ 2.23 2.24 -0.23 -0.22 -9.5﹪ -8.8﹪ 2.70 2.73 -0.99 -0.96 -26.0﹪ -26.8﹪ 3.80 3.84 -1.12 -1.08 -22.7﹪ 22.0﹪
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Ping Chang and Jeng-Shong Shih
Table 9. MLR Testing results of organic mixtures (continued from Table 8)
Sample D1
True 3.93
D2
7.86
D3
11.79
D4
15.72
E1
3.93
E2
7.86
E3
11.79
E4
15.72
Toluene Type1 6.46 2.53 64.4﹪ 9.87 2.01 25.5﹪ 14.28 2.49 21.1﹪ 20.62 4.90 31.1﹪ 4.71 0.78 19.9﹪ 7.16 -0.70 -8.9﹪ 12.44 0.65 5.5﹪ 16.37 0.65 4.1﹪
Type2 6.40 2.47 62.8﹪ 9.76 1.91 24.1﹪ 14.12 2.33 19.8﹪ 20.40 4.68 29.8﹪ 4.65 0.72 13.8﹪ 7.05 -0.82 -10.4﹪ 12.27 0.48 4.1﹪ 16.16 0.44 2.8﹪
True 0.95
1.90
2.85
3.80
Quantitative analysis for organic gas mixture, including toluene, butyl amine, acetic acid and butyl alcohol (interferent in this case), was calculated by multivariate linear regression analysis (MLR). Regression equations are shown in Table 7 and the testing results are shown in Table 8 and Table 9. MLR working-out of gas mixture with butyl alcohol was shown as Type 2 (butyl alcohol is an interferent). No obvious difference was observed between these two types. In other words, the system can work even the presence of interferent. In conclusion, various organic molecules, amine (butyl amine), carboxylic acid (acetic acid), alcohol (butyl alcohol) and aromatic molecule (toluene), can be distinguished clearly and determined by the six-channel (polyvinyl alcohol, fullerene, polystyrene, stearic acid, polyethylene adipate and polyvinyl pyrrolidene) piezoelectric detection system. A 6-3-4 back propagation neural network was used to recognize the organic molecules can be distinguished very clearly. The network also worked in gas mixture cases. Toluene, acetic acid and butyl amine were distinguished
Acetic acid Type1 Type2 1.10 1.14 0.15 0.19 19.5﹪ 15.4﹪ 1.72 1.79 -0.18 -0.11 -9.5﹪ 5.8﹪ 2.41 2.50 -0.45 -0.35 -15.6﹪ -12.4﹪ 3.20 3.32 -0.60 -0.14 -15.7﹪ -12.6﹪
True 0
Butyl amine Type1 Type2
0
0
0
0
0.67
0
1.34
0
2.01
0
2.68
0.64 -0.03 -3.1﹪ 1.2 -0.14 -10.4﹪ 1.58 -0.43 -21.3﹪ 2.03 -0.65 -24.3﹪
0.66 -0.06 -1.3﹪ 1.24 -1.10 -7.6﹪ 1.64 -0.37 -18.4﹪ 2.11 -0.57 -21.4﹪
from gas mixture with interferent, alcohol. With an error of about 5-20%, we suggest, the method can be used to detect the components of organic mixtures both qualitatively and quantitatively.
Acknowledgment The authors would like to thank the National Science Council of Republic of China in Taiwan for the financial support.
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Manuscript Received: Sept. 11, 2002 and Accepted: Oct. 11, 2002
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