基于BP神经网络算法的四杆机构轨迹分析
|
摘要
由于四连杆曲线类型的复杂性,数学上几乎无法准确给出连杆曲线的公式,而四连杆曲线在机械工程领域的应用几乎无处不在,因此对于四连杆曲线的研究历来受到许多学者的关注。目前采用人工神经网络算法对连杆曲线的研究受到了广泛关注,本文将引入神经网络算法中的BP网络算法来对四连杆曲线进行分析。
本文首先描述了四连杆曲线的分类,然后针对不同分类的连杆曲线进行了分析,得出了连杆曲线与四杆参数存在着一定的非线性关系。借助Delphi编制的软件可将四连杆参数准确地绘制出对应分类的连杆曲线,再利用matlab.提取了连杆曲线的数字化特征值——不变矩,建立了四连杆参数数值与对应的连杆曲线不变矩之间的样本库。通过样本库,以不变矩作为输入量,利用BP网络算法得出了连杆曲线与四杆机构参数之间的权值系数。最终借助权值系数得到一条待分析曲线对应的四杆机构参数。由于不变矩具有放大,缩小的不变性,所以,当待分析的曲线与BP计算后得到的曲线形状相似时,则可根据对应的比例获得相应的四连杆参数。
本文以卵圆形曲线和8字形曲线等两条待求四连杆曲线为例,采用上述方法对曲线进行了处理,所得四连杆曲线的相对误差一般能满足设计,从而验证了BP网络算法对于卵圆形曲线和8字形曲线与四连杆参数之间均具有较好的非线性关联,也就验证了本方法在连杆曲线综合方面具有一定的可行性、实用性。
The formula of coupler curve almost can't be accurately given because of the complex of types of Four-bar coupler curver, while the application of Four-bar coupler curver in mechanical engineering is widely used. So the study to Four-bar coupler curver is noticed by many experts all through the ages. Now analyses of the Four-bar coupler curve based on the algorithm of artificial neural networks is widely noticed. The study of this paper on Four-bar coupler curver will bring the algorithm of BP neural network(NN).
At first this paper gives the types of Four-bar coupler curver, and then analyses against the different classifications of the curve. We can conclude there is a certain nonlinear relationship of Four-bar linkage curves and the parameters of Four-bar linkage. With Delphi software compiled the Four-bar linkage parameters can accurately draw a corresponding link curve, and with Matlab software digital characteristics (non-moment) of Four-bar linkages can be extracted, the sample database are built by the parameters of Four-bar linkages and the the corresponding characters (non-moment)of the Four-bar coupler cures. By this sample database, and characters of Four-bar coupler curve as the input, power coefficient of the parameters of Four-bar linkages and the corresponding characters can be get. At last the parameters of Four-bar linkages corresponding characters (non-moment)of the Four-bar coupler cure can be calculated. As the non- moment zoom invariance, therefore, when the question curves and the Four-bar coupler curve which be calculated by the algorithm of BP neural networks are similar, the parameters of Four-bar linkages can be get by corresponding proportion.
Oval shaped curve and 8-type curve for two Four-bar linkages that curve will be used for the example of this paper. The curves are dealt with by using the methods which have been given before. The relative error of Four-bar linkage curves meet with the requirements of design in a general way. This method verifies better nonlinear by using the BP network algorithm to the 8-type curve (or oval shaped curve) and Four-bar linkage. At the same time this method also proved this way has a comprehensive feasibility, practicality.
本文首先描述了四连杆曲线的分类,然后针对不同分类的连杆曲线进行了分析,得出了连杆曲线与四杆参数存在着一定的非线性关系。借助Delphi编制的软件可将四连杆参数准确地绘制出对应分类的连杆曲线,再利用matlab.提取了连杆曲线的数字化特征值——不变矩,建立了四连杆参数数值与对应的连杆曲线不变矩之间的样本库。通过样本库,以不变矩作为输入量,利用BP网络算法得出了连杆曲线与四杆机构参数之间的权值系数。最终借助权值系数得到一条待分析曲线对应的四杆机构参数。由于不变矩具有放大,缩小的不变性,所以,当待分析的曲线与BP计算后得到的曲线形状相似时,则可根据对应的比例获得相应的四连杆参数。
本文以卵圆形曲线和8字形曲线等两条待求四连杆曲线为例,采用上述方法对曲线进行了处理,所得四连杆曲线的相对误差一般能满足设计,从而验证了BP网络算法对于卵圆形曲线和8字形曲线与四连杆参数之间均具有较好的非线性关联,也就验证了本方法在连杆曲线综合方面具有一定的可行性、实用性。
The formula of coupler curve almost can't be accurately given because of the complex of types of Four-bar coupler curver, while the application of Four-bar coupler curver in mechanical engineering is widely used. So the study to Four-bar coupler curver is noticed by many experts all through the ages. Now analyses of the Four-bar coupler curve based on the algorithm of artificial neural networks is widely noticed. The study of this paper on Four-bar coupler curver will bring the algorithm of BP neural network(NN).
At first this paper gives the types of Four-bar coupler curver, and then analyses against the different classifications of the curve. We can conclude there is a certain nonlinear relationship of Four-bar linkage curves and the parameters of Four-bar linkage. With Delphi software compiled the Four-bar linkage parameters can accurately draw a corresponding link curve, and with Matlab software digital characteristics (non-moment) of Four-bar linkages can be extracted, the sample database are built by the parameters of Four-bar linkages and the the corresponding characters (non-moment)of the Four-bar coupler cures. By this sample database, and characters of Four-bar coupler curve as the input, power coefficient of the parameters of Four-bar linkages and the corresponding characters can be get. At last the parameters of Four-bar linkages corresponding characters (non-moment)of the Four-bar coupler cure can be calculated. As the non- moment zoom invariance, therefore, when the question curves and the Four-bar coupler curve which be calculated by the algorithm of BP neural networks are similar, the parameters of Four-bar linkages can be get by corresponding proportion.
Oval shaped curve and 8-type curve for two Four-bar linkages that curve will be used for the example of this paper. The curves are dealt with by using the methods which have been given before. The relative error of Four-bar linkage curves meet with the requirements of design in a general way. This method verifies better nonlinear by using the BP network algorithm to the 8-type curve (or oval shaped curve) and Four-bar linkage. At the same time this method also proved this way has a comprehensive feasibility, practicality.
引文
[1]郑文纬,吴克坚.机械原理[M].北京:高等教育出版社,1996.
[2]张世民.平面连杆机构[M].北京:高等教育出版社,1983.
[3]刘勇,肖人彬.平面机构轨迹综合及其计算机辅助创新设计方法研究.华中科技大学博士学位论文,2005:14-29
[4]扬基厚,高峰.四杆机构空间模型与性能图谱.机械工业出版社,1989
[5]J.A.朗内斯,G.L.讷内耳.四连杆机构分析图谱[M].李学荣译.北京:机械工业出版社,1966,1-730.
[6]詹奎华,高强.连杆曲线规律变异的尺度研究[J].机械工程学报2006,23(17).
[7]詹奎华,黄锡坤.连杆曲线轨迹综合的特征图谱[J].机械传动,2005,29(5):8-28.
[8](美)WilliamK.Pratt著邓鲁华,张延恒等译.数字图像处理[M].机械工业出版社,2005.1:60-433
[9]朱福喜,朱三元,伍春香.人工智能基础[M]清华大学出版社,2004.9P2-P14.
[10]曹惟庆.连杆曲线识别的模糊数学方法.陕西机械学院学报,1992,8(2):21-28
[11]HoeltzelD.A.ChiengW.H.Pattern matching synthesis as an automated approach to mechanism design.ASME Journal of Mechanical Design,1990,112(4):190-199
[12]李震,桂长林.连杆曲线特征分析的数学形态学方法.机械工程学报,2002,38(2):27-30
[13]JohnR.M.Rapid search and selection of path generating mechanism from a library.Mechanism and Machine Theory,1994,29(3):223-235
[14]ZahnC.T.RoskiesR.Z.Fourier descriptors for plane closed curves.IEEE Transactions on Pattern Analysis and Machine Intelligence,1972,21(3):269-281
[15]PersoonE,FuKS.Shape discrimination using Fourier descriptors.IEEE Transactions on Pattern Analysis and Machine Intelligence,1986,8(3):388-397
[16]UiiahI KotaS.Optimal synthesis of mechanisms for path generationusing Fourier descriptors and global search methods.ASME Journal of Mechanical Design,1997,119(10):504-510
[17]孙晓斌,肖人彬.基于最大形状特征谱求解的机构轨迹精简数值表示方法.自然科学进展,2002,12(7):773-780
[18]孙晓斌,肖人彬,王雪.基于曲线形状特征量化提取的轨迹机构检索生成方法.机械工程学报,2000,36(11):97-105
[19]MartinT.hagan,Howard B.Demuth,MarkH.Beale.Neural Network Design.第一版.戴葵译.北京:机械工业出版社,2002
[20]朱大奇,史慧编著.人工神经网络原理及应用[M].科学出版社2006.3:09-92.
[21]郭军,胡贯容.BP神经网络算法研究华中科技大学硕士学位论文 2005,11,10
[22]窦万锋,齐维浩,杨先海.平面连杆曲线特征参数提取的自相关变换法.机械科学与技术,1995,50(5):31-35
[23]孙玉林,谢进.基于神经网络技术的连杆曲线识别和分类的研究.西南交通大学,硕士学位论文2001,04,01
[24]M.K.Hu."VisualPatternRecognitionbyMomentInvariants"[J].IRETrans.InformationTheory,1962,8(2):179-188.
[25]姚敏等编著.数字图象处理[M].机械工业出版社,2006.1:281-284
[26]HuoJP,CaoWQ.Fuzzymathematicsmethodforlocussynthesisofplanar Four-barlingage,ChineseJ.OfMechanicalEngineering(EnglishEdition).1990.3(1):22-28
[27]杨淑莹编著,李兰友主审.图像模式识别-VC++技术实现[M].清华大学出版社北京交通大学出版社2005.5:115-134.
[28]杨文龙等.软件工程(第2版)[M]..电子工业出版社,2004.9
[29]何江华.计算机仿真导论[M].北京:科学出版社,2001.26-54
[30]康凤举.现代仿真技术与应用[M].北京:国防工业出版社,2001.1-25
[31]朱家诚,王炎欢.机构仿真软件的研究与开发合肥工业大学硕士学位论文,2006.5
[32]JasonT.Roff著张瑜杨继萍等译.UML基础教程[M].清华大学出版社,2003.10:1-13
[33]刘超,张莉.可视化面向对象建模技术[M].北京航空航天大学出版社,1999
[34]蒋能学.面向对象系统设计[M].电子工业出版社,2003.10
[35]刘艺.Delphi面向对象的编程思想[M].机械工业出版社,2005.11
[2]张世民.平面连杆机构[M].北京:高等教育出版社,1983.
[3]刘勇,肖人彬.平面机构轨迹综合及其计算机辅助创新设计方法研究.华中科技大学博士学位论文,2005:14-29
[4]扬基厚,高峰.四杆机构空间模型与性能图谱.机械工业出版社,1989
[5]J.A.朗内斯,G.L.讷内耳.四连杆机构分析图谱[M].李学荣译.北京:机械工业出版社,1966,1-730.
[6]詹奎华,高强.连杆曲线规律变异的尺度研究[J].机械工程学报2006,23(17).
[7]詹奎华,黄锡坤.连杆曲线轨迹综合的特征图谱[J].机械传动,2005,29(5):8-28.
[8](美)WilliamK.Pratt著邓鲁华,张延恒等译.数字图像处理[M].机械工业出版社,2005.1:60-433
[9]朱福喜,朱三元,伍春香.人工智能基础[M]清华大学出版社,2004.9P2-P14.
[10]曹惟庆.连杆曲线识别的模糊数学方法.陕西机械学院学报,1992,8(2):21-28
[11]HoeltzelD.A.ChiengW.H.Pattern matching synthesis as an automated approach to mechanism design.ASME Journal of Mechanical Design,1990,112(4):190-199
[12]李震,桂长林.连杆曲线特征分析的数学形态学方法.机械工程学报,2002,38(2):27-30
[13]JohnR.M.Rapid search and selection of path generating mechanism from a library.Mechanism and Machine Theory,1994,29(3):223-235
[14]ZahnC.T.RoskiesR.Z.Fourier descriptors for plane closed curves.IEEE Transactions on Pattern Analysis and Machine Intelligence,1972,21(3):269-281
[15]PersoonE,FuKS.Shape discrimination using Fourier descriptors.IEEE Transactions on Pattern Analysis and Machine Intelligence,1986,8(3):388-397
[16]UiiahI KotaS.Optimal synthesis of mechanisms for path generationusing Fourier descriptors and global search methods.ASME Journal of Mechanical Design,1997,119(10):504-510
[17]孙晓斌,肖人彬.基于最大形状特征谱求解的机构轨迹精简数值表示方法.自然科学进展,2002,12(7):773-780
[18]孙晓斌,肖人彬,王雪.基于曲线形状特征量化提取的轨迹机构检索生成方法.机械工程学报,2000,36(11):97-105
[19]MartinT.hagan,Howard B.Demuth,MarkH.Beale.Neural Network Design.第一版.戴葵译.北京:机械工业出版社,2002
[20]朱大奇,史慧编著.人工神经网络原理及应用[M].科学出版社2006.3:09-92.
[21]郭军,胡贯容.BP神经网络算法研究华中科技大学硕士学位论文 2005,11,10
[22]窦万锋,齐维浩,杨先海.平面连杆曲线特征参数提取的自相关变换法.机械科学与技术,1995,50(5):31-35
[23]孙玉林,谢进.基于神经网络技术的连杆曲线识别和分类的研究.西南交通大学,硕士学位论文2001,04,01
[24]M.K.Hu."VisualPatternRecognitionbyMomentInvariants"[J].IRETrans.InformationTheory,1962,8(2):179-188.
[25]姚敏等编著.数字图象处理[M].机械工业出版社,2006.1:281-284
[26]HuoJP,CaoWQ.Fuzzymathematicsmethodforlocussynthesisofplanar Four-barlingage,ChineseJ.OfMechanicalEngineering(EnglishEdition).1990.3(1):22-28
[27]杨淑莹编著,李兰友主审.图像模式识别-VC++技术实现[M].清华大学出版社北京交通大学出版社2005.5:115-134.
[28]杨文龙等.软件工程(第2版)[M]..电子工业出版社,2004.9
[29]何江华.计算机仿真导论[M].北京:科学出版社,2001.26-54
[30]康凤举.现代仿真技术与应用[M].北京:国防工业出版社,2001.1-25
[31]朱家诚,王炎欢.机构仿真软件的研究与开发合肥工业大学硕士学位论文,2006.5
[32]JasonT.Roff著张瑜杨继萍等译.UML基础教程[M].清华大学出版社,2003.10:1-13
[33]刘超,张莉.可视化面向对象建模技术[M].北京航空航天大学出版社,1999
[34]蒋能学.面向对象系统设计[M].电子工业出版社,2003.10
[35]刘艺.Delphi面向对象的编程思想[M].机械工业出版社,2005.11