Avalable onlne www.jocpr.com Journal of Chemcal and Pharmaceutcal Research, 4, 6(6):36-4 Research Artcle ISSN : 975-7384 CODEN(USA) : JCPRC5 Grey predcton model n world women s pentathlon performance predcton appled research Su Jn and Techeng Guo Insttute of Physcal Educaton, Northeast Normal Unversty, Changchun, Jln, Chna Mltary Sports Department, Changchun Unversty of Scence and Technology, Changchun, Jln, Chna ABSTRACT Grey system theory s a knd of deal method to handle wth small samples dynamc development problems, and compettve sports problems possessed poor data nformaton, small sample and dynamcs, let grey system have an advantage over tradtonal probablty statstcs and fuzzy mathematcs n ts problems researchng, grey mathematcs applcaton n compettve sports performance predcton and analyss s more wdely. The paper apples documents lterature, counts prevous world women s pentathlon best performance from to 3. Combne wth world women s pentathlon best performance, the paper establshes GM (, ) grey model and GM (, 6) grey model on t. By comparng precse of GM(, ) model wth GM(, 6) model, t researches on GM(, N) model s applcaton n sports compettveness, states GM(, N) model method applcaton n multple tems sports compettveness, and selects GM(, 6) predcton model as grey model to apply nto compettve sports performance predcton. Meanwhle, apply GM (, 6) grey predcton model group to screen establshed model, and fnally defne to model wth sample data from 5 to3 and defne world women s pentathlon performance predcton model. Key words: women s pentathlon, GM (, ) model, grey relatonal analyss, GM (, 6) model INTRODUCTION In compettve sports, athlete compettve result nfluences factors are qute varous, lots of factors are unknown, neact, and factors affect and nteract each other, t s dffcult to make clear analyss on them one by one. But as a entrety system, compettve sports performance change and development have some nternal rules, each factor comprehensve effects let compettve sports performance has uncertantes. Tradtonal uncertan factors researchng mathematcal methods manly are regresson analyss, varance analyss, prncpal component analyss and other mathematcal statstcal methods to make statstcal analyss of system. Mathematcal statstcs method requres a great deal of samples and data, data changng should have certan rules, relatons among factors to be statc and so on, requrements on system s hgher, data samples should have better dstrbuton rules, and ts analyss cannot surely get effectve statstcal rules, even t gets statstcal rules, n most cases t also cannot make analyss and predcton on system. Grey predcton system modelng accordng to grey system behavor features data, utlzes accumulatng sequence to overcome orgnal sequence volatlty, randomness, ecavate nformaton data s eplct nformaton and hdden nformaton so that arrve at relatve precse short-term predcton model. For sports compettve performance predcton problem s poor data nformaton and dynamcs as well as other features, grey predcton model has already become one of major method n compettve sports performance predctng, lots of scholars have made research and applcaton on t, and got lots of achevements, as well as put forward many opnons. Among them, Ma Xang-Ha () researched on Chnese ecellent decathlon athlete performance, by carryng out grey relatonal analyss on t and grey GM (, ) predcton model s modelng, he analyzed Chnese decathlon athlete development trend []; Sun Qang () by establshng Olympc Games men s 4m competton performance same dmenson gray recurrence GM (, ) model, he solved 36
Su Jn and Techeng Guo J. Chem. Pharm. Res., 4, 6(6):36-4 grey model mddle and long term compettve sports performance predcton [];Wang Dao-n, Fan Xn-Sheng(5) took Chnese 3th to 8 th Olympc Games acheved gold medals numbers as orgnal data to establsh grey model, they stated grey model applcaton n compettve sports competton[3]; u Ja-Jn(6) analyzed the 4 th to the 8 th fve sessons Olympc Wnter Games women s shot compettve performance development trend, he proposed GM(, ) s more ft for sports compettve performance predcton grey model establshng that possessed slghtly swng data sequence [4];u Ja-Jn, Wang Dong, u Shun-Mn(999) by carryng out GM(, )model group modelng on men s hammer player B Zhong-Nan best performance, they researched on grey model group predcton methods n sports compettve performance[5]. The paper takes world women s pentathlon performance predcton as an eample, t makes statstcs of ~3 such 3 years world women s pentathlon best performances, makes grey relatonal analyss of ther total performance and other each event performance, establshes GM(, )and GM(, 6) grey predcton model, and researches grey model s applcaton n compettve sports by predctng. World women s pentathlon prevous champons performances analyss In order to predct world women s pentathlon compettve performance development trend, the paper makes statstcs of year ~3 such 3 years world women s pentathlon champons performances, and based on them, t establshes grey relatonal analyss and grey predcton model. The statstcal data s as Table : Table : Year ~3 prevous women s pentathlon hghest performance table [6] Year Total score 6m hurdle(s) Hgh jump(m) Shot (m) ong jump(m) 8m(s) 485 8.5.8 6.3 6.69 43.3 46 8.56.78 3.66 6.4 43.59 3 4933 8.9.89 4.48 6.6 35.58 4 4759 8.48.88 5.8 6.45 4.69 5 4948 8.9.93 3.9 6.65 33.47 6 473 8.3.8 3. 6.44 3.94 7 4944 8..88 4.43 6.59 33.4 8 4867 8.54.99 3.85 6.4 36.4 9 4784 8.3.86 3.77 6.54 36.63 4937 8.4.9 4. 6.44 3.55 473 8..8 4.8 6.34 38.99 53 8.38.84 6.5 6.57 3.5 3 485 8.5.89 3.4 6.57 3.53 Women s pentathlon competton s composed of 6m hurdle, hgh jump, shot, long jump and 8m fve events, ts fnal result s got by calculatng the fve events performances wth certan methods. In order to research on women s pentathlon total performance and establsh predcton model on t, t can frstly analyze ts total scores development trend. Fgure : Year ~3 prevous women s pentathlon hghest performance total scores change chart By Fgure, t can see that prevous total scores are among 46~5, and ther changes s on volatlty, t goes up and down, fluctuates, so rregular.and data quantty s lttle, nformaton quantty s lttle, and women s pentathlon competton performance development change s a dynamc process, tradtonal mathematcal method s dffcult to analyze t and judge ts change trend. Grey theory uses accumulatng sequence to do data mnng on orgnal data sequence, and apples generated sequence nto modelng, so that mnes ts nternal rules from less quantty, changng data, establshes model and analyzes world women s pentathlon annual best performance change and development trend. 3. World women s pentathlon annual best performance GM (, ) model GM (, ) model s grey predcton model s most wdely appled model. In grey theory applcatons, 9.8% researches apply nto grey predcton model, and among them 75.6% of used grey predcton model s GM(, ) 37
Su Jn and Techeng Guo J. Chem. Pharm. Res., 4, 6(6):36-4 grey predcton model, and ts thess quanttes s ncreasng at annual 9.69%~.8% speed.gm (, ) model method s smple, applcaton range s wde, t can be appled nto lots of tradtonal mathematcal method unsolved problems felds, and grey predcton model takes the leadng poston. Due to world women s pentathlon total performance data features, the paper adopts GM (, ) model to carry out model analyss of t. 3. Data test By data statstcs, t carres out grey model orgnal data sequence generaton on year ~3 world women s annual best performance total performance. Generated data sequence s as followng: = (, (), (3),, (3)) In order to ensure GM (, ) grey predcton model s accuracy, t needs to carry out testng on modelng obtaned λ falls n the nterval ( e, ) n+ + orgnal sequence data. If ts orgnal sequence ultmate rate (k) e n, then t can use ts data to carry out grey predcton modelng. Otherwse t should process wth orgnal data. Input n = 3 and t can get nterval(.8669,.46). By sequence ultmate rate formula: ( k ) λ( k) =, k =,3,,3 It can get that obtaned ultmate rate formula falls n the nterval(.937,.499), t can drectly use orgnal sequence to model on predcton system. 3. GM (, ) model establshment Accumulatng and mean handlng wth new data column By accumulatng operator AG carryng out accumulatng wth new data sequence, weaken ts randomness, and can get accumulatng sequence: = (, (),, (3)) And by formula z =.5 +.5, t solves ts average value generaton sequence z. Construct data matr B and data vector Y: (3) Calculate u : T T T. u = ( a, b) = ( B B) B Y = 9.3 (4)Model establshment: d +. = 9.3 dt z () () z (3) (3) B =, Y = M M M z () () It can solve: ( k + ) = 6399e.8k 594 (5) Then t can solve year ~3 women s pentathlon best performance predcted value as followng Table : 38
Su Jn and Techeng Guo J. Chem. Pharm. Res., 4, 6(6):36-4 3.3 GM (, ) model testng Table : Year ~3 women s pentathlon best performance predcton table Year 3 4 5 6 7 Total score 485. 478.6 4793. 483.8 484.4 485. 4835.7 Year 8 9 3 Total score 4846.4 4857. 4867.8 4878.6 4889.4 49. Model s each test ndcator s as followng Table 3 show. Table 3: GM (, ) model testng table Year Orgnal value Model value Resdual Relatve error Ultmate rate devaton 485 485. 46 478.6-6.6.347 -.56 3 4933 4793. 39.8.83.6 4 4759 483.8-44.8.94 -.389 5 4948 484.4 33.6.7.36 6 473 485. -..38 -.5 7 4944 4835.7 8.3.9.446 8 4867 4846.4.6.4 -.8 9 4784 4857. -73..53 -.96 4937 4867.8 69..4.88 473 4878.6-55.6.39 -.476 53 4889.4 3.6.47.558 3 485 49. -49.. -.357 By Table 3, t can get predcton model relatve error s not above 3%, ultmate devaton s not above.7. Resdual qualfed model Relatve error sequence s: Then t can solve average relatve error s: () Correlaton degree qualfed model Absolute correlaton degree g s orgnal sequence correlaton degree, t solves: (3) Mean square error rato qualfed model S and S are respectvely orgnal sequence square error rato value as: = (,, ) = n k g =.966, =.9 and correspondng grey predcton sequence and resdual sequence (k) C = S S / =.9466 By Table 3 data, t can solve model precse test data as followng Table 4. Table 4: GM (, ) predcton model precse table Precse grade Relatve error Absolute correlaton degree Mean square error rato value Grade Four.9.966.9466 absolute ε varances, t can solve mean By Table 4, t s clear that drectly uses tradtonal GM(, ) grey model to predct world women s pentathlon annual best performance, ts relatve error s.9 that s second grade precse, absolute correlaton degree s.966 that s frst grade precse, mean square error rato s.9466 that s four grade precse. To ensure establshed predcton model precse, t takes each ndcator lowest precse as predcton precse. Therefore, t s clear that GM (, ) grey predcton model predcted precse s grade four, t s dffcult to precsely make effectve predcton on world women s pentathlon annual best performance. 39
Su Jn and Techeng Guo J. Chem. Pharm. Res., 4, 6(6):36-4 3.4 GM (, ) model group applcaton In order to more effectve apply GM(, ) grey model to predct world women s pentathlon annual best performance, t adopts GM(, ) model group to model on ts data, n the hope of more effectve utlzng GM(, ) grey predcton model, more accurate researchng on world women s pentathlon performance development change trend. GM (, ) grey model group s on the bass of GM (, ) grey model, t respectvely carres out dfferent dmensons modelng on orgnal statstcal data. The paper takes year 3 data as base pont; t gradually cuts data from far and near, establshes four dmensons to thrteen dmensons totally ten GM (, ) grey predcton models. By comparng each dmenson relatve error, absolute correlaton degree and mean square error rate, t researches on GM (, ) predcton model s predcton precse on world women s pentathlon annual best performance. It gets precse table as Table 5. Table 5: GM (, ) model group precse test table Dmenson Precse grade Relatve error Absolute correlaton degree Mean square error rato value 4 Grade three.54.946.765 5 Grade three.57.9755.97 6 Grade four.55.78.958 7 Grade three.45.9786.934 8 Grade three.39.9958.854 9 Grade three.64.984.98 Grade three.6.9937.947 Grade three.66.988.953 Grade three.65.998.863 3 Grade three.9.966.9466 By Table 5, t s clear that GM(, ) grey predcton model s predcton modelng precse on world women s pentathlon annual best performance s qute low. In ten models, t has one model precse as grade four and all the rest are grade three. GM (, ) predcton model cannot effectvely carry out predcton modelng on world women s pentathlon annual best performance. 4. Women s pentathlon performance correlaton degree analyss Women s pentathlon s composed of fve events, every event performance wll have certan effects on total performance, and ts effects are both bg and small, every sport event dfferent development trend also surely affects pentathlon total performance development trend. Grey relatonal analyss s used to analyze total performance and each event sport performance dynamc relatons wth tme changng and ther features, whch provdes references for women s pentathlon total performance predcton. [] Record world women s pentathlon annual best performance total score and each event performance sequence as: = (, (), (3),, (3)) =,,, 5 [] Take world women s pentathlon annual best performance total score sequence as reference sequence, make mean transformaton on each sequence, carry out standard processng wth t, and solves ts mean sequence. [3] Calculate ts correlaton coeffcent: Among them, ρ s resoluton coeffcent, the paper takes t as.5. [4] Calculate ts correlaton degree: r = mn mn ( k) + ρ man man ( k) k k ξ = + ρ man man n n = ξ Input Table statstcal data nto above steps, t can solve each event performance and total performance grey correlaton degree values as Table 6. Table 6: Each event performance total performance grey correlaton degree value Hurdle Hgh jump Shot ong jump 8m Correlaton degree.856.84.674.8738.775 By Table 6, t s clear that t s long jump performance that has largest nfluence on women s pentathlon total performance, ts grey correlaton degree s.8738, the secondary s hurdle, hgh jump, 8m and shot ther grey k 4
Su Jn and Techeng Guo J. Chem. Pharm. Res., 4, 6(6):36-4 correlaton degree are respectvely.856,.84,.775,.674.grey correlaton calculaton can defne each sport performance mpact on women s all-around total performance. Though take dfferent resoluton coeffcent wll get dfferent correlaton degrees, ther sze order wll not change, correlaton sequence s essence of correlaton analyss. Though each sport performance and total performance correlaton degree are both bg and small, each correlaton degree has no bg dfferences, when predct on women s pentathlon performance, each sport performance s mportant to total performance predcton. 5. Women s pentathlon performance GM(, 6)model By above analyss, t s clear that GM (, ) predcton model effects n world women s pentathlon annual best performance predctng applcaton s not deal, t s dffcult to make effectve predcton on ts performance change development trend. By grey correlaton analyss, t s clear that women s pentathlon performance s closely connected wth ts each event performance that belongs to multple factors problems. In order to more precse predct ts performance change trend, the paper establshes multple varables grey predcton model that takes women s pentathlon performance total performance and other fve events performance as varables, establshes GM(, 6)grey predcton model for system, so that more precse and effectve research on women s pentathlon performance development change trend. To data sequence,( =,,,5), t carres out AGO processng, weakens ts randomness and gets world women s pentathlon annual best sport performance and each event performance accumulatng sequence,( =,,,5). () To adjonng mean, t generates sequence z = ( z (), z (3),, (3)), then t has: z z () z (3) B = M z (3) M () (3) (3) O 5 () 5 (3), Y M 5 (3) = () (3) M (3) (3) Set u ] T = [ a, b, b,, b5, then GM(, 6) model wnterzaton equaton s: + az = b + b3 3 + + b5 5 It can solve by formula: a b b u = = b3 b 4 b5 T ( B B).9 333. T 6.5 B Y = 6.3 9. 7.6 Table 7: GM (, 6) model error value Year Orgnal value Model value Resdual Relatve error 485 485. 46 3995.5 66.5.355 3 4933 5456.6-53.6.6 4 4759 4975.3-6.3.455 5 4948 53. -55.. 6 473 4675.6 37.4.79 7 4944 496.3-7.3.35 8 4867 4868. -.. 9 4784 4796. -.9.5 4937 4897.8 39..79 473 4698.3 4..5 53 557. -44..88 3 485 44844.5 6.5.3 4
Su Jn and Techeng Guo J. Chem. Pharm. Res., 4, 6(6):36-4 By wnterzaton equaton, t solves year ~3 world women s pentathlon performance predcted value, and makes comparatve analyss and test on solved predcted value and orgnal value, t gets ts model error values table as followng Table 7. () By Table 7, t s clear that establshed GM(, 6) grey predcton model by predctng and analyzng year ~ 3world women s pentathlon annual hghest performance, ts mamum relatve error s 3.55%, only year and such two years relatve errors surpass %, other years relatve errors are relatve deal. In order to more precse test model accuracy, make use of solved predcton value to precede wth grey predcton model each test ndcator calculaton; t solves each test ndcator as Table 8: Table 8: GM (, 6) predcton model precse table Precse grade Relatve error Absolute correlaton degree Mean square error rato value Grade four.58.58.759 By Table 8, t s clear that model relatve error s.46 that precse grade s grade two, absolute correlaton degree s.58 that precse grade s grade four, mean square error rato s.759 that precse grade s grade four. Model precse s lower, t s dffcult to make effectve predcton, n order to establsh precse predcton model, the paper apples GM (, 6) grey model group to screen the model, each dmenson model each test ndcator and model precse grade s as followng Table 9. Table 9: GM (, 6) model group precse test table Dmenson Precse grade Relatve error Absolute correlaton degree Mean square error rato value 4 Grade four.76.5.79 5 Grade four.56.58.75 6 Grade four.48.553.4796 7 Grade four.43.7838.785 8 Grade three.353.996.58 9 Grade two.39.993.487 Grade four.96.9577.84 Grade three.7.93.5393 Grade four.7.996.7 3 Grade four.58.58.759 By Table 9, t s clear that world women s pentathlon annual best performance grey predcton model only the nne dmensons precse arrves at grade two, then the paper fnally defnes to use ts predcton model to carry out GM (, 6) model modelng on data durng year 5 to 3. CONCUSION The paper analyzes compettve sports performance predcton, dscusses grey predcton model s feasblty n compettve sports performance predcton modelng, t provdes gudance for appled mathematcs n compettve sports performance predcton and decson makng as well as other aspects, drves appled mathematcs applcaton n compettve sports decson makng, and lets compettve sports decson makng more scentfc; use statstcal data modelng analyss, and apply grey model group model to model for compettve sports performance predcton, use grey model group to screen proper data samples dmensons to model, t more fleble apples grey predcton model, and mproves grey predcton precse; researches on compettve sports comprehensve sports event. To multple factor affected sports performances, t proposed to make grey relaton analyss of them, make GM (, N) grey predcton model, fully utlzes known data and condtons, and establshes precse predcton model. REFERENCES [] ZHU Hong-bng, IU Jan-tong, WANG Gang, etc,. Journal of Captal College of Physcal Educaton, 3, 5:8-. [] WANG We. Journal of Nanjng Insttute of Physcal Educaton, 4, 8(6):85-87. [3] ZHAO Yun hong, ZHOU Yao. Chna Sport Scence and Technology,, 38():39-4. [4] CHEN ang, SAI Qng-bn. Journal of Captal College of Physcal Educaton, 6, 8(5):85-88. [5] SONG A-ng, CHEN Ka. Journal of Captal College of Physcal Educaton, 3, 5(4):68-69, 6. [6] CHEN ang, TIAN De-bao. Journal of Captal College of Physcal Educaton, 6, 8(6):7-8. [7] Tong png, Yuan Janguo. Journal of Shangha Physcal Educaton Insttute,, 5():44-47. [8] IU Ja-jn. Journal of Guangzhou Physcal Educaton Insttute, 6, 6():54-56. [9] IU Ja-jn et al. Zhejang Sport Scence, 999, :6-64. 4