Application of fuzzy neural network in the pattern classification of table tennis rotating flight trajectory

Transcription

1 Applcaton of fuzzy neural network n the pattern classfcaton of table tenns rotatng flght trajectory Abstract Fe Cheng Shangqu Normal Unversty, Shangqu , Chna In order to mprove the accuracy and effcency n the pattern classfcaton of table tenns rotatng flght trajectory, the fuzzy neural network s proposed n ths paper. Predct of the trajectory s calculated by Error Back Propagaton (BP) neural network. Select the same data and method wth FNN algorthm and create BP predcton network, whose output s also poston nformaton of after 0 frames. The neural network learns a lot of hstorcal data offlne, and the best can be saved to predct the new trajectory, whch proves the feasblty of BP neural network. Fnally, we compare BP neural and mproved FNN algorthm, verfyng the superorty of BP n accuracy and superorty of FNN n tme consumng. In summary, we consder the FNN algorthm s more sutable for the Table tenns robot n predctng of trajectory. When usng FNN to classfy the trajectory. Smlarly select the characterstc, poston, speed of every frame of rotaton table tenns trajectory as the characterstc. Experments verfy the feasblty and applcablty of FNN n classfcaton of rotaton table tenns trajectory. Keywords: Fuzzy neural network, pattern classfcaton, table tenns, rotatng flght trajectory 1.INTRODUCTION The cover of the tmes n US: Chna: A whole new game, whch report the development of table tenns (TT) n Chna. Indeed, whch no other sports lke Chnese table tenns constantly make mracles, won gold and slver medals n the world sports, and rsng sde of another sde of brllant banners on the world spots stage. Nor so popular to hundreds of mllons of Chnese people, whch deeply nvolve and nfluenced on the all aspects of Chnese socety. Chnese table tenns on behalf of the connotaton and extenson of Chnese compettve sports s the core meanng of compettve sports, the best value, functons successfully emboded. Although TT s small, t brngs endless joy and exctng to us, gve us countless sensaton. Table tenns orgnated n England, as a carrer of Western culture, frstly ntroduced to Chna was not rejected lke other cultures by the local culture, and there s no sgnfcant conflct between Eastern and Western cultures. adverse, t rooted and grow n Chna, the most mportant reason s the exchange and dssemnaton of culture, s based on the nteracton of global culture, a hgh degree of dentty based on the value of table tenns, Chnese people accepted t, so the TT development and flourshed n Chna. Lookng from the TT spread of hstory n the world, t has nextrcably lnked n natonal poltcal, economc, and cultural n ts varous phases. Today, the World Table Tenns arena domnated by Chnese, the other countres table tenns growng have a potental declne trend, how to make the table tenns gan a sustanable development, the concern on cross-cultural communcaton seems partcularly urgent. In the tmes of the 1st century, combed hundreds of years of table tenns to the modern evoluton hstory, deeply study on the TT spread culture of dfferent hstorcal stages, should be awarded by the academa and the communty when they revewed hstorcal evoluton n ths stage, at the same tme fnd a rght path for table tenns as Pathfnder for Chnese sports system, fnal spread of the Chnese cultural soft power, to have a broader perspectve about the powers of nspecton and evaluaton of the constructon of sports. Table tenns s composed of many contents. It not only possesses varous plays but also has a lot of compose of sklls and tactcs. As the contnuous development of table tenns, we should augment our recognton, converse our concepton, renew our methods, and grasp the rules of table tenns. Accordng to the partcular state of the athlete, we should adopt effectve method, n order to mantan our country s leadng status n the world. J s (J and Dng, 013) paper analyses the present condton of the table tenns from macroscopc aspect. Research subjects: 5 excellent players. The paper apples documents, vstng, logc analyss, case analyss and statstcs, vdeo-observaton and three-phase method to research. The development of nowadays table tenns 678

2 makes the match come nto the overall opposng phase, ncludng sklls, tactcs, body and psychology. The bgball, 11-pont system each game and unblocked servce made t more ntense. After the new rules were adopted, t requres the players more careful and more accurate when they use any skll. On the base of the steady state, augment the ntatve conscousness. Alex s (Sheppard and L, 007) research reveals: after 11-pont system was adopted, the elte player s usng rate of the phase of recepton ncreased greatly. It makes the match change more fercely before 4 boards. The adopton of new rules requres the players more careful and more accurate when they use any skll, at the same tme; they should strengthen the jons of sklls between and 4 and between 3 and 5. As the standard of athletes gradually approach, the conscousness of table tenns s more and more mportant. The conscousness s the premse of the sklls and tactcs. It drectly affects the level of sklls and tactcs. So we should strengthen the cultvaton of the conscousness. The adopton of new rules wll arse some changes of the table tenns s theory, system, model and method. We should serously analyss the changes that the new rules brng, know the tendency of the table tenns, grasp the new opportunty, challenge the opponent and the future, ntent to brng forth new deas and development, keep up our country s domnant poston n the world.. MATERIALS AND METHODS Currently, the dentfcaton problem of the rotary table tenns has not been solved well. It carred out some relevant researches on the flght trajectory of rotary table tenns, ncludng the trajectory predcton of the rotary table tenns and the analyss of the rotary table tenns. Table tenns trajectory s recevng ncreasng attenton from computer vson researchers. The computer vson ncludes three aspects, whch are human object recognton, object trackng and table tenns trajectory. Among them, Table tenns trajectory s the hghest-level part. Robust table tenns trajectory algorthm has mportant theoretcal sgnfcance and great applcaton value, whch can be wdely used n the feld of ntellgent vdeo survellance, vdeo retreval and human-computer nteracton. At the same tme, the dffculty of the research s manly reflected n the complex background, multple types of actons, large amount of data and real-tme requrements. Table tenns trajectory process ncludes three mportant aspects, whch are the detecton and trackng of the human body, feature extracton and table tenns trajectory. In recent years, table tenns trajectory technology based on the spatal-temporal nterest ponts s wdely appled,whch has the advantage that t does not depend on the underlyng human detecton and trackng algorthm, but depends on the aspects of feature extracton and table tenns trajectory. Ino s (Ino and Kojma, 009) paper follows the table tenns trajectory method based on the spatal-temporal nterest ponts. As to extractng feature, he detects spatal-temporal nterest ponts n the three-dmensonal vdeo samples, and ntroduces the background dfference method to obtan the regon of nterest. The regon of nterest and the mnmum regon of STIPs are fused to obtan the fnal regon of nterest. Once agan, we extract the local feature nformaton, such as hstogram of orented gradent, hstogram of orented optcal flow and wavelet energy nformaton. Ma s paper (Ma et al., 014) uses the cumulatve hstogram to merge the sequence mage features and generate vdeo egenvectors. As to table tenns trajectory, he adopts the drect classfcaton methods of KNN and Ada Boost. KNN algorthm s smple, but low recognton rate. Ada Boost algorthm has a hgh recognton rate, but s more complcated because t needs a weak classfer tranng process. Compared to prevous work, the contrbuton of Zhang s paper (Zhang et al., 013) proposed a new feature representaton called STIG (Spatal-Temporal Interest Grd). STIG s based on ROI and STIP. Through combnng global features and local features, t can effectvely hold the space connecton nformaton among each pato-temporal nterest ponts. As to ROI, t s the fuson of the global foreground moton regon and local mnmum rectangle of STIP regon, whch obtaned by usng the bdrectonal analyss method. In addton, the ROI provdes the bass for other feature extracton. Amy s paper (Bufton et al., 014) studes the trajectory predcton problems of table tenns of png pong robot system, and propose two new trajectory predcton methods: the trajectory predcton method of the rotary table tenns based EKF and the trajectory predcton method of the rotary table tenns based UKF, both methods can estmate the ball s moton state n the state of the angular velocty s unknown. Further, the EKF predcton method to predct frst derved n the moton model of the rotary table tenns are accordance wth the force of crcumstances, and then construct the equatons of process and equatons of observaton by the model, at last predct the flght trajectory of the rotary table tenns. For UKF predcton method, frst of all does the U transform of samplng ponts, and then through the teratve of predcton process and update process, fnally get the predcted trajectory of the rotary table tenns. Respectvely, experment wth the rotaton data made by ptchng machne and the rotaton data made by human, the MALAB expermental results show that the predcton accuracy of EKF and UKF can both meet the png pong robot system needs, but the latter cost a 679

3 shorter tme, and analyses the pros and cons of them. In addton, accordng to the predcted flght trajectory, we desgned a pattern recognton classfer of trajectory based BP neural network. Frst, pre-processng the nput trajectory data, and then create a new BP network for pattern recognton, the nput s the three-dmensonal speeds of the table tenns on fve desgnated secton of the flght trajectory, the output s the correspondng rotaton type, and the neural network learn a lot of hstorcal data offlne, and fnally the traned network model can be used for the table tenns trajectory pattern recognton. Fuzzy system s a theory that s based on the fuzzy set (Wang et al., 014), t processes the followng treatment for a complcated ssue: fuzzy measurement, fuzzy recognton, fuzzy reasonng and fuzzy control. In the classcal theory, the characterstc functon s only allowed to take two values of 0 and 1, and the fuzzy set adopts the concept of membershp functon, the characterstc functon s extended to [0, 1]. Fuzzy set: supposng A:U[0, 1] s a map on unverse U, then A s the fuzzy set of U,U (x) s the membershp functon of A.U(x) reflects the membershp degree of x on the fuzzy set A. Fuzzy system s good at expressng and nterpretng knowledge; t s a descrpton of fuzzness based on precse mathematcal language. The basc computng unt of neural network s an artfcal neuron, whch smulates the structure and functon of neurons n the bran and has a strong self-learnng ablty. Through the contnuous learnng of adjustment, the artfcal neuron can be fnally presented by the specfc structure of network. Structure of the proposed fuzzy neural network s llustrated n Fg. 1. y Layer 4 w1 w w3 Layer 3 Layer Layer 1 x1 x xm Fgure 1. Structure of the proposed fuzzy neural network As n llustrated n Fg.1, the fuzzy neural network contans four layers: 1) Input nodes, ) Membershp functon nodes, 3) Rules nodes and 4) Output nodes. Fuzzy neural network s desgned based on a seres of IF-THEN rules, whch s used to descrbe the nput/output mappng relatonshp (Yu et al., 014): Rule k f x s A and x s A and x s A (1) ( ) : 1 1k k n nk then y w, k {1,,, N} () k Where x and y refer to the nput varable and output varable, and the symbol Ak refers to the precondton part. Furthermore, wk means the output acton strength that s correspondng to Rule(k). Moreover, N refers to the number fuzzy rules, and n denotes the number of nput varables. Based on the above defntons, the detals of the fuzzy neural network model are explaned as follows. (1) Input nodes layer In ths layer, each node s regarded as an nput varable, and the node only can transmt nput values to ts neghbour and upper layer. 680

4 v x, {1,,, n} (3) 1 ()Membershp functon nodes layer In the second layer, nodes should be dvded to N clusters, and then each cluster should follow a fuzzy rule. In partcular, each node of ths layer s able to calculate the value of membershp functon. Assume that an external nput s represented as v, and then the Gaussan membershp functon s descrbed as followed. 1 1 ( v ) m j vj exp, {1,,, n}, j {1,,, N} (4) j Where m j andδ j refer to the centrod and the wdth of the Gaussan membershp functon respectvely. (3)Rules nodes layer Dfferent from the above layers, n ths layer, the number of nodes means the number of fuzzy rules, and node n ths layer s used to calculate the rule actvaton strength. Output values of ths layer are lsted n the followng equaton. 3 v j vj, j {1,,, N} (5) (4)Output nodes layer Based on the above four layers, output values of ths layer are computed as follows. v 4 v w 3 j j j 3 v (6) j j The data obtaned from the assessment sheet research development s the result of the development of table tenns learnng meda, the data valdaton results of three valuators, data from teacher and student questonnares, the data value of student learnng outcomes. The data processng algorthm s shown n the followng: The basc equaton of the proposed algorthm s shown n the equaton (1) (Lv and Hu, 016): u U ( t k) U k k (7) ( t k ) k k ' c ' c 1 c ct ' c1 ' Uc c 1 ct k = 0, 1,, The equaton of snusodal modulaton wave s: u U sn t (8) s s s Set F = ω c /ω s 1, modulaton degree M = U s U c

5 For u p, the samplng pont s: U t t k U U ' c ' s sn s ( c 1 ) c Set ω s t = Y, ω c t = X, thenx = πk + π α 1 πmsny As shown n the form ofω c t = Xs n the nterval between πk + αandπ(k + 1) + α. Between a and b, when the sne wave modulaton s larger than the trangular carrer, the u p s gotten. The tme functon of u p s: u P1 k 1 M sny 0 X k 1 M sny ( X, Y ) k 1 M sny E/6 X k 1 M sny (9) The double Fourer seres of functon u p (x, y) s gven: A u X Y A nx B ny A mx 00 P1(, ) ( on cos on sn ) ( mo cos n1 n1 B sn my ) [ A cos( mx ny ) B sn( mx ny )] mo mn mn m1 1 In the above formula ( ) j( mx ny ) Amn jbmn u P1( X, Y) e dxdy (10) Take the formula (9) nto formula (10) E 6 k 1 M sny j( mx ny ) Amn jbmn e dxdy 0 k 1 M sny E ( 1) 1 sn 1 e jm n e jmm Y e jny dy e jmmsny e jny dy 0 0 [ ] j6m By Bessel functon, jn 1 jmm sny jny e 1 e e dy J ( ) 0 n mm 1 jmm sny jny 1 e e e dy J ( ) 0 n mm jn Then, 68

6 jn jn E jm( 1 ) e 1 1e Amn jbmn e [ Jn( mm) Jn( mm) ] j6mn (11) E jm( 1 ) jn j Jn( mm ) e [1 e ] 6mn The we get: C t D L C C u x x (1) C( x,t) C( x,t) C( x,t) t0 x0 x 0, C, 0 0, 0 x t 0 t 0 (13) After Laplace change, the standard normal dstrbuton functon s solved as follows: C 1 Φ x ut DLt 0.1 (14) Assume the relatve concentratons 0.16 and 0.84 occur at the tme of t 0.16 and t 0.84, then we can get: 1 x ut 8 t x ut t 0.16 D L 0.84 (15) The followng equaton (10)-(11) s shown as: I U / R 4 KT f / R (16) T T U 4KTR f (17) T 1 e Instrument s tools or facltes that are used by researcher n collectng data n order to work more easly and better results, n terms of more effcent, complete, and systematc, so easly processed. At ths stage of the research nstrument developed by researcher n collectng data n order to work more easly and better results, n terms of more accurate, complete, and systematc so t s more easly processed. 3.RESULTS AND DISCUSSION For a multple attrbute database, each propertes of the database s contnuous varable, f you want to extract the rules of the relatonshp between n propertes and the other m propertes, then the number of nputs s n whch can be expressed as x 1, x,..., x n, and the correspondng m outputs, can be expressed as a y 1, y,..., y m. In ths knd of problem, by usng the membershp degree functon, they can be translated nto the membershp degree value of ther correspondng fuzzy nputs and fuzzy outputs. Usng these as tranng samples, the followng form s expected to obtan: If (x 1 θv 1 ),x θv, x n θv n then (y 1 θξ 1 ),(y θξ ) and (y m θξ m ), θ(=, <, >,,, )s the relatonshp symbol; v, ξ are the fuzzy attrbutes (bg, medum, small etc). 683

7 The steps of usng fuzzy neural network system for mnng are as follows. Ths refers to the preprocessng of sample data, and characterstc values are mapped to the nterval of [0,1]. Supposng there are f samples (x 1, x,..., x f ), each sample x has n sample ndcators z 1, z,..., z n, x j refers to the number j ndcator of the number sample, then the n ndcators of f samples are shown n Table 1. Table 1Sample Data Indcator z1 z zn x1 x11 x1 x 1 n x x1 x x n x f x f 1 f x x fn The structure of fuzzy neural network s shown n Fgure. Fgure. Fuzzy Neural Network Structure The frst layer s nput layer, t can sent the nput value nto the next layer, the nodes number n ths layer s n. The second layer s the membershp functon layer; the membershp decreed of each nput component on the correspondng lngustc varable fuzzy set can be calculated n the n ths layer the membershp degree functon, each node stands for the a lngustc varable value. The thrd layer s the fuzzy rule of matchng. The applcaton degree of each rule s calculated, the node number n ths layer s m; the thrd layer and the fourth layer are fully connected. The data of the thrd layer s normalzed n the fourth layer, the node number n ths layer s m. The ffth layer s an output layer; n ths layer the output data s obtaned by weghted coeffcent, and then through the membershp functon, the jursdcton of the output under the fuzzy language varables can be determned. =1,,, n, n s the dmenson of the nput varables, j=1,,, m, m s the dvson number of fuzzy classfcaton, x j and σ j are the center and wdth of the membershp functon, respectvely,.e. translatng the nput value nto the lngustc varable (bg, medum, small, etc.) n the second layer. a layer s a nput layer,whch can translate x=(x 1, x,..., x n ) nto the next layer. b layer can calculate the membershp degree functon μ j of the jursdcton of the nput values under the fuzzy set. In order to test the tranng speed of the proposed approach, we construct an experment to demonstrate the convergence speed of the fuzzy neural network tranng process (shown n Fg. 3). 684

8 Value of errors Tranng Curve Objectve Curve Iteraton tmes Fgure 3. Error rate varyng under dfferent teraton tmes It can be observed from Fg. 3, tranng process can be converted to the objectve value after 500 teratons. 300 groups of data are selected from the 500 groups of data for tranng the network, the rest of the 00 groups of data are used for verfyng the accuracy of the algorthm. Frst of all, standardzng the data, then nputtng the standardzed characterstc values nto the fuzzy neural network, at last, usng the error back propagaton algorthm to adjust and correct c j, σ j, ω 1, ω andω 3. Tranng sample data after 615 teratons, network convergence, and error teraton steps shown n Fgure 4 s as follows. Fgure 4. The Sum of Squared Errors of Fuzzy Neural Network After the tranng, the revsed ω 1, ω andω 3 are 0.544, 0.51 and 0.451, respectvely. Settng 0.1 as the threshold λ of the rato of the samples on the total samples, the followng mportant rules are obtaned as shown n Table below. Table 4. Extracton Rules rule 1 rule rule 3 rule 4 rule 5 rule 6 rule 7 rule 8 rule 9 P P P P3 Q Q Q0 Q1 Q0 Q1 Q Q Q0 Q S S1 S 0 S S1 S1 S 0 S 0 S S1 A A4 A A Sample Rate CONCLUSION There are two puzzles of Table tenns robot system: It s hard for robot to response n a short tme, when table tenns movement n hgh speed condton; Table tenns robot cannot judge the type of opponents ht the ball (e.g. Backspn, Topspn, Regular), can t judge the rotaton and the drecton of rotaton, whch wll cause the robot to return the ball n sngle strategy, poor adaptablty. To solve these two problems, ths paper launches the research work on the trajectory of the Table tenns on Table tenns robot system, manly ncludng two parts: the 685

9 predcton of trajectory and classfcaton of rotaton table tenns trajectory. Predcton of the trajectory s the base of research n Table tenns robot. Ths paper presents an approach to predct the trajectory of table tenns ball based on the Fuzzy Neural Network (FNN) algorthm. Frstly, we get the real experment data between human and machne. Then we extract the poston and speed nformaton of10consecutve frames as the characterstc, whch s the nput of FNN algorthm. Then we pre-process the nput trajectory data and create a new FNN network for predcton, whose output s the poston nformaton of after0frames. Through several experments we found defcency of orgnal FNN algorthm, so we mprove FNN algorthm. The mproved FNN learns a lot of hstorcal data off lne and saves weght matrx of the hdden layer to save the traned FNN model. At last, we verfy the feasblty and applcablty of FNN n predcton of trajectory by experments. Predct of the trajectory by Error Back Propagaton (BP) neural network. Select the same data and method wth FNN algorthm and create BP predcton network, whose output s also poston nformaton of after0frames. The neural network learns a lot of hstorcal data offlne, and the best can be saved to predct the new trajectory, whch proves the feasblty of BP neural network. Fnally, we compare BP neural and mproved FNN algorthm, verfyng the superorty of BP n accuracy and superorty of FNN n tme consumng. In summary, we consder the FNN algorthm s more sutable for the Table tenns robot n predctng of trajectory. When usng FNN to classfy the trajectory. Smlarly select the characterstc, poston, speed of every frame of rotaton table tenns trajectory as the characterstc. Experments verfy the feasblty and applcablty of FNN n classfcaton of rotaton table tenns trajectory. Fnally, we compare BP neural and mproved FNN algorthm. Experments show that compared wth BP. the accuracy of FLM s relatvely a lttle low but the consumng tme s much less. 5. REFERENCES Akhtaruzzaman M., Shafe A.A., Khan M.R.(016). Gat Analyss: Systems, Technologes, and Importance, Journal of Mechancs n Medcne and Bology, 16(07), Do: /S Bufton A., Campbell A., Howe E., Straker L.(014). A comparson of the upper lmb movement knematcs utlzed by chldren playng vrtual and real table tenns, Human Movement Scence, Do: /j.humov Bačć B.(016). Predctng golf ball trajectores from swng plane: An artfcal neural networks approach, Expert Systems wth Applcatons, 65, Ino Y., Kojma T.(009). Knematcs of table tenns topspn forehands: effects of performance level and ball spn, Journal of Sports Scences, Do: / J P., Dng Z.Y.(013). A New Fuson Method of Table Tenns Sensor Informaton System,Sensors & Transducers, 160(1), J W.E., Guo Q.J., Zhong S., Zhou E.(013). Improved K-medods Clusterng Algorthm under Semantc Web, InProceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng.013, Do: /ccsee Jalal A., Km Y.H., Km Y.J.(017). Robust human actvty recognton from depth vdeo usng spatotemporal mult-fused features, Pattern recognton, 61, Lv Q.S., Hu H.F.(016). Research on parallel computng model and classfcaton algorthm based on data mnng process, Internatonal Journal of Securty and Its Applcatons, 9(5), 31-40, Do: /jdta Ma G.D., Lu Y.H., Lu K.M.(014). Influence of Repeated Bouts of Table Tenns Tranng on Cardac Bomarkers n Chldren. Pedatrc Cardology , Do: /s x. Prest L.L., La C.M.(016). 3D skeleton-based human acton classfcaton: a survey, Pattern Recognton, 53, Do: /j.patcog Sargano A.B., Angelov P., Habb Z.(017). A comprehensve revew on handcrafted and learnng-based acton representaton approaches for human actvty recognton, Appled Scences, 7(1), 110.Do: /app Sheppard A., L F.X.(007). Expertse and the control of ntercepton n table tenns, European Journal of Sport Scence, Do: / Wang Z.K., Boularas A., Müllng K., Schölkopf B., Peters J.(014). Antcpatory acton selecton for human robot table tenns, Artfcal Intellgence, Yu Z.G., Huang Q., Chen X.C., Zhang W., Gao J.Y., Quan Q.(014). Desgn of a Redundant Manpulator for Playng Table Tenns towards Human-Lke Stroke Patterns, Advances n Mechancal Engneerng, 19-3.Do: /014/ Zhang H., Lu W., Hu J.J., Lu R.Z.(013). Evaluaton of elte table tenns players' technque effectveness. Journal of Sports Scences,