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Verification of a logarithmic model for estimation of gas concentrations in a mixture for a tin oxide gas sensor response
Sensors and Actuators B 92 (2003) 269–278
Verification of a logarithmic model for estimation of gas concentrations in a mixture for a tin oxide gas sensor response Shigeki Hirobayashi∗ , Mohammed Afrose Kadir, Toshio Yoshizawa, Tatsuo Yamabuchi Faculty of Technology, Toyama University, Gofuku, Toyama 930-8555, Japan Received 18 June 2001; received in revised form 24 February 2003; accepted 28 February 2003
Abstract Changes in electrical conductivity due to a reaction occurring between the original adsorbents and the gases present in the surrounding atmosphere were measured for a tin dioxide-based gas sensor. In this study, a model of the gas sensor response using a relationship between the gas concentration in a mixture and the sensor resistance is proposed. The values of coefficients are determined by a least-squares fit of measured data. Using two gas sensors having different characteristics, the concentrations of gases in a mixture can be evaluated. The proposed method has been applied to the evaluation of the gas concentrations in ammonia–ethanol and CO–ethanol mixtures. Furthermore, we verified our model for a gas mixture of carbon monoxide, propane and methane gases, namely for a three-gas system. The results of the present study indicated that the evaluation of gas concentrations in a mixture is feasible using the proposed model of gas sensor response, which can be used as an inexpensive monitor for air pollution. © 2003 Published by Elsevier Science B.V. Keywords: Gas concentration; Gas sensor; Indoor-air pollutants; Gas mixture
1. Introduction The electrical conductivity of oxide semiconductors such as tin oxide gas sensors is altered by the absorption of reductive gases and oxidative reactions on the surface of the catalyzers. These sensors have high reproducibility and stability, and are often used for indoor monitoring systems such as home gas-leak alarms and instruments for the assessment of air pollution levels [1–3]. However, these sensors usually do not have high gas selectivity, and their sensing characteristics depend largely on changes in the indoor environment [4], such as temperature and humidity. Therefore, in this study we have maintained a constant temperature and humidity. Accordingly, the gas sensor system itself tests gas selectivity, which affects the gas sensor response characteristics [5,6]. Previously, gas sensor response characteristics have been modeled using a number of variables in an attempt to detect gas concentration and to classify gases [7–9]. However, general modeling requires gas concentration measurements for each object gas, which requires significant time and effort. In particular, the measurement of each pure gas contained in the mixture gas is necessary. Sugahara et al. [10] proposed ∗ Corresponding author. Tel.: +81-764-456889. E-mail address: [email protected] (S. Hirobayashi).
0925-4005/03/$ – see front matter © 2003 Published by Elsevier Science B.V. doi:10.1016/S0925-4005(03)00311-3
a method of integrating several sensors with different characteristics and/or the new concepts of pattern recognition, such as fuzzy logic and neural network. Using an artificial neural network and a fuzzy neural network they designed the gas discrimination and gas concentration–estimation system, respectively. Mart´ın et al. [11] proposed a model for detecting the individual components of the two gases, presenting a systematic study for enhancing all parameters of a neural network, including preprocessing techniques. However, these models require many gas concentration measurements for each object gas, which requires significant time and effort. When there is an increase in the classification and concentration of a gas, estimation of gas sensor characteristics is not easy. Therefore, mixture gas sensor characteristics are estimated by comparing sensor characteristics for a previously known pure gas. Typically, gas sensor characteristics are obtained experimentally for each pure gas making up a mixture gas, and mixture gas concentrations are calculated accurately using the sensor characteristic equation. In the present study, we extended the sensor characteristic equation to two mixture gases and performed an experiment to verify the sensor characteristics in three mixture gases. The efficiency of the proposed model is confirmed by the experimental result.
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can be approximated as follows: Rs = α log C + β,
Fig. 1. Circuit diagram of sensor system.
2. Modeling of sensor characteristic based on actual measurement The sensor elements used in the present study were TGS826 and TGS800 sensors (Figaro Engineer Inc.). The TGS826 is sensitive to ethanol (C2 H5 OH), carbon monoxide (CO), propane (C3 H8 ) and methane (CH4 ); this sensor also has a high sensitivity to ammonia (NH3 ). The TGS800 has high sensitivity to alcohol gas, i.e., the sensor can be used to judge whether a fuel gas is leaking, and an alarm is activated when alcohol gas is generated. In the present study, two combinations of mixture gases were used for the two-gas system: gas mixture of ammonia and ethanol and mixture of carbon monoxide and ethanol. The electrical resistance of a gas sensor decreases as the gas concentration C (ppm) increases. Fig. 1 shows a circuit diagram of the gas sensor. In the figure, Vc (V) is the power voltage (5 V), Rs () the electrical resistance of the gas sensor, and r () the output voltage resistance. The output voltage is defined according to Kirchhopff’s law as follows: Vr =
Vc r . Rs + r
(1)
We know that the sensor resistance decreases with increasing gas concentration C (ppm). Therefore, the sensor resistance
(2)
where α and β are the coefficients. This equation shows that the sensor resistance is proportional to the logarithm of the concentration C, and is satisfied when the temperature and relative humidity of the ambient are fixed. In our experiment we maintain such conditions using the setup shown in Fig. 2. Gas sensor resistance is shown in Fig. 3(a) and (b) as a function of the gas concentration in the gas mixture. We maintained the concentration of ethanol Ce (ppm) and that of ammonia Ca (ppm) in the temperature- and humidity-controlled chamber shown in Fig. 2. The temperature and relative humidity were maintained constant at approximately 25 ◦ C and 55%, respectively, and the concentration of each gas was adjusted by a syringe. Ammonia was varied from 180 to 1080 ppm (measured six times, in 180 ppm units) and ethanol concentration was varied from 100 to 600 ppm (measured six times, in 100 ppm units). At lower ethanol concentration, there is a greater sensitivity to ammonia concentration, as shown in Fig. 3(a) and (b), and the sensor resistance decreased with increasing ammonia concentration as expected. The straight lines and their slopes differ according to ammonia concentration in both the low and high gas concentration ranges. These results reveal that maintaining a unique-characteristic straight line is difficult. Therefore, we attempted to extend Eq. (2) to be applicable to the concentrations of two different gases. In Fig. 3(a) and (b), straight-line approximations are obtained at approximately 1000 ppm. This confirms the effects of a convergence and a measurement error of sensor output at this concentration. Thus, for the conditions in Fig. 3(a) and (b), we injected an ammonia concentration of 180–720 ppm and an ethanol concentration of 100–400 ppm, respectively, into the subject region. Straight-line plots were obtained by approximation from Eq. (2) using the least-squares method.
Fig. 2. Thermo-hydrostat used for gas sensing experiments.
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Fig. 4. Distribution of coefficients (a) α and (b) β in Eq. (4) using TGS826 sensor unit. Fig. 3. Measured values and approximated linear fitting for a gas mixture of ammonia and ethanol using (a) TGS826 and (b) TGS800.
β(Ce ) = α3 log Ce + α4 ,
(5)
Eq. (2) verifies that the sensor resistance is linearly proportional to the logarithmic concentration. For ammonia concentration (with respect to ethanol concentration), the resistance characteristics, shown in Fig. 3, are expressed as a straight line, similar to Eq. (2). The mixture gas characteristic equation is then as follows:
where α1 –α4 are constants. Combining Eqs. (3)–(5), the sensor resistance of ammonia and ethanol gas is then given by
Rs (Ca , Ce ) = α(Ce ) log Ca + β(Ce ),
In the present work, the measurement of the concentrations of two mixture gases is based on the above equation. Table 1 shows the values of the coefficients (α1 –α4 ), obtained by the least-squares method for the TGS826 and TGS800 gas sensors.
(3)
where Ca is the ammonia gas concentration and Ce the ethanol concentration. The characteristic equation of a mixture gas such as ammonia and ethanol can be determined from a generalized characteristic equation for a mixture gas with unknown coefficients α and β. Fig. 4 shows the characteristic of coefficients α and β of Eq. (3) with respect to the concentration of the other gas Ce (ppm). A straight-line approximation can be obtained using the least-squares method at various ethanol gas concentrations, and the plots fitted well to this linear approximation [12]. A simple linear equation such as Eq. (2) can then be applied to the other gas concentration. That is, α(Ce ) = α1 log Ce + α2 ,
(4)
Rs (Ca , Ce ) = α1 log Ca log Ce + α2 log Ca + α3 log Ce + α4 .
3. Verification of represented model equation The characteristic equation (Eq. (6)) is based on experimental data and is an extension of Eq. (2). In this section we examine Eqs. (2) and (6) in detail. The values of α 2 and α 3 are defined as the logarithms of alcohol and ethanol concentrations, respectively, α 4 is the initial concentration coefficient and α 1 is the coefficient peculiar to the mixture
Table 1 Coefficients of approximate equation for gas mixture of ammonia and ethanol α1 TGS826 TGS800
α2
1.1210 × 0.5974 × 104 104
α3
−3.2567 × −1.6253 × 104 104
(6)
α4
−4.0032 × −2.8450 × 104 104
1.2557 × 105 8.4795 × 104
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Fig. 5. Relationship between estimated values and measured data for a gas mixture of ammonia and ethanol using (a) TGS826 and (b) TGS800.
gas as obtained from Eq. (5). As long as α 1 is not zero, Eq. (6) is a curved surface when plotted against logarithmic concentrations of either ammonia or ethanol, indicating the existence of a correlation coefficient between the two gases. Namely, coefficient α 1 differs from coefficients α 2 and α 3 for each linear concentration term, which necessary because the characteristic sum of individual gases does not generally agree with the mixture gas characteristics. Furthermore, because representation of the extension of Eq. (2) is based on experimental data, the application of the concentration of this model, Eq. (6), is limited to the region that can be approximated by Eq. (2) for each pure gas. Using Eq. (6), we verified the characteristic of a mixture gas sensor composed of two pure gases. We quantitatively investigated the unevenness of distortion between the measured data and estimated values using the model described by Eq. (6). Cross-validation is necessary in the application of weight regression analysis [13]. A well-known method of cross-validation is to decide which variables are effective for use as a standard variable by means of one set of data, estimate a bias regression coefficient, apply the obtained bias regression coefficient to another set of the same kind of data, and then calculate the correlation coefficient between the actual measurement value and the obtained estimated value. For our calculation we divided the obtained data into two sets and estimated a bias regression coefficient. We then calculated the correlation coefficient. The bias regression coefficient was obtained using the least-squares method. We used the first set of data to estimate the regression coefficient, as shown in Table 1. We then applied this coefficient to the second set of data. Fig. 5(a) and (b) shows the relationships between the measured data and the estimated values for a gas mixture of ammonia and ethanol obtained using TGS826 and TGS800. A strong correlation is obtained when the slope of this coefficient is near 1. The values of our calculated coefficients are 0.9969 and 0.9966
for TGS826 and TGS800, respectively, indicating strong correlations. We quantitatively investigated the unevenness of distortion between the measured and estimated values using the model shown in Eq. (6). Fig. 6(a) and (b) shows histograms of the distortion of TGS826 and TGS800, respectively. Both figures show that the estimated values are greater than the measured values in the high-concentration region of the sensor characteristics. In addition, the distribution is slightly more centered and the error is large in the high-concentration region above the modeling subject region. However, in the modeling subject region, both results can generally be estimated to have a small error. In other words, the mixture gas sensor characteristic can be approximated with small errors.
4. Experiment for verification of representative concentration and compound gas mixture ratio Using the model described by Eq. (6), we determined the concentration of each composition for two mixture gases using the TGS826 and TGS800 sensors. As both of these sensors have low resistance characteristics, the concentration of each gas in a mixture gas can be estimated. In other words, the two sensor resistances in Eq. (6) can be expressed as RTGS826 = f (Ca , Ce ),
(7)
RTGS800 = g(Ca , Ce ).
(8)
As RTGS826 and RTGS800 are constant, the only variables in measurements in a real environment are the concentrations Ca and Ce . Since the number of equations and variables are equal, we can calculate the concentration of each gas. The calculated concentrations are consistent with the data from
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Fig. 6. Histograms of distortion between measured values and approximate linear fitting for a gas mixture of ammonia and ethanol using (a) TGS826 and (b) TGS800.
the estimation experiment, as shown in Table 1, demonstrating the validity of this model, which is shown in Fig. 7. Fig. 7 shows the estimated concentration together with the measured concentration for the proposed model for a
mixture gas of ammonia and ethanol. The arrows begin at the measured sensor resistance corresponding to the estimated concentration, and end at the concentration obtained by correct time measurement. The modeling region
Fig. 7. Error between estimated and measured gas concentrations for a gas mixture of ammonia and ethanol (arrows indicate errors).
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is the low-concentration region, which is separated from the high-concentration region by a dotted line. As expected, the estimated error is large in the high-concentration region due to the low sensitivity of sensors under such conditions, however the estimation is very accurate in the modeling concentration region. Next, using the same gas sensors (TGS826 and TGS800), we performed another experiment using a mixture gas of carbon monoxide and ethanol. Fig. 8(a) and (b) represents the measured data (dots) and estimated values (solid line) for each gas sensor, TGS826 and TGS800, respectively. Values for the coefficients of each function, as calculated by the least-squares method, are shown in Table 2. In this experiment we injected 100–700 ppm of carbon monoxide and 100–400 ppm of ethanol into the modeling subject region. We found that the estimated values were higher than the measured values in the high-concentration region. Fig. 9(a) and (b) shows the relationship between the estimated values and the measured data using the TGS826 and TGS800 gas sensors for a gas mixture of carbon monoxide and ethanol. In this case, the values of the calculated coefficients are 0.9968 and 0.9965, indicating a strong correlation. Fig. 10(a) and (b) are histograms that show the distortion of the measured data and estimated values. The distortion is quite low compared to the previous ethanol/ammonia mixture gases. Fig. 11 shows the measured data and estimated values for a mixture gas of carbon monoxide and ethanol. The figure shows that for this mixture gas, although the estimated distortion is quite large outside the modeling subject concentration region, the concentration can be estimated
Fig. 8. Measured values and approximated linear fitting for a gas mixture of carbon monoxide and ethanol using (a) TGS826 and (b) TGS800.
with reasonable accuracy using this model within the target region. In the present work, the sensor expressed by Eq. (2) is extended using the proposed model to Eq. (6). This model
Table 2 Coefficients of approximate equation for gas mixture of carbon monoxide and ethanol α1 TGS826 TGS800
α2
0.5321 × 0.9525 × 104 104
α3
−1.4189 × −2.6656 × 104 104
α4
−3.4969 × −3.5654 × 104 104
1.0666 × 105 1.0761 × 105
Fig. 9. Relationship between estimated values and measured data for a gas mixture of carbon monoxide and ethanol using (a) TGS826 and (b) TGS800.
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Fig. 10. Histograms of distortion between measured values and approximate linear fitting for a gas mixture of carbon monoxide and ethanol using (a) TGS826 and (b) TGS800.
has four unknown coefficients (α1 –α4 ), which can be solved by changing the concentration of mixture gas and measuring the concentration using each sensor at least four times. Accurate estimation of gas concentration is possible using a
simple numerical formula such as the proposed model. However, as the direction of vectors (α1 , α2 , α3 , α4 ) are similar, Eqs. (7) and (8) are identical so difference of gas sensitivity are necessary for sensor selection.
Fig. 11. Error between estimated and measured gas concentration for a gas mixture of carbon monoxide and ethanol (arrows indicate error).
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5. Gas sensor characteristic equation for a three-gas mixture
Table 3 Coefficients of approximate equation for a mixture of carbon monoxide, propane and methane gases using TGS800
For this verification experiment, we used the TGS800 gas sensor. As an example of a three-gas mixture, propane, carbon monoxide, and methane were mixed at various ratios and measured in a temperature- and humiditycontrolled chamber (temperature: 25 ◦ C, relative humidity: 55%). Sensor resistance in a two-gas mixture is given by
β1 β3 β5 β7
Rs = α1 log Cp log Cc + α2 log Cp + α3 log Cc + α4 ,
(9)
where the concentrations of the two gases are Cc and Cp for carbon monoxide and propane in this case, and α k (k = 1–4) are constants. Rs can be generalized for low and high concentrations, and α k will vary accordingly.
−0.266 1.198 1.124 −5.102
× × × ×
104 104 104 104
β2 β4 β6 β8
1.198 −5.486 −5.122 2.378
× × × ×
104 104 104 105
In order to obtain a characteristic equation for the three-gas mixture, we substitute the constants α k in the characteristic equation for the two-gas mixture (Eq. (9)) with a function for another concentration, in this case the concentration for carbon monoxide Cc . Each of the four constants, α k , are modeled using a linear approximation according to αk = β2k−1 log Cc + β2k ,
(10)
where k = 1–4. When Eq. (10) is substituted into Eq. (9), we get the characteristic equation for the three-gas mixture, written as Rs (Cm , Cc , Cp ) = β1 log Cm log Cc log Cp +β2 log Cc log Cp + β3 log Cm log Cp +β4 log Cp + β5 log Cm log Cc + β6 log Cc +β7 log Cm + β8 .
(11)
Extending this equation to a pure gas, the equation can be used to estimate these variables based on the sensor characteristics of three pure gases. However, the concentration of a mixture gas assumed in an uncontrolled space is difficult to obtain. If the concentrations of other molecules are assumed not to change by chemical reaction, the sensor characteristic of the mixture gas can be estimated using the pure gas sensor characteristics.
Fig. 12. Distributions of measured points (solid symbols) and estimated points (open symbols) using TGS800 for methane concentrations of (a) 1967 ppm, (b) 5900 ppm and (c) 9833 ppm.
Fig. 13. Relationship between estimated values and data measured using TGS800 for a gas mixture of propane, carbon monoxide and methane.
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Fig. 14. Histogram of distortion between estimated values and data measured using TGS800.
6. Verification of sensor characteristic in a three-gas mixture As a verification experiment, propane was varied from 1967 to 9833 ppm (measured five times, in 1967 ppm units), and methane and carbon monoxide were both varied from 1967 to 9833 ppm (measured three times, in 3933 ppm units), giving 45 (5 × 3 × 3) samples for which measured data was obtained for estimation. We examined an intersection for verification of the proposed model and took several measurements at the same concentration, the mean value of which was used in analysis. Fig. 12(a)–(c) compares the estimated values and measured data for methane concentrations of 1967, 5900 and 9833 ppm, respectively. In each concentration region, the measured data agree quite closely with the estimated values. This experiment demonstrates the validity of this model for all concentration regions. We separated the 45 samples of measured data into two groups and then estimated the regression coefficients β k (k = 1–8) and calculated the correlation coefficient. The regression coefficient was obtained using the least-squares method. Table 3 lists the values, and Fig. 13 shows the relationship between the measured data and the values estimated by this method. There is a strong correlation when the slope of this coefficient is close to 1. The value of our calculated correlation coefficient is 0.9978. Fig. 14 shows a histogram of the distortion between the measured data and the estimated values of propane concentration in the mixture gas of methane, propane and carbon monoxide. The figure shows the average error as propane concentration was varied from 1967 to 9833 ppm. At high concentrations, the error tends to increase.
7. Conclusions The characteristics of two mixture gases (ammonia and ethanol, and carbon monoxide and ethanol) were examined and using sensor characteristic equation, concentrations estimation of these mixture gases has done. We also verified the validity of a sensor characteristic equation for a mix-
ture of three gases. The three-gas mixture examined was a mixture gas of propane, carbon monoxide and methane. Sensor resistance was shown to be proportional to the logarithmic concentration of each composite gas, particularly in gas mixtures, and was found to become nonlinear when sensor resistance was low. Thus, we have developed a model for sensor characteristics based on experimental data. Using the guided sensor characteristic equation, we found a strong correlation between estimated values and measured data. At all measurement points, we approximated measured data with error of less than 3%. The proposed technique has been shown to approximate the sensor resistance characteristics of mixture gases using a simple function with high accuracy, and can be used to determine the concentration of mixtures of several gases. References [1] T. Oyabu, Chem. Sens. Technol. 5 (1994) 255. [2] T. Oyabu, M. Honda, T. Amamoto, Y. Kajiyama, Sens. Actuat. B 13 (1993) 462. [3] T. Oyabu, Sens. Actuat. B 10 (1993) 143. [4] T. Seiyama, Chem. Sens. Technol. 1 (1988) 1. [5] S. Hirobayashi, H. Kimura, T. Oyabu, Sens. Actuat. B 60 (1999) 78. [6] S. Hirobayashi, S. Sakamori, H. Kimura, T. Oyabu, Trans. Inst. Electron. Eng. Jpn. 118-E (5) (1998) 260. [7] H. Nambo, S. Hirobayashi, H. Kimura, T. Oyabu, Proceedings of the Seventh International Meeting on Chemical Sensors, Technical Digest, 1998, p. 181. [8] T. Oyabu, H. Kimura, S. Ishizaka, Sens. Mater. 7 (6) (1995) 431. [9] T. Oyabu, S. Hirobayashi, H. Kimura, Sens. Mater. 9 (3) (1997) 177. [10] K. Sugahara, R. Konishi, B. Yet, T. Osaki, Trans. Inst. Electron. Eng. Jpn. 121-E (5) (2001) 243. [11] M.A. Mart´ın, J.P. Santos, J.A. Agapito, Sens. Actuat. B 77 (2001) 468. [12] S. Hirobayashi, T. Yamabuchi, T. Yoshizawa, Trans. Inst. Electron. Eng. Jpn. 119-E (7) (1999) 390. [13] R. Kohavi, Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), 1995, p. 1137.
Biographies Shigeki Hirobayashi completed his master’s course at Kogakuin University in 1994 and withdrew from his doctoral course in 1995 to become a research associate at Kanazawa University. He then became a lecturer at
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Toyama University in 1999, where he is currently an associate professor and holds a Deng. Dr. Hirobayashi has been engaged in research on acoustic waves and vibration theory, acoustic signal processing, acoustic field control, and modeling of fluid transfer systems, and is a member of the Institute of Electronics Information and Communication Engineers, the Institute of Electrical Engineers of Japan, the Acoustic Society of Japan, the Acoustic Society of America, and the Society of Instrument and Control Engineers.
a technical officer at the Faculty of Engineering of Toyama University. Since 1994, Mr. Yoshizawa has been a research assistant at the Faculty of Engineering of Toyama University. Current research interests include numerical simulation using the finite-element method and digital signal processing. Mr. Yoshizawa is a member of the Institute of Electronics, Information and Communication Engineers of Japan and the Japan Society for Simulation Technology.
Mohammed Afrose Kadir was born in Dhaka, Bangladesh in 1964, and obtained his BEng degree from the Department of Electrical and Electronics Engineering at B.I.T., Khulna, Bangladesh in 1988. He was an employee of IOML (Toshiba), Bangladesh from 1989 to 1997. Mr. Kadir received his MEng degree from the Department of Electronic and Computer Engineering at Toyama University, Japan in 2000, and is currently a PhD student in the Department of Intellectual Information Systems Engineering at Toyama University. He is currently involved in research concerning the application of gas sensors, and is a member of the Institute of Engineers Bangladesh, the Institute of Electrical and Electronics Engineers Inc. (IEEE), USA and the IEEE Communication Society.
Tatsuo Yamabuchi was born in 1942 in Toyama, Japan, and was awarded his BEng, MEng, and DEng degrees in electrical communication engineering from Tohoku University in 1965, 1967 and 1972, respectively. Since 1972, Dr. Yamabuchi has been with the Department of Electrical Engineering, Faculty of Engineering, at Toyama University, where he has worked as an instructor, an assistant professor, and a professor in the Department of Electronics and Computer Science. In 1997, Dr. Yamabuchi joined the newly established Department of Intellectual Information Systems Engineering as a professor. At present, Dr. Yamabuchi is working on the finite-element method analysis of electromechanical resonators and filters, acoustic fields amid radiation and electromagnetic fields. Dr. Yamabuchi is a member of the Acoustic Society of Japan, the Institute of Electronics, Information and Communication Engineers (Japan), the Institute of Electrical and Electronics Engineers, the Japan Society for Simulation Technology, the Institute of Electrical Society of Japan and Information Processing Society of Japan.
Toshio Yoshizawa was born in Toyama, Japan, in 1948, and was awarded his BEng degree in electrical engineering from Toyama University, Toyama, Japan, in 1971. Mr. Yoshizawa worked at Nippon Minicomputer Co. Ltd., Tokyo, from 1971 to 1974, and from 1975 to 1994 worked as
Verification of a logarithmic model for estimation of gas concentrations in a mixture for a tin oxide gas sensor response Shigeki Hirobayashi∗ , Mohammed Afrose Kadir, Toshio Yoshizawa, Tatsuo Yamabuchi Faculty of Technology, Toyama University, Gofuku, Toyama 930-8555, Japan Received 18 June 2001; received in revised form 24 February 2003; accepted 28 February 2003
Abstract Changes in electrical conductivity due to a reaction occurring between the original adsorbents and the gases present in the surrounding atmosphere were measured for a tin dioxide-based gas sensor. In this study, a model of the gas sensor response using a relationship between the gas concentration in a mixture and the sensor resistance is proposed. The values of coefficients are determined by a least-squares fit of measured data. Using two gas sensors having different characteristics, the concentrations of gases in a mixture can be evaluated. The proposed method has been applied to the evaluation of the gas concentrations in ammonia–ethanol and CO–ethanol mixtures. Furthermore, we verified our model for a gas mixture of carbon monoxide, propane and methane gases, namely for a three-gas system. The results of the present study indicated that the evaluation of gas concentrations in a mixture is feasible using the proposed model of gas sensor response, which can be used as an inexpensive monitor for air pollution. © 2003 Published by Elsevier Science B.V. Keywords: Gas concentration; Gas sensor; Indoor-air pollutants; Gas mixture
1. Introduction The electrical conductivity of oxide semiconductors such as tin oxide gas sensors is altered by the absorption of reductive gases and oxidative reactions on the surface of the catalyzers. These sensors have high reproducibility and stability, and are often used for indoor monitoring systems such as home gas-leak alarms and instruments for the assessment of air pollution levels [1–3]. However, these sensors usually do not have high gas selectivity, and their sensing characteristics depend largely on changes in the indoor environment [4], such as temperature and humidity. Therefore, in this study we have maintained a constant temperature and humidity. Accordingly, the gas sensor system itself tests gas selectivity, which affects the gas sensor response characteristics [5,6]. Previously, gas sensor response characteristics have been modeled using a number of variables in an attempt to detect gas concentration and to classify gases [7–9]. However, general modeling requires gas concentration measurements for each object gas, which requires significant time and effort. In particular, the measurement of each pure gas contained in the mixture gas is necessary. Sugahara et al. [10] proposed ∗ Corresponding author. Tel.: +81-764-456889. E-mail address: [email protected] (S. Hirobayashi).
0925-4005/03/$ – see front matter © 2003 Published by Elsevier Science B.V. doi:10.1016/S0925-4005(03)00311-3
a method of integrating several sensors with different characteristics and/or the new concepts of pattern recognition, such as fuzzy logic and neural network. Using an artificial neural network and a fuzzy neural network they designed the gas discrimination and gas concentration–estimation system, respectively. Mart´ın et al. [11] proposed a model for detecting the individual components of the two gases, presenting a systematic study for enhancing all parameters of a neural network, including preprocessing techniques. However, these models require many gas concentration measurements for each object gas, which requires significant time and effort. When there is an increase in the classification and concentration of a gas, estimation of gas sensor characteristics is not easy. Therefore, mixture gas sensor characteristics are estimated by comparing sensor characteristics for a previously known pure gas. Typically, gas sensor characteristics are obtained experimentally for each pure gas making up a mixture gas, and mixture gas concentrations are calculated accurately using the sensor characteristic equation. In the present study, we extended the sensor characteristic equation to two mixture gases and performed an experiment to verify the sensor characteristics in three mixture gases. The efficiency of the proposed model is confirmed by the experimental result.
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can be approximated as follows: Rs = α log C + β,
Fig. 1. Circuit diagram of sensor system.
2. Modeling of sensor characteristic based on actual measurement The sensor elements used in the present study were TGS826 and TGS800 sensors (Figaro Engineer Inc.). The TGS826 is sensitive to ethanol (C2 H5 OH), carbon monoxide (CO), propane (C3 H8 ) and methane (CH4 ); this sensor also has a high sensitivity to ammonia (NH3 ). The TGS800 has high sensitivity to alcohol gas, i.e., the sensor can be used to judge whether a fuel gas is leaking, and an alarm is activated when alcohol gas is generated. In the present study, two combinations of mixture gases were used for the two-gas system: gas mixture of ammonia and ethanol and mixture of carbon monoxide and ethanol. The electrical resistance of a gas sensor decreases as the gas concentration C (ppm) increases. Fig. 1 shows a circuit diagram of the gas sensor. In the figure, Vc (V) is the power voltage (5 V), Rs () the electrical resistance of the gas sensor, and r () the output voltage resistance. The output voltage is defined according to Kirchhopff’s law as follows: Vr =
Vc r . Rs + r
(1)
We know that the sensor resistance decreases with increasing gas concentration C (ppm). Therefore, the sensor resistance
(2)
where α and β are the coefficients. This equation shows that the sensor resistance is proportional to the logarithm of the concentration C, and is satisfied when the temperature and relative humidity of the ambient are fixed. In our experiment we maintain such conditions using the setup shown in Fig. 2. Gas sensor resistance is shown in Fig. 3(a) and (b) as a function of the gas concentration in the gas mixture. We maintained the concentration of ethanol Ce (ppm) and that of ammonia Ca (ppm) in the temperature- and humidity-controlled chamber shown in Fig. 2. The temperature and relative humidity were maintained constant at approximately 25 ◦ C and 55%, respectively, and the concentration of each gas was adjusted by a syringe. Ammonia was varied from 180 to 1080 ppm (measured six times, in 180 ppm units) and ethanol concentration was varied from 100 to 600 ppm (measured six times, in 100 ppm units). At lower ethanol concentration, there is a greater sensitivity to ammonia concentration, as shown in Fig. 3(a) and (b), and the sensor resistance decreased with increasing ammonia concentration as expected. The straight lines and their slopes differ according to ammonia concentration in both the low and high gas concentration ranges. These results reveal that maintaining a unique-characteristic straight line is difficult. Therefore, we attempted to extend Eq. (2) to be applicable to the concentrations of two different gases. In Fig. 3(a) and (b), straight-line approximations are obtained at approximately 1000 ppm. This confirms the effects of a convergence and a measurement error of sensor output at this concentration. Thus, for the conditions in Fig. 3(a) and (b), we injected an ammonia concentration of 180–720 ppm and an ethanol concentration of 100–400 ppm, respectively, into the subject region. Straight-line plots were obtained by approximation from Eq. (2) using the least-squares method.
Fig. 2. Thermo-hydrostat used for gas sensing experiments.
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Fig. 4. Distribution of coefficients (a) α and (b) β in Eq. (4) using TGS826 sensor unit. Fig. 3. Measured values and approximated linear fitting for a gas mixture of ammonia and ethanol using (a) TGS826 and (b) TGS800.
β(Ce ) = α3 log Ce + α4 ,
(5)
Eq. (2) verifies that the sensor resistance is linearly proportional to the logarithmic concentration. For ammonia concentration (with respect to ethanol concentration), the resistance characteristics, shown in Fig. 3, are expressed as a straight line, similar to Eq. (2). The mixture gas characteristic equation is then as follows:
where α1 –α4 are constants. Combining Eqs. (3)–(5), the sensor resistance of ammonia and ethanol gas is then given by
Rs (Ca , Ce ) = α(Ce ) log Ca + β(Ce ),
In the present work, the measurement of the concentrations of two mixture gases is based on the above equation. Table 1 shows the values of the coefficients (α1 –α4 ), obtained by the least-squares method for the TGS826 and TGS800 gas sensors.
(3)
where Ca is the ammonia gas concentration and Ce the ethanol concentration. The characteristic equation of a mixture gas such as ammonia and ethanol can be determined from a generalized characteristic equation for a mixture gas with unknown coefficients α and β. Fig. 4 shows the characteristic of coefficients α and β of Eq. (3) with respect to the concentration of the other gas Ce (ppm). A straight-line approximation can be obtained using the least-squares method at various ethanol gas concentrations, and the plots fitted well to this linear approximation [12]. A simple linear equation such as Eq. (2) can then be applied to the other gas concentration. That is, α(Ce ) = α1 log Ce + α2 ,
(4)
Rs (Ca , Ce ) = α1 log Ca log Ce + α2 log Ca + α3 log Ce + α4 .
3. Verification of represented model equation The characteristic equation (Eq. (6)) is based on experimental data and is an extension of Eq. (2). In this section we examine Eqs. (2) and (6) in detail. The values of α 2 and α 3 are defined as the logarithms of alcohol and ethanol concentrations, respectively, α 4 is the initial concentration coefficient and α 1 is the coefficient peculiar to the mixture
Table 1 Coefficients of approximate equation for gas mixture of ammonia and ethanol α1 TGS826 TGS800
α2
1.1210 × 0.5974 × 104 104
α3
−3.2567 × −1.6253 × 104 104
(6)
α4
−4.0032 × −2.8450 × 104 104
1.2557 × 105 8.4795 × 104
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Fig. 5. Relationship between estimated values and measured data for a gas mixture of ammonia and ethanol using (a) TGS826 and (b) TGS800.
gas as obtained from Eq. (5). As long as α 1 is not zero, Eq. (6) is a curved surface when plotted against logarithmic concentrations of either ammonia or ethanol, indicating the existence of a correlation coefficient between the two gases. Namely, coefficient α 1 differs from coefficients α 2 and α 3 for each linear concentration term, which necessary because the characteristic sum of individual gases does not generally agree with the mixture gas characteristics. Furthermore, because representation of the extension of Eq. (2) is based on experimental data, the application of the concentration of this model, Eq. (6), is limited to the region that can be approximated by Eq. (2) for each pure gas. Using Eq. (6), we verified the characteristic of a mixture gas sensor composed of two pure gases. We quantitatively investigated the unevenness of distortion between the measured data and estimated values using the model described by Eq. (6). Cross-validation is necessary in the application of weight regression analysis [13]. A well-known method of cross-validation is to decide which variables are effective for use as a standard variable by means of one set of data, estimate a bias regression coefficient, apply the obtained bias regression coefficient to another set of the same kind of data, and then calculate the correlation coefficient between the actual measurement value and the obtained estimated value. For our calculation we divided the obtained data into two sets and estimated a bias regression coefficient. We then calculated the correlation coefficient. The bias regression coefficient was obtained using the least-squares method. We used the first set of data to estimate the regression coefficient, as shown in Table 1. We then applied this coefficient to the second set of data. Fig. 5(a) and (b) shows the relationships between the measured data and the estimated values for a gas mixture of ammonia and ethanol obtained using TGS826 and TGS800. A strong correlation is obtained when the slope of this coefficient is near 1. The values of our calculated coefficients are 0.9969 and 0.9966
for TGS826 and TGS800, respectively, indicating strong correlations. We quantitatively investigated the unevenness of distortion between the measured and estimated values using the model shown in Eq. (6). Fig. 6(a) and (b) shows histograms of the distortion of TGS826 and TGS800, respectively. Both figures show that the estimated values are greater than the measured values in the high-concentration region of the sensor characteristics. In addition, the distribution is slightly more centered and the error is large in the high-concentration region above the modeling subject region. However, in the modeling subject region, both results can generally be estimated to have a small error. In other words, the mixture gas sensor characteristic can be approximated with small errors.
4. Experiment for verification of representative concentration and compound gas mixture ratio Using the model described by Eq. (6), we determined the concentration of each composition for two mixture gases using the TGS826 and TGS800 sensors. As both of these sensors have low resistance characteristics, the concentration of each gas in a mixture gas can be estimated. In other words, the two sensor resistances in Eq. (6) can be expressed as RTGS826 = f (Ca , Ce ),
(7)
RTGS800 = g(Ca , Ce ).
(8)
As RTGS826 and RTGS800 are constant, the only variables in measurements in a real environment are the concentrations Ca and Ce . Since the number of equations and variables are equal, we can calculate the concentration of each gas. The calculated concentrations are consistent with the data from
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Fig. 6. Histograms of distortion between measured values and approximate linear fitting for a gas mixture of ammonia and ethanol using (a) TGS826 and (b) TGS800.
the estimation experiment, as shown in Table 1, demonstrating the validity of this model, which is shown in Fig. 7. Fig. 7 shows the estimated concentration together with the measured concentration for the proposed model for a
mixture gas of ammonia and ethanol. The arrows begin at the measured sensor resistance corresponding to the estimated concentration, and end at the concentration obtained by correct time measurement. The modeling region
Fig. 7. Error between estimated and measured gas concentrations for a gas mixture of ammonia and ethanol (arrows indicate errors).
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is the low-concentration region, which is separated from the high-concentration region by a dotted line. As expected, the estimated error is large in the high-concentration region due to the low sensitivity of sensors under such conditions, however the estimation is very accurate in the modeling concentration region. Next, using the same gas sensors (TGS826 and TGS800), we performed another experiment using a mixture gas of carbon monoxide and ethanol. Fig. 8(a) and (b) represents the measured data (dots) and estimated values (solid line) for each gas sensor, TGS826 and TGS800, respectively. Values for the coefficients of each function, as calculated by the least-squares method, are shown in Table 2. In this experiment we injected 100–700 ppm of carbon monoxide and 100–400 ppm of ethanol into the modeling subject region. We found that the estimated values were higher than the measured values in the high-concentration region. Fig. 9(a) and (b) shows the relationship between the estimated values and the measured data using the TGS826 and TGS800 gas sensors for a gas mixture of carbon monoxide and ethanol. In this case, the values of the calculated coefficients are 0.9968 and 0.9965, indicating a strong correlation. Fig. 10(a) and (b) are histograms that show the distortion of the measured data and estimated values. The distortion is quite low compared to the previous ethanol/ammonia mixture gases. Fig. 11 shows the measured data and estimated values for a mixture gas of carbon monoxide and ethanol. The figure shows that for this mixture gas, although the estimated distortion is quite large outside the modeling subject concentration region, the concentration can be estimated
Fig. 8. Measured values and approximated linear fitting for a gas mixture of carbon monoxide and ethanol using (a) TGS826 and (b) TGS800.
with reasonable accuracy using this model within the target region. In the present work, the sensor expressed by Eq. (2) is extended using the proposed model to Eq. (6). This model
Table 2 Coefficients of approximate equation for gas mixture of carbon monoxide and ethanol α1 TGS826 TGS800
α2
0.5321 × 0.9525 × 104 104
α3
−1.4189 × −2.6656 × 104 104
α4
−3.4969 × −3.5654 × 104 104
1.0666 × 105 1.0761 × 105
Fig. 9. Relationship between estimated values and measured data for a gas mixture of carbon monoxide and ethanol using (a) TGS826 and (b) TGS800.
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Fig. 10. Histograms of distortion between measured values and approximate linear fitting for a gas mixture of carbon monoxide and ethanol using (a) TGS826 and (b) TGS800.
has four unknown coefficients (α1 –α4 ), which can be solved by changing the concentration of mixture gas and measuring the concentration using each sensor at least four times. Accurate estimation of gas concentration is possible using a
simple numerical formula such as the proposed model. However, as the direction of vectors (α1 , α2 , α3 , α4 ) are similar, Eqs. (7) and (8) are identical so difference of gas sensitivity are necessary for sensor selection.
Fig. 11. Error between estimated and measured gas concentration for a gas mixture of carbon monoxide and ethanol (arrows indicate error).
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5. Gas sensor characteristic equation for a three-gas mixture
Table 3 Coefficients of approximate equation for a mixture of carbon monoxide, propane and methane gases using TGS800
For this verification experiment, we used the TGS800 gas sensor. As an example of a three-gas mixture, propane, carbon monoxide, and methane were mixed at various ratios and measured in a temperature- and humiditycontrolled chamber (temperature: 25 ◦ C, relative humidity: 55%). Sensor resistance in a two-gas mixture is given by
β1 β3 β5 β7
Rs = α1 log Cp log Cc + α2 log Cp + α3 log Cc + α4 ,
(9)
where the concentrations of the two gases are Cc and Cp for carbon monoxide and propane in this case, and α k (k = 1–4) are constants. Rs can be generalized for low and high concentrations, and α k will vary accordingly.
−0.266 1.198 1.124 −5.102
× × × ×
104 104 104 104
β2 β4 β6 β8
1.198 −5.486 −5.122 2.378
× × × ×
104 104 104 105
In order to obtain a characteristic equation for the three-gas mixture, we substitute the constants α k in the characteristic equation for the two-gas mixture (Eq. (9)) with a function for another concentration, in this case the concentration for carbon monoxide Cc . Each of the four constants, α k , are modeled using a linear approximation according to αk = β2k−1 log Cc + β2k ,
(10)
where k = 1–4. When Eq. (10) is substituted into Eq. (9), we get the characteristic equation for the three-gas mixture, written as Rs (Cm , Cc , Cp ) = β1 log Cm log Cc log Cp +β2 log Cc log Cp + β3 log Cm log Cp +β4 log Cp + β5 log Cm log Cc + β6 log Cc +β7 log Cm + β8 .
(11)
Extending this equation to a pure gas, the equation can be used to estimate these variables based on the sensor characteristics of three pure gases. However, the concentration of a mixture gas assumed in an uncontrolled space is difficult to obtain. If the concentrations of other molecules are assumed not to change by chemical reaction, the sensor characteristic of the mixture gas can be estimated using the pure gas sensor characteristics.
Fig. 12. Distributions of measured points (solid symbols) and estimated points (open symbols) using TGS800 for methane concentrations of (a) 1967 ppm, (b) 5900 ppm and (c) 9833 ppm.
Fig. 13. Relationship between estimated values and data measured using TGS800 for a gas mixture of propane, carbon monoxide and methane.
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Fig. 14. Histogram of distortion between estimated values and data measured using TGS800.
6. Verification of sensor characteristic in a three-gas mixture As a verification experiment, propane was varied from 1967 to 9833 ppm (measured five times, in 1967 ppm units), and methane and carbon monoxide were both varied from 1967 to 9833 ppm (measured three times, in 3933 ppm units), giving 45 (5 × 3 × 3) samples for which measured data was obtained for estimation. We examined an intersection for verification of the proposed model and took several measurements at the same concentration, the mean value of which was used in analysis. Fig. 12(a)–(c) compares the estimated values and measured data for methane concentrations of 1967, 5900 and 9833 ppm, respectively. In each concentration region, the measured data agree quite closely with the estimated values. This experiment demonstrates the validity of this model for all concentration regions. We separated the 45 samples of measured data into two groups and then estimated the regression coefficients β k (k = 1–8) and calculated the correlation coefficient. The regression coefficient was obtained using the least-squares method. Table 3 lists the values, and Fig. 13 shows the relationship between the measured data and the values estimated by this method. There is a strong correlation when the slope of this coefficient is close to 1. The value of our calculated correlation coefficient is 0.9978. Fig. 14 shows a histogram of the distortion between the measured data and the estimated values of propane concentration in the mixture gas of methane, propane and carbon monoxide. The figure shows the average error as propane concentration was varied from 1967 to 9833 ppm. At high concentrations, the error tends to increase.
7. Conclusions The characteristics of two mixture gases (ammonia and ethanol, and carbon monoxide and ethanol) were examined and using sensor characteristic equation, concentrations estimation of these mixture gases has done. We also verified the validity of a sensor characteristic equation for a mix-
ture of three gases. The three-gas mixture examined was a mixture gas of propane, carbon monoxide and methane. Sensor resistance was shown to be proportional to the logarithmic concentration of each composite gas, particularly in gas mixtures, and was found to become nonlinear when sensor resistance was low. Thus, we have developed a model for sensor characteristics based on experimental data. Using the guided sensor characteristic equation, we found a strong correlation between estimated values and measured data. At all measurement points, we approximated measured data with error of less than 3%. The proposed technique has been shown to approximate the sensor resistance characteristics of mixture gases using a simple function with high accuracy, and can be used to determine the concentration of mixtures of several gases. References [1] T. Oyabu, Chem. Sens. Technol. 5 (1994) 255. [2] T. Oyabu, M. Honda, T. Amamoto, Y. Kajiyama, Sens. Actuat. B 13 (1993) 462. [3] T. Oyabu, Sens. Actuat. B 10 (1993) 143. [4] T. Seiyama, Chem. Sens. Technol. 1 (1988) 1. [5] S. Hirobayashi, H. Kimura, T. Oyabu, Sens. Actuat. B 60 (1999) 78. [6] S. Hirobayashi, S. Sakamori, H. Kimura, T. Oyabu, Trans. Inst. Electron. Eng. Jpn. 118-E (5) (1998) 260. [7] H. Nambo, S. Hirobayashi, H. Kimura, T. Oyabu, Proceedings of the Seventh International Meeting on Chemical Sensors, Technical Digest, 1998, p. 181. [8] T. Oyabu, H. Kimura, S. Ishizaka, Sens. Mater. 7 (6) (1995) 431. [9] T. Oyabu, S. Hirobayashi, H. Kimura, Sens. Mater. 9 (3) (1997) 177. [10] K. Sugahara, R. Konishi, B. Yet, T. Osaki, Trans. Inst. Electron. Eng. Jpn. 121-E (5) (2001) 243. [11] M.A. Mart´ın, J.P. Santos, J.A. Agapito, Sens. Actuat. B 77 (2001) 468. [12] S. Hirobayashi, T. Yamabuchi, T. Yoshizawa, Trans. Inst. Electron. Eng. Jpn. 119-E (7) (1999) 390. [13] R. Kohavi, Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), 1995, p. 1137.
Biographies Shigeki Hirobayashi completed his master’s course at Kogakuin University in 1994 and withdrew from his doctoral course in 1995 to become a research associate at Kanazawa University. He then became a lecturer at
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Toyama University in 1999, where he is currently an associate professor and holds a Deng. Dr. Hirobayashi has been engaged in research on acoustic waves and vibration theory, acoustic signal processing, acoustic field control, and modeling of fluid transfer systems, and is a member of the Institute of Electronics Information and Communication Engineers, the Institute of Electrical Engineers of Japan, the Acoustic Society of Japan, the Acoustic Society of America, and the Society of Instrument and Control Engineers.
a technical officer at the Faculty of Engineering of Toyama University. Since 1994, Mr. Yoshizawa has been a research assistant at the Faculty of Engineering of Toyama University. Current research interests include numerical simulation using the finite-element method and digital signal processing. Mr. Yoshizawa is a member of the Institute of Electronics, Information and Communication Engineers of Japan and the Japan Society for Simulation Technology.
Mohammed Afrose Kadir was born in Dhaka, Bangladesh in 1964, and obtained his BEng degree from the Department of Electrical and Electronics Engineering at B.I.T., Khulna, Bangladesh in 1988. He was an employee of IOML (Toshiba), Bangladesh from 1989 to 1997. Mr. Kadir received his MEng degree from the Department of Electronic and Computer Engineering at Toyama University, Japan in 2000, and is currently a PhD student in the Department of Intellectual Information Systems Engineering at Toyama University. He is currently involved in research concerning the application of gas sensors, and is a member of the Institute of Engineers Bangladesh, the Institute of Electrical and Electronics Engineers Inc. (IEEE), USA and the IEEE Communication Society.
Tatsuo Yamabuchi was born in 1942 in Toyama, Japan, and was awarded his BEng, MEng, and DEng degrees in electrical communication engineering from Tohoku University in 1965, 1967 and 1972, respectively. Since 1972, Dr. Yamabuchi has been with the Department of Electrical Engineering, Faculty of Engineering, at Toyama University, where he has worked as an instructor, an assistant professor, and a professor in the Department of Electronics and Computer Science. In 1997, Dr. Yamabuchi joined the newly established Department of Intellectual Information Systems Engineering as a professor. At present, Dr. Yamabuchi is working on the finite-element method analysis of electromechanical resonators and filters, acoustic fields amid radiation and electromagnetic fields. Dr. Yamabuchi is a member of the Acoustic Society of Japan, the Institute of Electronics, Information and Communication Engineers (Japan), the Institute of Electrical and Electronics Engineers, the Japan Society for Simulation Technology, the Institute of Electrical Society of Japan and Information Processing Society of Japan.
Toshio Yoshizawa was born in Toyama, Japan, in 1948, and was awarded his BEng degree in electrical engineering from Toyama University, Toyama, Japan, in 1971. Mr. Yoshizawa worked at Nippon Minicomputer Co. Ltd., Tokyo, from 1971 to 1974, and from 1975 to 1994 worked as