An Improved BP Neural Network Based on GA for 3D Laser Data Repairing

Transcription

1 An Iproved BP Neura Network Based on GA for 3D Laser Data Reparng Shouqan Yu Lxa Rong Weha Chen Xngng Wu Schoo of Autoaton and Eectrca Engneerng Bejng Unversty of Aeronautcs & Astronautcs Bejng, Chna Abstract Affected by scannng object, envronent, scannng speed and user s operaton.etc, soe nforaton of the object s surface can t be detected by the aser scanner. Ang at the data oss n aser detectng, the paper presents an proved BP neura network based on GA for 3D aser data reparng, the novety of ths ethod s adoptng Genetc Agorth(GA) to optze the confgure and weght of network, and at the sae te cobnng Back Propagaton(BP) Agorth to fnd opta approxaton. The suaton shows the proved BP neura network based on GA has a faster constrngency speed and better reparng precson than tradtona BP neura network and GA agorth. Lasty, the paper gves the resut of reparng the pont coud coected by 3D nforaton reconstructon syste usng ths network. Keywords Data reparng, GA, BP network, Laser scanner Ⅰ INTRODUCTION The ethod of aser range has the obvousy superorty copared wth others, especay n recent years, the technoogy of aser scanner deveoped at hgh speed, so t s preferred for the appcaton n dstance detectng. But when usng aser scanner detectng, because affected by scannng object, envronent, scannng speed and user s operaton.etc, the data coected fro scanner s not ntegrated, the pont coud exsts deforty, so the surface of object reconstructed accordng to the pont coud w exst hoe, especay n the copcated object reconstructon. Ang at ths probe, the schoars hoe and abroad dd ebedded researches, and presented soe hoe reparng ethod[][], for exape, ancenty data reparng generay adopted paraboa tangenta contnuaton ethod, but f the deforty area s bg, the reparng precson cannot be ensured. In recent years, wth the deveopent of the technoogy of artfca ntegence (AI), t adopted n the cacuaton of approxaton extensvey. In [3], the author presents a ethod of data reparng usng BP network, athough BP network has the superorty n nonnear approxaton, restranng sape nose and reparng deforty data, BP network has the dsadvantage n gettng nto oca east easy and tranng sowy, and the resut s not satsfactory. GA derves for the genetc evouton theory of nature, and t has soved a ot of optzaton queston, ts advantage s that t can get gobay opta souton even the functon s poyorphc or dscrete. There are a ot of researched on utzng GA to bud BP network hoe and abroad, they attept to cobne GA wth BP network [4, 5, 6], n [7], the author present a Granuarty-GA to optze the network, ths ethod can prove the precson, but t cannot avod the best sape changng contnuty of GA, and t w resut n a ow constrngency speed. Yang Bo presents a network cobned GA wth BP, ths ethod has a hgh precson and speed copared to ndvdua GA or BP, but t can as at soe specay stuaton, t s not sutabe for our 3D aser data reparng, because our 3D data s changng at a rea te. Ths paper presents a nove ethod on 3D aser data reparng, through cobnng GA wth BP to desgn, the ethod hods the advantages of GA and BP, and specay n GA, t not ony adjusts the weght but aso the confguraton of the network, ths can ake the agorth to sut the dfferent appcaton n reparng hoe. In the ethod of codng, we adopt a cobnaton of bnary and rea nuber, t not ony econozes the eory space but aso proves the precson, the suaton shows that the ethod presents n ths paper certany has a obvous effcency n both speed and precson, t s sutabe for our 3D aser data reparng. The paper s dvded to nto the foowng sectons:3d aser scannng syste(secton Ⅱ), BP network and GA(secton Ⅲ), GA-BP network n data reparng(secton Ⅳ), and at ast a suaton s presented to testfy the proved BP neura network based on GA. Ⅱ 3D LASER SCANNING SYSTEM The data reparng agorth s apped n a vson syste of a obe robot, the vson syste any s a 3D aser scannng syste, t conssts of a D aser scanner LMS9 produced by SICK AG and a turnng patfor, as fgure. shows. LMS9 s a D scanner and ts dstance detecton prncpe s expaned n paper [8]. In the vson syste through the turnng the patfor, the scanner can get a 3D data, as fgure. (a) shows. The data coeted fro 3D Fgure.. The vson syste based on LMS /08 /$ IEEE RAM 008

2 aser scannng syste s n poar coordnate, and t s not convenent for data dsposa, so we need to estabsh a Cartesan coordnate adoptng asng ght etter as the orgn, the scanner can get dstance between S and the object defned as SD and β, through patfor we can getα, wthα, β and SD, we can get the x, y and z coordnate of D n s-xyz coordnate, as fgure. (b) shows. (a) They satsfy Eq.() Fgure.3.Basc Mode of BP Network (b) Fgure.. The prncpe of 3D data coectng x= SD*cos β cos α y= SD*cos β sn α z= SD*sn β Ⅲ BP NETWORK AND GA A. BP Network BP network s a forward drecton and no feedback network, t conssts of nodes connected by net, t dvdes nto nput ayer, hdden ayer and output ayer, as fgure. 3 shows, hdden ayer aybe consst of ut-ayers, the neurons n every ayer doesn t connect wth each, sgna transfers aong ayers. The network n ths paper adopts snge hdden ayer, because frsty, the confgure of ut-hdden ayers s copex, and the aount of cacuaton s bg, t w cost assve te n tranng process, and then Robert Hecht- () Nesen has testfed that n soe stuaton, a three-ayer BP network consstng of snge nput, hdden and output ayers can approxate a contnuous functon n a cosed nterva at a hgh precson [7]. The weght of network s ( w, T ) j, θ s defned as the threshod of the th neuron n hdden ayer, wj s the weght of the j th neuron n nput ayer to the th neuron n hdden ayer, the energy functon s defned as Eq.() f ( x) = x e () + Supposng the sera nuber of tranng nuber s, nput ode s X( k) = { x ( k)}, the output of hdden j ayer Y( k) = { y ( k)}, antcpant output T( k) = { t ( k)} and actua output Ok ( ) = { O( k)}, k =,,...N. The output of the neuron n hdden ayer y ( k ) s cacuated as Eq. (3) net = wj( k) x ( k) θ ( k) y ( k) = f( net ) j The output of the neuron n output ayer O ( k ) s cacuated as Eq. (4) net = T( k) y( k) θ ( k) (4) O( k) = f( net) The tranng error of the th neuron n output ayer of the th k sape s cacuated as Eq. (5) (3) e( k) = ( t ( ) ( )) k O k (5) The hostc error of the k th tranng sape s cacuated as Eq.(6) ek ( ) = e( k) = ( t( ) ( )) k O k (6) Weght adjustng based on error feedback s the key of the network tranng, and the error for weght adjustng noray s two: one s the hostc error of every tranng sape. The other s the ean square error of a tranng sapes. In ths paper, the hostc error of every tranng sape adopts ek ( ) n Eq.(6) as the prncpe for weght adjustng, the genera step s frsty nput every sape to cacuate the output through forward drecton network, and then cacuatng ek ( ), the weght adjustng n every ayer as foows,

3 Supposng the weght adjustng s T, wj, and the weght of the neuron n hdden ayer to output ayer nput the α and β of pont n hoe area to get the SD. The fow of GA-BP as foows. T ( k + ) = T ( k) + ηδ ( k) y ( k) (7) η s study effcency, noray t beongs to (0.0, 0.9), δ (k) = (( t k) O ( k)) O ( k) ( O ( k)) (8) The threshod of output θ + = θ + ηδ (9) ' ( k ) ( k) ( k) ' η s study effcency of threshod, the weght of neurons n nput ayer to hdden ayer w ( k + ) = w ( k) + ηδ ( k) x ( k) (0) j j j η can be the sae wth η, and the threshod δ ( k) = y ( k) ( y ( k)) δ ( k) T ( k) () the threshod of hdden ayer θ + = θ + ηδ () ' ( k ) ( k) ( k) Adoptng Eq.()~Eq.(), studyng and tranng network t to the perforance functon s saer than ε, perforance functon noray s the su error of tranng sapes, denotes th study, f t satsfy Eq.(3), the network s copeted N E = t ( k) O ( k) < ε (3) k= k s the sera nuber of sape. B. Genetc Agorth GA has a hgh capacty n fndng a goba optu souton. It can fetch up the faut of BP network n gettng nto oca optu. Its features consst of the chroosoe codng, the functon of ndvdua ftness, genetc operator and soe paraeters n GA. The basc fow of GA s as fgure. 4 shows, Ⅳ GA-BP NETWORK IN DATA REPAIRING A. reparng agorth and the confgure of network In secton Ⅲ, the prncpe of coectng data fro 3D aser syste has been ntroduced, t s gettng the coordnate of data n Cartesan coordnate accordng to SD, β and α, the produce of hoe s because soe area cannot be detected, and the SD w be wrong, and t w ake the age anaorphc. The wrong age has two obvous features, naey the ponts has the sar nforaton neary andα and β w not have a poston except for SD, the schee of aser data reparng presented n ths paper pace the pont coud nto a eory, and then search the area exstng hoes, after seectng the area around the hoe as the tranng data for network, the GA-BP w approxate these ponts through ncessant study, actuay peentng the reparng, and then ) sape norazaton Fgure.4. The fow chart of GA x( k) x x ( k) = x x ax n n (4) y() k yn y ( k) = =, k=,,..., N (5) yax yn ) ensure the aowed errors of teratve process of GA and BP ε, and ε, set the step ength η of BP, puse δ,popuaton M, varaton probabty λ and evouton G, the nta souton s set randoy. 3) Accordng to choose operator and parents to pent Crossover and varaton cacuaton. 4) Decode every chroosoe, revert the confguraton and weght of network, nput tranng sape, cacuate the error E of network and adaptabty of order accordng to F. 5) Record the best chroosoe, enate the sapes wth the sa F, the prncpe of enaton s to ensure the new generated popuaton has the sae scae wth before. 6) Query the error of best sape whether saer than ε or the teratve tes achevng G, f no, turn to (4), otherwse contnung 7) Decode the best chroosoe, query E whether saer than ε, f yes turn to (), otherwse defne the error as 为 Mn_E, ntaze the tranng tes = 0 and ean square devaton E 0 =Mn_E 8) Input the sapes to cacuate E, f E - < E, then aend weght, ake η=η*b(b s the constant bgger than ), - and turn to (0), f E > E, do not change weght, and then ake η=η*r(r s the constant saer than ), and turn to(9)

4 9) If E < ε, turn to (), otherwse change the weght accordng to agorth and turn to (9). 0) End. The confguraton of network n the paper depends on the actua stuaton of the aser data coectng syste, the confgure ode as fgure 5 shows. In paper [9], t has proved that a neura network wth three ayers can approach the a functon wth any precson. neurons of nput ayer to the frst, second tenth neurons of the hdden ayer, and the frst, second tenth neurons of the hdden ayer to the neuron of the output ayer. As s shown n fgure.6, the weght of network s 0.4,0.,0.,0.3,- 0.4, 0.35, , The sera code n GA s dvded nto two parts, the frst part conssts of ten bts bnary syste and the second part conssts of 30 deca fractons. Fgure.6. The sera code Fgure. 5. The xed codng of network Input ayer: two neurons. They denote the horzonta and ptchng ange of the pont, naey the α and β n Eq.. Hdden ayer: two to ten neurons. Frsty, the nuber of neurons cannot be saer than nput ayer, so the ower t s, and then consderng the hardware peent, the neurons cannot be too uch, so 0 neurons s enough. Output ayer: one neuron, the output of the network s the dstance fro the scannng pont to the asng ght etter, so one neuron s enough. Based on the confgurabe feature of BP network, the neurons of nput, hdden, and output ayer are a connected. B. The paraeters of GA ) chroosoe codng and popuaton ntazaton GA cacuate operators on the popuaton consstng of ndvduas expressed by sera code, every sera code denotes a knd of confgure and cobnaton of weght vector of network. The structure of network adopts two-vaue encodng, and the weght of network adopts rea nuber encodng. Adoptng the prncpe upwards, to confgure forward drecton network, and n the process of GA, the prncpe of ndvdua encodng as foows, a) sera code adopts 0 bts bnary syste to express the budup of hdden ayer, for exape, n fgure 7, the sera code denotes the hdden ayer conssts of,,3 and 0 neurons. b) The weght of network adopts deca fracton to express, after standardzaton, the deca fracton w beong to (-,). Fro eft to rght, the 30 deca fractons denotes the 30 weghts, n turn t s the weghts of the frst and second In the ntazaton of popuaton, seectng chroosoe randoy, and then seectng the popuaton scae M (nora 0~00), the bggest teratve tes, the cross probabty, and the varaton probabty, etc. and the ntazaton s fnshed. ) the cacuaton of adaptabty and seecton operator of GA The ndvdua expressed by sera code w be changed nto the confgure of network through decodng, and then nputtng the a tranng sapes to cacuate the error between the output of network and antcpant output, and defne the recproca of error as the ftness of ndvdua, ftness = + O ( k) t ( k) k = (6) In Eq. (6) s the su of tranng sape, O ( k) and t ( k ) are respectve the actua and antcpant output of network. Ths paper adopts the ethod of proportona ftness to decde whch sera codes w be seected as the parents n the next cacuaton. The fow s that frsty cacuatng the ftness, supposng the ndvdua ftness s F F, and then cacuatng the su of the ftness of every ndvdua, Fj, and defne the tes of the th ndvdua coped to the next popuaton as COPY, COPY = F j = F j j= (7) Generay COPY s deca fracton, n the paper t w be rounded. 3) cross operator of GA Cross operator akes GA has a hgh searchng abty. In ths paper, GA adopts xed bnary syste and rea nuber codng ethod, the secton of bnary syste adopts rando operator, naey generatng a rando nuber beongng to

5 (0,), and then changes t nto 0 bts bnary syste as ask code, every bt of ask corresponds to every bt of bnary codng, and then referrng to the bt of ask code, f the bt s, the bnary codng of two ndvdua w exchange the correspondng bt, for exape, as fgure.7 shows, A and B are parents, through exchangng to get C and D, ask code s 00000, A: cross C: B: D: Fgure.7. The cross operator The cross cacuaton of rea nuber codng doesn t affect the resut of optzaton, n ths paper, the author adopts party dscretey crossng, naey seectng parta vectors, and then exchangng the to generate the new popuaton, for exape, eder ndvdua are p = ( u, u... u n ) and p = ( v, v... v n ), fro the bt to exchange, and the new ndvdua after crossng as s shown beow: c = ( u, u... u, v... v ), c = ( v, v... v, u... u ) k k+ n k k+ n 4) varaton operator of GA The secton of bnary syste denotes the confgure of network, the cobnaton n souton space s tte, so the setup of varaton cacuaton can be easy, and at the sae te, varaton probabty adopts fxed and esser varaton probabty, generay to retan the coparabty between new and od popuaton and the stabty of evouton, varaton probabty s noray seected beonged to (0.000, 0.). The secton of rea nuber codng denotes the cobnaton of weght. Varaton cacuaton s portant to the agorth adoptng rea nuber codng, because cross cacuaton doesn t have a obvous affect to t, so t any depends on varaton to get the new ndvdua, the varaton probabty shoud be bg, and the souton space s bg, and of course the precson s hgh, here we adopt a sef adaptve varaton probabty, the hgher the ftness of ndvdua s, the ess the varaton probabty s, and the ower the ftness of ndvdua s, the bgger the varaton probabty s, as Eq.8 shows, P s the varaton probabty of ndvdua, sze s the copostor accordng to the ftness of ndvdua and P s the bggest varaton probabty. [: : sze] 0.0 P = P (8) sze The varaton cacuaton of the rea nuber secton dffers wth the bnary syste, for exape, p = ( u, u... u n ) s the ndvdua vector n souton space, F s ts ftness and F ax s F the bggest ftness, defne varaton teperature T =, Fax so the heft of ndvdua can be cacuate by Eq. 9 u k uk ( T, uk ak), 若 r% = = uk + ( T, bk uk), 若 r% = 0 (9) In Eq.9, r s rando sgness ntegers, and T ( T, y) = y ( r ). Ⅴ SIMULATON STUDIES Usng the GA-BP neura network to reparng the hoe caused by osng data of the aser scanner s based on neura network s exceent abty for approach each swatch. Therefore the choosng of swatches s portant to the perforance of the data reparng. The foowng experent and suaton s based on the foowng Dscrete Pont quadratc surface: Z = X + Y X,Y [-4,4] (0) Both varabes step of scatterng s 0., thus X and Y are array wth 40 ebers. Suppose, the osng data s wthn the 6 6 area X [-,-0.5], Y [,.5]. The surface whch needs reparng s shown n fgure. 8. Fgure.8. The surface needed repred Choose the foowng three groups of swatches nubers,,3. Swatches : X [-.0,0.5], Y [0,3.0] Swatches : X [-.5,.5], Y [-,3.5] Swatches 3: XY, [-4, 4] Executng the arthetc wth each of the three knds of swatch 0 tes and ake a statstc accordng to the foowng four paraeters. Tranng error t: The t of average error of the neura network s actua output accordng to the antcpate output of a swatch when tranng the neura network. The neura network can stop tranng when the Tranng error eets the t. Reparng error: The average error of the traned network s actua output accordng to the antcpate output of the osng area. Tes of tranng: count of the tranng cyces whch s taken on by neura network fro the startng t ts eetng the Tranng error t. Te: It s the te taken on by the arthetc s each executng. The deta nforaton s shown by the tabe and the average reparng perforance wth each group of swatches s shown n Tabe and fgure.9.

6 Tranng error t Swatch group Tabe PERFORMANCE TATISTICS Tes of tranng Reparng error Te(second) ( (a) (b) (c) Fgure. 9. Accordng to the tabe and fgure.8 The bgger the nuber of the swatch s the ore tranng cyces s needed to tran neura network every te and the ore seconds taken by each tranng cyce. The nuber of swatch has a very portant affecton to the precson of reparng. The best nuber of the swatch s not too any or too ess. But t s uch worse when there s too any swatch than too ess. The fner the Tranng error t s, the ore tranng cyce s taken by the arthetc to eet t and uch better the reparng error s. In a word the agorth can reparng the ost data areas we,f the swatches are chosen sutaby. The best swatches are a around the ost data areas and not too far away fro the. Usuay, the nuber of swatches s the arger, the better the arthetc s perforance s as fgure.0 shows. Rparng perforance of each group of swatch a: swatch 3; b: swatch ; c: swatch Fgure. 0. Surface repared by proved GA-BP network CONCLUSION In the paper, n order to repar the hoe of reconstructed surface, whch caused by the ost data of the aser scanner we present a ethod that usng the neura network and data around the ost data area to do the reparng work. In face of the on ne data reparng appcaton we ntroduce an knd of proved BP neura network based on GA. In ths ethod, we optze the structure and the weghts of the BP network, as ake the ethod ore adaptve. The suaton shows that ths ethod can not ony repar the hoe n an effcent way but aso have a very good reparng perforance. In a word, copared to the tradtona ethod, ths ethod can get a better perforance n approachng the ost data. ACKNOWLEDGEMENT Ths work s supported by 863 Progra of Chna under the research project 006AA04Z8 and Natura Scence Foundaton of Chna under the research project REFERENCES [] J. Scheffer, Deang wth ssng data, Res. Lett. Inf. Math.Sc, Mar.00., pp [] Y.. Zhong and W.C. Yang, On Spfyng Processng of Copex Measureent Data for Makng Reverse Engneerng Easer, Journa of Northwestern Poytechnca Unversty. X'an, vo. 4, 997, pp [3] P. Gu and X. Yan, Neura network approach to the reconstructon of free for surfaces for reverse engneerng, CAD, vo.7, Jan.995, pp.54-6 [4] B. F. Davd, An ntroducton to suated evoutonary optzaton, IEEE Transactons on Neura Networks, May 994,pp.3-4 [5] K. J. K and S.B. Cho, Evovng Artfca Neura Networks for DNA Mcroarray Anayss, 003 [6] B. Yang, X.H. Su and Y.D. Wang BP neura network optzaton based on an proved genetc agorth, Proceedngs of the Frst Internatona conference on Machne Learnng and Gybernetcs. Bejng, Dec.00, pp [7] M.Vttoro, Genetc evouton of the topoogy and weght dstrbuton of neura networks, IEEE Transactons on Neura Networks, May.994,pp [8] Z. X. Ca, J. X. Yu, X. B. Zou and Z.H. Duan A 3-D Perceptua Method Based on Laser Scanner for Mobe Robot, IEEE Internatona conferrence on Robotcs and Boetcs. pp [9] R.H. Nesen, Theory of the back- propagaton neura network, Proceedngs of the Internatona Jont Conference on Neura Networks. Washngton USA, Jan. 989,pp