GREY FORECASTING AND NEURAL NETWORK MODEL OF SPORT PERFORMANCE

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1 Journal of heoretical and Applied Inforation echnology 3 st March 03 Vol 49 No JAI & LLS All rights reserved ISSN: wwwatitorg E-ISSN: GREY FORECASING AND NEURAL NEWORK MODEL OF SPOR PERFORMANCE Weilong u, Hui Liu, 3 Hai Huang,, 3 Physical Education College of Handan College, Handan , Hebei, China E-ail: xuweilong0804@63co, zhongguowushu008@yahoococn ABSRAC Results are the ost iportant factor in copetitive sports If we can scientifically predict race results, it is bound to becoe a research focus of the sports copetitions In this paper, we use the gray prediction ethod and neural network theory to establish two prediction results odel Nuerical experients show that the odel has high prediction accuracy Keywords: Sport Perforance, Grey Syste, Forecast, Neural Networks INRODUCION How uch of the huan understanding of the real world divides the obective world into three systes: inside the syste is copletely full of white syste; syste of internal inforation to the outside world is ignorant, but only through their contact with the outside world to be observational study black syste; the portion of the inforation within the syste is known, another part of the inforation is unknown, and various factors in the syste with uncertain relationship between gray syste he gray prediction ethod is a ethod to predict the syste contains both the known inforation and contains uncertainties It is widely used to predict the process of randoly ordered gray, so as to find potential law he gray prediction ethod distinguishes trends dissiilarity between syste factors by correlation analysis ethod, and uses generation processing ethod to process raw data and generates strong regularity tie series, and then establishes corresponding differential equation odel, so features aount prediction things for a certain tie in the future or the tie of reaching a characteristic quantity With the rapid developent of high-tech, the overall level of copetitive sports has seen an unprecedented iproveent But understanding the laws affecting the sports perforance of people is ust like our understanding of huan beings both failiar and unfailiar Obviously, fro the existing knowledge of the huan, Our awareness of sports law is liited However, factors that affect sports perforance is varied We already know soe, and soe are still cognitive So, fro the view of syste theory, we can consider the syste of influencing sports perforance as grey syste herefore, the gray prediction ethod is very useful Neural network is inspired by the huan brain and constitutes a network of inforation processing systes It has highly nonlinear dynaic processing power and does not need to know the distribution of the data in the for and variable relationship When the input and output relationship of soe coplex syste is coplex and difficult to use expression of the general forula, the neural network is very easy to ipleent highly nonlinear relationship he neural network has achieved very good results in the field of applied research, for exaple pattern recognition, autoatic control In recent years, the neural network odel is successfully applied to the econoy forecast research So, we use neural networks to study athletic perforance prediction GREY FORECASING MODEL ypically, in the field of sports, orderly recording the best result of continuous sports for several years, you can get a set of tie series on the athletic perforance In this paper, we forecast the results trend of the five-year results of feale track and field one hundred eters race, and the perforance sees able able : the perforance Year Result

2 Journal of heoretical and Applied Inforation echnology 3 st March 03 Vol 49 No JAI & LLS All rights reserved ISSN: wwwatitorg E-ISSN: For the weakening of the randoness of the original tie-series, first, the original tie series data is processed by the data processing ethod of accuulated or accuulated save, the new tie series is called generate coluns he calculation ethod of one tie cuulative is ( ( k ) + ( k i Where {, (), ( n)} is generate coluns and { is original tie series, (), ( n)} he calculation ethod of tie cuulative is ( ) k i ( ) ( For non-negative data, the accuulating ties are ore, so the randoness of generated colun is weaker When the accuulate ties are enough, the tie series is changed fro rando sequence into non-rando sequence At this point, we generally use available exponential curve to approxiate he calculation ethod of repeated reduce is ( ( ( k ) It subtracts both before and after data of original tie series, so we get the generate coluns Let, (), (3), (4), (5) be original tie series, then we obtain the accuulated generating sequence {69,75,3433,4553,567} Establish Model Assue tie series has n observations, {, (), ( n)}, is the new sequence after accuulated generating, {, (), ( n)} hen the differential equation is d dt + α µ Where α developed grey is nuber and µ is endogenous control grey nuber α Let αˆ be estiated paraeters vector, we µ use the ethod of least squares to get where B ˆ α ( B B) B Yn [ + ()] [ () + (3)] [ ( n ) + ( n) ] Y n () (3) ( n) We solve the differential equation and then get the prediction odel:, k 0,, n Y n µ α k ˆ (0 ( k + ) ) e + α In the exaple, [ + ()] [ () + (3)] [ (3) + (4)] [ (4) + (5)] µ α B, , then 3 ˆ 530 B B 3685 ( B B) Fro α ( B B) B Yn B Y n 448, we get ˆα 58 So, we have α , µ 58 hen, 06

3 Journal of heoretical and Applied Inforation echnology 3 st March 03 Vol 49 No JAI & LLS All rights reserved ISSN: wwwatitorg E-ISSN: d dt µ 79, α µ α We get the prediction odel 00075k ( k + ) 6376e Model Check Grey prediction test usually contains residual test, association test and posterior test Residual est ˆ We calculate by prediction odel, and ˆ ˆ repeated reduce to generate, and then calculate absolute error sequence and relative error sequence of original sequence and ˆ, ie ˆ Φ, i,, n In the exaple, we put k 0,,,3, 4 into the prediction odel and then we get ˆ ˆ {79,98,349,454,5667} {79,9,,3,4} {0,04,037,00,0} Φ {0,%,3%,00%,097%} he relative error is less than 3%, so, accuracy of the odel is higher Association est First, we calculate correlation coefficient in{ } + ρ ax{ } η + ρ ax{ } where ρ is resolution and generally take ρ 0 5 In this exaple, in{ ( i )} in{0,04,037,000,0} 0 ax{ } in{0,04,037,000,0} 037 So, the correlation coefficient is η ( {,044,033,099,064} Second, we calculate associate degree Let arithetic ean be γ n n k η(, so γ is the associate degree of ( and ( n ˆ γ η( ( ) n 5 k 068 So, the odel satisfies ρ 0 5 and γ > 0 6 Posterior est First, we calculate he standard deviation of original sequence: [ S n Second, we calculate absolute error sequence standard deviation: S [ n hird, we calculate variance ratio: S 06 C 0463 S 035 Finally, we calculate sall error probability: { 06743S } P p < Let e i, S S, so { e } P p i <, S 0 ] ] 07

4 Journal of heoretical and Applied Inforation echnology 3 st March 03 Vol 49 No JAI & LLS All rights reserved ISSN: wwwatitorg E-ISSN: and we have S 6743S 0 9, and 0 0 e {045,0096,08,044,0037} i So, we have that e i < S0 qualified Fro the prediction forula ( k + ) 6376e ( k + ) hen, the odel is 00075k ( ( e ), we take k 5, so we get the result of 0 is second 3 NEURAL NEWORK PREDICION MODEL 3 Introduction of Neural Network he neural network is able to siulate the huan brain s receive doain of partial adustent and overwrite each, and does not have local iniu probles, and have learning fast and high fitting precision It can change the weight value of the indicators, and to ake it ore consistent with the actual situation x x x n i input layer hidden layer Figure : structure h h h RBF neural network is three forward networks he first layer is the input layer and is coposed of a signal source node; the second layer is hidden layer: the nuber of hidden units is deterined by the needs of proble, and transforation function of hidden unit is RBF, which is nonlinear function; the third layer is output layer, it akes the role of the response to the input pattern Since the apping of input to output is nonlinear and the apping of hidden layer space to output space is linear, so we can greatly accelerate the learning speed and avoid local inia probles he structure of RBF neural network is the following RBF neural network can approxiate any arbitrary precision continuous function, particularly w w w y output layer suited to solve classification probles, approxiation is shown below Let Figure : approxiation ( x, x, x n ( h, h, h ) be the aount of input network, H ) be radial basis vector, where h Gaussian basis is functions ( c, c, n C, c ) is center vector of network -th node, B ( b, b, b ) is wide base vector, where b is base width paraeter he weight vector is W ( w, w, w ) So, the output of network at tie k is y ( wh w h + w h + + w h Assue y ( is ideal output, we get the perforance index function is 3 Model Establish E( ( y( y( ) Assue ( x, x,, x ) is output of network, so we have input, n output and evaluation rank In the network, connection weights between the second and third tiers w i is the indicator weight value of odel First layer: input layer Fro figure, we have that the input layer has neurons he input and output is O i x i obect u ( y( RBF I i x i, i,,,,, n Second layer: hidden layer RBF neural network has n evaluation ranks Fro figure, we know that hidden layer has n neurons In this paper, we divide the evaluation rank into four kinds: A } { excellent, { i + y ( 08

5 Journal of heoretical and Applied Inforation echnology 3 st March 03 Vol 49 No JAI & LLS All rights reserved ISSN: wwwatitorg E-ISSN: good, qualified, unqualified}, so we take n 4, that is four fuzzy subset, and then we need four paraeters a, a, a3, a4 We use trigonoetric function to represent the ebership function µ (x), see Figure 3 µ(x) A A A3 A4 d p and increasing the calculation accuracy he gradient descent ethod is following Let w ( w ( k ) + η h ( y( y ( ) + α( w ( k ) w ( k )) and b ( y( y ( ) w h C 3 b, so b ( b ( k ) + η b + α( b ( k ) b ( k )) Let c ( y( y ( ) w i x c i b, so 0 a a a 3 a 4 c ( c ( k ) + η c + α( c ( k ) c ( k )) i i i i i Figure 3: ebership function When the output is I i O i, i,,,,, n, the hidden layer will output all levels i of ebership value O A ( x ) hird layer: output layer Output layer ainly copletes coprehensive evaluation of the input indicators, and then we get the evaluation rank and evaluation vector: i 3 i O i I 3 3 Oi w Ii where i,, and,, n However, RBF neural network has shortcoings, for exaple, slow convergence, and local iniu of the energy value and so on In order to solving this proble, we use odified network to perfect network connection weight In the paper, we use the reverse of network to calculate the output value, and then get the error of output value and actual value, and then use the forward of network to test the obtained value and odify the connection weight value, so to achieve the purpose of reducing network error Let d p t p y p be output error, so the error function is ep ( t p y p ) hen, we use the gradient descent ethod of RBF neural network learning algorith to odify positive weight vector W, so to achieve the purpose of reducing where η is learning rate, α is oentu factor Finally, using Jacobean array, we get the result y( y ( c x w h u( u( b Assue W is the adusted value of W, using gradient descent ethod, we get the iterative algorith forula W e η + α W W ( n) p ( n) We use the forula of W to iterate When the error is satisfied, we end the network training 33 Application In this paper, we use the ale one hundred contest of Olypic gae to train network he data of ale one hundred contests see able able : actual and predicted value nuber first second predicted relative first error Fro able, we get that the calculated value obtained by neural network prediction odel and the actual value have higher fitting accuracy 09

6 Journal of heoretical and Applied Inforation echnology 3 st March 03 Vol 49 No JAI & LLS All rights reserved ISSN: wwwatitorg E-ISSN: CONCLUSION In this paper, we use the gray prediction ethod and neural network theory to establish two prediction results odel Since the ipact of copetitive sports results can be attributed to the gray syste, the gray prediction ethod can be used to forecast the future of sport achieveents We need to note that: calculation should be retained long enough significant digits and reduce calculation error Copetitive sport is a ulti-factor, ulti-level, ulti-target linkages and utual restraint syste Its prediction of the results is very difficult raditional forecasting ethods are based on the discrete recursive odel and have obvious liitation However, neural network identification is not subect to the liitations of the non-linear odel he neural network forecasting odel coprehensively observes, analyzes and forecasts the developent and changes in the syste, so that the accuracy of the prediction is greatly iproved REFERENCES: [] ZP Wang, and G Sun, Deonstration on the Athletic Achieveents Forecasting Based on Back Propagation Neural Network, Journal of Naning Institute of Physical Education, Vol 0, No 4, 006, pp 09- [] C Zhuang, and ZP Wang, Coparing of Gray and Neural Network Model of Forecasting in Athletic Achieveents, Journal of Naning Institute of Physical Education(Social Science), Vol 0, No 6, 006, pp [3] ZM Zhang, Prediction of the result of en s 00 run in the Olypic Gaes based on the grey GM(,) odel, Journal of Physical Education, Vol 8, No 4, 0, pp -4 [4] GF Wang, W Zhao, J Liu, SH Feng, EJ ue, L Chen and B Wang, Olypic Perforance Prediction based on GA and Regression Analysis, CHINA SPOR SCIENCE AND ECH NOLOGY, Vol 47, No, 0, pp 4-8 [5] JJ Liu, Research on the New Methods of Gray Envelope in Sports Field, Journal of Guangzhou Sport University, Vol 6, No, 006, pp [6] Aiin Yang, Chunfeng Liu, Jincai Chang and Li Feng, OPSIS-Based Nuerical Coputation Methodology for Intuitionistic Fuzzy Multiple Attribute Decision Making, Inforation-an International Interdisciplinary Journal, Vol 4,No0,0, pp [7] Aiin Yang, Chunfeng Liu, Jincai Chang, iaoqiang Guo, Research on Parallel LU Decoposition Method and It s Applica tion in Circle ransportation,journal of Software, Vol 5, No,00, pp50-55 [8] Aiin Yang, Guanghua Zhao, Yuhuan Cui, Jingguo Qu, he Iproveent of Parallel Predict-Correct Gres() Algorith and its Application for hin Plate Structures, Journal of Coputers, Vol5, No0,00, pp64-69 [9] GF Wang, EJ ue and F ang, Application of Unsupervised Method Based on Evolutionary Neural Network in Evaluation of the Iportance of Indexes in Sports Measureent, China Sport Science, Vol 3, No, 0, pp [0] Q Huang and Y Shi, Research on the Application of Data Mining in the Guidance of Sports raining, Journal of Guangzhou Sport University, Vol 9, No 6, 009, pp 06-0 [] S Ji and Li, rack and field copetition forecast based on neural network odel, Sport, No 46, 0, pp - [] C Wu and SP Chen, Application of Neural Network Cobined Model in Liu iang s Contest Results Predicting, Journal of Guangzhou Maritie Colleget, Vol 9, No, 0, pp [3] JJ Liu, GY Sun and M Dai, Application of Grey Systeic heory and Method in Sports Scientific Research, China Sport Science and echnology, Vol 4, No 3, 005, pp [4] JJ Liu, Analysis on Grey Prediction of Sports Coplex Syste, China Sport Science and echnology, Vol 43, No, 007, pp 3-5 [5] ZQ Chen, DF Yang and MJ Huang, he Research on Model of Gray Syste Regress Prediction of Multivariate Cluster on Physical Education, China Sport Science and echnology, Vol 37, No, 00, pp 3-6 [6] CG Jiang, On PE eaching Evaluation in Vocational Schools Based on Multi-level Gray Evaluation Model, Sports Foru, Vol, No 5, 00, pp 4-6 [7] JL Liu and Y ue, Research on the Influence Factors of Sporting Goods Exportation Based on Gray Relational Analysis, Journal of Guangzhou Sport University, Vol 3, No 6, 0, pp

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