Send Orders for Reprnts to reprnts@benthamscence.ae The Open Automaton and Control Systems Journal, 2015, 7, 415-420 415 Open Access Lnearzaton Method of Carrer Catalytc Gas Sensor Characterstcs Usng Hgh-Order Polynomal Huang Weyong 1,*, Gao Yuqng 2 and Tan Xulng 3 1 Xuzhou Key Laboratory of Vrtual Realty and Mult-dmensonal Informaton Processng, Xuzhou Insttute of Technology, Xuzhou Jangsu, P.R. Chna 2 Jangsu Key Laboratory of Large Engneerng Equpment Detecton and Control, Xuzhou Insttute of Technology, Xuzhou Jangsu, P.R. Chna 3 School of Informaton and Electrcal Engneerng, Xuzhou Insttute of Technology, Xuzhou Jangsu, P.R. Chna Abstract: To mprove detectng performance of gas concentraton n coal-mne, a new lnearzaton method of carrer catalytc gas sensor characterstcs based on hgh-order polynomals was ntroduced. Frstly, the calbraton data of sensor was used to establsh the tranng sample set. Then, the hgh-order polynomal was employed to establsh nonlnear regresson nverse model of sensor characterstcs. Fnally, the polynomal coeffcents were ntellgently tuned by mproved clone selecton algorthm (ICSA) and the crtera of mean absolute error (MAE) mnmzaton. Expermental results showed that the method proposed n ths paper s effectve, and the performance of lnearzaton model s superor to that of the tradtonal least square method. Keywords: Carrer catalytc gas sensor, Lnearzaton, Hgh-order polynomal, Clone selecton algorthm. 1. INTRODUCTION Nowadays carrer catalytc gas sensor plays an mportant role n coal-mne gas measurement systems. Due to the nonlnear characterstcs of carrer catalytc gas sensors, external envronment, electronc component agng, and many other uncertan factors, there s a complex nonlnear relatonshp between the actual put voltage of sensor and gas concentraton [1]. Because the nonlnear characterstcs of carrer catalytc sensor drectly affect and even determne the performance of the gas measurement system, seekng an effectve mathematcal model to realze the lnearzaton of carrer catalytc gas sensor characterstcs s of great sgnfcance, so as to ensure the measurement accuracy of gas concentraton n coal-mne. Consderng that tradtonal methods, such as look-up table, pecewse lnearzaton and so on, have the shortcomng of low accuracy and they can not be applcable to hgh accuracy occasons, many researchers have carred on the thorough research n the feld of sensor characterstcs lnearzaton. CHEN proposed a least-squares method [2], but the method was based on the descent of sum of error square to fnd the optmal soluton, easly trappng n local mnmum pont and not gettng the global optmal soluton. Especally when the data ponts are larger, the method s prone to oscllaton phenomenon, even unable to obtan polynomal *Address correspondence to ths author at the School of Informaton and Electrcal Engneerng, Xuzhou Insttute of Technology, Jangsu, 221111, P.R. Chna; Tel: 13776786967; E-mal: h_weyongs@163.com coeffcent [3]. Lu proposed a knd of lnearzaton method based on neural network [4]. Because neural network s based on the law of large numbers usng the emprcal rsk crteron wth the complex model to ft the lmted samples, the lnearzaton model usng neural network s unstable and has poor generalzaton ablty [5]. In order to get hgher precson, Sun proposed a knd of least squares support vector machnes (LSSVM) method [6], but ths method s dffcult to be drectly appled n the detectng systems of mne gas. Both theory and practce show that the hgh-order polynomal can ft any nonlnear curve, and s easy to be mplemented n the detectng devces wth sngle-chp mcrocomputer. The current paper adopts hgh-order polynomal for lnearzaton of catalytc gas sensor characterstcs, so as to get better detectng performance. As the polynomal coeffcents determne drectly the polynomal performance, the selecton and optmzaton of polynomal coeffcent has become an mportant ssue to be resolved. Clone selecton algorthm (CSA) [7] by Castro accordng to the theory of mmunty n the clone selecton mechansm s a new optmzaton algorthm wth heurstc ntellgence, whch not only has a faster convergence speed n the search range, but also can overcome the problem of premature convergence that many other evolutonary computaton algorthms have [8]. Clone selecton algorthm has acheved excellent results n many practcal applcatons wth the superor performances to the classcal approaches, and also provdes a new way for the selecton and optmzaton of hgh-order polynomal coeffcent. 1874-4443/15 2015 Bentham Open
416 The Open Automaton and Control Systems Journal, 2015, Volume 7 Weyong et al. The put error of lnearzaton model s an mportant evaluaton crtera reflectng the system accuracy, and the mean square error (MSE) s usually used n the optmzaton of polynomal coeffcent optmzaton. Research shows that when optmzng hgh-order polynomal coeffcent, adoptng MSE evaluaton crtera has some defcences: when lers or sngular ponts exst n the sample set, ther effects wll be magnfed, whch can reduce overall modelng accuracy of the system. Whle the evaluaton crtera of mean absolute error (MAE) mnmzaton s appled, the robustness of lnearzaton model system s better [9]. To ths end, a new lnearzaton method of carrer catalytc gas sensor characterstcs by usng hgh-order polynomal and an mproved clone selecton algorthm (ICSA) was ntroduced n an attempt to tune ntellgently the polynomal coeffcents. The expermental results showed that the proposed method n ths paper s feasble, and can yeld better performance than the conventonal least square method. Ths paper s organzed as follows: Secton 1 lnes brefly the related work. Secton 2 states the lnearzaton prncple of sensor characterstcs usng hgh-order polynomal. Secton 3 presents the prncple and algorthm of ICSA. The procedure for selectng and optmzng polynomal coeffcent based on ICSA s presented n Secton 4, followed by the experment results and the conclusons n Secton 5 and n Secton 6. 2. LINEARIZATION MODEL OF SENSOR USING HIGH-ORDER POLYNOMIAL The lnearzaton of catalytc gas sensor characterstcs usng hgh-order polynomal s to establsh an nverse model of the sensor characterstcs usng multple sensor calbraton data by adjustng the polynomal coeffcents to fnd the mnmum dfference between the model put and the test data. If the hysteress and creep effect of sensor are not consdered, the lnearzaton model of catalytc gas sensor characterstcs can be descrbed wth n-order polynomal as follows: ˆx = a n u n + a n!1 u n!1 +!+ a 2 u 2 + a 1 u + a 0 (1) where, u s the put voltage of sensor, ˆx s measurement value of gas concentraton, n s the order of polynomal, (=n,n-1, 2,1,0) s polynomal coeffcent to be selected and optmzed. Due to a n formula (1) reflectng the nverse characterstcs of sensor, how to determne the a values become the key to mplement the characterstcs lnearzaton of catalytc gas sensor. By calbratng the sensor to obtan nput/put data of sensor, researchers used to select the polynomal coeffcents usng least square method. The polynomal coeffcents were stored n sngle-chp mcrocomputer and when the put voltage of sensor was detected, the real value of gas could be calculated by Formula (1). Because the prncple of least square method s smple and ts programmng s not dffcult, the least square method has become an mportant means for parameters estmaton by expermental data. a As mentoned above, the least square method n many cases can not obtan the optmal soluton, and even s unable to obtan the polynomal coeffcents that we want to obtan. The development of ntellgent optmzaton technology makes t possble for people to tune parameters of mathematcal model, whch can make the establshed model more credble [10]. Clone selecton algorthm was adopted n ths paper to select and optmze the polynomal coeffcent, so as to get better detectng results. 3. IMPROVED CLONE SELECTION ALGORITHM The basc prncple of clone selecton algorthm s that the functon to be optmzed and ts constrants s vewed as antgen, the soluton of the problem s vewed as antbody and the affnty between the antbody, antbody-antgen s vewed as the objectve functon of the problem [11]. In order to tune automatcally the polynomal coeffcents, an mproved clone selecton algorthm s lned n the paper. Its block dagram s shown n Fg. (1). The correspondng steps are explaned n detal as follows: Step 1: Intalzaton: Randomly generate n antbodes correspondng to a possble soluton, as the ntal populatons A, consttutng the ntal populaton space n I. Step 2: Evaluaton and selecton: Calculate the affnty functon of antbody n the populaton, and dvde N antbodes nto two parts: canddate set Ar and memory set Am. Step 3: Clonng: Clone k antbodes wth the hghest affnty, clonng number beng proportonal to the affnty. Step 4: Mutaton: Accordng to a specfed probablty, randomly perform the operaton of mutaton on the cloned antbodes at a certan scale. Step 5: Re-evaluaton and re-selecton: Re-calculate the affnty of antbodes cloned and mutated. If the affnty s even hgher than the orgnal, replace the orgnal antbody wth the new antbody, so as to form a new memory set. Step 6: Extncton: Delete d antbodes wth lowest affnty n Ar, generate randomly d antbodes, and add them to the populaton, n order to ensure the dversty of antbodes, whch smulate 5% B cells naturally dyng process n the bologcal clone selecton. Step 7: Stop: If the stop crteron s satsfed, then put the result, or else return to step 2. Because hgh-order polynomal coeffcent s approprate or does not have a decsve nfluence on performance of lnearzaton model of catalytc gas sensor characterstcs, t drectly affects the measurement result. Consderng that clone selecton algorthm has excellent optmzng performance, ths paper uses the algorthm to tune polynomal coeffcent wth sample data of sensor calbraton. 4. USING ICSA TO OPTIMIZE POLYNOMIAL CO- EFFICIENT Accordng to the characterstcs of the sensor and mproved clone selecton algorthm, the block dagram usng
Lnearzaton Method of Carrer Catalytc Gas Sensor The Open Automaton and Control Systems Journal, 2015, Volume 7 417 start ntalze populaton calculate affnty of antbodes evaluate and select produce canddate sets Ar produce memory sets Am clone on k antbodes wth hghest affnty generate randomly d antbodes to replace antbodes wth lowest affnty crossover and mutaton on antbodes re-evaluate and re-select generate new canddate sets update memory sets compose new populaton N satsfed end condton? end Y Fg. (1). Block dagram of mproved clone selecton algorthm. Fg. (2). Prncple dagram of sensor characterstcs lnearzaton. hgh order polynomal to ft characterstc curve s shown n Fg. (2). In Fg (2), x s the nput of sensor from the actual system, u s the sensor put, and ˆx s the put of polynomal fttng model. The parameters of the fttng model are tuned ntellgently by mproved clone selecton algorthm descrbed above accordng to the crtera of mean absolute error mnmzaton. The flow chart of tunng polynomal coeffcents s shown n Fg. (3). Beng dfferent from the conventonal method usng the tradtonal method of least squares, the modelng method n ths paper does not employ the error sum of squares descent method to seek the optmal polynomal coeffcents, but uses an mproved clonal selecton algorthm to search the optmal soluton n the global scope, so as to get an optmal polynomal to establsh nverse model of sensor. 5. EXPERIMENT AND RESULTS To facltate comparatve research, ths paper uses calbraton data of catalytc sensor 0~4% of methane gas as the basc data resource [2], and adopts three order polynomal to ft put characterstcs of sensor. In order to make modelng error mnmzed and has good consstency, the mean absolute error s employed to evaluate the modelng performance. The expresson of mean absolute error s shown n formula (2): MAE = 1 n n xˆ x = 1 where, x s the put of model, x s real value, n s the ˆ number of sample. (2)
418 The Open Automaton and Control Systems Journal, 2015, Volume 7 Weyong et al. start Sensor calbratng establshng data sample optmzng coeffcent of hghorder polynomal usng ICSA Hgh- order polynomal modelng satsfed end condton? end Y N Fg. (3). Flow chart of tunng polynomal coeffcents. 4.5 4 real value measurng value 3.5 3 put /% 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 nput /% Fg. (4). Input-put curve of sensor. To elmnate the effect of large range of the sensor put voltage on the modelng performance of the, the formula (3) s appled to normalze put voltage of sensor to the nterval [0, 1]. z u max{ u } = where, u s the sample value numbered max{ u } s the maxmum value of = 1,!,9. (3) u z s the normalzed value of u Nne learnng samples are used to tran 3-order polynomal and the coeffcents of polynomal are tuned by mproved clone selecton algorthm. The parameters of the mproved clone selecton algorthm are shown n Table 1. When MAE reaches to 0.04, the algorthm stops runnng to get the optmal coeffcent of the polynomal (a 3, a 2, a 1 and a 0 ) = (-0.009, -0.7487, 4.8555, 0.00000). The polynomal s expressed as follows: 3 2 ˆx = 0.0009u 0.7487u + 4.8555u (4) The polynomal above s the nverse model of sensor. After 9 tranng data are nput nto the nverse model, the fnal put results were obtaned and lsted n Table 2. The nputput curve of sensor was dsplayed n Fg. (4).
Lnearzaton Method of Carrer Catalytc Gas Sensor The Open Automaton and Control Systems Journal, 2015, Volume 7 419 Table 1. Parameters settngs of ICSA. ICSA Parameter Settng Total Generaton 100 Intal Populaton Sze 100 Length of Codng 22 Clone Factor 10 Suppresson Threshold 5 Cross Probablty 0.9 Mutaton Probablty 0.01 Table 2. Input-put data of sensor. Gas Real Value /% 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Sensor Output Voltage/mv 0 14 30 46 63 80 95 110 138 Gas Measurng Value/% 0.0000 0.4849 1.0201 1.5353 2.0605 2.5630 2.9874 3.3941 4.1059 It can be seen from Table 2 and Fg. (4), the measurement results are very close to the true value. To evaluate the lnearty of sensor, the ndependent lnearty L s used as evaluaton ndcators. m L =± 100% X Δ X max mn where, Δ s the maxmum absolute devaton; m X X max mn s sensor range, whch s the algebrac dfferental of the upper lmt and lower lmt of measurement. From Table 1 and formula (4), L (5) s 2.6475%, whle L s 4.2500% when usng the least square method [2]. It can be seen that the lnearzaton method proposed n ths paper can mprove effectvely the lnearty of sensor, and can get hgher measurement accuracy. On the other hand, the lnearzaton method usng least squares polynomal has 0.035% zero-error [2]. In order to avod zero-error, the value of zero-error must be subtracted from the measurement result obtaned, whch not only ncreases error of the other measurement ponts, but also denes the theoretcal bass of the method. Whle the lnearzaton method proposed n ths paper has no zero-error, does not have the defect of zero-pont adjustment and can obtan hgher measurement accuracy. It must be noted that the method proposed n ths paper does not ncrease the complexty of algorthm when the hgher than 3-order polynomal s employed to establsh nonlnear regresson nverse model of sensor. And ths method s also sutable for all knds of one-dmensonal or hgh-dmensonal sensors. CONCLUSION In ths paper, a new lnearzaton method of carrer catalytc gas sensor characterstcs usng hgh-order polynomal was ntroduced. The optmal coeffcents of polynomal were tuned by mproved clone selecton algorthm and the crtera of mean absolute error mnmzaton. The expermental results show the effectveness of the method. Compared to the tradtonal least square method, the method proposed n ths paper can mprove effectvely the lnearty of sensor, and can get hgher measurement accuracy, especally beng sutable for detecton system of mne gas based on sngle-chp mcrocomputer. CONFLICT OF INTEREST The authors confrm that ths artcle content has no conflct of nterest. ACKNOWLEDGEMENTS Ths work was fnancally supported by the Open Foundaton of Jangsu Key Laboratory of Large Engneerng Equpment Detecton and Control (JSKLEDC201212), the Foundaton of Basc Research Project (Natural Scence Foundaton) of Jangsu Provnce of Chna (BK20131124), and Xuzhou Key Laboratory of Vrtual Realty and Multdmensonal Informaton Processng. REFERENCES [1] Z. Yu, Z. Y. Zhang, D. J. Xu, Constant temperature catalytc gas sensor detecton method and applcaton n gas detecton, Instrument Technque and Sensor, vol. 46, pp.126-128, 2007. [2] K. H. Chen, W. K. Lu, Research of functon relatonshp between put voltage and gas volume fracton of carrer catalytc gas sensor, Industry and Mne Automaton vol. 39, pp. 92-95, 2013.
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