基于灰色理论和神经网络的弯曲回弹预测研究
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摘要
回弹是弯曲成形中不可避免的物理现象。由于回弹的存在,使得成形后的零件形状和尺寸发生较大的变化,难以达到设计的要求。因此,如何提高弯曲回弹预测的精度,一直是工业界研究的热点和难点。
近年来,代理模型法开始越来越多的应用在冲压成形上,尤其是弯曲回弹的预测。然而,由于在弯曲过程中,回弹受到了诸多因素的影响,不同形状的零件回弹规律差别又很大,目前代理模型法对弯曲回弹预测精度还不理想,回弹问题还有待进一步的研究。另外,在工业实践中,通常采用调整和控制工艺参数来减小回弹量。基于此,本文根据影响弯曲回弹预测精度的几个难点：如何调节工艺参数减小回弹、回弹预测模型的选择以及高精度回弹近似模型的建立,应用组合预测建立代理模型的方法,开展了针对弯曲回弹的预测研究。
首先利用灰色关联分析各工艺参数对回弹的影响程度,以影响较大的工艺参数作为设计变量,结合灰色模型和BP神经网络模型各自的优点,将组合的灰色神经网络代理模型应用于弯曲回弹的预测。该模型针对于弯曲回弹的特点,作了以下改进：采用多因子输入的灰色预测模型为主模型进行粗预测,神经网络为辅助模型修正其误差,并通过寻找最佳权值以优化灰色模型中微分所对应的背景值,来获得预测效果最佳的灰色模型,以提高灰色神经网络代理模型的回弹预测精度。
然后,以NUMISHEET'93的典型弯曲模型——U形件为例,分析影响U形件回弹的工艺参数,获取原始数据；通过灰色关联分析筛选出主要影响因素,分别为压边力、凹模与板料间的摩擦系数以及模具间隙；再以这三个因素为设计变量,利用改进灰色神经网络建立近似模型,对成形后的回弹进行预测验证,预测平均相对误差仅为2.26%；最后,把该预测效果与其他文献所使用的代理模型进行对比。结果表明：应用基于灰色理论和灰色神经网络代理模型组合预测的方法预测U形件弯曲回弹,设计变量少,预测精度高,既提高了回弹预测的精度,又提升了控制工艺参数减小回弹的效率。
Springback is an inevitable physical phenomenon in the process of bending. Because of the presence of the springback, the shape and size of the forming parts are largely changed and it is difficult to meet the design requirements. Therefore, how to improve the prediction accuracy of bending springback has been a hot and difficult point in industry.
Recently, the surrogate model method is increasingly applied in metal forming process, especially for the prediction of the springback. However, due to the springback affected by a great number of factors, different shape parts have different springback laws. And the prediction accuracy of the surrogate model method applied in the bending springback is not ideal. So the springback remains to be further studied. In addition, at industrial practice, controlling process parameters is the general way to reduce the springback. Based on the several difficulties in affecting the accuracy of the bending springback prediction, which included how to adjust the process parameters to reduce the springback, and how to choose the springback prediction method, as well as how to establish high-precision springback approximate model, the method of combination forecasting creating surrogate model is applied to carry out the research in the bending springback prediction.
Firstly, the influence degree of various process parameters in the springback is determined by grey relation analysis method. Then, the greater influence degree of the process parameters are choosen as the design variables.A new grey neural network model, which combines the advantages of grey model and BP neural network model, is developed to predict the bending springback. The model has several improvements in the prediction of bending springback, including employ multi-factor input grey prediction model. Grey model is used to do a coarse prediction task as the main model firstly, and then the auxiliary model-BP neural network is applied to correct errors. At last, a best grey model is obtained through finding the best weight values to optimize the background value corresponding to the differential in the grey model, in order to improve the springback prediction accuracy of grey neural network model.
Secondly, the U-shaped piece, which is the typical bending model form NUMISHEET'93, is taken as an example. And the analysis of the impact parameters of the U-shaped piece in springback process is conducted in order to obtain the original data. Then the main influence factors, which are the blank holder force, the friction coefficient between the die and the sheet metal and the die clearance, are determined by grey relational method. At last, an approximate model of grey neural network is established with these three factors as design variables. Experiments are conducted using the model to predict springback after forming and the result show s that the average relative error is only2.26%. Finally, the prediction effect of this method is compared to the other surrogate models of other literature. The result shows that the surrogate model method based on the combination of grey relation and improved grey neural network model, which has less design variables, not only greatly improves springback prediction accuracy, but also significantly enhances the efficiency of the controlling process parameters to reduce the springback.
近年来,代理模型法开始越来越多的应用在冲压成形上,尤其是弯曲回弹的预测。然而,由于在弯曲过程中,回弹受到了诸多因素的影响,不同形状的零件回弹规律差别又很大,目前代理模型法对弯曲回弹预测精度还不理想,回弹问题还有待进一步的研究。另外,在工业实践中,通常采用调整和控制工艺参数来减小回弹量。基于此,本文根据影响弯曲回弹预测精度的几个难点：如何调节工艺参数减小回弹、回弹预测模型的选择以及高精度回弹近似模型的建立,应用组合预测建立代理模型的方法,开展了针对弯曲回弹的预测研究。
首先利用灰色关联分析各工艺参数对回弹的影响程度,以影响较大的工艺参数作为设计变量,结合灰色模型和BP神经网络模型各自的优点,将组合的灰色神经网络代理模型应用于弯曲回弹的预测。该模型针对于弯曲回弹的特点,作了以下改进：采用多因子输入的灰色预测模型为主模型进行粗预测,神经网络为辅助模型修正其误差,并通过寻找最佳权值以优化灰色模型中微分所对应的背景值,来获得预测效果最佳的灰色模型,以提高灰色神经网络代理模型的回弹预测精度。
然后,以NUMISHEET'93的典型弯曲模型——U形件为例,分析影响U形件回弹的工艺参数,获取原始数据；通过灰色关联分析筛选出主要影响因素,分别为压边力、凹模与板料间的摩擦系数以及模具间隙；再以这三个因素为设计变量,利用改进灰色神经网络建立近似模型,对成形后的回弹进行预测验证,预测平均相对误差仅为2.26%；最后,把该预测效果与其他文献所使用的代理模型进行对比。结果表明：应用基于灰色理论和灰色神经网络代理模型组合预测的方法预测U形件弯曲回弹,设计变量少,预测精度高,既提高了回弹预测的精度,又提升了控制工艺参数减小回弹的效率。
Springback is an inevitable physical phenomenon in the process of bending. Because of the presence of the springback, the shape and size of the forming parts are largely changed and it is difficult to meet the design requirements. Therefore, how to improve the prediction accuracy of bending springback has been a hot and difficult point in industry.
Recently, the surrogate model method is increasingly applied in metal forming process, especially for the prediction of the springback. However, due to the springback affected by a great number of factors, different shape parts have different springback laws. And the prediction accuracy of the surrogate model method applied in the bending springback is not ideal. So the springback remains to be further studied. In addition, at industrial practice, controlling process parameters is the general way to reduce the springback. Based on the several difficulties in affecting the accuracy of the bending springback prediction, which included how to adjust the process parameters to reduce the springback, and how to choose the springback prediction method, as well as how to establish high-precision springback approximate model, the method of combination forecasting creating surrogate model is applied to carry out the research in the bending springback prediction.
Firstly, the influence degree of various process parameters in the springback is determined by grey relation analysis method. Then, the greater influence degree of the process parameters are choosen as the design variables.A new grey neural network model, which combines the advantages of grey model and BP neural network model, is developed to predict the bending springback. The model has several improvements in the prediction of bending springback, including employ multi-factor input grey prediction model. Grey model is used to do a coarse prediction task as the main model firstly, and then the auxiliary model-BP neural network is applied to correct errors. At last, a best grey model is obtained through finding the best weight values to optimize the background value corresponding to the differential in the grey model, in order to improve the springback prediction accuracy of grey neural network model.
Secondly, the U-shaped piece, which is the typical bending model form NUMISHEET'93, is taken as an example. And the analysis of the impact parameters of the U-shaped piece in springback process is conducted in order to obtain the original data. Then the main influence factors, which are the blank holder force, the friction coefficient between the die and the sheet metal and the die clearance, are determined by grey relational method. At last, an approximate model of grey neural network is established with these three factors as design variables. Experiments are conducted using the model to predict springback after forming and the result show s that the average relative error is only2.26%. Finally, the prediction effect of this method is compared to the other surrogate models of other literature. The result shows that the surrogate model method based on the combination of grey relation and improved grey neural network model, which has less design variables, not only greatly improves springback prediction accuracy, but also significantly enhances the efficiency of the controlling process parameters to reduce the springback.
引文
[1]ALY EL-DOMIATY, A.H.SHABAIK. Bending of work-hardening metals under the influence of axial load [J]. Journal of Mechanical Working Technology.1984,10(1):57-66
[2]Gau Jenn-Terng, Kinzel Gary L. A new model for springback prediction in which the Bauschinger effect is considered [J]. International Journal of Mechanical Sciences.2001, 43(8):1813-1832
[3]Farhang Pourboghrat, Michael E. Karabin, Richard C. Becher. Hybrid membrane/shell method for calculating springback of anisotropic sheet metals undergoing axisymmetric loading [J]. International Journal of Plasticity.2000,16(6):677-700
[4]Xue P, Yu TX, Chu E. Theoretical prediction of springback of metal sheets after double-curvature forming operation [J]. Intenational Journal of Materials Processing Technology,1999,89-90:65-71
[5]Xue P, Yu TX, Chu E. An energy approach for predicting springback of metal sheets after double-curvature forming part Ⅰ:axisymmetric stamping [J]. International Journal of Mechanical Sciences.2001,43(8):1893-1914
[6]Xue P, Yu TX, Chu E. An energy approach for predicting springback of metal sheets after double-curvature forming part Ⅱ:Unequal double-curvature forming [J]. International Journal of Mechanical Sciences,2001,43(8):1915-1924
[7]Zhongqin Lin, Gang Liu, Weili Xu. Study on the effects of numerical parameters on the precision of springback prediction [C]. Proceedings of the sixth international LS-DYNA users conference.2000,5:25-33
[8]M.J.Finn, P.C.Galbraith, L.Wu, etc. Use of a coupled explicit-implicit solve for calculating spring-back in automotive body panels [J]. Journal of Material Processing Technology. 1995,50(1-4):395-409
[9]Huang You-Min, Leu Daw-Kwei. Elasto-plastic finite element analysis of sheet metal U-bending process [J]. Journal of Materials Processing Technology.1995,48(1-4): 151-157
[10]安治国.径向基函数模型在板料成形工艺多目标优化设计中的应用[D].重庆大学博士学位论文.2009
[11]Ohata, T., Nakamura, Y., Katayama, T., et al. Development of optimum process design system for sheet fabrication using response surface method [J]. Journal of Materials Processing Technology.2003,143-144(1):667-672
[12]Breitkopf Piotr, Naceur Hakim, Rassineux Alain, et al.. Moving least squares response surface approximation:Formulation and metal forming applications [J]. Computers and Structures.2005,83(17-18):1411-1428
[13]Jakumeit, J., Herdy, M., & Nitsche, M. Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm [J]. Structural and Multidisciplinary Optimization.2005,29(6):498-507
[14]张彬等.基于人工神经网络的拉形回弹预测技术研究[J].塑性工程学报.2003,10(2)：28-31
[15]林忠钦,刘罡,李淑慧等.应用正交试验设计提高U形件的成形精度[J].机械工程学报.2002,38：83-89
[16]A. Forcellese, F. Gabrielli, R. Ruffini. Effect of the training set size on springback control by neural network in an air bending process[J]. Materials Processing Technology,1998, 80:493-500
[17]安治国,周杰,赵军等.基于径向基函数响应面法的板料成形仿真研究[J].系统仿真学报.2009,21(6)：1557-1561
[18]张立力.板材成形回弹数值模拟和模具补偿方法的研究[D].机械科学研究院硕士学位论文.2001
[19]《冲模设计手册》编写组.冲压设计手册模具手册之四[M].机械工业出版社,1988：161
[20]李书涛等.工艺参数对板料成形性能的影响[J].锻压技术.2002,3：22-26
[21]张高贤.U形件成形工艺参数优化研究[D].浙江大学硕士学位论文.2004
[22]罗佑新,张龙庭,李敏.灰色系统理论及其在机械工程中的应用[M].长沙：国防科技大学出版社.2001
[23]丁雪梅.基于BP算法的股票预测技术研究[D].哈尔滨师范大学硕士学位论文.2003
[24]张伟平.冰蓄冷空调系统的负荷预测和末端房间解耦控制[D].兰州理工大学硕士学位论文.2006
[25]李小燕.灰色神经网络预测模型的优化研究[D].武汉理工大学硕士学位论文.2009
[26]徐雅冬.U形件弯曲回弹预测及优化方法的研究[D].天津理工大学硕士学位论文.2008
[27]赵叶峰.U形件弯曲回弹的数值模拟及预测与优化控制[D].扬州大学硕士学位论文.2005
[28]杨川.基于径向基代理模型的板料回弹预测研究[D].西南交通大学硕士学位论文. 2009
[29]许剑.谈板料弯曲中回弹产生的原因及控制措施[J].科技风.2009,255-256
[30]刘罡.基于回弹控制的提高轿车冲压件成形精度方法研究[D].上海交通大学博士学位论文.2001
[31]李文平.弯曲回弹变分原理及其数值模拟研究[D].燕山大学博士学位论文.2006
[32]谢延敏,于沪平,陈军,等.基于灰色系统理论的方盒件拉深稳健设计[J].机械工程学报.2007,43(3)：54-59
[33]陈炎嗣,郭景仪.冲压模具设计与制造技术[M].北京：北京出版社,1991
[34]李硕本等.冲压工艺理论及新技术[M].机械工业出版社,2002
[35]谢延敏,于沪平,陈军,等.韧性断裂准则在板料成形中应用研究进展[J].哈尔滨工业大学学报.2009,41(1)：169-173
[36]张婷.基于灰色神经网络组合模型的能源需求预测[D].天津大学硕士学位论文.2007
[37]谢延敏.基于Kriging模型和灰色关联分析的板料成形工艺稳健优化设计研究[D].上海交通大学博士学位论文,2007
[38]张毅,杨建国.基于灰色理论预处理的神经网络机床热误差建模[J].机械工程学报.2011,47(7)：134-139
[39]邢听.灰色神经网络改进算法及其应用研究[D].华中科技大学硕士学位论文.2011
[40]孙芳芳.浅议灰色关联度分析方法及其应用[J].科技信息.2010,(17)：880-882
[41]高贝贝.基于灰色神经网络的农产品数量安全预测模型的研究[D].首都师范大学硕士学位论文.2012
[42]李妍.基于灰色神经网络的液压泵故障诊断研究[D].燕山大学硕士学位论文.2011
[43]王莹莹.基于灰色神经网络模型的煤炭物流需求预测研究[D].北京交通大学硕士学位论文.2012
[44]黄金湘.基于Dynaform的汽车门槛内板零件回弹特性分析[J].金属铸锻焊技术.2011,40(9)：176-179
[45]韩飞,莫健华,龚攀.基于遗传神经网络的数字化渐进成形回弹预测[J].华中科技大学学报.2008,36(1)：121-124
[46]刘艳.高强度钢板冲压成形回弹规律数值模拟[D].上海交通大学硕士学位论文.2007
[47]曹克利.高强度钢板冲压件回弹的研究[D].哈尔滨工业大学硕士学位论文.2008
[48]章敬东,刘小辉,邓飞其,刘永清.灰色神经网络组合算法在复杂非线性预测中的应用[J].计算机工程与应用,2003,12：56-58
[49]史德明,李林川,宋建文.基于灰色预测和神经网络的电力系统负荷预测[J].电网 技术.2001,25(12)：14-17
[50]聂昕.板料冲压成形的回弹研究及其在工程上的应用[D].湖南大学硕士学位论文.2006
[51]张冬娟.板料冲压成形回弹理论及有限元数值模拟研究[D].上海交通大学硕士学位论文.2006
[52]刘迪辉.薄板冲压回弹仿真计算及应用技术研究[D].湖南大学硕士学位论文.2005
[53]胡玉琢.改进型灰色神经网络模型在水质预测中的应用[D].重庆大学硕士学位论文.2010
[54]葛少云,贾鸥莎,刘洪.基于遗传灰色神经网络模型的实时电价条件下短期电力负荷预测[J],电网技术.2012,36(1)：224-229
[55]陈淑燕,王炜.交通量的灰色神经网络预测方法[J].东南大学学报.2004,34(4)：541-544
[56]王梦寒,刘文,赖啸.基于GR神经网络的汽车U形纵梁多工步冲压成形回弹预测分析[J].金属铸锻焊技术.2011,40(23)：82-84
[57]王大勇,傅利斌,李伟等.U截面型钢压弯回弹的试验研究及预测分析[J].锻压技术.2011,36(1)：140-143
[58]官英平,王风琴,赵军.宽板V型自由弯曲智能化控制过程的影响因素分析[J].锻压技术.2005,3：35-38
[59]潘婷婷.基于灰色神经网络的旅游上市公司财务危机[D].苏州大学硕士学位论文.2011
[60]曹建华.基于灰色神经网络模型的网络流量预测算法研究[D].江南大学硕士学位论文.2008
[61]陈相东,王彬.多因素灰色预测模型及其应用[J].数学的实践与认识.2012,42(1)：80-83
[62]张龙庭,罗佑新.试验数据处理的多因素灰色模型GM(1,N)及其应用[J].机械设计.2003,20(3)：23-24
[63]王汉林.灰色神经网络模型的建立及其在复杂非线性预测问题中的应用[D].吉林大学硕士学位论文.2004
[64]姜韬.灰色神经网络在多核体系结构空间探究中的应用[D].武汉理工大学硕士学位论文.2010
[65]张军.灰色预测模型的改进及其应用[D].西安理工大学硕士学位论文.2008
[66]王志远.基于灰色神经网络的股票分析预测研究[D].郑州大学硕士学位论文.2011
[2]Gau Jenn-Terng, Kinzel Gary L. A new model for springback prediction in which the Bauschinger effect is considered [J]. International Journal of Mechanical Sciences.2001, 43(8):1813-1832
[3]Farhang Pourboghrat, Michael E. Karabin, Richard C. Becher. Hybrid membrane/shell method for calculating springback of anisotropic sheet metals undergoing axisymmetric loading [J]. International Journal of Plasticity.2000,16(6):677-700
[4]Xue P, Yu TX, Chu E. Theoretical prediction of springback of metal sheets after double-curvature forming operation [J]. Intenational Journal of Materials Processing Technology,1999,89-90:65-71
[5]Xue P, Yu TX, Chu E. An energy approach for predicting springback of metal sheets after double-curvature forming part Ⅰ:axisymmetric stamping [J]. International Journal of Mechanical Sciences.2001,43(8):1893-1914
[6]Xue P, Yu TX, Chu E. An energy approach for predicting springback of metal sheets after double-curvature forming part Ⅱ:Unequal double-curvature forming [J]. International Journal of Mechanical Sciences,2001,43(8):1915-1924
[7]Zhongqin Lin, Gang Liu, Weili Xu. Study on the effects of numerical parameters on the precision of springback prediction [C]. Proceedings of the sixth international LS-DYNA users conference.2000,5:25-33
[8]M.J.Finn, P.C.Galbraith, L.Wu, etc. Use of a coupled explicit-implicit solve for calculating spring-back in automotive body panels [J]. Journal of Material Processing Technology. 1995,50(1-4):395-409
[9]Huang You-Min, Leu Daw-Kwei. Elasto-plastic finite element analysis of sheet metal U-bending process [J]. Journal of Materials Processing Technology.1995,48(1-4): 151-157
[10]安治国.径向基函数模型在板料成形工艺多目标优化设计中的应用[D].重庆大学博士学位论文.2009
[11]Ohata, T., Nakamura, Y., Katayama, T., et al. Development of optimum process design system for sheet fabrication using response surface method [J]. Journal of Materials Processing Technology.2003,143-144(1):667-672
[12]Breitkopf Piotr, Naceur Hakim, Rassineux Alain, et al.. Moving least squares response surface approximation:Formulation and metal forming applications [J]. Computers and Structures.2005,83(17-18):1411-1428
[13]Jakumeit, J., Herdy, M., & Nitsche, M. Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm [J]. Structural and Multidisciplinary Optimization.2005,29(6):498-507
[14]张彬等.基于人工神经网络的拉形回弹预测技术研究[J].塑性工程学报.2003,10(2)：28-31
[15]林忠钦,刘罡,李淑慧等.应用正交试验设计提高U形件的成形精度[J].机械工程学报.2002,38：83-89
[16]A. Forcellese, F. Gabrielli, R. Ruffini. Effect of the training set size on springback control by neural network in an air bending process[J]. Materials Processing Technology,1998, 80:493-500
[17]安治国,周杰,赵军等.基于径向基函数响应面法的板料成形仿真研究[J].系统仿真学报.2009,21(6)：1557-1561
[18]张立力.板材成形回弹数值模拟和模具补偿方法的研究[D].机械科学研究院硕士学位论文.2001
[19]《冲模设计手册》编写组.冲压设计手册模具手册之四[M].机械工业出版社,1988：161
[20]李书涛等.工艺参数对板料成形性能的影响[J].锻压技术.2002,3：22-26
[21]张高贤.U形件成形工艺参数优化研究[D].浙江大学硕士学位论文.2004
[22]罗佑新,张龙庭,李敏.灰色系统理论及其在机械工程中的应用[M].长沙：国防科技大学出版社.2001
[23]丁雪梅.基于BP算法的股票预测技术研究[D].哈尔滨师范大学硕士学位论文.2003
[24]张伟平.冰蓄冷空调系统的负荷预测和末端房间解耦控制[D].兰州理工大学硕士学位论文.2006
[25]李小燕.灰色神经网络预测模型的优化研究[D].武汉理工大学硕士学位论文.2009
[26]徐雅冬.U形件弯曲回弹预测及优化方法的研究[D].天津理工大学硕士学位论文.2008
[27]赵叶峰.U形件弯曲回弹的数值模拟及预测与优化控制[D].扬州大学硕士学位论文.2005
[28]杨川.基于径向基代理模型的板料回弹预测研究[D].西南交通大学硕士学位论文. 2009
[29]许剑.谈板料弯曲中回弹产生的原因及控制措施[J].科技风.2009,255-256
[30]刘罡.基于回弹控制的提高轿车冲压件成形精度方法研究[D].上海交通大学博士学位论文.2001
[31]李文平.弯曲回弹变分原理及其数值模拟研究[D].燕山大学博士学位论文.2006
[32]谢延敏,于沪平,陈军,等.基于灰色系统理论的方盒件拉深稳健设计[J].机械工程学报.2007,43(3)：54-59
[33]陈炎嗣,郭景仪.冲压模具设计与制造技术[M].北京：北京出版社,1991
[34]李硕本等.冲压工艺理论及新技术[M].机械工业出版社,2002
[35]谢延敏,于沪平,陈军,等.韧性断裂准则在板料成形中应用研究进展[J].哈尔滨工业大学学报.2009,41(1)：169-173
[36]张婷.基于灰色神经网络组合模型的能源需求预测[D].天津大学硕士学位论文.2007
[37]谢延敏.基于Kriging模型和灰色关联分析的板料成形工艺稳健优化设计研究[D].上海交通大学博士学位论文,2007
[38]张毅,杨建国.基于灰色理论预处理的神经网络机床热误差建模[J].机械工程学报.2011,47(7)：134-139
[39]邢听.灰色神经网络改进算法及其应用研究[D].华中科技大学硕士学位论文.2011
[40]孙芳芳.浅议灰色关联度分析方法及其应用[J].科技信息.2010,(17)：880-882
[41]高贝贝.基于灰色神经网络的农产品数量安全预测模型的研究[D].首都师范大学硕士学位论文.2012
[42]李妍.基于灰色神经网络的液压泵故障诊断研究[D].燕山大学硕士学位论文.2011
[43]王莹莹.基于灰色神经网络模型的煤炭物流需求预测研究[D].北京交通大学硕士学位论文.2012
[44]黄金湘.基于Dynaform的汽车门槛内板零件回弹特性分析[J].金属铸锻焊技术.2011,40(9)：176-179
[45]韩飞,莫健华,龚攀.基于遗传神经网络的数字化渐进成形回弹预测[J].华中科技大学学报.2008,36(1)：121-124
[46]刘艳.高强度钢板冲压成形回弹规律数值模拟[D].上海交通大学硕士学位论文.2007
[47]曹克利.高强度钢板冲压件回弹的研究[D].哈尔滨工业大学硕士学位论文.2008
[48]章敬东,刘小辉,邓飞其,刘永清.灰色神经网络组合算法在复杂非线性预测中的应用[J].计算机工程与应用,2003,12：56-58
[49]史德明,李林川,宋建文.基于灰色预测和神经网络的电力系统负荷预测[J].电网 技术.2001,25(12)：14-17
[50]聂昕.板料冲压成形的回弹研究及其在工程上的应用[D].湖南大学硕士学位论文.2006
[51]张冬娟.板料冲压成形回弹理论及有限元数值模拟研究[D].上海交通大学硕士学位论文.2006
[52]刘迪辉.薄板冲压回弹仿真计算及应用技术研究[D].湖南大学硕士学位论文.2005
[53]胡玉琢.改进型灰色神经网络模型在水质预测中的应用[D].重庆大学硕士学位论文.2010
[54]葛少云,贾鸥莎,刘洪.基于遗传灰色神经网络模型的实时电价条件下短期电力负荷预测[J],电网技术.2012,36(1)：224-229
[55]陈淑燕,王炜.交通量的灰色神经网络预测方法[J].东南大学学报.2004,34(4)：541-544
[56]王梦寒,刘文,赖啸.基于GR神经网络的汽车U形纵梁多工步冲压成形回弹预测分析[J].金属铸锻焊技术.2011,40(23)：82-84
[57]王大勇,傅利斌,李伟等.U截面型钢压弯回弹的试验研究及预测分析[J].锻压技术.2011,36(1)：140-143
[58]官英平,王风琴,赵军.宽板V型自由弯曲智能化控制过程的影响因素分析[J].锻压技术.2005,3：35-38
[59]潘婷婷.基于灰色神经网络的旅游上市公司财务危机[D].苏州大学硕士学位论文.2011
[60]曹建华.基于灰色神经网络模型的网络流量预测算法研究[D].江南大学硕士学位论文.2008
[61]陈相东,王彬.多因素灰色预测模型及其应用[J].数学的实践与认识.2012,42(1)：80-83
[62]张龙庭,罗佑新.试验数据处理的多因素灰色模型GM(1,N)及其应用[J].机械设计.2003,20(3)：23-24
[63]王汉林.灰色神经网络模型的建立及其在复杂非线性预测问题中的应用[D].吉林大学硕士学位论文.2004
[64]姜韬.灰色神经网络在多核体系结构空间探究中的应用[D].武汉理工大学硕士学位论文.2010
[65]张军.灰色预测模型的改进及其应用[D].西安理工大学硕士学位论文.2008
[66]王志远.基于灰色神经网络的股票分析预测研究[D].郑州大学硕士学位论文.2011