Qualitative and quantitative gas analysis with non-linear interdigital sensor arrays and artificial neural networks

B CHEMICAL

ELSEVIER

Sensors and Actuators B 26-27 (1995) 289-292

Qualitative and quantitative gas analysis with non-linear interdigital sensor arrays and artificial neural networks Gerhard Niebling, Artur Schlachter Lehrstuhl fiir Technisehe Elektronik, Technische Universitiit Mi~nchen, Arcistrasse 21, 80333 Munich, Germany

Abstract

Interdigital sensors are well suited to the quantitative and qualitative analysis of gases and vapours. The surfaces of the sensors are coated with substances which are also used in gas chromatography. The signals for the gas analysis are the relative changes of the electrical conductance and capacity. The disadvantages of these sensor elements are their non-selectivity and their non-linear transfer characteristics. Artificial neural networks are used for pattern recognition of multicomponent sensor systems. The paper describes a modification of the conventional signal evaluation technique using neural networks to evaluate the concentrations of a gas mixture. Keywords: Gas analysis; Interdigital sensors; Chemosensors; Neural networks; Signal processing

1. Introduction

1.1. Neural network

The quantitative analysis of a gas mixture with nonselective and non-linear sensor elements is achievable with a combination of several different sensor elements in an array. The usual process of quantitative gas analysis is the determination of a model which describes (exactly or approximately) the relation between the sensor signals of the array and the concentrations of the gas components. Different regression techniques can be used to estimate the concentrations of a gas mixture when applying a chemosensor array. For sensors with a linear transfer characteristic the mathematical expression of the model is a matrix calculated by linear regression methods like PCA (principal component analysis) or PLS (partial least squares) [1]. Regression procedures for non-linear sensors, e.g. TLS (transformed least squares) [2], MARS (multivariate adaptive regression splines) [3] and PPR (projection pursuit regression) [4], are either parametric (PCA, PLS, TLS) or non-parametric techniques (MARS, PPR). The goal of a parametric regression technique is to find a parameter set describing the functional dependence of sensor signals and gas concentrations, whereas a non-parametric technique (e.g. a smoothing routine) provides a model which gives an approximate relation between the measured data and the sensor signals.

The methods of pattern recognition with artificial neural networks belong to the non-parametric techniques. The multilayer perceptron which is discussed in this paper is one of the most commonly used neural networks in the field of classification [5]. The basic element of an artificial neural network is a node (Fig. 1). A node has some weighted inputs and one analogue output. The nodes are ordered in several layers (Fig. 2).

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X(l'l)3 ~ _ _ , ~

~_~,

X(l-l)2

Xlj

X(l-l)l ~ WLjl Fig. 1. Single node.

>

v

layer 1 Fig. 2. Two-layer neural network.

layer 2

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G. Niebling~ A. Schlachter / Sensors and Actuators B 26-27 (1995) 289-292

The next step is the estimation of OFlau~/ [-~ UW-m l

(6)

~,j = OF/Ou,j

~ ~.ode (of the layerbefore) |node (of the actuallayer) layer

layer

(6~=f'(X,j)

a~ =Xzj(1-X~)a~.)

Fig. 3. Nomenclature.

The previous terms ~ - 1 ) can be computed from 3t:

Nomenclature

~__ 1)i = ~ Wlji~lj j~l

The basic nomenclature is shown in Fig. 3. The values X are node inputs or outputs. The values w are weight factors. The terms 6* and 6 are explained later. The first index (on the left side) marks an actual layer l, the second index marks a node in this layer, and the third index (for weights) marks a node number in the layer before, ( l - 1).

(7)

where m is the number of units in layer l. Finally, aF/~wzji can be calculated: (8)

aF/Ow,ji = 6,jX(,_ I )i

With a gain term • and an optional 'recollection' factor a the weights can be adapted: (9)

Awg.~.w = - • aF/Ow,, + a Aw~'? Forward p a s s

At the beginning of the forward pass an input vector is laid on the first layer and the signal information is shifted through the network. The output values of a single node with n inputs are calculated as follows: n l = 1, 2

Uij ~-- E X ( l _ l ) i W l j i i~o

(1)

1

Xtj =f(u0.) - 1 + exp( - u0.)

(2)

f is the sigmoid transfer function (Eq. (2)) of a single node. Xto is a 'pseudo' input (always with value 1). This means that the weights w(t+ ~o are the offset values of this node j in the layer l + 1. The fitting of the offset values is included in the learning process. 1.2. Back-propagation

(10)

2. Quantitative gas analysis with neural networks Experiments with synthetic data sets have been performed in order to study the behaviour of neural networks. The calibration data set for the training phase consisted of 25 points (Figs. 4 and 5). The trained networks were tested with a data set of 189 points (Figs. 6-8). gas concentrations ~

sensor signals

algorithm

The back-propagation training algorithm described by Rumelhart et al. [6] uses a gradient search technique to minimize a cost function F equal to the mean square difference between the desired output dr and the actual output vector X~. (two layers). The following description gives a short introduction to the algorithm. The cost function is given by F=O.5(Xw-dj)

w~ w= wgld + Aw~ w

2

(3)

Fig. 4. Sensor signals vs. gas concentrations (calibration data). sensor signals ~

gas concentrations

The necessary condition for the minimum is (4)

bF /i)w = O

1,0

Backward pass

The backward pass starts with the calculation of OF/OXo (an example calculation for the two-layer network

is given in parentheses): (5)

6~ =aF/OXtj

d;)

Fig. 5. Gas concentrations vs. sensor signals (calibration data).

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G. Niebling~ A. Schlachter / Sensors and Actuators B 26-27 (1995) 289-292

The model for the synthetic data sets was found empirically by measurements with interdigital sensors. The aim of the experiments was the estimation of the concentrations of a binary gas mixture.

2.1. Conventional method

li

Usually an inverse model C-1 is estimated in order to obtain the gas concentrations of the sensor signals. Fig. 5 shows the inverted relation of Fig. 4.

Fig. 8. Gas concentrations vs. sensor signals (test data).

Experiment 1 We used a neural network with five inner units in order to approximate the inverse model C -1. Fig. 6 shows the result after 20 000 learning steps made with the calibration data set. The parameters • and a of the learning algorithm were 0.4 and 0.9. 2.2. Reverse calibration (RC)

with an iterative process using a modified backward pass. In the beginning a rough estimation of the gas concentrations sought is laid on the inputs of the neural net. The forward pass is performed in the same way as described before, the backward pass also, but the calculation continues until the terms /71

Experiment 2 With the network parameters of experiment 1 we trained a network in order to approximate the sensor characteristic. Fig. 7 shows the result. After a sufficient approximation of the sensor characteristic is achieved the gas concentration can be found

~ = ~ wu,~lj

The weights of the network remain unchanged. The input values Xoj are adapted (Eqs. (12) and (13)) until stable values are achieved. These values are finally the estimations for the gas concentrations (Fig. 8): AX;7 ~= - ~

sensor signals - - ~

gas concentrations

I.

(11)

j=l

+/3 AX;' a

X~0?w=A~a + AX'd;w

(12) (13)

The experiments show that the approximation of the sensor characteristic is better than the approximation of the inverse relation.

3.

Experimental

3.1. Interdigital chemosensors I

Fig. 6. Approximation of the inverse model C - t (test data).

gas concentrations @

sensor signals

i Fig. 7. Approximation of the sensor characteristic C (test data).

The basic function of an interdigital sensor (Figs. 9 and 10) is based on the polarizability of the sensor coatings and the ionic conductance caused by the dissociation of the adsorbed molecules [7,8]. A quartz wafer is used as substrate because of its high chemical stability and its electrical properties. The electrodes are buried in the substance (Fig. 10) in order to get a plane surface for the sensitive coating. The sensitive coatings were laid on with an airbrush technique to a thickness of about 0.2-1.0 mm.

3.2. Signal evaluation We performed experiments with mixtures of acetone and methanol vapours. As an example, Fig. 11 shows the relative conductance versus the concentrations of a methanol-acetone mixture. The measurements were

292

G. Nieblin~ A. Schlachter / Sensors and Actuators B 26-27 (1995) 289-292 s _

made with an array of different coated interdigital sensors and evaluated with a neural network applying the modified method described above. Fig. 12 shows the result of the evaluation.

metallization

Fig. 9. Structure of an interdigital sensor. B=5~m

4. Conclusions

A = 5 p.m

The experiments show that the use of the reverse calibration (RC) technique (experiment 2) supplies better results than the conventional method (experiment

////////////////

1).

quartz plate Fig. 10. 'Buried' electrodes.

4.0 ~.~

Although the experiments were only realized for the transfer characteristics of interdigital sensors the results can be transmitted to other classes of transfer characteristics. The application of the RC technique is a new, interesting aspect of quantitative gas analysis with the use of a neural network for function fitting.

References

Fig. 11. Signal of the SE 25 coated sensor.

0

2

6

METHANOL[~] Fig. 12. Indicated vapour concentrations (full circles) vs. the true concentrations (open circles on the dotted lines).

[1] S. Wold, H. Martens and H. Wold, The multivariate calibration problem in chemistry solved by the PLS method, Lecture Notes in Mathematics, Vol. 973, Springer, Berlin, 1983, pp. 286-293. [2] C. Hierold and R. Miiller, Quantitative analysis of gas mixtures with non-selective gas sensors, Sensors and Actuators, 17 (1989) 587-592. [3] J.H. Friedman, Multivariate adaptive regression splines, Ann. Statist., 19 (1991) 1-141. [4] J.H. Friedman and W. Stuetzle, Projection pursuit regression, J. Am. Stat. Assoc., 76 (376) (1981). [5] G. Niebling, Identification of gases with classical pattern recognition methods and artificial neural networks, Sensors and Actuators B, 18 (1994) 259-263. [6] D.E. Rumelhart, G.H. Hinton and R.J. Williams, Learning internal representations by error propagation, in D.E. Rumelhart and J.E. McClelland (eds.), Parallel Disuibuted Processing: Explorations in the Microstructures o f Cognition, Vol. 1, MIT Press, Cambridge, MA, 1986, pp. 318-362. [7] E.C.M. Hermans, CO, CO2, CH4 and H20 sensing by polymer covered interdigitated electrode structures, Sensors and Actuators, 5 (1984) 181-186. [8] R.S. Jachowicz and S.D. Senturia, A thin-film capacitance humidity sensor, Sensors and Actuators, 2 (1982) 171-186.