基于小波神经网络的变参数振动钻削仿真与预测
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摘要
多元变参数振动钻削是一种为适应新型材料的出现而进行的优化切削过程，在切削过程中为提高孔加工质量而提出的最优化加工方法。该方法在钻削过程的不同区段，要求采用该区段的最优振动参数和切削参数。但出于实验设备等客观因素的限制，在实验中大幅度地频繁改变参数是不实际的，因此，用计算机来全方位地分析和仿真切削过程是必须的。这就要求在对系统辩识的基础上根据切削理论、振动理论、控制理论等对系统进行形象的描述并构造振动钻削的仿真模型，实现对振动钻削的动态仿真。
传统的研究方法是采用多元正交多项式回归参数优化设计，通过获得一些经验公式来进行实验研究。这种方法需要根据切削理论、振动理论、控制理论等对系统进行形象的描述，进而构造仿真模型，它的数据处理量大，且性能指标与因素之间存在复杂的非线性关系，难以精确描述。近年来，随着神经网络技术的不断发展，也有采用神经网络模型对黄铜材料进行了振动钻削的过程仿真与参数优化的例子，并取得了比较好的结果。
小波变换(Wavelet Transform)是20世纪70年代中期由法国科学家Grossman和Morlet在进行地震信号分析时提出的，通过信号处理的实际需要由经验建立了反演公式。小波变换是一个时间和频率的局域变换，因而能有效的从信号中提取信息，通过伸缩和平移等运算功能对函数或信号进行多尺度细化分析(Multiscale Analysis)，解决了Fourier变换不能解决的许多困难问题，从而小波变化被誉为“数学显微镜”。它是调和分析发展史上里程碑
摘要
式的标志。
小波神经网络是小波分析理论与神经网络理论相结合的产物，从网络的
形式上来看是将小波分解与前馈神经网络相融合，通常是将常规单隐层神经
网络的隐节点的519叮oid函数由小波函数来代替，相应的输入层到隐层的权
值及隐层的阀值分别由小波函数的尺度和平移参数所代替。
本文提出将神经网络和小波函数结合起来应用到振动钻削过程仿真与参
数优化中，拓展了计算智能的应用领域，并取得了良好的结果。
全文共分6章。
第1章主要介绍了神经网络和小波理论的起源和发展，讨论了计算智能
技术在机械加工和振动钻削领域应用的现状及发展趋势，继而确定了本文的
研究内容和方向。
第2章主要介绍了神经网络和小波理论的基础知识和它们的应用领域及
发展方向。
第3章讨论了在变参数振动钻削过程中神经网络建模，给出了相关概念。
变参数振动钻削是一种最优化的加工方法，在钻削过程的不同区段，要求采
用该区段的最优振动参数和切削参数。这必然要求得到亚层材料的每一层材
料钻入、钻中、钻出各个区段的最优参数，这就引出了参数优化问题。神经
网络模型不需要预先知道钻削过程的先验知识，只要给出测量数据和期望输
出的数据，就可以通过神经网络建立输出和输入之间很好的非线性映射，找
到它们之间的非线性规律，从而实现对非样本的预测。
第4章通过比较应用于神经网络的各类算法的优缺点，选定共辘梯度算
法作为在振动钻削过程的小波神经网络算法，并给出了基于局部学习的共辘
梯度算法(L CG)，该算法与普通的共扼梯度算法相比明显改善提高了小波神
经网络性能:由于小波网络的参变量多，它比小波分解具有更多的自由度和
摘要
更强的逼近能力，适当选取参数就可达到较好的逼近能力，因此讨论了振动
钻削过程仿真中基于局部学习的小波网络权值初始化原则和网络训练方法;
利用灰色关联度分析法，寻找和挖掘振动钻削过程中输入数据和输出数据之
间所隐含的内在规律，并进行因素主次划分，在此基础上提出了用灰色理论
关联分析法来选取小波神经网络的输入参数。
第5章主要应用前两章所得结论，具体实现振动钻削仿真、参数优化和预测，
通过在仿真过程中三个区段原始数据与仿真数据比较曲线，分析了输入量(振
动频率F、振幅A、给进量f)与输出量(入钻定位误差R、孔扩量△D、出口
毛刺高度H)之间的关系。通过实验获得测量数据，对小波神经网络进行训练，
利用网络的泛化能力，进行参数寻优。利用小波神经网络来进行预测(黄铜
材料为例)，并得到了良好的结果。
最后一章为全文作了总结，指出了本文所做的工作和存在不足。本文的
研究工作是结合国家自然科学资助基金项目“多元时变参数振动钻削新型材
料的理论与实验研究”展开进行的，并得到吉林省科技厅“叠层材料变参数
振动钻削虚拟系统的研究”项目的立项支持。
Multi-element varying-parameters vibration drilling is an optimal machining method supported for adapting the appearance of new-type material, optimizing the cutting process and improving the quality of hole machining. In the different section of drilling process, the method needs adopt the optimal vibration parameters and cutting parameters. But for the limitation of experiment equipments and other external factors, it is impossible for continually changing the parameters very extensively. So it is necessary to analyze and simulate cutting process roundly by using computers. It demands us to use cutting theory, vibration theory, control theory to describe the system visually, structure the simulation model of vibration drilling and implement the dynamic simulation of vibration drilling. All the work must be based on system identification.
The multi-element orthogonal polynomial regression is used for traditional optimization technique of parametric optimum design, and the experimental research is done by some experiential formula. This research need describe the system visually by using cutting theory, vibration theory, control theory etc, then the simulation model can be structured. It must deal with data greatly, and the non-linear relationship between capability guideline and factors is very complex and difficulty to describe accurately. In recent years, with the development of Neural Network techniques, there are some examples of Neural Network models to simulate the vibration drilling process and optimize the parameters of brass materials, and the estimated results is very right.
Wavelet Transform theory has been put forward by Grossman and Morlet, two France scientists in 1970's, when they analyzed the signs of the earthquake. They founded the inversion formulas based on practical demand and experiment. The Wavelet Transform is a part change of the time and the frequency. So the signs can be picked up effectively. The signs and the functions can be also multi-scale analyzed by the operational function such as flexing and parallel moving. And many difficult questions that Fourier cannot be figured out have been solved now. The Wavelet Transform is famous as the mathematical microscope. It is a sign as a landmark for the analysis phylogeny.
The Wavelet neural network is a result combined by the wavelet analysis and the neural network. If we think it from a form of the network, it is a combination of Wavelet analysis and the feed front type. Usually, the sigmoid function of the concealed nodes, which is in the
neural network of the formal single concealed layer, is replaced by Wavelet function. The corresponding weight, which is from input layer to concealed layer, and concealed layer threshold value are replaced by yardstick of Wavelet function and parallel moving parameters.
This dissertation puts forward a method that unites the neural network and the Wavelet function, and then applies it to the drilling process' simulation and parametric optimum. The method has broadened the application field of computer intelligence. And the good result has been obtained.
The whole dissertation consists of six parts.
The first chapter introduces the origin and development of the neural network and the wavelet theory, and discusses the current situation and develop trend with regard to the computer intelligent technology on mechanism machining and vibration drilling field. And then ascertain the studying content and direction of this article.
Chapter 2 introduces the basic knowledge and applying field and develop trend of the neural network and the Wavelet theory.
Chapter 3 introduces the neural network model which is in the process of varying parameter's vibration drilling. And the correlative concepts have been also presented. Varying parameter's vibration drilling is the best optimum methods of process. In the varying drilling section, the optimum parameters of vibration and drilling need to be adopted. It must obtain the best optimum parameters of the every layer material for the beginning drilling and the midd
传统的研究方法是采用多元正交多项式回归参数优化设计，通过获得一些经验公式来进行实验研究。这种方法需要根据切削理论、振动理论、控制理论等对系统进行形象的描述，进而构造仿真模型，它的数据处理量大，且性能指标与因素之间存在复杂的非线性关系，难以精确描述。近年来，随着神经网络技术的不断发展，也有采用神经网络模型对黄铜材料进行了振动钻削的过程仿真与参数优化的例子，并取得了比较好的结果。
小波变换(Wavelet Transform)是20世纪70年代中期由法国科学家Grossman和Morlet在进行地震信号分析时提出的，通过信号处理的实际需要由经验建立了反演公式。小波变换是一个时间和频率的局域变换，因而能有效的从信号中提取信息，通过伸缩和平移等运算功能对函数或信号进行多尺度细化分析(Multiscale Analysis)，解决了Fourier变换不能解决的许多困难问题，从而小波变化被誉为“数学显微镜”。它是调和分析发展史上里程碑
摘要
式的标志。
小波神经网络是小波分析理论与神经网络理论相结合的产物，从网络的
形式上来看是将小波分解与前馈神经网络相融合，通常是将常规单隐层神经
网络的隐节点的519叮oid函数由小波函数来代替，相应的输入层到隐层的权
值及隐层的阀值分别由小波函数的尺度和平移参数所代替。
本文提出将神经网络和小波函数结合起来应用到振动钻削过程仿真与参
数优化中，拓展了计算智能的应用领域，并取得了良好的结果。
全文共分6章。
第1章主要介绍了神经网络和小波理论的起源和发展，讨论了计算智能
技术在机械加工和振动钻削领域应用的现状及发展趋势，继而确定了本文的
研究内容和方向。
第2章主要介绍了神经网络和小波理论的基础知识和它们的应用领域及
发展方向。
第3章讨论了在变参数振动钻削过程中神经网络建模，给出了相关概念。
变参数振动钻削是一种最优化的加工方法，在钻削过程的不同区段，要求采
用该区段的最优振动参数和切削参数。这必然要求得到亚层材料的每一层材
料钻入、钻中、钻出各个区段的最优参数，这就引出了参数优化问题。神经
网络模型不需要预先知道钻削过程的先验知识，只要给出测量数据和期望输
出的数据，就可以通过神经网络建立输出和输入之间很好的非线性映射，找
到它们之间的非线性规律，从而实现对非样本的预测。
第4章通过比较应用于神经网络的各类算法的优缺点，选定共辘梯度算
法作为在振动钻削过程的小波神经网络算法，并给出了基于局部学习的共辘
梯度算法(L CG)，该算法与普通的共扼梯度算法相比明显改善提高了小波神
经网络性能:由于小波网络的参变量多，它比小波分解具有更多的自由度和
摘要
更强的逼近能力，适当选取参数就可达到较好的逼近能力，因此讨论了振动
钻削过程仿真中基于局部学习的小波网络权值初始化原则和网络训练方法;
利用灰色关联度分析法，寻找和挖掘振动钻削过程中输入数据和输出数据之
间所隐含的内在规律，并进行因素主次划分，在此基础上提出了用灰色理论
关联分析法来选取小波神经网络的输入参数。
第5章主要应用前两章所得结论，具体实现振动钻削仿真、参数优化和预测，
通过在仿真过程中三个区段原始数据与仿真数据比较曲线，分析了输入量(振
动频率F、振幅A、给进量f)与输出量(入钻定位误差R、孔扩量△D、出口
毛刺高度H)之间的关系。通过实验获得测量数据，对小波神经网络进行训练，
利用网络的泛化能力，进行参数寻优。利用小波神经网络来进行预测(黄铜
材料为例)，并得到了良好的结果。
最后一章为全文作了总结，指出了本文所做的工作和存在不足。本文的
研究工作是结合国家自然科学资助基金项目“多元时变参数振动钻削新型材
料的理论与实验研究”展开进行的，并得到吉林省科技厅“叠层材料变参数
振动钻削虚拟系统的研究”项目的立项支持。
Multi-element varying-parameters vibration drilling is an optimal machining method supported for adapting the appearance of new-type material, optimizing the cutting process and improving the quality of hole machining. In the different section of drilling process, the method needs adopt the optimal vibration parameters and cutting parameters. But for the limitation of experiment equipments and other external factors, it is impossible for continually changing the parameters very extensively. So it is necessary to analyze and simulate cutting process roundly by using computers. It demands us to use cutting theory, vibration theory, control theory to describe the system visually, structure the simulation model of vibration drilling and implement the dynamic simulation of vibration drilling. All the work must be based on system identification.
The multi-element orthogonal polynomial regression is used for traditional optimization technique of parametric optimum design, and the experimental research is done by some experiential formula. This research need describe the system visually by using cutting theory, vibration theory, control theory etc, then the simulation model can be structured. It must deal with data greatly, and the non-linear relationship between capability guideline and factors is very complex and difficulty to describe accurately. In recent years, with the development of Neural Network techniques, there are some examples of Neural Network models to simulate the vibration drilling process and optimize the parameters of brass materials, and the estimated results is very right.
Wavelet Transform theory has been put forward by Grossman and Morlet, two France scientists in 1970's, when they analyzed the signs of the earthquake. They founded the inversion formulas based on practical demand and experiment. The Wavelet Transform is a part change of the time and the frequency. So the signs can be picked up effectively. The signs and the functions can be also multi-scale analyzed by the operational function such as flexing and parallel moving. And many difficult questions that Fourier cannot be figured out have been solved now. The Wavelet Transform is famous as the mathematical microscope. It is a sign as a landmark for the analysis phylogeny.
The Wavelet neural network is a result combined by the wavelet analysis and the neural network. If we think it from a form of the network, it is a combination of Wavelet analysis and the feed front type. Usually, the sigmoid function of the concealed nodes, which is in the
neural network of the formal single concealed layer, is replaced by Wavelet function. The corresponding weight, which is from input layer to concealed layer, and concealed layer threshold value are replaced by yardstick of Wavelet function and parallel moving parameters.
This dissertation puts forward a method that unites the neural network and the Wavelet function, and then applies it to the drilling process' simulation and parametric optimum. The method has broadened the application field of computer intelligence. And the good result has been obtained.
The whole dissertation consists of six parts.
The first chapter introduces the origin and development of the neural network and the wavelet theory, and discusses the current situation and develop trend with regard to the computer intelligent technology on mechanism machining and vibration drilling field. And then ascertain the studying content and direction of this article.
Chapter 2 introduces the basic knowledge and applying field and develop trend of the neural network and the Wavelet theory.
Chapter 3 introduces the neural network model which is in the process of varying parameter's vibration drilling. And the correlative concepts have been also presented. Varying parameter's vibration drilling is the best optimum methods of process. In the varying drilling section, the optimum parameters of vibration and drilling need to be adopted. It must obtain the best optimum parameters of the every layer material for the beginning drilling and the midd
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