Analytica Chimica Acta 417 (2000) 101–110
Quantitative artificial neural network for electronic noses Yu Lu, Liping Bian, Pengyuan Yang∗ Department of Chemistry, Fudan University, Shanghai 200433, PR China Received 9 August 1999; received in revised form 30 March 2000; accepted 6 April 2000
Abstract This paper reports a quantitative artificial neural network (ANN) to implement an electronic nose (enose). A new approach was proposed by the combination of ANN with fundamental aspects of analytical chemistry, especially with the concept of relative error (RE) in quantitative analysis. Thus, both the qualitative and quantitative requirements for ANN in implementing enose can be satisfied. Converging criterion while training the ANN can be set according to RE function (RE-Func) designed in this work. Fast converging speed and good prediction accuracy could be promised with the use of RE-Func. In addition, transform functions in logarithmic, sigmoid and their combined forms to pre-process training data sets were evaluated. Also training methods, such as order of training data magnitude and treatment of data passed the RE requirement checking in last iteration, were optimized. The enose was constructed to response quantitatively towards alcohol vapor within concentration range of 0.001–1 mg/l in the presence of petroleum gas and water vapor. The prediction error was <10%. No qualitative mistake of prediction was observed for samples of alcohol and petroleum vapors, or for their mixtures. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Enose; ANN; Quantitative analysis; Alcohol vapor
1. Introduction Quantitative analysis of gases, by means of so called electronic nose (enose) composed of artificial neural network (ANN) with semiconductor sensor arrays, has attracted more and more attentions [1,2]. In the real world, the gas concentration measured can vary from a few ppm to more than a thousand ppm, which may be 2–3 order of magnitude over the concentration range. Thus, a practical enose must response to a wide concentration range of gases quantitatively, in addition to ∗ Corresponding author. Tel.: +86-21-65642009; fax: +86-21-65641740. E-mail address:
[email protected] (P. Yang)
its excellent ability of pattern recognition in qualitative analysis [3]. There are already quite a number of studies dealing with the quantitative problems associated with the enose using semiconductor sensor arrays or other sensor arrays [1,4–6]. In its nature, the ANN is most likely suitable to solve many problems of pattern recognition which is in the area of qualification of analytical chemistry. When the ANN is applied to the quantitative analysis, many classical neural network models, such as back-propagation (BP) cannot predict smelled gas concentration correctly [5]. The main reason for this failure is possibly due to the ‘0–1’ feature for both the sigmoid transfer function and outputs of neurons.
0003-2670/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 3 - 2 6 7 0 ( 0 0 ) 0 0 9 2 2 - 3
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Therefore, the BP-ANN model must be modified to face the wide concentration range in the real application. Llobet et al. [1] proposed a method using transient and steady state responses of a sensor array to perform a quantitative analysis for gases. However, the tested concentrations were only of three types: 25, 50 and 100 ppm. De Agapito et al. [4] described a fuzzy logic model, with which the concentration of a gas may have some linguistic labels, such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Although the concentration of a gas sample can be classified in such way, this model may only solve the concentration problem semi-quantitatively. A new fuzzy-logic approach has been proposed by Vlachos in 1996 [5]. This model does not suffer from abrupt transitions and can be trained very efficiently by increasing the amount of training data. As its defect, a relatively large error was found when the sample concentration is high. In a modified multi-layer perceptron model [6], Moore et al. applied a partially connected network and obtained a very good linear response in concentration range from 0 to more than 10,000 ppm for individual gas tested. However, they also found that when a gas mixture was measured, the modified ANN gives a poor qualitative result for some gases, such as CO. In other words, the new model enhances the quantitative ability while degrades its qualitative merit for gas pattern recognition at the same time. As a consequence, the interference problem might be raised up when the enose is utilized to a gas mixture. Is there any other smart way to overcome the quantitative problems in ANN? When we apply the ANN approach to a chemical system, have we neglected some important features of this system? To answer these questions, recently, Wang and Kowalski proposed a concept of ‘ChemNet’, as well as its theory and application [6]. The creative idea behind ChemNet is to incorporate chemical theories into neural network structure, so that the ANN system can store a priori knowledge when building a model. This combination is one step closer to the true underlying model than those classical or traditional ANN models. Clearly, this new approach has brought the quantitative ANN into a new stage. Hereby, we report a quantitative ANN model based on the theory of analytical chemistry, especially the
concept of relative error (RE) in quantitative analysis. Its application to the real gas mixture analysis is also discussed.
2. Theoretical 2.1. Relative error in quantitative analysis As well known, analysts can evaluate whether an analytical result is satisfactory by comparing the tested result (Rx ) with the ideal one (Ri ), then an analytical conclusion can be drawn according to the value of RE RE =
R x − Ri Ri
(1)
The value of RE is a concentration-related parameter. In general, a larger RE is expected for low concentrations and especially for a concentration near the limit of detection (LOD). In contrast, a smaller RE may be used for higher concentrations. Clearly the RE is not a constant over the whole concentration range. A hyperbolic type profile would well describe the curve shape of RE requirement over the whole concentration range, which is shown as the dashed curve in Fig. 1. For this RE reason, when the tested concentration is small, generally analysts do not require analytical
Fig. 1. Requirement of relative error in analysis. Dashed curve, ideal relative error for analytical instruments; solid curve, real relative error requirement in this work.
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Fig. 2. ANN architecture of enose. The first layer is called as gas sensor layer; the second, hidden layer; the last, output concentration layer. Signals are transferred from layer to layer and their values are decided by both the transfer function used by each neuron and the connection weights between two different neurons.
instruments to give the same accurate data as those of larger concentrations. This situation should be considered when an enose is applied to the gas mixture with a wide concentration range. 2.2. ANN model The architecture of ANN commonly utilized in this work, so-called three-layer feed-forward ANN [8], is shown in Fig. 2. The mathematical formulation of the neurons in this three-layer ANN is X xi,k−1 wij + bj (2) yj k = F where yj k is output of the jth node in the kth layer, wij the connection weight between the ith node and the jth node from i to j, bj the bias of the jth node and F(x) is the transfer function. A selected member of sigmoid family is used usually as the transfer function, for instance [10] F (x) =
1 + tanh(x/x0 ) 2
(3)
where x0 is a constant to control the slope of the transfer function. 2.3. BP learning and integration of RE Most of the practical ANNs are trained by the method of BP learning, whose process has been described clearly in [7]. To take consideration of the RE
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discussed before, a piece of rule is made that when the RE of a predicted result is smaller than the permitted one for this concentration level, the predicted result is regarded as correct. In theory, when all the data in the training set pass this check, the ANN is considered fully trained and can be used to predict concentrations of unknown samples. With this rule, the RE nature of analytical chemistry has been taken into ANN. To apply this rule, the permitted RE for each concentration must be pre-learnt in the ANN. A function called RE-func, RE(x), is introduced to realize in computer application of ANN. To build a RE-func is just an easy task. In general, the RE representing the requirement of permitted error can be formulated as hyperbola (see the dashed curve as shown in Fig. 1). For instance, the required error in an intermediate concentration range could be |1c| ≤ e
(4)
where c is the concentration and e is the permitted error within this concentration range. Then the RE-Func in this range should be RE(c) =
e c
(5)
And for very low and very high concentration cases, the RE-Func might be simply a constant within a concentration range RE(c) = re
(6)
where re is the constant RE requirement. Thus, the combination of several equations as in the forms of Eqs. (5) and (6) gives the RE-Func for the whole concentration range to be considered. The profile of this real RE-Func is plotted as a solid curve showing in Fig. 1. In the numerical iterations, the convergence of training process is judged by the RE value of the ANN output as follows: yc − yik ≤ RE(c) yc
(7)
where yc is the output value expected from the training set.
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2.4. Selection of pre-process function The pre-process function, with which ideal concentration (teacher signal) is turned into the value range of 0–1, is a realistic problem in ANNs for quantitative analysis, because ANN models available can only deal with data in this very 0–1 range. Unfortunately, only a little emphasis has been put on this matter in earlier works, but it is indeed a problem worthy of consideration [6]. In fact, any function producing values between 0 and 1 can be used as the pre-process function. Two different kinds of conversion methods are used and compared here. An example of logarithmic function is given as x0 =
log x + m 2m
(8)
where x is the original concentration, x0 the processed ‘teacher signal’ for the ANN, and 2m is the order of magnitude expected for applied concentration range (10m –10−m ). And an example of sigmoid one has the form as below x π (9) x 0 = sin max 2 where max is the maximal concentration during the whole analytical process. Both the functions are shown in Fig. 3A and B. Theoretically, the logarithmic function is apparently suitable for qualitative analysis for its great ability differing ‘no’ (zero) from ‘yes’ (larger than zero). However, it is hard to employ this function for quantitative analysis because its output is likely between the range of 0.5–1 in most cases, no matter the input value is very small (e.g. value of 1) or quite large (e.g. value of 500), based on Eq. (8). When the ANN predicts concentration of an unknown sample, it is difficult to distinguish quantitatively from such a narrow range. In the other hand, the output of sigmoid function covers 0–1 smoothly so that it fits adequately into quantitative analysis, although it hardly has the merit of qualitative analysis as in the case of logarithmic one. Thus, a wiser way seems to take these two functions together
Fig. 3. Pre-processing transform functions: (A) logarithmic function; (B) sigmoid function and (C) combination of logarithmic and sigmoid function.
where lim is the transform point, the point to combine these two functions together: logarithmic function is used when x is below lim; while sigmoid function is used when x is larger than lim. The profile of this function is shown in Fig. 3C. By this means, both qualitative and quantitative requirement of analysis could be fulfilled in theory.
log x + m x ≤ lim 2m x0 = x − lim log lim + m log lim + m + sin arcsin 1 − x > lim 2m max − lim 2m
(10)
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3. Experimental
3.3. Experimental procedure
3.1. Hardware and software
Before each measurement, the air signals Gair of four sensors were collected. The alcohol vapor samples with particular concentration were made up with standard alcohol vapor sample and air. Then the samples were introduced into the apparatus at the rate of 10 ml/min until the sensor array gets stabilized, which was monitored by a voltage meter connected to the output pin of the sensor array. After that, those stable signals Ggas of the sensor array were collected again, from which the responses of the four sensors were normalized as Eq. (11) and recorded
All calculations and data process were done with an IBM-compatible PC (80486 DX2 66 MHz or above). The programs to implement ANN were written in Borland C++ 4.5 for Windows 3.1 and Windows 95. 3.2. Experimental set-up The metal-oxide semiconductor sensor-array consists of four different sensors (manufactured by East Electronics Group, Beijing, China) which exhibit individual sensitivity to alcohol vapor, alkanes, petrol vapor and ethyne. The experimental set-up is illustrated in Fig. 4, and the whole apparatus was airtight. As shown in Fig. 4, gas samples were injected quantitatively and then passed through pipes and finally entered a measurement chamber, in which the sensor array lied. A gas chromatograph (GC-102, Shanghai Analytical Instrument Corp.) was connected in a cascade way to monitor those gas concentrations online. This additional monitoring by GC can ensure that the concentrations of all gas samples made up are correct.
G=
Ggas − Gair Gmax
(11)
where Gmax is the maximum input signal allowed by the electronic system. The concentrations of alcohol vapor samples made of during the experiments are listed in Table 1. Alcohol samples with eight levels of concentration were used with no interference gas added. Other alcohol samples in the presence of water vapor or hexane vapor or their mixture (see Table 1), were also measured. Altogether 102 samples of these concentrations were measured and were taken as the training sets. Finally, another 27 samples, 15 measured and 12 interpolated, which had not been used as training data, were taken as the testing sets (‘unknown’ samples) and their concentrations were predicted by the already trained ANN. The results of prediction were compared Table 1 Concentrations of tested samples
Fig. 4. Experimental set-up. Gas sample was stored and rarefied in the syringes; when injected, the sample flew from C port of the second tee, through the six-way valve and then into the sensor-chamber. A GC was connected with the six-way to detect online whether the concentration of the sample was right.
No.
Concentration (mg/l)
Ideal output
1 2 3 4 5 6 7 8 M1 M2 M3 M4 M5
0.012 0.025 0.062 0.12 0.25 0.49 0.74 0.99 0 (with 2 mg/l hexane) 0 (with 4 mg/l hexane) 0 (with 400 mg/l water vapor) 0.062 (with 2 mg/l hexane) 0.062 (with 400 mg/l water vapor)
5.0 9.9 25 49 99 198 297 396 0 0 0 25 25
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with the ideal concentrations of these 27 ‘unknown’ samples. Because those concentrations to be considered were just in the range of 0–1 mg/l, to draw a more representative conclusion of the methods discussed in this work, concentration values of measured samples were multiplied with 400. Then these new values were inputted into the ANN as input data. Therefore, the whole concentration range in this case could be from 0 to 500. The set of maximum value of 500 (used in Eqs. (9) and (10) was considered to avoid over-scale error when a sample with a possible concentration larger than 400 was measured.
3.5. The neural network The ANN used here is a three-layer feed-forward network (see Fig. 2) with BP learning as its teaching algorithm. There are four nodes in the input layer, each of which represents one semiconductor sensor. And in the hidden layer, benefited from use of concept of relative error, there can be only four nodes. It is understood generally that an improper set-up for the hidden nodes may be difficult for the ANN to converge to the best state in enose applications. As to the output layer, since only concentration of alcohol vapor will be determined, there is just one node. Transfer function in this ANN is the same as in Eq. (3).
3.4. Data processing 3.6. The training algorithm Data in the training sets and the testing sets (‘unknown’ samples) are all composed of responses of four sensors. The ideal concentration values of the training sets are also included. The concentrations of the samples in both sets, teacher signal in training sets and ideal output result in testing sets, can be found in Table 1. The parameter of m (see Eq. (10)) was set to 3 in this study such that the order of magnitude is 6 for the concentration range. All the input data were pre-processed by the function shown in Eq. (10) such that they were all transformed between 0 and 1. To have a quantitative output at the same time, the transformation from data in ANN output (between 0 and 1) to those real concentration values should be also considered. This kind of function is called post-process function. The post-process functions for the logarithmic and sigmoid function are listed in Eqs. (12) and (13), respectively. 0
x = 106x −3 2 arcsin(x 0 ) x = max π
(12) (13)
A successful training can be made as following. The training order of concentration was designed from small to large. At the end of iteration, the convergence of training process was checked against Eq. (7). The training data passed the RE requirement were marked and eliminated temporarily from training sets for next turn. Altogether 4,000,000 epochs were needed for the whole training process. The details of the algorithm are discussed in Section 4.4.
4. Results and discussions 4.1. ANN training and results As previous mentioned, Table 1 lists the concentrations of alcohol vapor used during the experiments. Table 2 shows the predicted results of testing sets when optimized conditions for ANN are applied. In Table 2, sample numbers with asterisks are interpolated concentrations. The other ones are tested sample numbers already explained in Table 1. The interpolated data were estimated from the response curves of sensors towards the gas samples. Each RE permitted listed in Table 2 was applied according to the error requirement for an individual concentration. Concentrations of
And as the combination of these two kinds of pre-process functions, the overall post-process functions is presented in Eq. (14). In these equations, meanings of the symbols are the same as discussed before. 0 106x −3 x ≤ lim log lim + 3 max − lim x= arcsin x 0 − + lim x > lim 6 arcsin(1 − ((log lim + 3)/6))
(14)
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unknown samples were predicted with the ANN under following conditions. Transform point was set to 10; training order was from small data to the larger ones; and training data passed in the last iteration would not be trained in the current training turn. To evaluate the convergence of a training process, the accuracy of trained ANN is defined by error rate e, of calculation e=
ne nt
(15)
where ne refers to the number of mis-predicted samples, which means an exceeding of the permitted RE, and nt refers to the number of all predicted samples. Obviously in an ideal situation, the value of e should be close to 0 after the ANN has been trained. In Table 2, an error rate e, of 11.1% still exists. This error rate is considered to be rather satisfactory for an ANN designed for quantitative analysis of gas mix-
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ture. There is only one interpolated sample labeled as I4 with quite large prediction error in Table 2. The reason of its relatively large deviation of this interpolated sample is still unknown in present stage. To achieve a best model of ANN, three key aspects must be investigated. These aspects are: applying the concept of relative error, choosing appropriate value of the transform point (lim) parameter, and training data sets using the optimized algorithm. The following sections will focus on these studies. 4.2. Effects of RE In this study, the enose is expected to a following accuracy requirement: 1c ≤ ±10 c ∈ [0, 80] 1c ≤ ±16 c ∈ (80, 160] (16) 1c ≤ ±10% c ∈ (160, 500] c
Table 2 Result of trained ANN applied in Enose No.
Predicted concentration/400 mg/l
Ideal concentration/400 mg/l
RE permitted
RE experimental
I1a I2a I3a I4a I5a I6a I7a I8a I9a I10a I11a I12a 1 2 3 4 5 6 7 8 9 4 M1 M2 M3 M4 M5
0.14 7.0 9.3 51 266 349 0.0042 6.7 8.5 32 239 334 0.0012 7.4 15 31 49 109 214 314 365 24 0.0014 0.0012 31 0.0014 32
2.5 4.9 7.4 103 247 346 1.2 4.9 6.2 57 223 322 0 4.9 9.9 25 49 99 198 297 396 25 0 0 25 0 254
4.0 2.0 1.3 0.15 0.10 0.10 8.1 8.1 0.10 8.1 0.10 0.10 5.0 2.0 1.0 0.40 0.20 0.16 0.10 0.10 0.10 0.40 5.0 5.0 0.40 5.0 0.40
>5 0.41 0.26 0.51 0.074 0.0074 1.00 0.35 0.38 0.44 0.073 0.039 1.2 0.49 0.51 0.26 0.011 0.10 0.082 0.057 0.078 0.016 1.4 1.2 0.26 1.4 0.27
a Interpolated data estimated from the response curves of sensors vs. sample concentration and other numbers can be found in Table 1. Convergence condition, 80% of all the data in training set passed the 50% RE requirement; converging speed, 4×106 epochs.
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To reflect this requirement, the RE(x) should be set as follows: 0.5 x≤ε ε 10 ε < x ≤ 80 x (17) RE(x) = 16 80 < x ≤ 160 x 10 x > 160 where ε refers to 0.001, which is a proper value to avoid the problem of the divided-by-zero error when a very small teacher signal is met. This RE-Func is the same as the solid curve shown in Fig. 1. Thus, the REs are set to constants in a very low or high concentration range, while the REs are inversely proportional to concentrations in a middle range. In order to enhance the accuracy of the ANN model used, the RE was reduced to its half value in the training process such that the RE parameter used was stricter than the one designed for this ANN. In addition, the training process was stopped when about 85% of the total data sets met the strict RE requirement instead of 100%. Because the random errors in the experimental measurement, a non-conditional observance of converging criteria could lead to a possible over-training effect [11]; or even the net could not converge at all if the 100% of data sets are required to meet the strict RE. It was found that this training method can let almost all data pass the originally designed RE requirement (not its stricter form). Prediction results show that a good accuracy can be promised in this case. As discussed before, in the case of enose, with error requirement shown in Eq. (17), the employment of RE-Func ensures that the ANN would converge even when the responses of the sensor array are not so ideal and when experimental uncertainties can not be avoided. Actually, using of a constant permitted RE or a constant absolute error on the whole concentration range has led to divergence in this case. The most exciting merit for this ANN model is that no declining of qualitative advantage has been made while quantitative accuracy has been enhanced. Table 2 lists clearly that both single gas and mixture samples were trained and predicted at almost the same accuracy in this ANN. What is more with this
ANN model is that both the requirement of speed and accuracy can be reached. The reason of why training speed is improved is that each predicted result need not fit to the ideal one and the ANN approaches the satisfied output in a more smart way. In addition, because each predicted result is just within a permitted error range according to its concentration level, in general, the accuracy of ANNs can be improved and the over-fitting problem in a common ANN model can be partially solved. 4.3. Transform point in pre-processing The transform point (lim) decides whether the pre-process function is more like a logarithmic one or a sigmoid one (see Eqs. (8) and (9)), so that this transform point seems to be the hinge in the training process. This decision is essential to both requirements of qualitative and quantitative analysis. Several numbers were used as the transform point: 0.01, 0.1, 0.5, 1, 10, 50, 100, 250, 490. The smaller transform points represent logarithmic function, while the larger points work for those more like sigmoid function. Still those medium numbers show the combination of logarithmic and sigmoid functions. The converging speed was compared in Table 3 and the predicting accuracy (error rate) was illustrated in Fig. 5 to show the importance of finding a proper transform point. To ensure the ANN would make good predictions, a stricter converging criterion should be taken when training it. In both Table 3 and Fig. 5, the Table 3 Effect of transform point on converging speeda Transform point
100% RE (epochs)
50% RE (epochs)
0.01 0.1 0.5 1 10 50 100 250 490
80000 700000 400000 400000 900000 70000 80000 80000 90000
4000000 800000 Unfinished Unfinished 4000000 600000 700000 700000 700000
a 50% RE represents a strict converging criteria with a reduced RE to its half value, while 100% RE shows a normal requirement for RE-Func. Those unfinished were interrupted due to the too long training time they cost.
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Table 4 Training methods
Fig. 5. Effects of transform point on accuracy: (A) converging criterion complied with the RE-Func; (B) converging criterion: RE is reduced to its half value in the training process. (—䉬—) Total error %; (---䉬---) error % (<10); (− −䊏− −) error % (10–250); (− −䉱− −) error % (250–500).
50% RE stands for a reduced RE to its half value in the training process as mentioned before, while the 100% RE remains a normal value required by RE-Func. Obviously, the stricter the criterion was, the harder the ANN could converge while being trained. The comparison clearly shows that the value of 10 might be taken as the transform point when accuracy is more important, while logarithmic function shall be used when speed is more required. As shown in Fig. 5, large transform point, which implies logarithmic profile, would cause a large error when it is used for the concentration prediction from the signal input. Thus, the logarithmic function works better only under low concentration, while sigmoid function gives more accurate results for higher concentrations. In Table 3, it seems that logarithmic function is suitable for quick training. The combination of these two functions is the eclectic choice. 4.4. Optimizing the training algorithm Another interesting feature is the algorithm used in process of ANN training. There are two major factors in the present training algorithm. The first factor
Method no.
Training order
Passed data
1 2 3 4
From small to large From small to large All at the same time All at the same time
Eliminated Retained Eliminated Retained
is the concentration order in training run. The training order can be chosen either with whole data sets or from small to large concentrations. Here the training order from small to large concentrations means that the network trained with smaller one(s) should meet the RE requirement first before adding larger one(s) into training sets. The other factor in the training algorithm is the removing or retaining treatment of data when the RE requirement is satisfied in the last iteration. For those concentrations already reached the RE requirement, they can be either eliminated temporarily from training sets, or simply be retained for next run. Four different kinds of training process involved the discussed two factors were tested, and the training methods are listed in Table 4 in detail. The results of the ANN trained with these four processes listed in Table 5 are expressed mainly by two factors, the converging speed and accuracy, similar to those shown in Table 3and Fig. 5. All four training ways used conditions as listed in Table 2 except different training method. As can be learnt through Table 5, Process 3 is the optimum algorithm for this ANN when converge speed is the main requirement because ANN trained with this method converged the fastest. For the promise of accuracy, it is clear that both Processes 1 and 3 can be used. It can also be judged from Table 5 Effect on speed of training methoda Method no.
Study epochs
Total e
e1 (<10)
e2 (Between 10 and 250)
e3 (Between 250 and 500)
1 2 3 4
4000000 4000000 500000 600000
0.11 0.18 0.11 0.15
0.17 0.17 0.17 0.17
0.091 0.27 0.091 0.18
0 0 0 0
a The method numbers are according to Table 4. Convergence condition, 80% of all the data in training set passed the 50% RE requirement. e is the error rate of predicted concentrations of unknown samples. e1 , e2 and e3 are error rate for individual concentration ranges.
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comparisons that the treatment of passed data seems to be more important.
5. Conclusion The idea of combination of chemical theories with mathematical formulations of ANN has been developed and applied to set up a quantitative ANN for enose. The concept of RE in analytical chemistry has been introduced into the error treatment in ANN model. The RE-ANN model has been established to enhance the quantitative accuracy of ANN for enose applications while the qualitative merit of the ANNs has not been sacrificed. In addition, discussions of pre- and post-processing function of concentration data and also the training algorithm have been proved to be very important, in which lies possibility of improvements for both predicting accuracy and training speed of ANN. Future research is needed to combine this idea with other well-developed ANN models [4–7,9] to make ANNs much closer to practical applications. The employment of RE in ANNs applications is expected to increase the feasibility for realizing more and more practical enoses as well as in other analytical areas.
Acknowledgements The research is supported by Ministry of Science and Technology of China (Contract No. 96-A23-03-07) and partially by NFS of China. References [1] E. Llobet, J. Brezmes, Y. Vilanovc, J.E. Sueiras, X. Correig, Sens. Actuators B 41 (1997) 13–21. [2] J.W. Gardner, P.N. Barlett, Sens. Actuators B 18/19 (1994) 211. [3] M.A. Craven, J.W. Gardner, P.N. Bartlett, Trends Anal. Chem. 15 (1996) 486–493. [4] A. De Agapito, L. De Agapito, M. Schneider, R. Garcia Rosa, T. De Pedro, Sens. Actuators B 15–16 (1993) 105–109. [5] D. Vlachos, J. Avaritsiotis, Sens. Actuators B 33 (1996) 77–82. [6] S.W. Moore, J.W. Gardner, E.L. Hines, W. Gopel, U. Weimar, Sens. Actuators B 15/16 (1993) 344–348. [7] Z. Wang, B.R. Kowalski, Anal. Chem. 67 (1995) 1497–1504. [8] J.W. Gardner, E.L. Hines, H.C. Tang, Sens. Actuators B 9 (1992) 9–15. [9] L. Zhang, J.-H. Jiang, P. Liu, Y.-Z. Liang, R.-Q. Yu, Anal. Chim. Acta 344 (1997) 29–39. [10] J. Zupan, J. Gasteiger, in: Neural Networks for Chemists, VCH, Weinheim, Federal Republic of Germany, 1993, 27 pp. [11] I.V. Tetko, D.J. Livingstone, A.I. Luik, J. Chem. Inf. Comput. Sci. 35 (1995) 826–833.