Open Access Nonlinear Correction of Sensor Based on Immunization Programs

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1 Sed Orders or Reprits to The Ope Automatio ad Cotrol Systems Joural, 2014, 6, Ope Access Noliear Correctio o Sesor Based o Immuizatio Programs Lirog Lu 1, Xiaodog Niu 2, Jiyag Zhou 1,* ad Chuhua Shi 1 1 Biomedical Egieerig, Chagzhi Medical College, Chagzhi, Shaxi, , Chia 2 Departmet o Physics, Chagzhi Medical College, Chagzhi, Shaxi, , Chia Abstract: Sesor applicatios i medical istrumetatio measuremet are very extesive, but mostly the iput ad output o the sesor is oliear, which brigs a great icoveiece or the measure o medical istrumets. This paper itroduces biological immue system o the basis o the evolutio plaig, thereby ormig immuizatio programs to use o-liear calibratio o the sesor. This method jois oliear correctio lis ater sesor ampliicatio ad A/D coverter lis ad uses the immuizatio program to obtai the polyomial coeiciets o the oliear correctio li. Simulatios show that usig immuizatio programs to have o-liear calibratio to sesor, gives high correctio accuracy, aster covergece speed ad very good stability. Keywords: Immuizatio programs, o-liear calibratio, sesor. 1. INTRODUCTION Sesor [1] is a device which ca covert measuremet ito the power output. Sesor plays a importat role i the developmet o medical istrumets ad medical experimets. I the ideal state, there is a liear relatioship betwee the iput ad output o the sesor, by measurig the amout o the output, we ca id the iput size. However, i practical applicatios, most o the relatioship betwee sesor output ad iput is o-liear. To solve this problem, people use may methods to correct the o-liearity o sesor. However, these corrective methods at this stage exist with deects such as high cost, poor accuracy ad poor stability [2, 3]. Evolutioary Programmig [4] which is a evolutioary algorithm origiated i the 1960s is a radom search algorithm obtaied by simulatig the process o atural evolutio. I evolutioary pla, use o the cross ad reorgaizatio operator is ot recommeded, which ca relect the idividual iterplay. However, oly use o mutatio operator such as Gaussia mutatio operator is suggested i most cases, because its algorithm is simple. Mutatio operator ca modiy a idividual with a certai probability, but maybe the mutatio idividual is ot suitable as a paret, which ca be cocluded as there beig a degradatio. All practical problems themselves have certai characteristics, usig these eatures it will improve solvig speed, but evolutioary programmig does t tae advatage o these eatures. The two poits above iluece the ruig speed o the algorithm. The ability to maitai evolutioary programmig solutios group diversity is isuiciet, ad easy to premature covergece [5]. Biological immue system [6] is a importat system o the body to perorm a immue respose ad immue uctio, it ca recogize sel ad others ad rapidly remove ad elimiate oreig bodies to esure the saety o the body. Biological immue system has uctios o producig a variety o atibodies, sel-regulatio ad immue memory. The idea o this system s wor is applied i egieerig practice, such as the attitude cotrol o satellite; or more details reer to the literature [7]. Diagosis o RNA-based viruses sometimes eeds the help o oliear correctio [8], so the method must udergo urther research to id more beeits or the developmet o the society. Apply the mechaism o biological immue system to evolutioary programmig algorithm by drawig the ability o immue system to produce ad maitai the diversity o atibodies ad sel-regulatio. I the overall ramewor o evolutioary algorithms, immue mechaism is itroduced to orm immuizatio program (reerred to as IP). This paper studies the applicatio o the immuizatio program to solve o-liear calibratio o sesor system. Experimetal results show that applicatio o the immuizatio program or oliear calibratio ca ot oly improve the correctio accuracy, but also greatly improve the speed ad stability. 2. CORRECTION MODEL The correctio model is show i Fig. (1). I Fig. (1), X is the measured variable as the iput sigal o the sesor. Ater the sesor, X becomes a o-liear output sigal, the ater ampliicatio ad A/D coverter lis, the output becomes Y, which is also o-liear with X, ially ater IP correctio, Z becomes the output. IP correctio maily perorms data processig ad oliear correctio to mae sure that the relatioship betwee the ial output Z ad iput o sesor X is liear. *Address correspodece to this author at the Biomedical Egieerig, Chagzhi Medical College, Chagzhi, Shaxi, , Chia; Tel: ; llr1982@163.com / Betham Ope

2 1706 The Ope Automatio ad Cotrol Systems Joural, 2014, Volume 6 Lu et al. Fig. (1). Correctio model. Produce N+m Fig. (2). IP low chart. Give the relatioship betwee Y ad X is: Y = ( X ) that betwee Z ad Y is: Z = g(y ), i g(y ) =!1 (Y ), the Z = g(y ) =!1 (Y ) = X (1) As we ca see, the whole circuit output Z ad its iput X is equal, which is certaily liear, amely, o-liear correctio succeeds. The purpose o this paper is to use IP to see correctio li Z = g(y ), amely, Z =!1 (Y ). The variable Z ca be expressed as: Y a Y (2) Where, a 0,...,a are coeiciets to be determied, the value o is determied by required accuracy. I this paper, =3, amely Y 3 (3) Where, a 0 are coeiciets to be determied, whe coeiciets i (3) are determied, the correctio li Z =!1 (Y ) is also determied. 3. STEPS OF USİNG IP TO İMPLEMENT NON- LİNEARİTY CORRECTİON OF SENSOR By applyig the mechaism o biological immue system to evolutioary programmig algorithms, immuizatio programs are ormed. IP low chart is show i Fig. (2). The steps o usig IP to solve the oliear correctio problem o sesor system are as ollows:

3 Noliear Correctio o Sesor Based o Immuizatio Programs The Ope Automatio ad Cotrol Systems Joural, 2014, Volume Table 1. Sesor output F ad correspodig actual iput cocetratio value Cp. F (HZ) Cp () (1) Recogitio o atige is the problem to be solved. Recogitio o atige is to id the objective uctio correspodig to the problem. I this paper, the objective uctio o sesor oliearity correctio is: (x) = (Z! X ) 2 = a 0 Y 3! X ( ) 2 (2) The iitial productio o atibodies. We ca use computer to radomly produce N+m idividuals as the iitial populatio ad put m idividuals ito memory ba. (3) Idividual itess calculatio. Idividual itess is determied by the ollowig ormula: F(x) = 1 (x) = 1 = (Z! X ) 2 1 (a 0 Y 3! X ) 2 (4) Gaussia mutatio. Gauss mutatio operator is mostly used i IP. I the process o mutatio, calculate liear square root o each idividual itess uctio value to obtai the stadard deviatio o idividual variatio, each compoet plus a radom obeyig logormal. Give X is idividual,! is the stadard deviatio o Gaussia mutatio. Chromosomal idividual has L gee locatios. The, ( X,! ) = (( x 1,x 2,,x L ),! ). Ater Gaussia mutatio, x i (t +1) = x i (t) + N(0,! (t +1)) (6) Where,! (t +1) = F( X (t)) + # (7) Where, N( 0, σ ( t + 1)) deotes radom variables whose mea is 0 ad variace is σ ( t +1), F( X ( t)) idicates the itess o curret idividual,! is coeiciet to be deter-! mied, usually, the value o!! #$ is 1 ad 0 respectiively. (5) Calculatio o atibody aiity ad cocetratio. The computig object o the N ew idividuals o Gaussia mutatio, ad m idividuals i memory ba. Aiity o the atibody ad atige. We ca regard the aiity o the atibody ad atige as the match degree betwee the objective uctio ad easible solutio, which ca be regarded as idividual itess here. The aiity uctio i this paper is: ( A g ) = 1 (x) = 1 = (Z! X ) 2 1 (a 0 Y 3! X ) 2 (4) (5) (8) meas the aiities betwee atibody ad atige. Aiity o the atibody ad atibody. Aiity o the atibody ad atibody is the similarity degree betwee atibodies [6]. I this paper, we deie the aiity betwee atibody x ad atibody y as: xy, b x, y = (9) ( A ) (A ) g Where, L is the same gee locatio betwee atibody x ad atibody y, L is the legth o atibody x ad y. We deie the cocetratio o the atibody as: C V = 1 ( A N b (10) j!n N is total atibodies i populatio. Whe ( A b > T, ( A b = 1, whe ( A b! T, ( A b = 0. T is a costat set i advace. C V represets the proportio o similar atibodies i populatio. (6) Coditios judge. Determie whether the termiatio coditio is satisied. Yes meas ed o the output, otherwise, cotiue. (7) The ormatio o a ew paret populatio. The ormatio o a ew paret is based o a idividual breedig expected probability. Simpliied desired idividual probability propagatio ca be calculated [9] as: P = ( A g ) C V x, y (11) As is see, (A ) is higher, P is bigger. CV is bigger, P is smaller. Namely, we hope or the high-itess ad lowcocetratio idividual to breed to maitai the diversity o populatio. (8) New atibodies productio. I accordace with the roulette wheel selectio mechaism to mae selectio operatio, the selected probability o a idividual is the idividual desired reproductio with ormula (11) to calculate. (9) Tur to step (3) 4. ANALYSIS OF CASE g I order to veriy the ature o the proposed method, we have doe a lot i the MATLAB simulatio. The iput ad output data is rom cocetratio sesor i [10]. The variable i Table 1 meas the output o sesor; Cp meas the iput o the sesor.

4 1708 The Ope Automatio ad Cotrol Systems Joural, 2014, Volume 6 Lu et al. Fig. (3). Actual value ad ip ittig curve. Fig. (4). The optimal value chage ater 100 iteratios. From the table, it is show the relatioship betwee the output ad correspodig practical iput s cocetratio value Cp is o-liear. Here, we must add o-liear correctio li i the output o the sesor, so that there is a liear relatioship betwee the ial output ad iput. Correctio li Y 3 = a 0 + a 2 $ max # max 2 + a 3 $ # max Where, max=2500 HZ, a 0 are coeiciets to be determied. The paper uses IP to determie the polyomial coeiciets o o-liear correctio li. We tae iteratios as100, the media o a 0 is 20, idividual umber is 50, ad memory ba is Operate IP ad the results ca be see as ollows: Fig. (3) shows the actual iput cocetratio ad cotrast value o IP ittig curve. Circles represet the actual output requecy correspodig to the actual iput cocetratio. The solid lie represets the output o the o-corrected li correspodig to the actual iput requecy i o-liear correctio li as show by Fig. (3): correspodig to the same requecy, the actual value o the iput desity ad the output value ater o-liear correctio is essetially the same, amely, the iput ad output o the etire cocetratio sesor system is substatially the same, i order to achieve the liear output ad a o-liear calibratio o cocetratio sesor. Fig. (4) is the optimal solutio chage igure o usig IP or oliear correctio ater 100 iteratios, the horizotal axis represets the evolutio geeratio, ad the vertical axis represets the objective uctio value. The smaller the target uctio value, the better the o-liear correctio. As

5 Noliear Correctio o Sesor Based o Immuizatio Programs The Ope Automatio ad Cotrol Systems Joural, 2014, Volume we ca see, populatio coverges to the miimum ater 58 evolve geeratio. The miimum value o the objective uctio is ad available coeiciets to be determied are a 0 = = = = Namely, Z = ! $ max # max $ # With examples o the aalysis, it ca be see that the use o IP or o-liear correctio o sesor, the iput ad output o a etire cocetratio sesor is basically the same ad objective uctio value may reach , idicatig that this correctio method has a higher precisio accuracy. I additio, curve coverges ca also be see to the miimum o the objective uctio ater 58 geeratio, idicatig that this correctio method has a aster covergece rate. Ruig the program 100 times, 99 ca coverge to the miimum value o the objective uctio, idicatig that this correctio method has a very good stability. CONCLUSION As the core compoet o medical measuremets, the accuracy ad stability o sesor will directly aect the accuracy ad stability o the etire medical measuremets. Sice most sesors s iput ad output cosists o-liear characteristics, thereore they brig much icoveiece to the medical equipmet measurig. This paper itroduces the biological immue system based evolutioary programmig, thus ormig immuizatio programs, ater ampliyig circuit ad A/D coverter circuit, o-liearity correctio li is itroduced, ad use the immuizatio program to obtai o-liear calibratio coeiciets o the polyomial lis. Thus, we ca coclude that the relatioship betwee output ad iput is liear, i.e., we will achieve o-liear calibratio o sesor. Fially, we use the IP to obtai a o-liear calibratio o cocetratio sesor i the literature [8]. Practice max 3 shows that the use o IP or o-liear calibratio has a high calibratio accuracy, aster covergece rate ad very good stability. CONFLICT OF INTEREST The authors coirm that this article cotet has o colict o iterest. ACKNOWLEDGEMENTS This wor is supported by Research ad Developmet Project Fud o Uiversity Techology i Shaxi (No ). REFERENCES [1] A. Che, Medical Sesor, 2 d ed. Sciece Press: Beijig, vol. 1, [2] J. Liu, Noliear correctio method o sesor based o aealig geetic algorithm, Trasducer ad Microsystem Techologies, vol. 30, pp , [3] C. Liu, F. Wag, K. Shi, X. Wag, ad Z. Su, Robust H cotrol or satellite attitude cotrol system with ucertaities ad additive perturbatio, Iteratioal Joural o Sciece, vol. 1, pp. 1-9, [4] T. Liu, ad H. Wag, Geetic support vector method o oliear correctio o sesor, Joural o Electroic Measuremet ad Istrumet, vol. 25, pp , [5] D. Che, ad C. Zhao, A improved adaptive immue evolutioary programmig method ad its applicatio, Joural o System Simulatio, vol. 18, pp , [6] F. Shi, ad H. Wag, 30 Aalysis Cases i MATLAB Itelliget Algorithms, Beihag Uiversity Press, 2011, pp [7] M. Zhou, ad S. Su, Priciple ad applicatio o geetic algorithm, Natioal Deese Idustry Press, pp , [8] C. Liao, G. Lee, ad H. Liu, T. Hsieh, ad C.H. Luo Miiature RT PCR system or diagosis o RNA-based viruses, Nucleic acids Research, vol. 33, p. 156, [9] X.L. Xu, W. Wag, ad Q. Gua, Adaptive Immue Algorithm or Solvig Job-Shop Schedulig Problem, Spriger-Verlag: Berli Heidelberg, [10] Y. She, A ew method or pulp cocetratio sesor calibratio ad dyamic oliear estimatio, Chiese Joural o Scietiic Istrumet, vol. 18, pp. 1-6, Received: September 16, 2014 Revised: December 23, 2014 Accepted: December 31, 2014 Lu et al.; Licesee Betham Ope. This is a ope access article licesed uder the terms o the Creative Commos Attributio No-Commercial Licese ( which permits urestricted, o-commercial use, distributio ad reproductio i ay medium, provided the wor is properly cited.