10-04-2017, 08:27 PM
The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor for Mixed Organic Vapours
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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 = -2.3 106 f2 m/A (1)
Where F 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
210 Ping Chang and Jeng-Shong Shih
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
Multi-channel sensor Nitrogen
Injecting port
Heater
Flow controller
Sample
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 211
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 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
netk = Wik Xi k (2)
H f net k k = ( ) (3)
(b) Compute the output vecter Y of the output layer
net W H j kj i j = (4)
Y f net j j = ( ) (5)
Step 5. Compute the distances d
(a) Compute the distances d of the output layer
j j j j = (T Y ) f ' (net ) (6)
(b) Compute the distances d of the hidden layer
k j kj
j
k = ( W ) f ' (net ) (7)
Step 6. Compute the modification of W and ( is the learning rate)
(a) Compute the modification of W and of the output layer
W H kj j k = (8)
j j = (9)
(b) Compute the modification of W and of the hidden layer
W X ik k i = (10)
k k = (11)
Step 7. Renew W and
(a) Renew W and of the output layer
Wkj = Wkj + Wkj (12)
j j j = + (13)
(b) Renew W and of the hidden layer
Wik = Wik + Wik (14)
k k k = + (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
Step 3. Input an unknown data matrix X
Step 4. Compute the output vector
(a) Compute the output vector H of hidden layer
net W X k ik i k = (16)
H f net k k = ( ) (17)
(b) Compute the output vecter Y of the output layer
net W H j kj i j = (18)
Y f net j j = ( ) (19)
212 Ping Chang and Jeng-Shong Shih
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.
Response of channel 1
Response of channel 2
Response of channel 3
Response of channel 4
Response of channel 5
Response of channel 6
Input Layer #6 Hidden Layer #3 Output Layer #4
Acetic acid
Butyl amine
Toluene
Butyl alcohol
Presence(+1)
Absence (-1)
Hz 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 D
New
= Old
(20)
: mean of the data of the unit
: standard deviation of the data of the unit
k = 2.58 (99%)
D D Min
Max Min New
= Old
(0.8 0.2) + 0.2
(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
Error
rate/units
Error rate
/examples
Training 40 0.625 % 7.5 %
Testing 20 0 % 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.
Presence (+1)
Absence (-1)
The Application of Back Propagation Neural Network of Multi-channel Piezoelectric Quartz Crystal Sensor 213
for Mixed Organic Vapours
Figure 3. The response of multichannel PZ sensor for
toluene
Table 2. Regression equations of linear regression analysis
for organic gases
Analytes Regression
channel
Regression
equation R2
Toluene Polystyrene Y=6.9075X+1.25 0.9998
Butyl
alcohol
Polyvinyl
pyrrolidene Y=7.1517X+15.14 0.9992
Acetic
acid
Polyvinyl
pyrrolidene Y=28.003X+33.35 0.9815
Butyl
amine Polystyrene Y=7.2733X+20.05 0.9917
*Stearic
acid Y=10.386X+115.15 0.9626
*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,
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.