- Email: [email protected]
Dynamic Modeling and Optimization of Micro-Hotplate Chemical Gas Sensors
Copyright
DYNAMIC MODELING AND OPTIMIZATION OF MICRO-HOTPLATE CHEMICAL GAS SENSORS Tekin Kunt' Thomas J. McAvoy·,1 Richard E. Cavicchi" Steve Semancik"
• Institute Engineering, •• National Science and
for Systems Research, Department of Chemical University of Maryland, College Park, MD 20742 Institute of Standards and Technology, Chemical Technology Laboratory, Gaithersburg, MD 20899
Abstract: The chemical process industries are facing tighter fugitive emission control standards. Cost efficient, portable, and sensitive sensors are needed to attack this leak detection problem in chemical plants. This paper reports a first step towards this aim, i.e. optimal tuning of micro-hotplate chemical gas sensors to recognize two similar vapors such as methanol and ethanol in air. Experiments are conducted by flowing gas over the sensor at a constant rate and concentration . Heater current pulse amplitudes (micro-hotplate temperatures) are varied randomly to generate a large database for training empirical models. After studying different data-based dynamic modeling techniques , wavelet networks (WNET) method proposed by Zhang and Benveniste was found to give the most accurate predictions for the methanol and ethanol responses . Keywords: Chemical microsensors, Detection systems, Sensor systems , Temperature profiles, Neural-network models, Alarm systems
1. INTRODUCTIO)/
developed at the National Institute of Science and Technology (NIST) can be tuned for optimal seperation of two similar vapors such as methanol and ethanol in air.
The chemical process industries are facing tighter fugitive emission control standards . To date , conventional analytical methods such as gas chromatography, optical spectroscopy or mass spertrometry are used in the majority of process analyzers (Hool et at.. 1994). Although these analytical techniques are relatively mature, cost is often prohibitive. On the other hand, the potential use of an artificial nose , as a less expensive alternative for the leak detection problem in chemical plants, was described in a previous paper (Kunt et al. , 1996). In this paper, we report a first step to\\'ards optimization of micro-hotplate gas sensors which form the front-end of an artificial nose for chemical process applications. 1\lore specifically, it is shown that micro-hotplate gas sensors I
The organization of this paper is as follows. In Section Two, a background on micro-hotplate chemical gas sensors is presented . Sections Three and Four are devoted to the modeling and optimization of micro-hotplate chemical gas sensors. Conclusions are given in Section Five.
2. MICRO-HOTPLATE GAS SENSORS Recent advances in micromachining have allowed development of a new generation of chemical sensors at the I\ational Institute of Science and Technology (NIST) (Suehle et at.. 1993; Cavicchi et al., 1994). Researchers at NIST designed and
Author to whom all correspondence should be addressed
91
Formaldehyde
Melhanol
55
90
95
100
105
Time (sec )
Fig. 2. Different gas signatures subject to a linear temperature profile "best" temperature pulse sequence which would maximize our ability to discriminate two similar alcohols (with respect to a cert.ain criterion). In order to solve this optimization problem, accurate predictive models were required. Since developing accurate models based on first principles is not feasible and a database can be generated in a short amount of time using micro-hotplate gas sensors, data-based dynamic models were used, as explained in the next section.
Fig. 1. Micro-hotplate chemical gas sensor fabricated a gas sensor consisting of an array of micro-hotplates on a silicon wafer using commercially available complementary metal oxide semiconductor (CM OS) technology. Each individual sensor contains a heater, a hotplate layer and a sensing film, usually tin dioxide (Sn02)' The size of each sensor is around 200/lm x 200/lm as shown in Figure 1. Its thermal response time, which is the time it takes to heat the micro-hotplate to a set temperature, is estimated to be ~ 1 msec.
3. DYNAMIC MODELING USING WAVELET NETWORKS
The fast thermal time constant, inherent to microhotplate gas sensors, offers many advantages over commercially available Taguchi metal oxide gas sensors. Reduced power consumption is the most obvious one. since micro-hotplates require 10 to 100 times less power than a conventional Taguchi sensor. Another advantage of micro-hot.plates is their array structure. Since these sensors are extremely small (comparable to the diameter of a human hair), an array of micro-hotplates with several hundred different sensors can be fabricated on the same chip. In t.his paper, however, only one sensor is examined where selectivity is achieved using rapid t.emperature modulation during the sensor 's operation. Temperature modulation enhances a sensor's detect.ion and classification capabilities since each gas has different kinetics , i.e. different time constants for adsorption / desorpt ion. and reaction processes. Cavicchi and co-workers (Cavicchi et al., 1995) haw shown the viability of t his approach by applying a linear t.emperature profile to a micro-hotplate gas sensor and measuring different response patterns for different chemicals (see Figure 2). Although these signatures were distinct for compounds such as methanol and formaldehyde. t hey were some\\'hat similar between alcohols, e.g. methanol and ethanol. Hence, the challenge was to find the
vVavelet theory provides very efficient algorithms for analyzing, approximating, estimating and compressing functions or signals. These algorithms , however, are usually limited to problems with small input dimension (less than three), since constructing and storing a wavelet basis for larger input dimensions can be costly (Sjoberg et al., 1995). On the other hand, artificial neural net.\vorb are successful in approximating functions with a large input dimension (Poggio and Girosi , 1990). Although the potential of using feedforward neural networks as universal approxirnat.ors has been shown (Hornik. 1989), the theory does not provide constructive and systematic synthesis procedures for determining both the network structure and its parameters. Several researchers have independently studied the connections between wavelet theory' and artificial neural networks. Pati and Krishnaprasad (Pati and Krishnaprasad. 1993) have used the discrete wavelet transformations for analyzing and synthesizing feedforward neural networks. Bakshi and Stephanopoulos (Bakshi and Stephanopoulos. 1993) have reported a wavelet based method for learning at multiple resolutions ullder the framework of \rave-:'-iets . In this paper. we are
92
using wavelet networks (WNET) like those developed by Zhang and Benveniste (Zhang and Benveniste, 1992; Zhang, 1994b). The approach allows us to explore the similarity between the discrete inverse wavelet transform and neural networks with one hidden layer . First, the wavelet network method is described , then results related to dynamic modeling of micro-hotplate gas sensors are presented.
(3) find "Uli by the least squares method. (4) select the " best." n regressors from W which minimize the Akaike 's final prediction error criterion (FPE) using stepwise selection by orthogonalization. FPE is defined as
and n p =n(d+2)+d+l
3.1 Wavelet Networks
where SSE(fn) = 2:::1 (fn(x;) -Yi)2 and np is the total number of parameters in a wavelet network. (5) adjust the parameters (ai, t" Wi) of the resulting network to further decrease the prediction error, 2:::1 (fn(Xi) - y;)2 , by a quasiNewton procedure.
Given a wavelet function W : ~d >-+ ~, its associated wavelet network is written as n
In(x)
=L
wiW(ai
* (x -
till
+9
(1)
i=l
where d is the input dimension, n is the number of wavelet bases, ai is the dilation parameter, ti is the translation parameter, Wi E ~, ai E ~d, ti E ~d , and * denotes a component-wise product of two vectors . The parameter 9 is introduced to help in dealing with nonzero mean functions, since the wavelet IJ! has zero mean . Here, IJ! belongs to the set of square-integrable functions, i.e. w(x) E L2 (~), and satisfies an admissibility condition, which implies that the mean value of lJ!(x) be zero (Daubechies, 1990),
J
3.2 Modeling of Micro-Hotplate Gas Sensors
In the previous section, a description of the wavelet network method is given . In this section , the dynamic modeling problem in the context of micro-hotpate gas sensors is presented along with the motivation behind choosing the wavelet networks method over another NARX (Nonlinear Autoregressive Exogenous) approach. To date, very little use has been made of the transient information in the sensor response (Gardner and Bartlett, 1994) . This was partly due to the slow time constant inherent in the thick film, and generally larger, metal oxide semiconductor gas sensors. On the other hand , the micro-hotplate conductometric gas sensors developed at NIST can be heated/cooled from room temperature to 500°C in a few milliseconds (Cavicchi et al., 1995). Dynamic modeling techniques are required to fully take advantage of the fast response characteristics embedded in these micro-hotpate gas sensors.
+ 00
lJ!(x)dx
=0
(2)
- 00
The wavelet function W is chosen as the so-called "Mexican hat" , W(x)
where
IIxl1 2
= (lIx11 2
-
d) exp( -11;11
2 )
(5)
(3)
= x T x.
All the parameters ai , ti, Wi, g, and n of the network in Equation 1 are to be adapted using training data. An outline of the training (learning) procedure is given below whereas the details are in (Zhang, 1994a):
Following the notation from the previous section , we can describe the sensor response (conductance) as Yi for a given temperature Ui. Since the sensor response will depend on the previous conductance values as well as the temperature history, the next conductance value can be described as
Given: A set of training data (Xi , Yi) where x, is an input (1 x d), and Yi is an output (1 xl) with i = 1, ... ,N, then
Yi+l
(1) set 9 to be the arithmetic mean of the training data . (2) construct a regressor library W of discretely dilated and translated versions of the \vavelet W. The training data is scanned and a subset of some regular (dyadic) lattice of dilated (Ui) and translated (t,) versions of W, whose supports contain the training data points , is selected.
= In(
Yi
,Yi-l , ··· ,Y,-(ny - I) ,
Ui+l ,U,-l ·· · , U i -(nu-2))
(6)
where nu and ny denote maximum time lags in the input and output. respectively. The function In is obtained using the wavelet networks approach discussed in the previous section. In this example, two previous temperature (nu = 2) and one previous conductance (ny = 1) values were enough to build a nonlinear dynamic model.
93
2.5
f\
, 5
, jf:i
05
,
o -05
..
- , .5
. . . . . . . . .0.- 2'----~'--~,--~,--~--~---
80
100
120
140 Time (sec)
160
180
...... 0...
.
..-
. . . . . . .-
.0
0 . . . . ._
.... i •
III
~
300~~~~~~~~~~~~~70~~7~2-~74-~7-6~7~8-~80--8~2-
200
TIme (sec)
Fig. 3. Comparison of different dynamic modeling techniques using Ethanol test data set in the multi-step ahead prediction mode
Fig. 4. Actual (solid line) and predicted (dashed line) responses for Ethanol and Methanol (top plot) using the optimum temperature profile (bottom plot)
The multi-step ahead prediction of the wavelet networks (WNET) for ethanol response data is shown in Figure 3 and compared with other N ARX predictors, such as the l'\eural Networks Partial Least Squares (NNPLS) (Qin and McAvoy, 1992), and continuous-time models (NNRUNGE) (Rico-~1artinez et al., 1992) . In the multi-step ahead prediction mode , the network predicts the next output using previous predictions for output instead of actual output values from Equation 6. In other words , the temperature profile alone is enough for predicting the conductance response of gas i (i .e. yi = .ri(U)) .
of the previous section , an off-line optimization problem can be formulated as (Kunt et al., 1996) (7)
where yMetOH = .rMetOH(U(t)) and yEtOH = .rEtOH(U(t)). The distance, d, between the two response curves is calculated using the Euclidean distance , i.e. IlyM etOH - yEtOHII~ , the squared two-norm . Note that there are other possible distance metrics that one can also use (Ratton et al., 1997).
The temperature profile u(t) which will maximize the Equation 7 should be bounded between minimum and maximum temperatures (in this case, 20°C and 425°C respectively) . Furthermore ,the difference between two successive temperature pulses should be less than 50°C, since the database used in the modeling was generated with the same constraint .
In general, two different dynamics which govern conductance responses in micro-hotplate gas sensors can be distinguished : a fast dynamic component arising from fast t.emperature changes and a slow change possibly due to complex surface and near surface "relaxation" phenomena. While the other :\ARX predictors are able to follow slow changes, they did not accurately predict the fast dynamics. Thus, modeling of microsensor response with different types of dynamics requires the adoption of techniques with multi-resolution capabilities , such as wavelet networks. Very accurate predictions using wavelet networks have been obtained , and used in off-line optimization of the temperature profiles .
4.
.-.0..-.
.
-,r
This off-line optimization problem is solved using the Sequential Quadratic Programming (SQP) algorithm provided in the MATLAB 2 Optimization Toolbox . Figure 4 shows the resulting response curves (both predictions and experimantal results) after the optimization . ,,"otc that the predictions for both gases fit very well with the experimental results . The computed optimal profile consists of temperature oscillations around 300°C with a small amplitude. The frequency of these oscillations depends on the particular distance metric used in the off-line optimization. When the gas is interrogated with this optimal temperature program. methanol response follows the tempera-
OPTnUZATIO~
OF r-.lICRO-HOTPLATE GAS SEl'\SORS
The aim of off-line optimization is to increase selectivity by choosing the "best" temperature profile . For a given temperature profile u(t), let the predicted conductance response for methanol (ethanol) be yM etOH (yEf OH) during the time inten·al [0, To] . Sinee a functional mapping, .ri, can be developed for each gas i. following the approach
~ Commercial produ cts arc id entified only to specify ex-
perimental procedure . This ill 110 way implies recommendat iOIl or endorsement b~· th e ,
94
ture profile whereas ethanol gives an out-of-phase response. \Ioreover. it takes about 20 seconds to decide which gas is present in the test chamber though the c."cie length can also be optimized. This approach can be furth er extended to deal with mixtures of gases .
Hornik , K . (1989). 1\1ultilayer feed forward networks are universal approximators. Neural Networks. Kunt , T ., L. Ratton et aL (1996) . Towards the development of an artificial nose for chemical process applications. Computers Chem . Engng. 20(Suppl .), S1437- S1442 . Pati , Y. and P. Krishnaprasad (1993). Analysis and synthesis of feedforward neural networks using discrete wavelet transformations . Neural Networks 4, 73- 85. Poggio , T. and F . Girosi (1990) . ;-';etworks for approximation and learning . Proceedings of the IEEE 78(9), 1481 - 1497. Qin , S. Joe and Thomas .1. 1\1cA voy (1992). ~onlinear PLS modeling using neural networks. Computers and Chemical Engineering 16(4) , 379-391. Ratton , 1., T . Kunt et al. (1997). A comparative study of signal processing techniques for clustering microsensor data. accepted for publication in the Sensors and Actuators B. Rico-Martinez , R., K. Krischer et al. (1992) . Discrete vs. continuous time non linear signal processing of Cu electrodissolution data. Chemical Engineering Communication 118, 25-48. Sjoberg, .1 ., Q . Zhang et al. (1995). Nonlinear black-box modeling in system identification: a unified overview . A utomatica 31 ( 12) , 16911724. Suehle , J.S. , RE . Cavicchi, M. Gaitan and S. Semancik (1993) . Tin oxide gas sensor fabricated using CMOS micro-hotplates and insitu processing. IEEE Electron Device Letters 14(3) , 118- 120. Zhang, Q. (1994a). Using wavelet network in nonparametric estimation . Technical Report 833. !RISA. Zhang, Q . (1994b) . Wavenet , public domain matlab toolbox . anonymous FTP : ftp.irisaJr /10cal/wavenet . Zhang, Q. and A. Benveniste (1992) . Wavelet networks . IEEE Trans. on Neural Networks 3 , 889-898 .
5. CONCLUSIO:\,S This paper has discussed the optimal tuning of micro-hotplate chemical gas sensors using off-line optimization and dynamic data-based modeling techniques . Temperature modulation is used to increase selectivity between methanol and ethanol gases injected into air. Data-based dynamic models are developed for predicting conductance resp onses of each gas for a given temperature profile . Among the different dynamic modeling techniques studied , the wavelet networks method gave very accurate predictive models. Using these predictive models in an off-line optimization scheme, an optimal temperature profile was computed and validated through actual experiments. This optimal temperature program produced methanol and ethanol responses that were out-of-phase. Although methanol and ethanol gases have been chosen to illustrate the optimal tuning of microhotplate gas sensors , the methodology described in this paper is generic and can be extended to various applications.
6. REFERENCES Bakshi , B. and G. Stephanopoulos (1993). WaveNet: a multiresolution , hierarchical neural network with localized learning. AICHE 10urnaI39 , 57-81. Cavicchi , R .E. , J .S. Suehle et al. (1994). Microhotplate temperature control for sensor fabrication , study and op eration . In : Proceedings of th e Fifth Int ernational Meeting on Chemical Sensors. pp. 1136- 1139. Cavi cchi, RE ., .1 .S. Suehle et al. (1995). Fast temperature programmed sensing for microhotplate gas sensors. IEEE Electron Device Letters 16(6) , 1- 3. Daubechies, 1. (1990) . The wavelet transform. time-frequency localization and signal analysis. IEEE Trans. Informat. Theory. Gardner, J. W. and P . !\ . Bartlett (1994) . A brief history of electronic noses . Sensors and Actuator's B 18-19.211- 220. HooL K., R. Bredeweg et aL (1994). Gas phase sensing in t he chemical industry: today"s practiced t echnology. In : NIST Wor'kshop on Gas S ensors: Strategies for Future Technologies (S. Semancik, Ed.). :'-lIST SP865. Gaithersburg . pp. 65 - 70.
95
DYNAMIC MODELING AND OPTIMIZATION OF MICRO-HOTPLATE CHEMICAL GAS SENSORS Tekin Kunt' Thomas J. McAvoy·,1 Richard E. Cavicchi" Steve Semancik"
• Institute Engineering, •• National Science and
for Systems Research, Department of Chemical University of Maryland, College Park, MD 20742 Institute of Standards and Technology, Chemical Technology Laboratory, Gaithersburg, MD 20899
Abstract: The chemical process industries are facing tighter fugitive emission control standards. Cost efficient, portable, and sensitive sensors are needed to attack this leak detection problem in chemical plants. This paper reports a first step towards this aim, i.e. optimal tuning of micro-hotplate chemical gas sensors to recognize two similar vapors such as methanol and ethanol in air. Experiments are conducted by flowing gas over the sensor at a constant rate and concentration . Heater current pulse amplitudes (micro-hotplate temperatures) are varied randomly to generate a large database for training empirical models. After studying different data-based dynamic modeling techniques , wavelet networks (WNET) method proposed by Zhang and Benveniste was found to give the most accurate predictions for the methanol and ethanol responses . Keywords: Chemical microsensors, Detection systems, Sensor systems , Temperature profiles, Neural-network models, Alarm systems
1. INTRODUCTIO)/
developed at the National Institute of Science and Technology (NIST) can be tuned for optimal seperation of two similar vapors such as methanol and ethanol in air.
The chemical process industries are facing tighter fugitive emission control standards . To date , conventional analytical methods such as gas chromatography, optical spectroscopy or mass spertrometry are used in the majority of process analyzers (Hool et at.. 1994). Although these analytical techniques are relatively mature, cost is often prohibitive. On the other hand, the potential use of an artificial nose , as a less expensive alternative for the leak detection problem in chemical plants, was described in a previous paper (Kunt et al. , 1996). In this paper, we report a first step to\\'ards optimization of micro-hotplate gas sensors which form the front-end of an artificial nose for chemical process applications. 1\lore specifically, it is shown that micro-hotplate gas sensors I
The organization of this paper is as follows. In Section Two, a background on micro-hotplate chemical gas sensors is presented . Sections Three and Four are devoted to the modeling and optimization of micro-hotplate chemical gas sensors. Conclusions are given in Section Five.
2. MICRO-HOTPLATE GAS SENSORS Recent advances in micromachining have allowed development of a new generation of chemical sensors at the I\ational Institute of Science and Technology (NIST) (Suehle et at.. 1993; Cavicchi et al., 1994). Researchers at NIST designed and
Author to whom all correspondence should be addressed
91
Formaldehyde
Melhanol
55
90
95
100
105
Time (sec )
Fig. 2. Different gas signatures subject to a linear temperature profile "best" temperature pulse sequence which would maximize our ability to discriminate two similar alcohols (with respect to a cert.ain criterion). In order to solve this optimization problem, accurate predictive models were required. Since developing accurate models based on first principles is not feasible and a database can be generated in a short amount of time using micro-hotplate gas sensors, data-based dynamic models were used, as explained in the next section.
Fig. 1. Micro-hotplate chemical gas sensor fabricated a gas sensor consisting of an array of micro-hotplates on a silicon wafer using commercially available complementary metal oxide semiconductor (CM OS) technology. Each individual sensor contains a heater, a hotplate layer and a sensing film, usually tin dioxide (Sn02)' The size of each sensor is around 200/lm x 200/lm as shown in Figure 1. Its thermal response time, which is the time it takes to heat the micro-hotplate to a set temperature, is estimated to be ~ 1 msec.
3. DYNAMIC MODELING USING WAVELET NETWORKS
The fast thermal time constant, inherent to microhotplate gas sensors, offers many advantages over commercially available Taguchi metal oxide gas sensors. Reduced power consumption is the most obvious one. since micro-hotplates require 10 to 100 times less power than a conventional Taguchi sensor. Another advantage of micro-hot.plates is their array structure. Since these sensors are extremely small (comparable to the diameter of a human hair), an array of micro-hotplates with several hundred different sensors can be fabricated on the same chip. In t.his paper, however, only one sensor is examined where selectivity is achieved using rapid t.emperature modulation during the sensor 's operation. Temperature modulation enhances a sensor's detect.ion and classification capabilities since each gas has different kinetics , i.e. different time constants for adsorption / desorpt ion. and reaction processes. Cavicchi and co-workers (Cavicchi et al., 1995) haw shown the viability of t his approach by applying a linear t.emperature profile to a micro-hotplate gas sensor and measuring different response patterns for different chemicals (see Figure 2). Although these signatures were distinct for compounds such as methanol and formaldehyde. t hey were some\\'hat similar between alcohols, e.g. methanol and ethanol. Hence, the challenge was to find the
vVavelet theory provides very efficient algorithms for analyzing, approximating, estimating and compressing functions or signals. These algorithms , however, are usually limited to problems with small input dimension (less than three), since constructing and storing a wavelet basis for larger input dimensions can be costly (Sjoberg et al., 1995). On the other hand, artificial neural net.\vorb are successful in approximating functions with a large input dimension (Poggio and Girosi , 1990). Although the potential of using feedforward neural networks as universal approxirnat.ors has been shown (Hornik. 1989), the theory does not provide constructive and systematic synthesis procedures for determining both the network structure and its parameters. Several researchers have independently studied the connections between wavelet theory' and artificial neural networks. Pati and Krishnaprasad (Pati and Krishnaprasad. 1993) have used the discrete wavelet transformations for analyzing and synthesizing feedforward neural networks. Bakshi and Stephanopoulos (Bakshi and Stephanopoulos. 1993) have reported a wavelet based method for learning at multiple resolutions ullder the framework of \rave-:'-iets . In this paper. we are
92
using wavelet networks (WNET) like those developed by Zhang and Benveniste (Zhang and Benveniste, 1992; Zhang, 1994b). The approach allows us to explore the similarity between the discrete inverse wavelet transform and neural networks with one hidden layer . First, the wavelet network method is described , then results related to dynamic modeling of micro-hotplate gas sensors are presented.
(3) find "Uli by the least squares method. (4) select the " best." n regressors from W which minimize the Akaike 's final prediction error criterion (FPE) using stepwise selection by orthogonalization. FPE is defined as
and n p =n(d+2)+d+l
3.1 Wavelet Networks
where SSE(fn) = 2:::1 (fn(x;) -Yi)2 and np is the total number of parameters in a wavelet network. (5) adjust the parameters (ai, t" Wi) of the resulting network to further decrease the prediction error, 2:::1 (fn(Xi) - y;)2 , by a quasiNewton procedure.
Given a wavelet function W : ~d >-+ ~, its associated wavelet network is written as n
In(x)
=L
wiW(ai
* (x -
till
+9
(1)
i=l
where d is the input dimension, n is the number of wavelet bases, ai is the dilation parameter, ti is the translation parameter, Wi E ~, ai E ~d, ti E ~d , and * denotes a component-wise product of two vectors . The parameter 9 is introduced to help in dealing with nonzero mean functions, since the wavelet IJ! has zero mean . Here, IJ! belongs to the set of square-integrable functions, i.e. w(x) E L2 (~), and satisfies an admissibility condition, which implies that the mean value of lJ!(x) be zero (Daubechies, 1990),
J
3.2 Modeling of Micro-Hotplate Gas Sensors
In the previous section, a description of the wavelet network method is given . In this section , the dynamic modeling problem in the context of micro-hotpate gas sensors is presented along with the motivation behind choosing the wavelet networks method over another NARX (Nonlinear Autoregressive Exogenous) approach. To date, very little use has been made of the transient information in the sensor response (Gardner and Bartlett, 1994) . This was partly due to the slow time constant inherent in the thick film, and generally larger, metal oxide semiconductor gas sensors. On the other hand , the micro-hotplate conductometric gas sensors developed at NIST can be heated/cooled from room temperature to 500°C in a few milliseconds (Cavicchi et al., 1995). Dynamic modeling techniques are required to fully take advantage of the fast response characteristics embedded in these micro-hotpate gas sensors.
+ 00
lJ!(x)dx
=0
(2)
- 00
The wavelet function W is chosen as the so-called "Mexican hat" , W(x)
where
IIxl1 2
= (lIx11 2
-
d) exp( -11;11
2 )
(5)
(3)
= x T x.
All the parameters ai , ti, Wi, g, and n of the network in Equation 1 are to be adapted using training data. An outline of the training (learning) procedure is given below whereas the details are in (Zhang, 1994a):
Following the notation from the previous section , we can describe the sensor response (conductance) as Yi for a given temperature Ui. Since the sensor response will depend on the previous conductance values as well as the temperature history, the next conductance value can be described as
Given: A set of training data (Xi , Yi) where x, is an input (1 x d), and Yi is an output (1 xl) with i = 1, ... ,N, then
Yi+l
(1) set 9 to be the arithmetic mean of the training data . (2) construct a regressor library W of discretely dilated and translated versions of the \vavelet W. The training data is scanned and a subset of some regular (dyadic) lattice of dilated (Ui) and translated (t,) versions of W, whose supports contain the training data points , is selected.
= In(
Yi
,Yi-l , ··· ,Y,-(ny - I) ,
Ui+l ,U,-l ·· · , U i -(nu-2))
(6)
where nu and ny denote maximum time lags in the input and output. respectively. The function In is obtained using the wavelet networks approach discussed in the previous section. In this example, two previous temperature (nu = 2) and one previous conductance (ny = 1) values were enough to build a nonlinear dynamic model.
93
2.5
f\
, 5
, jf:i
05
,
o -05
..
- , .5
. . . . . . . . .0.- 2'----~'--~,--~,--~--~---
80
100
120
140 Time (sec)
160
180
...... 0...
.
..-
. . . . . . .-
.0
0 . . . . ._
.... i •
III
~
300~~~~~~~~~~~~~70~~7~2-~74-~7-6~7~8-~80--8~2-
200
TIme (sec)
Fig. 3. Comparison of different dynamic modeling techniques using Ethanol test data set in the multi-step ahead prediction mode
Fig. 4. Actual (solid line) and predicted (dashed line) responses for Ethanol and Methanol (top plot) using the optimum temperature profile (bottom plot)
The multi-step ahead prediction of the wavelet networks (WNET) for ethanol response data is shown in Figure 3 and compared with other N ARX predictors, such as the l'\eural Networks Partial Least Squares (NNPLS) (Qin and McAvoy, 1992), and continuous-time models (NNRUNGE) (Rico-~1artinez et al., 1992) . In the multi-step ahead prediction mode , the network predicts the next output using previous predictions for output instead of actual output values from Equation 6. In other words , the temperature profile alone is enough for predicting the conductance response of gas i (i .e. yi = .ri(U)) .
of the previous section , an off-line optimization problem can be formulated as (Kunt et al., 1996) (7)
where yMetOH = .rMetOH(U(t)) and yEtOH = .rEtOH(U(t)). The distance, d, between the two response curves is calculated using the Euclidean distance , i.e. IlyM etOH - yEtOHII~ , the squared two-norm . Note that there are other possible distance metrics that one can also use (Ratton et al., 1997).
The temperature profile u(t) which will maximize the Equation 7 should be bounded between minimum and maximum temperatures (in this case, 20°C and 425°C respectively) . Furthermore ,the difference between two successive temperature pulses should be less than 50°C, since the database used in the modeling was generated with the same constraint .
In general, two different dynamics which govern conductance responses in micro-hotplate gas sensors can be distinguished : a fast dynamic component arising from fast t.emperature changes and a slow change possibly due to complex surface and near surface "relaxation" phenomena. While the other :\ARX predictors are able to follow slow changes, they did not accurately predict the fast dynamics. Thus, modeling of microsensor response with different types of dynamics requires the adoption of techniques with multi-resolution capabilities , such as wavelet networks. Very accurate predictions using wavelet networks have been obtained , and used in off-line optimization of the temperature profiles .
4.
.-.0..-.
.
-,r
This off-line optimization problem is solved using the Sequential Quadratic Programming (SQP) algorithm provided in the MATLAB 2 Optimization Toolbox . Figure 4 shows the resulting response curves (both predictions and experimantal results) after the optimization . ,,"otc that the predictions for both gases fit very well with the experimental results . The computed optimal profile consists of temperature oscillations around 300°C with a small amplitude. The frequency of these oscillations depends on the particular distance metric used in the off-line optimization. When the gas is interrogated with this optimal temperature program. methanol response follows the tempera-
OPTnUZATIO~
OF r-.lICRO-HOTPLATE GAS SEl'\SORS
The aim of off-line optimization is to increase selectivity by choosing the "best" temperature profile . For a given temperature profile u(t), let the predicted conductance response for methanol (ethanol) be yM etOH (yEf OH) during the time inten·al [0, To] . Sinee a functional mapping, .ri, can be developed for each gas i. following the approach
~ Commercial produ cts arc id entified only to specify ex-
perimental procedure . This ill 110 way implies recommendat iOIl or endorsement b~· th e ,
94
ture profile whereas ethanol gives an out-of-phase response. \Ioreover. it takes about 20 seconds to decide which gas is present in the test chamber though the c."cie length can also be optimized. This approach can be furth er extended to deal with mixtures of gases .
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5. CONCLUSIO:\,S This paper has discussed the optimal tuning of micro-hotplate chemical gas sensors using off-line optimization and dynamic data-based modeling techniques . Temperature modulation is used to increase selectivity between methanol and ethanol gases injected into air. Data-based dynamic models are developed for predicting conductance resp onses of each gas for a given temperature profile . Among the different dynamic modeling techniques studied , the wavelet networks method gave very accurate predictive models. Using these predictive models in an off-line optimization scheme, an optimal temperature profile was computed and validated through actual experiments. This optimal temperature program produced methanol and ethanol responses that were out-of-phase. Although methanol and ethanol gases have been chosen to illustrate the optimal tuning of microhotplate gas sensors , the methodology described in this paper is generic and can be extended to various applications.
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