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Detection of vapours and odours from a multisensor array using pattern recognition Part 1. Principal component and cluster analysis
Sensors and Actuators
109
B, 4 (1991) 109-115
Detection of Vapours and Odours from a Multisensor Array Using Pattern Recognition Part 1. Principal Component and Cluster Analysis JULIAN W. GARDNER Department
of Engineering,
University
of Warwick,
Conventry
Abstract Mathematical expressions describing the response of individual sensors and arrays of tin oxide gas sensors are derived from a barrier-limited electron mobility model. From these expressions, the fractional change in conductance is identified as the optimal response parameter with which to characterize sensor array performance instead of the more usual relative conductance. In an experimental study, twelve tin oxide gas sensors are exposed to five alcohols and six beverages, and the responses are studied using pattern-recognition methods. Results of regression and supervised learning analysis show a high degree of colinearity in the data with a subset of only five sensors needed for classification. Principal component analysis and clustering methods are applied to the response of the tin oxide sensors to all the vapours. The results show that the theoretically derived normalization of the data set substantially improves the classification of vapours and beverages. The individual alcohols are separated out into five distinct clusters, whereas the beverages cluster into only three distinct classes, namely, beers, lagers and spirits. It is suggested that the separation may be improved further by employing other sensor types or processing techniques.
Intruduction Considerable effort has been directed towards the use of metal oxides for gas detection, since the discovery by Brattain and 0925~4005/91/$3.50
CV4 7AL (U.K.)
Bardeen in 1953 that adsorption of a gas on the surface of a semiconductor can produce a significant change in electrical resistance [ 11. Although measurements have been made on a variety of materials (e.g., ZnO, TiOz, W03) in different forms (single crystal, polycrystalline, amorphous), the most successful commercial semiconducting gas sensor employs a porous, sintered tin oxide element doped by a precious metal. Unfortunately, the performance of semiconducting oxide sensors is often limited by such problems as long-term drift in base-line conductance, a poor specificity and sensitivity to humidity. In the mid 1980s Zaromb and Stetter [2] proposed the use of an array of sensors with partially overlapping sensitivities. This overlapping sensitivity approach to gas sensing has been adopted by several workers and applied not only to arrays of commercial tin oxide sensors but also to MOS and piezoelectric devices. In addition, several pattern-recognition techniques have been used to determine relationships in the multidimensional data sets from these gas sensor arrays; for a general review see Gardner and Bartlett [ 31. An important element in any patternrecognition method is the selection of an appropriate pre-processing algorithm to characterize the sensor response. The sensor response or sensitivity has been represented in a variety of ways including the relative resistance value, R&R,, [4]; log relative resistance value, ln(R&Rair) [ 51; conductance difference, G, - Gtii, or even the fractional conductance change, (G,, - GGr)/Gair [6], where Rgas, Rair, G,, Gtir are the resistances or conductances in gas or air respectively. 0 Elsevier Sequoia/Printed in The Netherlands
110
Furthermore, it is quite common to apply a divide normalization procedure, e.g., throughout by the average or maximum sensor response, or autoscale the sensor data (make the response of each sensor have a mean of zero and standard deviation of one over all the chemicals sensed). In this paper, a microscopic model of conduction in sintered tin oxide films is developed to determine the most appropriate of these parameters to define the sensor response and the merits associated with the choice .of the pre-processing technique are discussed. Next the measured response of an array of twelve sintered tin oxide gas sensors, an electronic nose [7], to five alcohols and six beverages is presented. Finally, these data have been analysed using both unsupervised (cluster analysis) and supervised (principal pattern-recognition component analysis) techniques and the ability of these techniques to classify vapours or odours is evaluated.
Use of a Microscopic Model to Determine the Optimal Response Parameter The mechanism of bulk conduction in tin oxide is normally described in terms of an n-type semiconductor, where the intrinsic donors are assumed to be oxygen vacancies V,. Thus, the associated donor concentration n’ may be determined by reaction ( la) : O*-(s)
sVo+n’+;O,(g) L
R + 0, -(s) 2
mR0 + n”
(14 (lb)
where the reduction in lattice oxygen, 0, -(s) causes an increase in the oxygen lattice vacancies V, and electron donor concentration. The second irreversible reaction ( 1b) follows the introduction of a combustible gas R, where the product RO is often gaseous (e.g., CO2 and H,O) and KZ”is the resulting donor The conductance change concentration. expected from this bulk model of a homogeneous non-stoichiometric oxide cannot explain the observed gas sensitivity of thin or
thick (doped) tin oxide film [S, 91. Therefore a barrier-limited conduction model was introduced by Heiland [ 81 for thin tin oxide films in which the electron mobility is limited at the surface by a space-charge region. The model was later extended to describe the behaviour of thick porous tin oxide films or pellets, where oxygen is free to diffuse into the bulk of the material. Consequently, the accepted model of a porous sintered oxide film is that of barrier-limited conduction [9, lo]. Assuming a symmetric potential barrier, when the conductance G is governed by thermionic emission [ 111, gives i 2e kT x exp(s)
cash(g)
(2)
where the donor concentration n is modified by the lattice oxygen (eqn. (l)), the barrier height Q, is dependent upon the difference between the thermionic work function of a vacuum (undoped) or precious metal (doped) and the electron affinity of the semiconductor, m* is the effective mass of the donor, k is Boltzmann’s constant and T the absolute temperature. The effect of the gas R may now be modelled as a lowering of the integranular barrier height A (in units of e/kT), and provided that the donor concentration n is governed by the bulk stoichiometry as stated earlier, we can reduce eqn. (2) to G = G,, exp(A) Using this microscopic model to calculate the response parameters to apply in patternrecognition techniques, we obtain the formulae shown in Table 1. The reduction in the barrier height A may be related to the gas-induced donor concentration n ’ (eqn. 1(b)) and bulk donor concentration n by A N ln( 1 + n”/n)
(4)
Assuming that the bulk carrier concentration is effectively given by the oxygen lattice (i.e., n x n’), then eqn. (4) is identical to that proposed by Mizei and Harsanyi [ 121, and later by Lantto et al. [IO]. The donor
111
TABLE 1. Response parameter height model
relationships:
barrier
Expressions
Conductance
Resistance
Difference Fractional change Relative
GJexp(A) - 11 exp(A) - 1
&[exp( -A) exp( -A) - 1
exp(A)
exp( -A)
11
concentrations 11’ and n” are related to the oxygen partial pressure in air and gas, [O,],i, and [ OJgas, which gives A = ~~{[~zlair/EQdgasI = W3
(5)
where 0 is the fractional occupancy of the lattice vacancies. The reaction kinetics have been solved by Williams [ 131 and produce A = ln( 1 + K;[ R]“/K,0)0,92 where K1’ and K2’ are the temperature-independent forward reaction rates in eqns. (la) and (lb) and [R] is the partial pressure of the gas R. The index m depends upon the lattice oxygen species; when the species is 02-(s), its value is i. Thus, A can be approximated and substituted into the response parameter relationships of Table 1. The results are shown in Table 2. There is considerable experimental evidence to support the theoretical relationship for the fractional change in conductance or resistance [ 141. From Table 2 it may be seen that the relative change is a poor response parameter when the partial pressure of gas is low, whereas the difference or fractional change in conductance is always (i.e., for all
TABLE 2. Response parameter relationships: gas concentration. Gh is Go(Kzo/K,o) and Rh is &(Kzo/K,") Expression
Conductance
Resistance
Difference
G&[R]”
-R;[R]”
Fractional change
$ [RI”
-$
Relative
1 +,K”/K,“)lN”
[ 1 + WZ”/~~)[
[RI”’
A<1 only
RI”1- ’
A) a sensitive parameter. In an array of i porous tin oxide sensors, the change in conductance is now related to the gas j partial pressure by
S, = &as -
G,i,) /G,i,
= uV[ RI”’
(6) The index m is dependent upon the oxide properties and temperature rather than the gas analysed, and CIis the ratio of reaction rates and depends upon the sensor type and gas. When sampling at fixed gas concentration, the difference or fractional conductance is most appropriate and a commonly used normalization procedure removes the concentration terms (7) When sampling of various components takes place it is preferable to linearize eqn. (6) by using the log-parameter, i.e., lnKG,,s - Gir)/G,i,] = mi log[R] + UU (8) It is then possible to carry out regression analysis on this set of equations, provided that the fractional conductance is not too near zero since the log term would introduce large errors. Several workers have used the log-relative parameter to define the sensor response [9, 151. Although this technique ameliorates the concentration effect in the sensor responses, it does not linearize the equations ln[G,,/G,i,]
N ag[ RI”’
(9) In this case the simple normalization of the signals over all sensors is not appropriate; instead a double logarithm is needed. Experimental Measurements Measurements on the response of an array of twelve different commercial tin oxide gas sensors were taken using the Warwick electronic nose. A full description of the experimental arrangement is given elsewhere [ 161. In brief, the conductance of each sensor was measured before and three minutes after either 0.4~1 of an alcohol or 25 ,~l of a
beverage was introduced into a 20 1 flask containing the sensor array. Eight sets of data were taken on five alcohols, namely, methanol (m), ethanol (e), I-butanol (b), propanol (p), and 2-methyl- 1-butanol (x); followed by ten sets of data on six beverages, namely two beers (w, s), two lagers (h, c) and two spirits (whisky (t) and brandy (b)).
Data Analysis The error on the fractional conductance change of the array was defined by the ratio of the sample standard deviation to the sample mean averaged over all twelve sensors. This error was found to be 16.4% when averaged over all the alcohol data. Several workers have normalized the response parameter using eqn. (7), but from the analysis above a more appropriate procedure is
The adoption of this normalization procedure removes the effect of a change in the sign of S, as would be observed in a mixed sensor array or could be caused by falling base-line drift. Moreover, the normalized parameter, gV,,is now the length of the response vector in n-dimensional space. Employing this procedure on the alcohol data, the error in fractional conductance change was observed to fall to 11S%. This reduction was probably due to the removal of the variation in vapour concentration during testing. Regression (and unsupervised hierarchical cluster analysis) revealed high correlations between the tin oxide sensors in the array. The correlation matrix of the normalized fractional change in conductance for the alcohols was calculated (and a similar one was found for the beverages). Strong correlations exist between sensors {1; 3, 5,6,9, 11, 12) and (7,s). Thus, the vapours and beverages could be measured using a subset of only five sensors, such as 1, 2, 4, 7 and 10.
Cluster Analysis (CA) In cluster analysis, points are grouped together according to their proximity in ndimensional space. A similarity value SIM, can be calculated to represent this proximity and is given by SIM, = 1 - d,/max(d,)
(11) where dii is the distance metric of the data points (i, j) in n-dimensional vector space and max(dJ is its maximum value. The similarity index is one for two identical points and zero for the two most distant, and the values are displayed on a dendrogram. Methods of finding clusters in multidimensional data from piezoelectric quartz [ 171 and SAW [ 181arrays have been reported. In this study the Lance and Williams distance metric has been chosen with flexible fusion [3]. Figure l(a) and (b) shows the dendrograms for the original and normalized alcohol fractional conductance data sets. Clearly, the normalization procedure enhances the cluster analysis since in the normalized data the five clusters (A-E) become more distinctly revealed. The technique was also applied to the beverage data, which again showed an improvement in analysing the normalized response, where three clusters
Fig. 1. Results of cluster analysis on original (a) and normalized (b) responses (fractional conductance change) of a twelve tin oxide sensor array to five alcohols (m = methanol, e = ethanol, p = propan-2-01, b = 1-butanol and x = 2-methyl- 1-butanol).
113
LaOor
oxide gas sensor arrays, it has been successfully applied by others [ 17, 181 to analyse the response of piezoelectric devices. In principal component analysis, the response matrix is expressed in terms of linear combinations of the orthogonal response vectors S,. So the rth principal component X, is a summation of the n response vectors S, for the vapours
& Beerr
j
h---Spirits
3!t-
Fig. 2. Results of cluster analysis on original (a) and normalized (b) responses (conductance change) of a twelve tin oxide sensor array to six beverages (h = lager A, c=lager B, w =beer A, s =beer B, t =whisky, b = brandy).
of lagers (A), beers (D’) and spirits (C’) were observed, Fig. 2. Unfortunately, the separation within these classes is poor. It should be noted that a cluster analysis of the relative conductance and fractional conductance change produces identical results, because a unit translation of each response vector will not change the relative distance between points. Principal Component Analysis (PCA) Principal component analysis is a powerful linear supervised learning pattern-recognition technique that is usually employed in conjunction with cluster analysis. Although it has not yet been applied to the output from tin
i=
(12) 1
where air are the eigenvectors, sometimes referred to as the loadings. The variance of X, is maximized under the constraints that f
air = 1
i=l
and that the principal components are independent. The percentage of data variance contained in each principal component is determined by the eigenvalue. In essence, the technique removes any redundancy in the data and thus reduces the dirnensionality of the problem. Table 3 shows the value of the eigenvalues and percentage variance for the first five principal components of the original and normalized response of the tin oxide array to alcohols and the percentage variance of the beverages. The magnitude of the eigenvalues depends upon the normalization procedure. When autoscaling is used the total is simply n, where n is the number of sensors in the array. However, autoscaling has not been used here for two reasons: first, the response parameters are similar in magnitude and secondly, autoscaling increases the fractional error on
Table 3. Eigenvalues of response data Principal component or eigenvector
Alcohols Original eigenvalue % var.
Xl x, x, x, X,
5.282 68.6 1.960 25.5 3.2 .0.245 1.2 0.095 0.7 0.052
Beverages Normalized eigenvalue % var.
Original % var.
Normalized % var.
0.081 0.023 0.005 0.002 0.002
98.6 0.8 0.3 0.1 0.0
74.8 19.0 2.6 1.9 0.8
70.4 20.0 4.4 2.2 1.5
I
-3 -4 (a)
I -2 0 2 Principal Component,
4 X,
-41 -.6
6 @)
Fig. 3. Results of principal component conductance change) to five alcohols.
analysis
1
I
-:4
-.2 Principal
0 2 Component,
of the original
4 X,
6
(a) and normalized
:~__;~~
I
t
I
-400 .-
-.06;.
I I
(a)
0 Principal
-.
h
Ec CC
I I
-1
_:
.L L-04
b
-.08 L 1 Component
Fig. 4. Results of principal change) to six beverages.
2 X1
component
(b) responses (fractional
-2 W
‘h I I 1
.l -1 0 Principal Conponcnt,
,2 X1
analysis of the original (a) and normalized
low signals, which could lead to erroneous results. In both sets of data, we can see from Table 3 that over 90% of the variance within the data is contained in the first two principal components. Figure 3 shows a plot of the first principal components (X, and X2) for the original and normalized alcohol responses, where an improvement can be seen in particular upon the normalized response for methanol and I-butanol. Again it should be noted that the PCA of the log-relative values is the same as the fractional conductance change provided normalization is not used. A more dramatic effect is noted with the beverage response (see Fig. 4), where the beers and lagers are now separated from each other and
(b) responses (conductance
in addition the spread in the spirits group is reduced. However, within these groups it is still difficult to separate out the individual beverages, and these results produce less separation than an earlier parameter study [ 161.
Conclusions A microscopic model of conduction in tin oxide gas sensors has been developed to select the appropriate sensor response parameter, and improves subsequent classification when compared with more conventional parameters. CA and PCA have been applied to alcohols and beverages and gave good
115
classification for alcohols, but restricted classification for beverages. Further improvements may be made to pattern recognition of vapours and odours by either employing a subset of only five tin oxide gas sensors with, perhaps, SAW devices or considering the application of more generalized pattern-recognition techniques, such as artificial neural networks [ 19,201.
References W. H. Brattain and J. Bardeen, Surface properties of germanium, Bell Syst. Tech. J., 32 (1953) 1. S. Zaromb and J. R. Stetter, Theoretical basis for identification and measurement of air contaminants using an array of sensors having partially overlapping sensitivities, Sensors and Actuators, 6 (1984) 225-243.
J. W. Gardner and P. N. Bartlett, in P. T. Moseley, D. E. Williams and J. 0. W. Norris (eds.), Techniques and Mechanisms in Gas Sensing, Adam Hilger, Bristol, 1991, pp. 347-380. K. Takahata, in T. Seiyama (ed.), Chemical Sensor Technology, Vol. 1, Kodansha, Tokyo, 1988, p. 39. H. Abe, S. Kanaya, Y. Takahashi and S. Sasaki, Extended studies of the automated odor sensing system based on plural semi-conductor gas sensors with computerised pattern recognition techniques, Anal. Chim. Acta, 215 (1988) 155-168. T. A. Jones, in P. T. Moseley and B. C. Tofield (eds.), Solid State Gas Sensors, Adam Hilger, Bristol, 1987, p. 51. J. W. Gardner, P. N. Bartlett, G. H. Dodd and H. V. Shurmer, in D. Schild (ed.), Chemosensory Information Processing, Vol. H39, Springer, Berlin, 1990, p. 131. G. Heiland, Homogeneous semiconducting gas sensors, Sensors and Actuators, 2 (1982) 343-361.
9 J. F. McAleer, P. T. Moseley, J. 0. W. Norris and D. E. Williams, Tin dioxide gas sensors, J. Chem. Sot., Faraday Trans. I, 83 (1987) 1323-1346. 10 V. Lannto, P. Romppainen and S. Leppavuori, A study of the temperature dependence of the barrier energy in porous tin oxide, Sensors and Actuators, 14 (1988) 149-163.
11 H. K. Henisch, Semiconductor Contacts, Clarendon Press, Oxford, 1984, p. 9. 12 J. Mizsei and J. Harsanyi, Resistivity and work function measurements on Pd-doped SnO, sensor surface, Sensors and Actuators, 4 (1983) 397402. 13 D. E. Williams, in P. T. Moseley and B. C. Tofield (eds.), Solid State Gus Sensors, Adam Hilger, Bristol, 1987, p. 115. 14 Figaro Engineering Inc., The basis of Figaro gas sensor, Technical Notes, Osaka, Japan. 15 M. Kaneyasu, A. Ikegami, H. Arima and S. Iwanaga, Smell identification using a thick film hybrid gas sensor, IEEE Trans. Components, Hybrids Man@ Technol., CHMT-IO (1987) 267273. 16 H. V. Shurmer, J. W. Gardner and P. Corcoran, Intelligent vapour discrimination using a composite 12 element sensor array, Sensors and Actuators, 131 (1990) 256-260.
17 W. P. Carey, K. R. Beebe, B. R. Kowalski, D. L. Illman and T. Hirschfeld, Selection of adsorbates for chemical sensor arrays by pattern recognition, Anal. Chem., 58 (1986) 149-153. 18 S. L. Rose-Pehrsson, J. W. Grate, D. S. Ballantine and P. C. Jurs, Detection of hazardous vapours including mixtures using pattern recognition analysis of responses from SAW devices, Anal. Chem., 60 (1988) 2801-2811.
19 J. W. Gardner, E. L. Hines and M. Wilkinson, Application of artificial neural networks in an electronic nose, Meas. Sci. Technot., I (1990) 446-451. 20 J. W. Gardner and E. L. Hines, Detection of vapours and odours from a multisensor array using pattern recognition. Part II. Artificial neural networks, to be published.
109
B, 4 (1991) 109-115
Detection of Vapours and Odours from a Multisensor Array Using Pattern Recognition Part 1. Principal Component and Cluster Analysis JULIAN W. GARDNER Department
of Engineering,
University
of Warwick,
Conventry
Abstract Mathematical expressions describing the response of individual sensors and arrays of tin oxide gas sensors are derived from a barrier-limited electron mobility model. From these expressions, the fractional change in conductance is identified as the optimal response parameter with which to characterize sensor array performance instead of the more usual relative conductance. In an experimental study, twelve tin oxide gas sensors are exposed to five alcohols and six beverages, and the responses are studied using pattern-recognition methods. Results of regression and supervised learning analysis show a high degree of colinearity in the data with a subset of only five sensors needed for classification. Principal component analysis and clustering methods are applied to the response of the tin oxide sensors to all the vapours. The results show that the theoretically derived normalization of the data set substantially improves the classification of vapours and beverages. The individual alcohols are separated out into five distinct clusters, whereas the beverages cluster into only three distinct classes, namely, beers, lagers and spirits. It is suggested that the separation may be improved further by employing other sensor types or processing techniques.
Intruduction Considerable effort has been directed towards the use of metal oxides for gas detection, since the discovery by Brattain and 0925~4005/91/$3.50
CV4 7AL (U.K.)
Bardeen in 1953 that adsorption of a gas on the surface of a semiconductor can produce a significant change in electrical resistance [ 11. Although measurements have been made on a variety of materials (e.g., ZnO, TiOz, W03) in different forms (single crystal, polycrystalline, amorphous), the most successful commercial semiconducting gas sensor employs a porous, sintered tin oxide element doped by a precious metal. Unfortunately, the performance of semiconducting oxide sensors is often limited by such problems as long-term drift in base-line conductance, a poor specificity and sensitivity to humidity. In the mid 1980s Zaromb and Stetter [2] proposed the use of an array of sensors with partially overlapping sensitivities. This overlapping sensitivity approach to gas sensing has been adopted by several workers and applied not only to arrays of commercial tin oxide sensors but also to MOS and piezoelectric devices. In addition, several pattern-recognition techniques have been used to determine relationships in the multidimensional data sets from these gas sensor arrays; for a general review see Gardner and Bartlett [ 31. An important element in any patternrecognition method is the selection of an appropriate pre-processing algorithm to characterize the sensor response. The sensor response or sensitivity has been represented in a variety of ways including the relative resistance value, R&R,, [4]; log relative resistance value, ln(R&Rair) [ 51; conductance difference, G, - Gtii, or even the fractional conductance change, (G,, - GGr)/Gair [6], where Rgas, Rair, G,, Gtir are the resistances or conductances in gas or air respectively. 0 Elsevier Sequoia/Printed in The Netherlands
110
Furthermore, it is quite common to apply a divide normalization procedure, e.g., throughout by the average or maximum sensor response, or autoscale the sensor data (make the response of each sensor have a mean of zero and standard deviation of one over all the chemicals sensed). In this paper, a microscopic model of conduction in sintered tin oxide films is developed to determine the most appropriate of these parameters to define the sensor response and the merits associated with the choice .of the pre-processing technique are discussed. Next the measured response of an array of twelve sintered tin oxide gas sensors, an electronic nose [7], to five alcohols and six beverages is presented. Finally, these data have been analysed using both unsupervised (cluster analysis) and supervised (principal pattern-recognition component analysis) techniques and the ability of these techniques to classify vapours or odours is evaluated.
Use of a Microscopic Model to Determine the Optimal Response Parameter The mechanism of bulk conduction in tin oxide is normally described in terms of an n-type semiconductor, where the intrinsic donors are assumed to be oxygen vacancies V,. Thus, the associated donor concentration n’ may be determined by reaction ( la) : O*-(s)
sVo+n’+;O,(g) L
R + 0, -(s) 2
mR0 + n”
(14 (lb)
where the reduction in lattice oxygen, 0, -(s) causes an increase in the oxygen lattice vacancies V, and electron donor concentration. The second irreversible reaction ( 1b) follows the introduction of a combustible gas R, where the product RO is often gaseous (e.g., CO2 and H,O) and KZ”is the resulting donor The conductance change concentration. expected from this bulk model of a homogeneous non-stoichiometric oxide cannot explain the observed gas sensitivity of thin or
thick (doped) tin oxide film [S, 91. Therefore a barrier-limited conduction model was introduced by Heiland [ 81 for thin tin oxide films in which the electron mobility is limited at the surface by a space-charge region. The model was later extended to describe the behaviour of thick porous tin oxide films or pellets, where oxygen is free to diffuse into the bulk of the material. Consequently, the accepted model of a porous sintered oxide film is that of barrier-limited conduction [9, lo]. Assuming a symmetric potential barrier, when the conductance G is governed by thermionic emission [ 111, gives i 2e kT x exp(s)
cash(g)
(2)
where the donor concentration n is modified by the lattice oxygen (eqn. (l)), the barrier height Q, is dependent upon the difference between the thermionic work function of a vacuum (undoped) or precious metal (doped) and the electron affinity of the semiconductor, m* is the effective mass of the donor, k is Boltzmann’s constant and T the absolute temperature. The effect of the gas R may now be modelled as a lowering of the integranular barrier height A (in units of e/kT), and provided that the donor concentration n is governed by the bulk stoichiometry as stated earlier, we can reduce eqn. (2) to G = G,, exp(A) Using this microscopic model to calculate the response parameters to apply in patternrecognition techniques, we obtain the formulae shown in Table 1. The reduction in the barrier height A may be related to the gas-induced donor concentration n ’ (eqn. 1(b)) and bulk donor concentration n by A N ln( 1 + n”/n)
(4)
Assuming that the bulk carrier concentration is effectively given by the oxygen lattice (i.e., n x n’), then eqn. (4) is identical to that proposed by Mizei and Harsanyi [ 121, and later by Lantto et al. [IO]. The donor
111
TABLE 1. Response parameter height model
relationships:
barrier
Expressions
Conductance
Resistance
Difference Fractional change Relative
GJexp(A) - 11 exp(A) - 1
&[exp( -A) exp( -A) - 1
exp(A)
exp( -A)
11
concentrations 11’ and n” are related to the oxygen partial pressure in air and gas, [O,],i, and [ OJgas, which gives A = ~~{[~zlair/EQdgasI = W3
(5)
where 0 is the fractional occupancy of the lattice vacancies. The reaction kinetics have been solved by Williams [ 131 and produce A = ln( 1 + K;[ R]“/K,0)0,92 where K1’ and K2’ are the temperature-independent forward reaction rates in eqns. (la) and (lb) and [R] is the partial pressure of the gas R. The index m depends upon the lattice oxygen species; when the species is 02-(s), its value is i. Thus, A can be approximated and substituted into the response parameter relationships of Table 1. The results are shown in Table 2. There is considerable experimental evidence to support the theoretical relationship for the fractional change in conductance or resistance [ 141. From Table 2 it may be seen that the relative change is a poor response parameter when the partial pressure of gas is low, whereas the difference or fractional change in conductance is always (i.e., for all
TABLE 2. Response parameter relationships: gas concentration. Gh is Go(Kzo/K,o) and Rh is &(Kzo/K,") Expression
Conductance
Resistance
Difference
G&[R]”
-R;[R]”
Fractional change
$ [RI”
-$
Relative
1 +,K”/K,“)lN”
[ 1 + WZ”/~~)[
[RI”’
A<1 only
RI”1- ’
A) a sensitive parameter. In an array of i porous tin oxide sensors, the change in conductance is now related to the gas j partial pressure by
S, = &as -
G,i,) /G,i,
= uV[ RI”’
(6) The index m is dependent upon the oxide properties and temperature rather than the gas analysed, and CIis the ratio of reaction rates and depends upon the sensor type and gas. When sampling at fixed gas concentration, the difference or fractional conductance is most appropriate and a commonly used normalization procedure removes the concentration terms (7) When sampling of various components takes place it is preferable to linearize eqn. (6) by using the log-parameter, i.e., lnKG,,s - Gir)/G,i,] = mi log[R] + UU (8) It is then possible to carry out regression analysis on this set of equations, provided that the fractional conductance is not too near zero since the log term would introduce large errors. Several workers have used the log-relative parameter to define the sensor response [9, 151. Although this technique ameliorates the concentration effect in the sensor responses, it does not linearize the equations ln[G,,/G,i,]
N ag[ RI”’
(9) In this case the simple normalization of the signals over all sensors is not appropriate; instead a double logarithm is needed. Experimental Measurements Measurements on the response of an array of twelve different commercial tin oxide gas sensors were taken using the Warwick electronic nose. A full description of the experimental arrangement is given elsewhere [ 161. In brief, the conductance of each sensor was measured before and three minutes after either 0.4~1 of an alcohol or 25 ,~l of a
beverage was introduced into a 20 1 flask containing the sensor array. Eight sets of data were taken on five alcohols, namely, methanol (m), ethanol (e), I-butanol (b), propanol (p), and 2-methyl- 1-butanol (x); followed by ten sets of data on six beverages, namely two beers (w, s), two lagers (h, c) and two spirits (whisky (t) and brandy (b)).
Data Analysis The error on the fractional conductance change of the array was defined by the ratio of the sample standard deviation to the sample mean averaged over all twelve sensors. This error was found to be 16.4% when averaged over all the alcohol data. Several workers have normalized the response parameter using eqn. (7), but from the analysis above a more appropriate procedure is
The adoption of this normalization procedure removes the effect of a change in the sign of S, as would be observed in a mixed sensor array or could be caused by falling base-line drift. Moreover, the normalized parameter, gV,,is now the length of the response vector in n-dimensional space. Employing this procedure on the alcohol data, the error in fractional conductance change was observed to fall to 11S%. This reduction was probably due to the removal of the variation in vapour concentration during testing. Regression (and unsupervised hierarchical cluster analysis) revealed high correlations between the tin oxide sensors in the array. The correlation matrix of the normalized fractional change in conductance for the alcohols was calculated (and a similar one was found for the beverages). Strong correlations exist between sensors {1; 3, 5,6,9, 11, 12) and (7,s). Thus, the vapours and beverages could be measured using a subset of only five sensors, such as 1, 2, 4, 7 and 10.
Cluster Analysis (CA) In cluster analysis, points are grouped together according to their proximity in ndimensional space. A similarity value SIM, can be calculated to represent this proximity and is given by SIM, = 1 - d,/max(d,)
(11) where dii is the distance metric of the data points (i, j) in n-dimensional vector space and max(dJ is its maximum value. The similarity index is one for two identical points and zero for the two most distant, and the values are displayed on a dendrogram. Methods of finding clusters in multidimensional data from piezoelectric quartz [ 171 and SAW [ 181arrays have been reported. In this study the Lance and Williams distance metric has been chosen with flexible fusion [3]. Figure l(a) and (b) shows the dendrograms for the original and normalized alcohol fractional conductance data sets. Clearly, the normalization procedure enhances the cluster analysis since in the normalized data the five clusters (A-E) become more distinctly revealed. The technique was also applied to the beverage data, which again showed an improvement in analysing the normalized response, where three clusters
Fig. 1. Results of cluster analysis on original (a) and normalized (b) responses (fractional conductance change) of a twelve tin oxide sensor array to five alcohols (m = methanol, e = ethanol, p = propan-2-01, b = 1-butanol and x = 2-methyl- 1-butanol).
113
LaOor
oxide gas sensor arrays, it has been successfully applied by others [ 17, 181 to analyse the response of piezoelectric devices. In principal component analysis, the response matrix is expressed in terms of linear combinations of the orthogonal response vectors S,. So the rth principal component X, is a summation of the n response vectors S, for the vapours
& Beerr
j
h---Spirits
3!t-
Fig. 2. Results of cluster analysis on original (a) and normalized (b) responses (conductance change) of a twelve tin oxide sensor array to six beverages (h = lager A, c=lager B, w =beer A, s =beer B, t =whisky, b = brandy).
of lagers (A), beers (D’) and spirits (C’) were observed, Fig. 2. Unfortunately, the separation within these classes is poor. It should be noted that a cluster analysis of the relative conductance and fractional conductance change produces identical results, because a unit translation of each response vector will not change the relative distance between points. Principal Component Analysis (PCA) Principal component analysis is a powerful linear supervised learning pattern-recognition technique that is usually employed in conjunction with cluster analysis. Although it has not yet been applied to the output from tin
i=
(12) 1
where air are the eigenvectors, sometimes referred to as the loadings. The variance of X, is maximized under the constraints that f
air = 1
i=l
and that the principal components are independent. The percentage of data variance contained in each principal component is determined by the eigenvalue. In essence, the technique removes any redundancy in the data and thus reduces the dirnensionality of the problem. Table 3 shows the value of the eigenvalues and percentage variance for the first five principal components of the original and normalized response of the tin oxide array to alcohols and the percentage variance of the beverages. The magnitude of the eigenvalues depends upon the normalization procedure. When autoscaling is used the total is simply n, where n is the number of sensors in the array. However, autoscaling has not been used here for two reasons: first, the response parameters are similar in magnitude and secondly, autoscaling increases the fractional error on
Table 3. Eigenvalues of response data Principal component or eigenvector
Alcohols Original eigenvalue % var.
Xl x, x, x, X,
5.282 68.6 1.960 25.5 3.2 .0.245 1.2 0.095 0.7 0.052
Beverages Normalized eigenvalue % var.
Original % var.
Normalized % var.
0.081 0.023 0.005 0.002 0.002
98.6 0.8 0.3 0.1 0.0
74.8 19.0 2.6 1.9 0.8
70.4 20.0 4.4 2.2 1.5
I
-3 -4 (a)
I -2 0 2 Principal Component,
4 X,
-41 -.6
6 @)
Fig. 3. Results of principal component conductance change) to five alcohols.
analysis
1
I
-:4
-.2 Principal
0 2 Component,
of the original
4 X,
6
(a) and normalized
:~__;~~
I
t
I
-400 .-
-.06;.
I I
(a)
0 Principal
-.
h
Ec CC
I I
-1
_:
.L L-04
b
-.08 L 1 Component
Fig. 4. Results of principal change) to six beverages.
2 X1
component
(b) responses (fractional
-2 W
‘h I I 1
.l -1 0 Principal Conponcnt,
,2 X1
analysis of the original (a) and normalized
low signals, which could lead to erroneous results. In both sets of data, we can see from Table 3 that over 90% of the variance within the data is contained in the first two principal components. Figure 3 shows a plot of the first principal components (X, and X2) for the original and normalized alcohol responses, where an improvement can be seen in particular upon the normalized response for methanol and I-butanol. Again it should be noted that the PCA of the log-relative values is the same as the fractional conductance change provided normalization is not used. A more dramatic effect is noted with the beverage response (see Fig. 4), where the beers and lagers are now separated from each other and
(b) responses (conductance
in addition the spread in the spirits group is reduced. However, within these groups it is still difficult to separate out the individual beverages, and these results produce less separation than an earlier parameter study [ 161.
Conclusions A microscopic model of conduction in tin oxide gas sensors has been developed to select the appropriate sensor response parameter, and improves subsequent classification when compared with more conventional parameters. CA and PCA have been applied to alcohols and beverages and gave good
115
classification for alcohols, but restricted classification for beverages. Further improvements may be made to pattern recognition of vapours and odours by either employing a subset of only five tin oxide gas sensors with, perhaps, SAW devices or considering the application of more generalized pattern-recognition techniques, such as artificial neural networks [ 19,201.
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