Gas mixture estimation model based on response equivalent and orthogonal decomposition of transient response signals

Transcript

1 37 4 Vol. 37 No JOURNAL OF NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY Aug. 15 doi /j. cn http / /journal. nudt. edu. cn * Legendre 15% Legendre TP1. 6 A Gas mixture estimation model based on response equivalent and orthogonal decomposition of transient response signals QIN Guojun 1 ZHONG Ming 3 ZHANG Wenna 1 HU Niaoqing 1 1. Key Laboratory of Science and Technology on Integrated Logistics Support National University of Defense Technology Changsha 4173 China. College of Mechanical Engineering Hunan International Economy University Changsha 4117 China 3. The PLA Unit 696 Wulumuqi 831 China Abstract Based on linear mixture assumption or training the classifiers by large amount of data many methods used to recognize and estimate gas mixtures were adopted the non-orthogonal decomposition of steady response signal. Considering orthogonal decomposition approaches were mainly applied to analyze transient response signals a gas mixture estimation model based on response equivalent and orthogonal decomposition of transient response signals was put forward. A novel nonlinear gas-mixing model was built after the analysis of MOS Metal Oxide Semiconductor gas sensor response characteristics based on the component equivalent expression for different gas responses. A new orthogonal basis function the EQL Extended Quasi-Legendre basis was proposed and applied to the decomposition of a transient response signal from the gas sensor. After the exponential relationship between the coefficients and the gas concentration was verified via regression analysis the components in the gas mixture were separated and their concentrations were estimated simultaneously. Experimental result shows that even though only the prior knowledge of single gas responses was applied to build the model the concentration determined from the transient response of the gas mixture can reach an error within 15%. Key words response equivalent orthogonal decomposition extended quasi-legendre basis transient response signal gas mixture estimation * A qgj@ nudt. edu. cn

2 4 173 o m i = α 1 /β m i m j o α m j β m j = γ 1 /β m i m j c m i α j βm j m i 5 5 m O i O j 5 o m i 11 o j m i O j m o m i N O i i = 1 N m x m = f m o m o m i + + o m N 6 5 m 1-15 O i x m = f m i N 1/β α m m j λ 1 j =1 α m j b m j c j b m j [ ( m i ) i ] 7 1 x m = N γ m j c j β m j 1 /β m [ i β ] m i 8 f m x m 1 /β m i = N γ m j 1 /β m i c j β m j /β m i 9 m O i x m 19 x mi = G m - 1 = f G air mi c i = γ m i c i β m i 1 m 9 G m m O i N G air m m c j N f mi m O i γ m i c j Freundlich β m i M 1 3 K x k m m = 1 M O i m k = 1 K N o m i M K o m i = c i λ m i λ m i O i m x k m 1 /βk m i = N γ k m j 1 /βk m i c j βk m j /βk m i 1 λ m i N 1 M K > N x m i = f m i o m i = α m i λ m i β m i c i β m i = α m i o m i β m i 3 α m i = γ m i /λ β m i m m O j 3 x m j = α m j o m j β m j = γ m j c j β m j 4 x m i = x m j i [ ] ( ) γ m j β m j N O j Legendre Metal Oxide Semiconduct MOS 1

3 t a L n t Legendre Legendre L t = 1 Fourier Wavelet Basel 1 L 1 t = sin( t - α Legendre ) Legendre MOS L k -1 t = sin( kt - k α ) - k -1 C k -1 j-1 L j-1 t 1 < k N + 1 t a L k t = cos( kt - k α ) - k -1 C k j L j t j = 1 k N Legendre Legendre N+m-1 L N+m = t m - C N+m j L j t m = 1 M j = Γ N M = span 1 11 sint cost sint cost sinnt cosnt t t M Fig. 1 1 ~ 8 Legendre Extended quasi-legendre standard orthogonal basis fuctions of L i t i = 8 Gram-Schmidt C k-1 j-1 C k j ( ) α = sin kt - k α L α j-1 t dt ( ) α = cos kt - k α L α j t dt C N+m j = α t m L j t dt α L j t dt L j-1 t dt L j t dt 1 a ~ i α = 1 N = 8 M = ~ 8 Legendre ~ 8 L n t Fourier

4 Legendre 3 Γ N M K + 1 A = a a K T 3. 1 AIRSENSE K r K = - PEN3 3 x i - ^x K i x K i i i 1 MOS 槡 x i ^x i # 6 G 1ml 5ml 1ml ml 5ml 1ml Legendre 1 K 3 1ml 5ml 4h L 3ml l 3 l l l 1 # l - l 1 Fig. Original responses and their reconstruction of sensor in diesel gas l G /G 3 6s 1Hz Fig. 3 Curves of fitting error changes with different K 6s K = 4 3. Legendre x t t a Legendre K ^x K t = K a k L k t 1 k = K = 4 1 # Legendre 4 6 a k k = K Legendre

5 Legendre 3 Legendre 4. 1 a k m 4 1 i 1 Legendre 4 M K m m = 1 1 γ k m i β k m i a k m m = 1 M i = 1 c p i K + 1 N k = 1 K c i i = 1 N a k m i c p k = 1 K p = 1 P P c i i = 1 N a k m i c p 4 N γ k m i β k m i i = 1 N a 1 1 /β 1 i = γ 1 1 /β 1 i c1 β 1 1 /β 1 i + γ /β 1 i c β 1 /β 1 i + + γ 1 N 1 /β 1 i cn β 1 N /β 1 i a K 1 1 /βk 1 i = γ P 1 1 /βk 1 i c1 βk 1 1 /βk 1 i + γ P 1 1 /βk 1 i c βk 1 /βk 1 i + + γ P 1 N 1 /βk 1 i cn βk 1 N /βk 1 i 13 a M 1 /β M i = γ M 1 1 /β M i c1 β M 1 /β M i + γ M 1 /β M i c β M /β M i + + γ M N 1 /β M i cn β M N /β M i a K M 1 /βk M i = γ K M 1 1 /βk M i c1 βk M 1 /βk M i + γ K M 1 /βk M i c βk M /βk M i + + γ K M N 1 /βk M i cn βk M N /βk M i 4. k = a 13 m 1 a m m = a p m i # # 3# 5# 6# 7# 8# 9# Legendre l 13 l 1 r l error 4 5 1# # 3# 5# = l ac - l es /l ac 1% l ac l es 6# 7# 8# 9# Fig. 4 4 Orthogonal decomposition coefficients of diesel gas signals and their fitting results

6 4 177 Fig. 5 5 Orthogonal decomposition coefficients of gear oil gas signals and their fitting results 1 1ml 5ml 15% Tab. 1 1 Estimation result of sample volumes for single gas and the mixture gas l ac /m l es /ml r l error /% l es /ml r l error /% % x m 1 5 x m 13

7 Legendre References 1 Gutierrez-Osuna R. Pattern analysis for machine olfaction a review J. IEEE Sensors Journal J GAO Daqi YANG Genxing. Recent developments and application prospects of electronic noses J. Journal of Transducer Technology in Chinese 3 De Vito S Massera E Piga M et al. On field calibration of an electronic nose for benzene estimation in an urban pollution monitoring scenario J. Sensors and Actuators B Chemical Sohna J H Hudson N Gallagher E et al. Implementation of an electronic nose for continuous odour monitoring in a poultry shed J. Sensors and Actuators B Chemical Martin M A Santos J P Agapito J A. Application of artificial neural networks to calculate the partial gas concentrations in a mixture J. Sensors and Actuators B Chemical J ZHANG Qinyi WANG Zhenyong SUN Wei et al. Application of electronic nose for quantification of ethanol & acetone and ethanol & benzene J. Journal of Transduction Technology in Chinese 7 J LIU Hongxiu LI Hongbo LI Weidong et al. Research on the fish freshness assessment based on electronic nose J. Acta Scientiarum Naturalium Universitatis Sunyatseni in Chinese 8 J YUAN Zuqiang WANG Xinlei. Application of gray system theory in quantitative analysis of electronic nose J. Transducer and Microsystem Technology in Chinese 9 Gao D Q Chen W. Simultaneous estimation of odor classes and concentrations using an electronic nose with function approximation model ensembles J. Sensors and Actuators B Chemical Gao D Q Chen M M Yan J. Simultaneous estimation of classes and concentrations of odors by an electronic nose using combinative and modular multilayer perceptions J. Sensors and Actuators B Chemical Pardo M Sberveglieri G. Remarks on the use of multilayer perceptrons for the analysis of chemical sensor array data J. IEEE Sensors Journal Bermejo S Sole-Casals J. Blind source separation for solidstate chemical sensor arrays C / /Proceedings of Sensor Array and Multichannel Signal Processing Workshop Kermit M Tomic O. Independent component analysis applied on gas sensor array measurement data J. IEEE Sensors Journal Rudnev V A Boichenko A P Karnozhytskiy P V. Classification of gasoline by octane number and light gas condensate fractions by origin with using dielectric or gaschromatographic data and chemo-metrics tools J. Talanta Yu H C Wang J Xiao H et al. Quality grade identification of green tea using the eigenvalues of pca based on the E-nose signals J. Sensors and Actuators B Chemical Hirobayashi S Kadir M A Yoshizawa T et al. Verification of a logarithmic model for estimation of gas concentrations in a mixture for a tin oxide gas sensor response J. Sensors and Actuators B Chemical Chaiyboun A Traute R Haas T et al. A logarithmic multiparameter model using gas sensor main and cross sensitivities to estimate gas concentrations in gas mixture for SnO gas sensors J. Sensors and Actuators B Chemical Huang D l Leung H. Simultaneous classification and concentration estimation for electronic nose J. IEEE Sensors Journal Abbas A Bouabdellah A. Theory of solids /gas mixtures multi-interfaces application to the steady state interactions between a sensor array based on metal oxide semiconductor detectors and a mixture of vapors J. Sensors and Actuators B Chemical Legendre J ZHOU Zhimin WANG Guozhao. A quasi-legendre basis and its application J. Journal of Zhejiang University Science Edition in Chinese 1 Vergara A Martinelli E Huerta R et al. Orthogonal decomposition of chemo-sensory cues J. Sensors and. Actuators B Chemical Khol D. Fundamentals and recent developments of homogenous semiconducting sensors M. Sensors and Sensory Systems for an Electronic Nose Gardner J W Bartlett P N USA Kluwer Academic Publishers Legendre J ZHANG Wenna QIN Guojun HU Niaoqing. Orthogonal decomposition of gas array signals based on a quasi-legendre basis J. Journal of Transduction Technology in Chinese