A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results Durig the Aual Traiig Cycle Krzysztof Przedowek 1, Krzysztof Wiktorowicz 2, Tomasz Krzeszowski 2 ad Jausz Iskra 3 1 Faculty of Physical Educatio, Uiversity of Rzeszow, Rzeszow, Polad 2 Faculty of Electrical ad Computer Egieerig, Rzeszow Uiversity of Techology, Rzeszow, Polad 3 Faculty of Physical Educatio ad Physiotherapy, Opole Uiversity of Techology, Opole, Polad Keywords: Abstract: 110m Hurdles, Predictive Models, Fuzzy Systems, R Programmig Laguage. This paper describes a fuzzy-based software tool for predictig results i the 110m hurdles. The predictive models were built o usig 40 aual traiig cycles completed by 18 athletes. These models iclude: ordiary least squares regressio, ridge regressio, LASSO regressio, elastic et regressio ad oliear fuzzy correctio of least squares regressio. I order to compare them, ad choose the best model, leave-oe-out cross-validatio was used. This showed that the fuzzy corrector proposed i this paper has the lowest predictio error. The developed software ca support a coach i plaig a athlete s aual traiig cycle. It allows the athlete s results to be predicted, ad i this way, for the best traiig loads to be selected. The tool is a web-based iteractive applicatio that ca be ru from a computer or a mobile device. The whole system was implemeted usig the R programmig laguage with additioal packages. 1 INTRODUCTION Nowadays a variety of computer tools ad methods play a importat role i sport traiig. Both competitors ad coaches are lookig for ew solutios that ca support the traiig process. Oe aspect of such support ca be the use of regressio models to predict results. Predictio ca be used to calculate performace results (Edelma-Nusser et al., 2002; Maszczyk et al., 2011; Przedowek et al., 2014) or to idetify sportig talet (Papić et al., 2009; Rocziok et al., 2013). For example, i the paper (Edelma- Nusser et al., 2002), the authors use artificial eural etworks to predict swimmers competitive performace. The eural models were cross-validated ad the results show that the modelig was very precise. The paper (Przedowek et al., 2014) describes the use of liear ad oliear multivariable models as tools to predict 400m hurdles results. Aother paper (Haghighat et al., 2013) presets a review of datamiig techiques that are used for predictio i various sportig disciplies. Despite the existece of methods for predictio i sport, there is lack of tools that could be used by a coach durig the traiig process, particularly i the 110m hurdles. Available software such as Kiovea, Physics Toolkit ad SkillSpector ca be used for the biomechaical aalysis of huma motio based o video sequeces (Omorczyk et al., 2014; Sañudo et al., 2014; Gavojdea, 2015). For example, Sañudo et al. (Sañudo et al., 2014) use Kiovea software to determie the mea propulsive velocity ad the maximal velocity durig a bech press. I the paper (Gavojdea, 2015), Kiovea ad Physics Toolkit are used to aalyze the double salto backward tucked. Aother applicatio, amed Lice (Gabi et al., 2012) is used i the desig of observatioal systems, video recordig, the calculatio of data quality ad the presetatio of results. I aother paper (Raders et al., 2010), the authors compare differet multi-camera systems used for football match aalysis. Papic et al. (Papić et al., 2009) developed a fuzzy expert system for scoutig ad evaluatig youg sports talet. A similar system is preseted i (Louzada et al., 2016), where the authors carried out talet idetificatio i soccer usig a web-orieted expert system. I the 110m hurdles, the coach ca use the tool to estimate the parameters of hurdle clearace (Krzeszowski et al., 2016). These parameters are estimated usig the particle swarm optimizatio algorithm ad they are based o aalysis of the images recorded with a 100 Hz camera. From the literature review, it ca be see that there is a eed to develop tools supportig sports traiig. The mai cotributio of this paper is, therefore to 176 Przedowek, K., Wiktorowicz, K., Krzeszowski, T. ad Iskra, J. A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results Durig the Aual Traiig Cycle. DOI: 10.5220/0006043701760181 I Proceedigs of the 4th Iteratioal Cogress o Sport Scieces Research ad Techology Support (icsports 2016), pages 176-181 ISBN: 978-989-758-205-9 Copyright c 2016 by SCITEPRESS Sciece ad Techology Publicatios, Lda. All rights reserved
A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results Durig the Aual Traiig Cycle Table 1: Descriptio of variables used to costruct the models. Variable Descriptio x x mi x max y Predicted 110m hurdles result [s] 14.02 13.26 15.13 x 1 Age [years] 21.9 18.0 28.0 x 2 Body height [cm] 187.3 181.0 195.0 x 3 Body mass [kg] 77.8 71.0 83.0 x 4 Body mass idex 22.1 20.3 23.5 x 5 Curret 110m hurdles result [s] 14.33 13.34 15.40 x 6 Maximal ad techical speed [m] 12513 5800 17970 x 7 Techical ad speed exercises [m] 5925 2470 10200 x 8 Speed ad specific hurdle edurace [m] 11961 3150 20400 x 9 Pace rus [m] 64087 25780 100300 x 10 Aerobic edurace [m] 328631 80600 550000 x 11 Stregth edurace [m] 20638 1850 46595 x 12 Stregth of lower limbs [kg] 291119 96400 658600 x 13 Truk stregth [amout] 38442 5240 145000 x 14 Upper body stregth [kg] 3352 1630 4850 x 15 Explosive stregth of lower limbs [amout] 1244 0 2214 x 16 Explosive stregth of upper limbs [amout] 656 213 1850 x 17 Techical exercises walkig pace [mi] 456 130 1110 x 18 Techical exercises ruig pace [mi] 574 195 1450 x 19 Rus over hurdles [amout] 778 362 1317 x 20 Hurdle rus i varied rhythm [amout] 1077 320 1850 develop a fuzzy-based software tool for results predictio i the 110m hurdles. This tool is created as a web applicatio that ca be ru from a computer or a mobile device. It allows traiig loads to be plaed across the aual traiig cycle so the athlete achieves their expected results. 2 MATERIAL The traiig data cotai 40 records. These records were collected from 18 highly traied athletes (mea result i the 110m hurdles: 14.02 s) aged betwee 18 ad 28. The athletes were members of the Polish Natioal Team. Each record cotais a athlete s parameters ad that athlete s traiig program across the aual traiig cycle. The models for result predictio were build usig 21 variables (Tab. 1). The iput variables x 1 x 5 represet the athlete s parameters, the iput variables x 6 x 20 represet the traiig loads ad the output variable y represets the predicted 110m hurdles result. The traiig loads were classified o the basis of work (Iskra ad Ryguła, 2001), but it should be oted that this classificatio ca be formulated i differet ways. I this paper, the values of these loads are the sum of all the loads of the same type realized durig the aual traiig cycle. The 110m hurdles results were registered before ad after the cycle. 3 PREDICTIVE MODELS 3.1 Problem Formulatio We cosidered the regressio problem with p iputs (predictors) X j ad oe output (respose) Ŷ. The goal was to build the predictive model Ŷ = f (X 1,...,X p ) based o a data set cotaiig observatios i the form of pairs (x i,y i ), where i = 1,...,, p = dim(x). I this paper, we use: liear models i the form of ordiary least squares (OLS), ridge regressio, least absolute shrikage ad selectio operator (LASSO) ad elastic et regressio, oliear model i the form of fuzzy rule base system (FRBS). The detailed descriptio of the liear models ca be foud i (Wiktorowicz et al., 2015). The fuzzy model is described i the ext sectio. Due to the small amout of data ( = 40), the models are compared usig the leave-oe-out crossvalidatio method (Arlot ad Celisse, 2010). The idea of this method is based o the separatio of subsets of learig data from the data set. Each subset is formed by removig oly oe record from the data set, which becomes the testig pair. The predictive quality of a model is expressed by the root of the mea square error of cross-validatio (RMSE CV ) calculated as 177
icsports 2016-4th Iteratioal Cogress o Sport Scieces Research ad Techology Support RMSE CV = 1 i=1 (y i ŷ i ) 2 (1) where ŷ i is the output of a model costructed o the data set after removig the pair (x i,y i ). Moreover, we use the fitess measure expressed by the root mea square error of traiig (RMSE T ) defied as 1 RMSE T = (y i ŷ i ) 2 (2) i=1 where ŷ i is the output of a model costructed o the full data set. 3.2 Fuzzy Regressio Model The fuzzy model proposed i this paper is costructed i the followig steps. 1. Cross-validatio of the OLS model Ŷ = f OLS (X 1,...,X p ) (3) for the data (x i,y i ). The error i the ith step of cross-validatio has the form where ŷ i = f OLS (x i ). d i = y i ŷ i (4) 2. Costructig the fuzzy (oliear) model ˆD = f FUZZY (X 1,...,X p ) (5) for the data (x i,d i ). This model predicts the errors obtaied i Step 1, that is it determies dˆ i = f FUZZY (x i ). The best fuzzy model ca be chose o the basis of cross-validatio coducted, for example, with varyig umbers of fuzzy sets. 3. Cross-validatio of the OLS model with the corrected error i the form d ew i = y i (ŷ i + ˆ d i ) (6) where ŷ i ad ˆ d i are determied by (3) ad (5), respectively. 3.3 Compariso of Models The regressio models were calculated i R (R Core Team, 2016). The lm.ridge fuctio from the "MASS" package (Veables ad Ripley, 2002) was used to calculate the OLS ad the ridge regressios. The LASSO regressio ad the elastic et regressio were obtaied with the eet fuctio icluded i the "elastic et" package (Zou ad Hastie, 2016). The fuzzy regressio model was calculated usig frbs.lear from the "frbs" package (Riza et al., cross-validatio error for ˆd 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 2 3 4 5 6 7 8 9 10 11 12 13 umber of fuzzy sets Figure 1: Cross-validatio error for ˆ d as a fuctio of the umber of fuzzy sets. The smallest error is obtaied for eight sets. 2015). The learig method was the Wag-Medel algorithm (Wag ad Medel, 1992). The parameters of the applied models are show i Table 2. I the fuzzy model, five Gaussia membership fuctios are used, the t-orm is "miimum", the defuzzificatio is the "weighted average method", ad the implicatio is "miimum". The umber of fuzzy sets was determied by calculatig the crossvalidatio errors. These errors are show i Fig. 1 as a fuctio of the umber of fuzzy sets (chagig from 2 to 13). From Fig. 1 it is see that the best model is obtaied for eight sets. The errors RMSE CV ad RMSE T for the models uder cosideratio are preseted i Table 3. It shows that the proposed fuzzy regressio model has the lowest RMSE CV ad the high- Table 2: Parameters of models. Regressio Parameters OLS RIDGE lambda = 16.1 LASSO lambda = 0, s = 0.04 ENET lambda = 0.16, s = 0.56 FUZZY method.type = "WM" um.labels = 8 type.mf = "GAUSSIAN" type.torm = "MIN" type.defuz = "WAM" type.implicatio.fuc = "MIN" Table 3: Summary of errors. Regressio RMSE CV [s] RMSE T [s] OLS 0.3807 0.1302 RIDGE 0.2276 0.1641 LASSO 0.2397 0.1495 ENET 0.1996 0.1562 FUZZY 0.0851 0.2852 178
A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results Durig the Aual Traiig Cycle Figure 2: Screeshot of the applicatio for result predictio i 110m hurdles. est RMSE T. It meas that it ca predict the result better tha the liear models, but it has the worst fit to the data. 4 GRAPHICAL USER INTERFACE The graphical user iterface was implemeted i R laguage usig the libraries shiy, shiythemes ad shiydashboard. This iterface is a web-orieted applicatio ad therefore it requires oly a web browser ad a Iteret coectio to be used. The curret versio of the developed system is available o https://hurdles.shiyapps.io/predictio. The applicatio cosists of two tabs labeled "Result predictio" ad "About". The "Result predictio" tab is used for eterig data ad for result predictio (Fig. 2). The iput variables are grouped ito five boxes: "Athlete s parameters", "Traiig loads edurace", "Traiig loads techique ad rhythm", Traiig loads stregth", ad "Traiig loads speed". The value of each iput ca be modified usig appropriately scaled sliders. For example, the box "Traiig loads edurace" preseted i Fig. 3 has five sliders for chagig the edurace traiig loads. Each slider has its rage determied o the basis of the miimum ad maximum values i the database (Tab. 1). For istace, the slider "Pace rus" rages from 25000m to 101000m with each step equal to oe meter. I the last box, labeled "Predictive model" (Fig. 4), the user ca choose oe of the developed re- 179
icsports 2016-4th Iteratioal Cogress o Sport Scieces Research ad Techology Support with differet traiig coditios. The whole applicatio, composed of the predictive models ad the graphical user iterface, was created i R programmig laguage. The simple iterface allows a athlete s parameters ad traiig loads to be chaged. I this way, the coach ca predict the expected result ad select idividual compoets of the traiig for a give athlete. Further work will focus o the developmet of the proposed applicatio, which ivolves implemetig idividual user accouts, the preparatio of a athlete databases ad creatig reports. I additio, a ew computatioal module will be developed for geeratig traiig loads. Figure 3: Screeshot of the box for eterig edurace traiig loads. ACKNOWLEDGEMENTS This work has bee supported by the Polish Miistry of Sciece ad Higher Educatio withi the research project "Developmet of Academic Sport" i the years 2016-2018, project o. N RSA4 00554. REFERENCES Figure 4: Screeshot of the box for result predictio. gressio models. Two textoutput fields display the curret ad predicted results. Predictio of the result is performed automatically after chagig the value i ay box i this tab. I this way, the user ca modify traiig loads ad observe the chages that occur i the expected result. The traiig program should correspod to the iputs specified i Tab. 1. The "About" tab cotais iformatio about the applicatio ad the authors. 5 CONCLUSIONS I this paper a fuzzy-based software tool for result predictio i the 110m hurdles was preseted. The predictio is based o the followig models: OLS regressio, ridge regressio, LASSO regressio, elastic et regressio ad OLS regressio with fuzzy correctio. The best predictio was obtaied by the proposed fuzzy model, but it has the lowest fitess to the data. The parameters of the models ca be also validated i future usig a idepedet group of athletes Arlot, S. ad Celisse, A. (2010). A survey of crossvalidatio procedures for model selectio. Statistics Surveys, 4:40 79. Edelma-Nusser, J., Hohma, A., ad Heeberg, B. (2002). Modelig ad predictio of competitive performace i swimmig upo eural etworks. Europea Joural of Sport Sciece, 2(2):1 10. Gabi, B., Camerio, O., Aguera, M. T., ad Castañer, M. (2012). Lice: Multiplatform sport aalysis software. Procedia - Social ad Behavioral Scieces, 46:4692 4694. Gavojdea, A.-M. (2015). The impact of usig the specialized software o studig the ladigs at ueve bars. I Coferece proceedigs of elearig ad Software for Educatio (else 2015), umber 3, pages 346 352. Haghighat, M., Rastegari, H., ad Nourafza, N. (2013). A review of data miig techiques for result predictio i sports. Advaces i Computer Sciece: a Iteratioal Joural, 2(5):7 12. Iskra, J. ad Ryguła, I. (2001). The optimizatio of traiig loads i high class hurdlers. Joural of Huma Kietics, 6:59 72. Krzeszowski, T., Przedowek, K., Wiktorowicz, K., ad Iskra, J. (2016). Estimatio of hurdle clearace parameters usig a moocular huma motio trackig method. Computer Methods i Biomechaics ad Biomedical Egieerig, 19(12):1319 1329. PMID: 26838547. 180
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