王伟等：基于CART决策树的冲压成形仿真数据挖掘 ·1379· 表7油箱壳拉深成形工艺规则 Table 7 Process rules for tank cover drawing CART决策树路径 CART工艺规则 Gini值 1.node0→node1→node#2→node#3 Iff≤215.6andu≤0.1025 Then class=general 0.00 2.node0→node1→node#2-→mode#4 Iff215.6 and 0.1025 Then class general 0.25 3.node0→node1→nodc#5→nodc6 lf215.6<f≤254.8andh≤4.5 Then class=general 0.43 4.node0→node+node#5→node#7→node8 If 215.6<f5254.8 and h>4.5 and r8.5 Then class good 0.00 5.node0→node#→node#5→node#7→node9 If 215.6<f254.8 and h x4.5 and >8.5 Then class good 0.32 6.node0→mode10→mode#11 If fx254.8 and r8.5 Then class good 0.46 7.node0一→mode#12→node#13 If f>254.8 and r>8.5 and h5.5 Then class bad 0.14 8.node0→node#12→node#14 If f>254.8 and r>8.5 and h>5.5 Then class bad 0.00 Gini值为0、成形质量分类为good,表明规则4获得 cial Intelligence.Beijing:Metallurgical Industry Press,2000 较佳的成形质量的概率为100%，该规则对应的实 (王国栋，刘相华.金属轧制过程人工智能优化.北京：冶金 工业出版社.2000) 际生产工艺规则为： [6]Hu J,Peng Y H,Li D Y,et al.Robust optimization based on f=(225.4kN,245kN), knowledge discovery from metal forming simulation.J Mater h =(5mm,6 mm,7 mm),r=7 mm Process Technol,2007,187-188:698 [7]Salehi MS,Serajzadeh S.A model to predict recrystallization ki- 4结论 netics in hot strip rolling using combined artificial neural network and finite elements.J Mater Eng Perform,2009,18(9):1209 (1)基尼指数是概率论中描述集合不确定性的 [8]Zheng G J,Zhang J W,Hu P,et al.Optimization of hot forming 指标，CART决策树方法以该指标最小化作为决策 process using data mining techniques and finite element method. Int J Automotire Technol,2015,16(2):329 树递归构建过程中最优特征和最优切分点选择的依 [9]Li Y,Wang J,Zhang Y J.Quality analysis method for hot strip 据，计算速度快、算法稳定；CART决策树方法不需 based on data mining.Chin J Eng,2015,37(Suppl 1):56 要建立复杂非线性模型，通过特征切分得到的决策 (李扬，王京，张勇军.基于数据挖掘的热轧带钢质量分析方 法.工程科学学报，2015,37（增刊1）：56) 树图就可以直观提取知识规则. [10]Wang Y L,Wang H C.Li Z G.Study on knowledge discovery (2)采用Python平台，结合主成分分析法、基于 based on results of sheet metal forming simulation.China Mech 性能度量的模型交叉验证方法，给出了基于CART Eng,2006,17(Supp1):257 决策树理论的知识发现技术路径.油箱壳知识发现 (王义林，王华昌，李志刚.基于板料成形数值模拟的知识 发现方法的研究.中国机械工程，2006,17（增刊1）：257) 实例表明，基于CART决策树理论的知识发现技术 [11]Wang Y C,Yin JL,Li D Y,et al.Knowledge discovery based 是解决数值模拟结果潜在知识挖掘困难的可行 on decision trees C4.5 for stamping process.Mech Sci Technol, 途径 2004,23(12):1506 (王迎春，尹纪龙，李大永，等.基于决策树算法C4.5的冲 参考文献 压工艺知识发现.机械科学与技术，2004,23(12)：1506) [12]Li D Y,Peng Y H,Yin J L.et al.Principal component and [1]Fang G.Zeng P.Finite element simulation for blanking process of fuzzy C-means clustering analysis of stamping simulation results. sheet metal.Acta Metall Sinica,2001,37(6):653 J Plast Eng,2007,14(3):40 (方刚，曾攀.金属板料冲裁过程的有限元模拟.金属学报， (李大永，彭颖红，尹纪龙，等.冲压成形仿真数据的主成分 2001,37(6):653) 与模糊聚类分析.塑性工程学报，2007,14(3)：40) [2]Li J Y,Fu J,Peng B Y,et al.Design and optimization of the [13]Breiman L,Friedman J,Olshen R,et al.Classification and Re- equivalent draw bead based on numerical simulation.Plast Eng, gression Trees.New York:Routledge,1984 2007,14(5):14 [14]Zhou Z H.Machine Learning.Beijing:Tsinghua University (李金燕，傅建，彭必友，等.基于数值模拟的等效拉延筋设 Press,2016 计与优化.塑性工程学报，2007,14(5)：14) (周志华.机器学习.北京：清华大学出版社，2016) [3]Gou Y F,Wang C.Zhang X W.Structure design and application [15]Rutkowski L,Jaworski M,Pietruczuk L,et al.The CART deci- for a new drawing die based on Dynaform.Forging Stamping Tech- sion tree for mining data streams.Inf Sci,2014,266:1 nod,2016,41(12):107 [16]Su C J,Yu T.Sheet Metal Forming CAE Analysis and Applica- (猴彦甫，王冲，张学文.基于Dynaform的一种新型拉延模结 tion:Dynaform Engineering Application.Beijing:National De 构设计与应用.锻压技术，2016,41(12)：107) fense Industry Press,2011 [4]Fayyad U M,Piatetasky-Shapiro G,Smyth P.From Data Mining (苏春建，于涛.金属板材成形CAE分析及应用：Dynaform to Knowledge Discovery:An Overview.Adrances in Knowledge Dis- 工程应用.北京：国防工业出版社，2011) covery and Data Mining.Menlo Park:American Association for [17]Nelli F.Python Data Analytics:Data Analysis and Science Using Artificial Intelligence,1996 Pandas,Matplotlib,and the Python Programming Language. [5]Wang G D,Liu X H.Metal Rolling Process Optimization of Artifi- Berkeley:APress,2015王 伟等: 基于 CART 决策树的冲压成形仿真数据挖掘 表 7 油箱壳拉深成形工艺规则 Table 7 Process rules for tank cover drawing CART 决策树路径 CART 工艺规则 Gini 值 1郾 node#0寅node#1 寅node#2寅node#3 If f臆215郾 6 and 滋臆0郾 1025 Then class = general 0郾 00 2郾 node#0寅node#1寅node#2寅node#4 If f臆215郾 6 and 滋 > 0郾 1025 Then class = general 0郾 25 3郾 node#0寅node#1寅node#5寅node#6 If 215郾 6 < f臆254郾 8 and h臆4郾 5 Then class = general 0郾 43 4郾 node#0寅node#1寅node#5寅node#7寅node#8 If 215郾 6 < f臆254郾 8 and h > 4郾 5 and r臆8郾 5 Then class = good 0郾 00 5郾 node#0寅node#1寅node#5寅node#7寅node#9 If 215郾 6 < f臆254郾 8 and h > 4郾 5 and r > 8郾 5 Then class = good 0郾 32 6郾 node#0寅node#10寅node#11 If f > 254郾 8 and r臆8郾 5 Then class = good 0郾 46 7郾 node#0寅node#12寅node#13 If f > 254郾 8 and r > 8郾 5 and h臆5郾 5 Then class = bad 0郾 14 8郾 node#0寅node#12寅node#14 If f > 254郾 8 and r > 8郾 5 and h > 5郾 5 Then class = bad 0郾 00 Gini 值为 0、成形质量分类为 good,表明规则 4 获得 较佳的成形质量的概率为 100% ,该规则对应的实 际生产工艺规则为: f = (225郾 4 kN,245 kN), h = (5 mm,6 mm,7 mm),r = 7 mm 4 结论 (1)基尼指数是概率论中描述集合不确定性的 指标,CART 决策树方法以该指标最小化作为决策 树递归构建过程中最优特征和最优切分点选择的依 据,计算速度快、算法稳定;CART 决策树方法不需 要建立复杂非线性模型,通过特征切分得到的决策 树图就可以直观提取知识规则. (2)采用 Python 平台,结合主成分分析法、基于 性能度量的模型交叉验证方法,给出了基于 CART 决策树理论的知识发现技术路径. 油箱壳知识发现 实例表明,基于 CART 决策树理论的知识发现技术 是解决数值模拟结果潜在知识挖掘困难的可行 途径. 参 考 文 献 [1] Fang G, Zeng P. Finite element simulation for blanking process of sheet metal. Acta Metall Sinica, 2001, 37(6): 653 (方刚,曾攀. 金属板料冲裁过程的有限元模拟. 金属学报, 2001, 37(6): 653) [2] Li J Y, Fu J, Peng B Y, et al. Design and optimization of the equivalent draw bead based on numerical simulation. J Plast Eng, 2007, 14(5): 14 (李金燕, 傅建, 彭必友, 等. 基于数值模拟的等效拉延筋设 计与优化. 塑性工程学报, 2007, 14(5): 14) [3] Gou Y F, Wang C, Zhang X W. Structure design and application for a new drawing die based on Dynaform. Forging Stamping Tech鄄 nol, 2016, 41(12): 107 (缑彦甫, 王冲, 张学文. 基于 Dynaform 的一种新型拉延模结 构设计与应用. 锻压技术, 2016, 41(12): 107 ) [4] Fayyad U M, Piatetasky鄄Shapiro G, Smyth P. From Data Mining to Knowledge Discovery: An Overview. Advances in Knowledge Dis鄄 covery and Data Mining. Menlo Park:American Association for Artificial Intelligence, 1996 [5] Wang G D, Liu X H. Metal Rolling Process Optimization of Artifi鄄 cial Intelligence. Beijing: Metallurgical Industry Press, 2000 (王国栋, 刘相华. 金属轧制过程人工智能优化. 北京: 冶金 工业出版社,2000) [6] Hu J, Peng Y H, Li D Y, et al. Robust optimization based on knowledge discovery from metal forming simulation. J Mater Process Technol, 2007, 187鄄鄄188: 698 [7] Salehi M S, Serajzadeh S. A model to predict recrystallization ki鄄 netics in hot strip rolling using combined artificial neural network and finite elements. J Mater Eng Perform, 2009, 18(9): 1209 [8] Zheng G J, Zhang J W, Hu P, et al. Optimization of hot forming process using data mining techniques and finite element method. Int J Automotive Technol, 2015, 16(2): 329 [9] Li Y, Wang J, Zhang Y J. Quality analysis method for hot strip based on data mining. Chin J Eng, 2015, 37(Suppl 1): 56 (李扬, 王京, 张勇军. 基于数据挖掘的热轧带钢质量分析方 法. 工程科学学报, 2015, 37(增刊 1): 56) [10] Wang Y L, Wang H C, Li Z G. Study on knowledge discovery based on results of sheet metal forming simulation. China Mech Eng, 2006, 17(Supp l): 257 (王义林, 王华昌, 李志刚. 基于板料成形数值模拟的知识 发现方法的研究. 中国机械工程, 2006, 17(增刊 1): 257) [11] Wang Y C, Yin J L, Li D Y, et al. Knowledge discovery based on decision trees C4. 5 for stamping process. Mech Sci Technol, 2004, 23(12): 1506 (王迎春, 尹纪龙, 李大永, 等. 基于决策树算法 C4. 5 的冲 压工艺知识发现. 机械科学与技术, 2004, 23(12): 1506) [12] Li D Y, Peng Y H, Yin J L, et al. Principal component and fuzzy C鄄means clustering analysis of stamping simulation results. J Plast Eng, 2007, 14(3): 40 (李大永, 彭颖红, 尹纪龙, 等. 冲压成形仿真数据的主成分 与模糊聚类分析. 塑性工程学报, 2007, 14(3): 40) [13] Breiman L, Friedman J, Olshen R, et al. Classification and Re鄄 gression Trees. New York: Routledge , 1984 [14] Zhou Z H. Machine Learning. Beijing: Tsinghua University Press, 2016 (周志华. 机器学习. 北京: 清华大学出版社, 2016) [15] Rutkowski L, Jaworski M, Pietruczuk L, et al. The CART deci鄄 sion tree for mining data streams. Inf Sci, 2014, 266: 1 [16] Su C J, Yu T. Sheet Metal Forming CAE Analysis and Applica鄄 tion: Dynaform Engineering Application. Beijing: National De鄄 fense Industry Press, 2011 (苏春建, 于涛. 金属板材成形 CAE 分析及应用:Dynaform 工程应用. 北京: 国防工业出版社, 2011) [17] Nelli F. Python Data Analytics: Data Analysis and Science Using Pandas, Matplotlib, and the Python Programming Language. Berkeley: APress, 2015 ·1379·