The Quality Prediction of Fiber-Optic Gyroscope Based on the Grey Theory and BP Neural Network

Transcription

1 Iteratioal Workshop of Advaed Maufaturig ad Automatio (IWAMA 6) The Quality Preditio of Fiber-Opti Gyrosope Based o the Grey Theory ad BP Neural Network Na Ji Hogia Cai* haghai Key Laboratory of Mehaial Automatio ad Robotis, hool of Mehatroi Egieerig ad Automatio haghai Uiversity haghai, Chia 8794@qq.om haghai Key Laboratory of Mehaial Automatio ad Robotis, hool of Mehatroi Egieerig ad Automatio haghai Uiversity haghai, Chia hai@staff.shu.edu. otrol. The test work aouts for 3% of the whole developmet proess for fiber-opti gyrosope. O the basis of a large umber of aumulated test data, we should aalyze the mai parameters of fiber-opti gyrosope data to foreast the quality of fiber-opti gyrosope so that we ould otrol the produt quality i advae. That will be a effetive way i improvig the quality of fiber-opti gyrosope []. Abstrat Fiber-opti gyrosope has beome a ew geeratio of leadig devie of iertial measuremet system. Fiber-opti gyrosope is small bath produt with high preisio ad high ost. Its developmet proess has the harateristis of heavy testig work, omple data aalysis, poor stability so that its produt quality is hard to otrol. Therefore, we use the grey theory ombied with BP eural etwork to build the model for the quality preditio of fiber-opti gyrosope. As the fiber-opti gyrosope is small bath produt ad its quality is iflueed by multiple fators, we add The ample eletor ad optimize the results i the traditioal grey preditio method. The ample eletor is used to proess the relevat historial data of similar fiber-opti gyrosope. The grey model is used to predit the quality of the fiber-opti gyrosope. Furthermore, we use BP eural etwork to orret residual error to improve the auray of preditio. We verified that the method has a high auray rate ad meets the produtio demads. Aordig to the preditio, it a take timely measures to otrol the produt quality i advae. Curretly there are lots of foreastig methods iludig epert foreastig method (suh as Braistormig, Delphi Tehique, et.),tred etrapolatio, epoetial smoothig, aalogy method, regressio aalysis, the iputs ad outputs aalysis, growth urve method, artifiial eural etwork models [3]. Wu ad hieh used a Markov hai model i quality futio deploymet to aalyze ustomer requiremets [4]. Deg et al. hybridized the geeti algorithm ad eural etwork for proess parameters optimizatio [5]. Wag et al. put forward grey system theory based preditio for topi tred o Iteret [6]. These algorithms have bee applied to the various idustry produt quality preditios. Based o the grey sequee method ad the grey relatioal spae aalysis, the grey theory a ahieve the aalysis, evaluatio, modelig, foreastig, deisio-makig, otrol ad optimizatio. David et al. itrodued the BP algorithm ito the traditioal quality otrol hart, traiig ad test, ad it is feasible that the artifiial eural etwork a predit abormal situatio i quality otrol [7]. Wag et al. set the proess parameters itelligetly for layered maufaturig by developig the BP eural etwork [8]. ajukta ad William preset a multi-variable model whih ombied the reursive eural etwork ad the ehaed evolutioary algorithm to moitor ad orret dyami proess [9]. It is effetive i otrollig the quality iflueed by multi-variable. Compared with other foreastig methods, the grey theory has the harateristis suh as: it is feasible ad sample data are small, with four data eough i theory; amples do ot eed to have a regular distributio; The omputig workload is small; The quatitative aalysis ad the qualitative aalysis of the results would be osistet; It a be used i the reet, mid, ad log-term preditio, ad the auray of preditio is high []. Wei established a improved model ombied the traditioal GM (,) ad RBF eural etwork ad use the advatages of both to build grey ompesatig RBF eural Keywords Fiber-opti gyrosope; grey theory; BP eural etwork; quality preditio I. INTRODUCTION Fiber-opti gyrosope has the uique advatages i the aerospae, aviatio, avigatio, weapo ad idustry areas as a ew geeratio of agular veloity sesitive devie []. At preset it has bee widely used as guided torpedo, fiber optial guided missile, subsurfae eploratio, groud vehile positio ad orietatio, airbore iertial avigatio system, et. espeially i the military field. Fiber-opti gyrosope has made a very wide rage appliatio whih is umathed by ay other gyrosope. Aordig to the fiber-opti gyrosope market report of Busiess Commuiatios Compay, the globe fiber-opti gyrosope market value has bee keepig the average aual ompoud growth rate 4.% i reet years. Aordig to the researh report of Global Idustry Aalysts, the Asia-Paifi regio is the global mai market of fiber-opti gyrosope, i whih the Uited tates ad Chia aout for 39% of the total. Therefore, may outries stregthe the researh of fiber-opti gyrosope. Fiber-opti gyrosope is small bath produt with high preisio ad high ost. As its developmet proess has heavy testig work, omple data aalysis ad poor stability, produt quality is diffiult to 6. The authors - Published by Atlatis Press 3

2 etwork foreastig mode, whih a selet optimal bakgroud value ad dyami idetifyig parameters []. However, the grey theory has its ow limitatio: the results sometimes are messy; it is ot as aurate as the regressio aalysis method i the situatio with large umber of sample data. Therefore may sholars put forward the orrespodig improved algorithms whe they use the grey theory. As the ovolutio trasform a improve the trasformatio sequee smoothess ad the mehaism of aumulatio geeratio, Che improved the sequee geeratio of grey model ad GM (, ) model ad established the grey model GM (,, t) with liear time []. Wag ad Zhag established the grey ombiatio preditio model based o at oloy algorithm [3]. Wa et al. established foreastig model for the material osumptio based o the grey theory ad eural etwork model, meawhile he preseted a ew kid of broadly ombiatio foreast model i whih he improved the futio for the geeralized weighted ad proposed the way to estimate weighted oeffiiet of the parameter [4]. Based o the aalysis of the above, the grey theory is a effetive method to predit with small sample data. With the help of the grey theory, the behavior ad the evolutio of the uertai system ould be orretly desribed ad effetively moitored. As fiber-opti gyrosope is small-bath ordered produt, it is suitable to use the grey theory to predit the produt quality [5-7]. However i order to further improve the auray of the result, we add The ample eletor ad optimize the result with BP eural etwork based o the traditioal grey preditio CGM (, ) model [8]. The sample proessor is to aalysis relevat historial data of the fiber-opti gyrosope. Combiig with the BP eural etwork, it orrets the data residual from the grey model i the results optimizer, beause BP eural etwork a avoid the distortig pheomeo whih is geerated from the sequee aumulatio offset. I this paper, we predit the produt quality of fiber-opti gyrosope by the ombiatio model of the grey theory ad BP eural etwork. We verify that the method has a high auray rate ad meets the produtio demads. II. PROBLEM DECRIPTION Fiber-opti gyrosope is a ew type sesor with o rotatio of quality whih a measure agular veloity ad rotatio agle of the objet relative to the iertial spae. The appliatios of fiber-opti gyrosope i aviatio, airbore systems ad military tehology are ireasig, espeially gai etesive attetio of the army. Takig Ameria, Japa, Frae as the mai body, the fiber-opti gyrosope researh work has made great progress. It ame ito ommerial as early as 99s. The preisio of moder fiber-opti gyrosope has amouted to. /h. The preditio ad otrol of quality is beomig more ad more importat of fiber-opti gyrosope eterprise produtio proess. We a realize advaed otrol produt quality, sietifi ad reasoable plaig ad effetively esure the quality of the produt by quality foreast. There are may importat testig idees, suh as the sale fator, zero bias, threshold, ad other idiators whih are refleted the quality of fiber-opti gyrosope [9]. The sale fator is the proportio of the maimum output to the maimum deviatio whih is the fiber-opti gyrosope output relates to the least square method fittig lie i the sope of the iputs agular veloity. Due to the workig poit of fiber-opti gyrosope varies with the hage of the agular veloity, the sale fator will also hage. The greater the iputs agular veloity is, the greater the oliearity is. o the sale fator is a importat ide to predit the quality of the fiber-opti gyrosope []. This artile proposes the grey theory ombied with BP eural etwork method to foreast the produt quality ad use the sample data of the sale fator i the fiber-opti gyrosope testig idees for validatio. The result proves the feasibility of the algorithm. III. ALGORITHM OF THE QUALITY PREDICTION The flow hat of the produt quality preditio model based o the grey theory ad BP eural etwork is show i Fig.. It iludes the sample seletio ad proessig, quality preditio (the grey theory), the optimizatio of result (BP eural etwork) ad trae aalysis. ample seletio ad proessig Produt testig data olletio elet historial data Get the origial data Proess the sample data Fig.. Flow hat of the produt quality preditio. A. ample seletio ad proessig The mai futio of sample seletio ad proessig is to dig the historial data of the fiber-opti gyrosope i order to provide more aurate iputs for CGM (, ) model. There are two ways to use the origial sample data: oe is the diret use of the origial sample data ad the other is seletig the optimal sample data i some way. For eample, the optimal sample data is hose by the grey fuzzy lusterig evaluatio method []. However, they do t pay attetio to the fat that differet sample data have distit differet effet. I this paper, osiderig that the latest data will be the most valuable to predit, so we hoose the latest produt data from the history samples as ew foreast data to ostitute a ew preditio sample. Assumig that the historial sample data of fiber-opti gyrosope test sale fator are as follows: Quality preditio Calulate the mea sequee Establish the umulative average sequee olve the parameter Establish the preditio model Test the model auray Whether meet the preisio? YE Quality preditio value Result optimizatio,,, Amog this: is the umber of sample size. NO Costrut the residual sequee of BP eural etwork Create ad trai the etwork Predit the residual error Optimize the result Quality preditio value Trae aalysis Whether the preditio value is qualified? NO Trae aalysis ad fid the problem Take measures Ed YE 3

3 New preditio sample data are:,,, s, Amog this, s is the umber of ew preditio sample size, we assume s=+ ad ew preditio sample are:,,,, B. Grey theory model CGM (, ) GM (, ) ad CGM (, ) are ommo grey foreastig models [-3]. GM (, ) model is relatively simple ad it is more ommoly used. However, Yao et al. preseted that the GM (, ) model is ot feasible for the situatio with poor iformatio ad the CGM (, ) has more advatages to predit i the uertai situatio with poor iformatio ad multiple-fator for it has more rigorous logi struture. Cosiderig the quality is iflueed by may fators, we hoose CGM (, ) model. The steps of the grey theory CGM (, ) model are as follows: ) Determie the foreast sample The sample whih was proessed by sample proessor will be the CGM (, ) model of the origial sample ().,,,, ) Calulate the average Ad: t.5 t t t 3,,,, t, 3,,, 3) Calulate the umulative average sequee k k t t, k 3,,,, We a obtai the umulative average sequee: k, 3,,, 4) Determie parameters Make s(f) as a ohomogeeous disrete epoetial futio. Assumig that f r s(f) is a ertai futio i time domai ad osiderig the geeral form of geeralized eergy system. We make f r a k k be a, b, R, k, 3,,, If { () (k)} is assoiated with satisfatio tred of ohomogeeous disrete epoetial futio we use the least square method. Parameters a ad b are ofirmed as follows: t t t 3 a l t t 3 a k a k e k e k k k k b a k a k e e k k is: a k k k e 5) Build up the foreast model The foreast model is: k t a e a ~ t b e (3) The performae ide of the foreastig data QuaCof QuaCof ~ t a e a 6) Verify the model auray q b e t t ~ t t q t e t q () (t) is residual i (5) ad e(t) is the relative error i (6). Normally we thik e(t) 5% is a good result. Or we use posterior-variae-test. The method is show below: Get the average of () (t): t t 3

4 Get the variae of () (t): t t Get the average of the residuals q () (t): Get the variae of q () (t): t t q q t t q q The ratio of the mea square C is: The probability of small error P is: C t P P q q.6745 The small the error ratio of mea square is, the better the result is. If C is smaller, the is bigger or is smaller. The historial test sale fator data variae is bigger ad the degree of disrete is greater if is bigger. The residual variae is smaller ad the degree of disrete is smaller if is smaller. C is small that meas although the historial test sale fator data are disrete, the differee betwee the predited ad atual values is ot too disrete. The bigger the probability of small error is, the better result we get. If P is bigger, it meas the differee betwee the residual ad the average residual is pretty less tha the give value Aordig to the ide of C ad P, we a omprehesively assess the auray of sale fator, as show i Table I. If the result is usatisfied, we eed to use the residual sequee to establish the BP eural etwork model to optimize the result. TABLE I. CORREPONDING RELATION BETWEEN IMPACT LEVEL AND CORE Preisio Grade P C Level >.95 <.35 Level >.8 <.5 Level3 >.7 <.65 Level4.7.8 C. Optimizatio Model The optimizatio steps based o the improved BP eural etwork is as follows: ) Costrut the residual sequee q () (t) of the BP eural etwork model The residual error is the differee of sample data () (t) before time t subtrat the predited value from CGM (, ). If the foreast order is, we use q () (t-), q () (t-),, q () (t-) to alulate the preditio result i time ad as the traiig sample iputs ito eural etwork (iputs matri). The q () (t) is the epetatios of etwork traiig (outputs matri). ) Normalize sample Normalize the sample data to [, ] ad the formula is as follows: y y ma mi i mi y y mi ma i is the origial data. y mi ad y ma are the sope of aturalizatio ad [-,] is the default value. 3) ort data The % iputs data are used as test data ad the % data are used as hage data; others are used as ormal iputs to trai. We etrat the above three groups of data radomly. 4) Create ad trai the etwork Aordig to the followig method to determie the umber of hidde layer odes. Assume that iput layer of BP eural etwork has m euros, output layer has euros, hidde layer has s odes, ad the we a get the (4): mi s m a a is ostat betwee oe to te. We ofirm the umber of iputs ad outputs harateristi parameters ad the umber of eah layer of euros, ad hoose a trasfer futio. 5) imulate etwork I order to further verify the etwork performae after traiig, the etwork should be simulated deeply. We use sample data for the traied etwork to simulate ad it a be used as a effetive tool for preditig residual sequee. 6) Determie ad optimize the q () (t) The residual sequee whih use traiig model of BP eural etwork to predit is q () (t) ad we ostrut the ew predited value. C t q t () (t) is the predited value aordig to the CGM (, ) model. Its preisio is higher tha GM (, ), but there is still residual ompared with atual value domai. We proess the residual with BP artifiial eural etwork, so we a get the more aurate residual error. Aordig to the above aalysis, () is the fial predited value. 33

5 IV. CAE TUDY We ivestigate ad survey data from a photoeletri tehology o., LTD. We selet bathes of fiber-opti gyrosope test sale fator as the sample data. Nie oseutive bathes of the ais sale fator i ormal temperature of the HI - L - I series fiber-opti gyrosope are show i the followig table. TABLE II. HI - L - I ERIE FIBER-OPTIC GYROCOPE CALE FACTOR AMPLE DATA Trial-maufature I II III Ⅳ Ⅴ ale Fator Trial-maufature Ⅵ Ⅶ Ⅷ Ⅸ ale Fator teps are as follows: ) Proess sample with the sample proessor The origial data as sale fator of HI- L-I series fiber-opti gyrosope are: There are ie data samples (=9). The latest bath data is I. Irease the th data i the origial historial samples ad the latest data is 6.7. The sample data are: ) Use CGM (, ) model to predit ample data are: The average series are alulated by (6): t The samples geerated by the average value aumulates aordig to (7) are: t Parameters a ad b are alulated by () ad (): a b Aordig to (3), the preditig model is: ~ a a t t b e e t e e We use posterior-variae-test to verify Aordig to the preditio model, preditig sequee is alulated ~ t The we get residual error sequee by (5). q t The variae of the residual sequee is alulated by (9) ad () Variae of the origial value sequee is: A posteriori differee ratio is alulated by (). C The little error frequey is alulated by (). P P q t q Aordig to Table I, the model preisio is Level 3. It is illustrated that CGM (, ) preditio model is feasible ad we a use it to predit produt quality. But we should establish residual error orretio model to further optimize the results. The foreast result of the grey theory model is: QuaCof a *9 b e a e ) Use the results orretor to optimize 34

6 Establish residual error sequee q () (t) of BP eural etwork model. Iput data is si groups ad eah group iputs three data P Output data is si groups ad eah group outputs oe data. t 779.7;39.66;444.36;647.96; 56.84;77.3 4) Normalize the sample Call the futio of Matlab: ormiput, ps map mi map ormiput, ts map mi mat 5) ortdata By partitioig the traiig sample, we use divideve() to etrat three kids of lassifiatio data radomly. The futio all is as follows: traiample, validateamples, testamples ormiput, ormt arget, divideve validateperet, ; testperet mi ma ormiput, et ewffnodenum, NodeNum, TypeNum, ; TF, TF, TF 3,' TRAINGD' Use the followig ode to trai a etwork: ettraiparamepohs.. ettraiparam.. goal ettraiparamlr...; ; e After etwork was reated we begi to trai the etwork ad all the trai futio. et, tr traitraiamplest.,,, ; 4; et, traiamples. p, validateamples, testamples 7) imulate the etwork I order to validate the etwork performae after traiig, we the further simulate the etwork. We use the sample data validated to simulate the traied etwork. It is a effetive tool for the residual sequee preditio. Fig. illustrates the overgee proess of traiig while it is lose to target. 6) Create ad trai the etwork et the etwork parameters: Node umber of the first hidde layer is. NodeNum ; Node umber of the first hidde layer is 6. NodeNum The dimesio of the output is. TypeNum et the layers of trasfer futio: 6; ; TF TF TF 3 ' trasig'; TF3 is a trasfer futio of output layer. Use the followig ode to reate a etwork: Fig.. BP eural etwork traiig. The etwork test after traied is show i Fig. 3. The "o" represets the atual value ad "*" represets the predited value. Fig. 4 shows the absolute error variatio. Aordig to Table III, the absolute preditio error is withi 3 ad relative error is less tha %. The preisio is high ad preditio error is small. o this etwork a be used as a residual error preditio. 35

7 the et bath residual is q () (t)=-8.8 with the traied BP eural etwork above. Predited value is () (t)=84.6 with the grey theory. o the preditive result after the residual orretio for BP eural etwork is t t q t ( 8.8) The predited value of the et bath of fiber-opti gyrosope sale fator is I fat, the atual data is The error is 3.3%, whih is smaller tha geeral requiremets 5%. Net we verified the sample of 65 produts i the first quarter of 3,ad we foud that the average error is aroud 3.%.o we verify that the algorithm desribed i this paper is feasible to foreast the quality of fiber-opti gyrosope. Fig. 3. Traied etwork preditio. V. CONCLUION I this paper, osiderig the harateristis of fiber-opti gyrosope, we predit the quality with the grey theory method ad optimize the results based o BP eural etwork. The grey theory is adopted as foreast mai body ad it is ombied with BP eural etwork to arry o the residual error orretio. The ase study verify the model is feasible. Aordig to the foreast results, we a take timely measures to otrol the produt quality i advaed. ACKNOWLEDGMENT This work is supported by haghai eoomi ad Iformatio Commissio uder Grat No. 56. The authors are grateful for the fiaial support, ad also would like to thak the aoymous reviewers ad the editor for their ommets ad suggestios. Fig. 4. Network error variatio value ompared with the real data TABLE III. Origial Residual equee ERROR CHECKING WITH BP NEURAL NETWORK MODEL BP Neural Networks imulatio Preditio Preditio Error % % % % % % Determie the ew predited value of q () (t).we predit REFERENCE [] Zhou, H. (). Appliatio ad developmet of fiber opti gyrosope. Tehology Foudatio of Natioal Defee, 4-5. [] Ma, J., Ye, M., Chao, D. H., Che,. Y., &Yu, M. (). Reliability estimatio of FOGs based o iformatio fusio tehology of multi-soures. Joural of Chiese Iertial Tehology, (6), [3] Chag, Pei, C., Li, J. J., &Dza, W. Y. (). Foreastig of maufaturig ost i mobile phoe produts by ase-based reasoig ad artifiial eural etwork models. Joural of Itelliget Maufaturig, 3 (3), [4] Wu, H. H., &hieh, J. I. (6). Usig a Markov hai model i quality futio deploymet to aalyse ustomer requiremets. The Iteratioal Joural of Advaed Maufaturig Tehology, 3(-), [5] Deg, Z. H., Zhag,. H., Liu, W. (9). A hybrid model usig geeti algorithm ad eural etwork for proess parameters optimizatio i NC amshaft gridig. The Iteratioal Jouralof Advaed Maufaturig Tehology, 45(9-), [6] Wag,. Q., Qi,L., &Che, C. (4). Grey ystem Theory based preditio for topi tred o Iteret. Egieerig Appliatios of Artifiial Itelligee, 9, 9-. [7] David, K., Leo, P., &William, R. (993). The Appliatio of Artifiial Neural Networks to Quality Cotrol Charts. ystem iees, 993,Proeedig of the Twety-ith Hawaii Iteratioal Coferee o, (pp ). IEEE. [8] Wag, W. L., Coley, J. G., Ya, Y. N. (). Towards itelliget settig of proess parameters for layered maufaturig. Joural of Itelliget Maufaturig, (),

8 [9] ajukta, P., &William, J. K. (997). Neural Networks ad Evolutioary Computatio for Real-time Quality Cotrol of Comple Proesses. Reliability ad Maitaiability ymposium. 997 Proeedigs,(pp ). IEEE. [] Yao, T.., Li, Y., &Liu,. F. (). egmetal Corretio Cootatio GM(,) Model. Joural of Grey ystem, 4(4), [] Wei, Q. Y. (). Quality Cotrol of mall-bath Produtio Based o the Improved Grey RBF Neural Network Model. Zhegzhou Uiversity, -53. [] Che, C. Y. (7). Aumulative geeratio of improved gray model ad GM (,, t). Joural of Mathematis Pratie ad Uderstadig, 37(),5-9. [3] Wag, F.. &Zhag, L.. (9). Combiatio Gray Foreast Model Based o the At Coloy Algorithm. Mathematis i Pratie ad Theory, 39(4), -6. [4] Wa, Y. C., He, Y. Q., &Cheg, Z. H. (3). Material osumptio based o grey system ad eural etwork geeralized weighted futio average ombiatio foreast model researh. ystems Egieerig Theory ad Pratie, 3(7),8-87. [5] Li, Husa, L. (). The use of the Taguhi method with grey relatioal aalysis ad a eural etwork to optimize a ovel GMA weldig proess. Joural of Itelliget Maufaturig, 3(5), [6] Niti, K.., aurav, D., &iba,. M. (). Establishig gree supplier appraisemet platform usig grey oepts. Grey ystems: Theory ad Appliatio, (3), [7] Tag,. Q. (). Error Modelig ad Compasatig of Fiber Opti Gyro Based o Wavelet Aalysis ad Grey Neural Network. Chiese Joural of Lasers,39 (), -6. [8] Zhag, F., Jia, Z. P., &ia, H. (). Node trust evaluatio i mobile ad ho etworks based o multi-dimesioal fuzzy ad Markov CGM(,) model. COMPUTER COMMUNICATION,35(5), [9] Na, Y.L., Li, L. K., Wu, Y. J., u, G. F., &Yu, H. Y. (). Measuremet error aalysis of FOG s sale fator. Joural of Chiese Iertial Tehology, (4), [] hloffel, G. (3). Uidiretioal fiber opti sesor for agular aeleratio measuremet. Optis Letters, 38(9), 5-5. [] Wag, B. J., &og, G.B. (). Egieerig biddig deisio-makig method based o fuzzy mathematis. Joural of Hebei Uiversity of tehology, 3(), 6-. [] Li, G. D., &Nagai, M. (3). A optimal preditio model for time series preditio i maufaturig systems. The Iteratioal Joural of Advaed Maufaturig Tehology, 67(9-), [3] Li, G. D., Masuda,., Wag, C. H. (). The hybrid grey-based model for umulative urve preditio i maufaturig system. The Iteratioal Joural of Advaed Maufaturig Tehology, 47(-4),