類神經網路與統計分析在撞球9號球開球上之應用

The Application of Neural Network and Statistic Analysis for 9-Ball Break in Billiard

本研究主要目的在探討撞球9號球開球中不同母球位置、母球速度及撞擊角度對進球數的影響，並嘗試以倒傳遞類神經網路結合最佳化演算法來預測最佳進球數下其開球變項為何。受試者為16位優秀9號球撞球選手，實驗設計為將球桌右半邊開球線，並從顆星邊至中央等分為7個母球置球點，每個選手分別在上述7個位置及平時比賽位置各開三次球，開球時要求以中桿方式出桿。過程以兩台高速攝影機(120Hz)同步擷取影片，並以Kwon 3D動作分析軟體來分析運動學參數。統計主要以卡方考驗來分析，並以SPSS 17.0版軟體來執行，顯著水準設為α=.05。類神經網路部分則採用2個隱藏層結構，以自行撰寫之程式配合Matlab 7.9版軟體來執行。研究結果如下：一、1號位置進球率顯著地大於3號、4號、5號、6號及7號位置之進球率；整體而言越靠近顆星位置其進球率也越高。二、在1號、2號、3號及4號位置開球，其各洞進球次數之卡方值有達顯著差異；結果顯示在上述這四個位置開球，子球有偏向進某些洞口的趨勢。三、類神經網路配合最佳化在1號位置之分析可發現，母球速度似乎不是影響進球數的主要因素。而在撞擊角度方面可發現只有在速度介於9.7~10.5 公尺秒s時，撞擊角度偏右顆星方向會有較佳進球數；在其餘速度範圍下，整體而言撞擊角度略偏左顆星方向似乎會有較佳的結果。

Purpose: The purpose of this study was to investigate the effect of different positions， velocity and impinging angle of the cue ball on scoring situation in 9-Ball billiard. In addition， the back-propagation neural network with optimization method was used to find the optimal solution in the break. Methods: The subjects were 16 excellent 9-Ball pool players. Experiment was conducted on the right half of the table. The breaking line from the right edge to the central point was equally divided into seven points. Every player broke three times in each of the seven points and usual game breaking point. The subject was requested to break in stop shot way. The procedure was recorded using two synchronized high-speed cameras (120Hz). Kwon 3D motion analysis software was used for data analysis. Chi-Square tests were used for statistical analysis. The significant level was set at α=.05. The structure of neural network used two hidden layers and analyzed by a Matlab program. Results: The scoring rate of the 1st position was significantly greater than that of the 3rd， the 4th， the 5th， the 6th ， and the 7th position. Overall， the position that was more closed to the cushion had higher score. In the 1st， the 2nd， the 3rd， and the 4th position， the differences of scores for each hole were significantly different in chi-square test. These results showed that when break in the above four positions， some holes may have higher scores than the other holes. The results of back-propagation neural network and optimization analysis in the1st position showed that the cue ball velocity did not seem to have a main effect on score. Only between the velocity of 9.7-10.5 m/s， the impinging angle toward right can have better score. In other velocity range， the impinging angle slightly toward left can have better results.