判别稀疏分解及其在机械故障特征提取中的应用

Sparse representation based signal processing methods (SRMs), including their applications to mechanical fault feature extraction, have been a hotspot. Among these methods, the ones with learned dictionaries are of particular interest to relevant scholars. Whereas, such SRMs usually fail to achieve multi-dictionary learning, leading to ineffective separation of the fault feature component and the interference component or ineffective separation of multiple fault feature components. To this end, a new adaptive signal processing method, discriminative sparse decomposition (DSD), is proposed in this project. DSD is able to achieve multi-dictionary learning so that components can be represented sparsely with multiple discriminative learned dictionaries, so it is specially suitable to handle multi-component separation problems. This project intends to study and perfect the theory of DSD, and to solve its key theoretical problems. On this basis the project also investigates DSD's applications to mechanical fault feature extraction, and then the systematical DSD-based mechanical fault feature extraction method is proposed. The research achievements of this project will be of important significance for promoting the development of signal processing technology and mechanical fault feature extraction technology.

基于稀疏表示的信号处理方法(简称稀疏表示方法)及其在机械故障特征提取中的应用已成为研究的热点。其中，使用学习字典的稀疏表示方法尤为受到关注。然而，现有使用学习字典的稀疏表示方法通常因无法实现多字典学习而不能有效分离故障特征分量与干扰分量或者分离多个故障特征分量。因此，本项目提出了一种新的自适应信号处理方法——判别稀疏分解(Discriminative Sparse Decomposition，DSD)。判别稀疏分解方法能够实现判别字典学习，从而可使用多个具有判别力的学习字典分别对各个分量进行稀疏表示，特别适合处理多分量分离的问题。本项目拟对判别稀疏分解方法的理论进行研究和完善，解决其关键理论问题。在此基础上，对判别稀疏分解方法在机械故障特征提取中的应用进行研究，提出系统的基于判别稀疏分解的机械故障特征提取方法。项目研究成果对信号处理技术和机械故障特征提取技术的发展都具有重要的意义。

项目开展了稀疏表示理论研究及其在机械故障特征提取中的应用研究，主要研究工作和创新性成果有：（1）研究字典学习的目标函数，利用故障振动信号蕴含的非局部自相似性来提升字典学习效果；（2）研究迭代字典学习算法，并以此解决稀疏表示方法在字典学习时存在降噪结果局部仍含有噪声的问题以及字典学习过程中全局平均与局部降噪不一致性的问题；（3）研究字典学习算法的参数选择问题，利用近似熵选择字典学习时分割信号段的长度；（4）研究机械微弱故障特征提取问题，利用基于SOSO增强以及基于群的K-SVD算法以增强故障冲击特点；（5）研究轴承定量故障诊断问题，利用迭代K-SVD以及阶跃-脉冲响应特点估计轴承的故障损伤程度；（6）研究齿轮传动和齿轮齿条传动机构的啮合特性以及开展应力分析，为故障机理研究和动力学故障信号仿真提供基础。