基于小波包神经网络和D-S理论的滚动轴承故障诊断方法

目 录
摘 要 i
ABSTRACT ii
第1章 研究对象背景介绍 1
第2章 小波包分析的基本原理 2
2.1 小波包变换 2
2.1.1 小波变换基本原理 2
2.1.2 Mallat算法 3
2.1.3 小波包分解与重构 3
2.2 故障模式的特征分析 4
2.2.1 小波包分解频段能量 4
2.2.2 故障类型特征向量的构造及特征分析 5
第3章 神经网络的基本原理 7
3.1 神经网络的发展简介 7
3.2 BP神经网络的基本理论 7
3.2.1 BP神经网络的结构 7
3.2.2 反向传播算法的本质 8
3.2.3 BP神经网络的停止准则 9
3.3 BP神经网络的Matlab实现 9
3.3.1 隐含层与隐含节点 10
3.3.2 激活函数的确定 10
3.3.3 学习率参数 10
第4章 D-S证据理论的基本原理 11
4.1 D-S证据理论 11
4.1.1 几个基本定义 11
4.1.2 Dempster组合规则 12
4.1.3 决策准则 12
4.2 基于神经网络分类可信度的基本概率分配函数的构造 12
第5章 仿真实验 14
5.1 数据的介绍 14
5.2 数据的预处理 14
5.3 故障诊断策略的流程图及实现 15
5.4 仿真的结果图及分析 19
5.4.1 准确率分析 19
5.4.2 计算复杂度及实时性分析 20
第6章 总结及展望 22

摘 要
通过故障诊断与容错控制课程的学习，我了解了非常多实用的故障检测、分类方法，本次课程作业针对滚动轴承这种非平稳振动信号采用的小波包分解的方法来检测故障的存在，运用神经网络来实现故障的分类，还结合D-S理论融合了多个传感器的诊断结果，提高了故障诊断的准确性并通过实验仿真证实。通过对比单一传感器的诊断结果和本次课程设计中采用方法的诊断结果，可以看出基于小波包神经网络和D-S理论的滚动轴承故障诊断方法能够提高滚动轴承故障诊断的准确率。
基于小波包变换的故障特征向量构造方法对滚动轴承时变、冲击信号的处理非常有效。小波包分解的得到的频段能量分布表征着滚动轴承不同的故障类型，通过检测各频段相对能量的变化可以有效地了解滚动轴承的运行状态。所以，可以采用小波包频段能量参数构建故障特征向量。
神经网络具有很好的自学习能力。它将小波包频段能量参数构建的故障特征向量作为输入，真实的故障状态作为输出，进而实现了对故障的分类。
最后，为表征和融合决策级的不确定性，采用了D-S证据理论。这种理论中定义的置信函数和似然函数，对信息的非精确和狭义不确定等认知方面的表示、度量、和处理比概率论更加灵活、有效。本文应用了这一理论，首先统计先验信息获得混淆矩阵进而构建出识别框架并完成基本概率赋值，然后利用给定的组合规则进行证据的融合，最终给出决策结果。
仿真的结果验证了这种诊断方法是有效性的并且具有更好的诊断效果。
关键词：故障诊断；小波包变换；滚动轴承；多传感器；D-S理论

ABSTRACT
Through the learning of fault diagnosis and fault-tolerant control courses, I learned a lot of practical fault detection and classification methods. This course’s job is to use the wavelet packet decomposition method for non-stationary vibration signals of rolling bearings to detect the presence of faults and to use nerves. The network is used to classify faults, and the DS results are combined with the diagnostic results of multiple sensors to improve the accuracy of fault diagnosis and confirm it through experimental simulation. By comparing the diagnostic results of a single sensor and the diagnostic results of the method used in the course design, it can be seen that the fault diagnosis method for rolling bearings based on wavelet packet neural network and D-S theory can improve the accuracy of fault diagnosis of rolling bearings.
The fault eigenvector construction method based on wavelet packet transform is very effective for the time-varying and impact signal processing of rolling bearings. In other words, the frequency band energy distribution obtained by the wavelet packet decomposition represents different types of faults in the rolling bearing. By detecting the relative energy changes in each frequency band, the running state of the rolling bearing can be effectively understood. Therefore, the wavelet packet energy parameters can be used to construct fault feature vectors.
Neural networks have good self-learning capabilities. It takes as input the fault eigenvectors constructed by wavelet packet frequency band energy parameters, and the actual fault status is used as an output, thereby further classifying the faults.
Finally, in order to characterize and fuse decision-level uncertainties, D-S evidence theory is used. Firstly, we obtain the confusion matrix by collecting the prior information and construct the recognition framework and complete the basic probability assignment. Then we use the given combination rules to fuse the evidence and finally give the decision result.
The results of the simulation verified that this diagnostic method is effective and has a better diagnostic effect.
Key Words: fault diagnosis; wavelet packet transform; rolling bearings; D-S the