基于分数阶时频分析的机械故障诊断方法研究

发布时间：2018-05-03 22:35

本文选题：时频分析 + 分数阶Fourier变换　；参考：《南昌航空大学》2017年硕士论文

【摘要】：本论文是在国家自然科学基金(51261024,51075372,51265039,50775208),国家重点研发计划项目(2016YFF0203000)、机械传动国家重点实验室开放基金(No.SKLMT-KFKT-201514)和江西省教育厅科技计划项目(No.GJJ12405,No.GJJ150699)资助下展开研究,利用分数阶Fourier变换具有的独特特点,将基于Fourier变换的传统信号处理方法推广到分数阶Fourier变换领域,提出了一些行之有效的分数阶非平稳信号处理方法,分数阶小波变换、分数阶S变换、分数阶广义S变换、分数阶局部均值分解等方法,并将之应用在旋转机器故障诊断中,取得了比较好的创新性成果。本文主要研究内容包括以下几个方面:第1章,阐述了课题研究的背景和研究意义,论述了时频分析方法的国内外现状,这里,主要从基于核函数的时频分析、基于信号分解的时频分析、参数化时频分析的三方面加以论述。同时,还论述了现有的时频分析方法在机械故障诊断中的应用现状,在此基础上,提出了本文所研究的内容以及对现有内容的创新之处。第2章,论述了分数阶小波变换的定义、性质和算法,在此基础上,提出了基于分数阶小波变换的机械故障诊断方法,并与传统小波变换进行了对比研究。该方法结合了小波变换和分数阶Fourier变换各自的优点,同时摒弃了各自的缺点,在分析中加入了一个可调节变量即分数阶阶数,使得该方法对非平稳信号的分析更加灵活。仿真研究表明,分数阶小波变换优于传统的小波变换,在对信号的滤波方面具有优势。最后,将提出的方法应用到转子碰磨故障中,实验结果验证了提出方法的有效性。第3章,论述了标准S变换的定义、算法及性质,本章将标准S变换和分数阶Fourier变换结合,构造了分数阶S变换,给出了分数阶S变换的定义式子和算法,并与标准S变换进行对比分析。该方法将S变换和分数阶Fourier变换各自的优点进行了结合,就能根据信号的特点来选择合适的分数阶阶数,从而做到对信号进行准确的分析。仿真结果表明,分数阶S变换具有明显的优势,不仅能反映信号的频率结构,而且得到了着比标准S变换更高的时频分辨率。最后,将提出的方法应用到滚动轴承故障诊断中,实验结果进一步验证了提出的方法的有效性。第4章,论述了广义S变换的定义、算法及性质,类似分数阶S变换的定义,构造了分数阶广义S变换,给出了分数阶广义S变换的定义和算法,并与标准S变换、广义S变换进行对比分析。该方法充分吸收了广义S变换和分数阶Fourier变换各自的优点,并将两者的优点进行了融合,使得分数阶广义S变换能灵活的对非平稳信号进行分析。仿真结果表明,分数阶广义S变换具有明显的优势,不仅能反映信号的频率结构,而且得到了比标准S变换、广义S变换更高的时频分辨率。最后,将提出的方法应用到滚动轴承故障诊断中,实验结果进一步验证了提出的分数阶广义S变换的有效性。第5章,结合局部均值分解和分数阶Fourier变换的各自优点,构造了分数阶局部均值分解,给出了其定义和算法,在此基础上,提出了基于分数阶LMD的Wigner分布的机械故障诊断方法,同时,将提出的方法与传统的Wigner分布进行了对比研究,仿真和实验结果表明,分数阶局部均值分解优于传统的Wigner分布,能有效地消除其交叉项,具有很高的时频分辨率,能有效低反映故障的特征频率。第6章,对本文的研究内容给以了总结,并给出了值得进一步研究问题。
[Abstract]:This paper is based on the National Natural Science Foundation (51261024510753725126503950775208), the national key research and development project (2016YFF0203000), the open fund of the National Key Laboratory of mechanical transmission (No.SKLMT-KFKT-201514) and the No.GJJ12405 (No.GJJ150699) of the Jiangxi Provincial Education Department (No.GJJ12405, No.GJJ150699), using fractional Fourie The unique characteristic of R transform is to extend the traditional signal processing method based on Fourier transform to the domain of fractional Fourier transform. Some effective fractional order nonstationary signal processing methods, fractional order wavelet transform, fractional order S transform, fractional order generalized S transform, fractional order partial mean decomposition and so on are proposed and applied. The main research contents of this paper include the following aspects: the first chapter, the following aspects: the background and the significance of the research, the status of the time frequency analysis method at home and abroad, and the time frequency analysis based on the kernel function and the time frequency analysis based on the signal decomposition, The three aspects of the parametric time-frequency analysis are discussed. At the same time, the application of the existing time-frequency analysis method in the mechanical fault diagnosis is also discussed. On this basis, the contents of this paper and the innovation of the existing content are put forward. In the second chapter, the definition, properties and algorithms of fractional small wave transform are discussed. A method of mechanical fault diagnosis based on fractional wavelet transform is proposed and compared with the traditional wavelet transform. The method combines the advantages of the wavelet transform and the fractional Fourier transform. At the same time, the method discarded their respective shortcomings and added an adjustable variable, the fractional order in the analysis, which makes the method not flat. The analysis of the stable signal is more flexible. The simulation study shows that the fractional wavelet transform is superior to the traditional wavelet transform and has advantages in the signal filtering. Finally, the proposed method is applied to the rotor rubbing fault. The experimental results verify the effectiveness of the proposed method. The third chapter discusses the definition, algorithm and properties of the standard S transform. In this chapter, the fractional order S transform is constructed by combining standard S transform with fractional order Fourier transform. The definition and algorithm of fractional order S transform are given, and the comparison analysis is made with standard S transform. This method combines the advantages of S transform and fractional Fourier transform, and can choose the appropriate fractional order according to the characteristics of the signal. The simulation results show that the fractional S transform has obvious advantages, which can not only reflect the frequency structure of the signal, but also get a higher time-frequency resolution than the standard S transform. Finally, the proposed method is applied to the fault diagnosis of the rolling bearing, and the experimental results are further verified. The fourth chapter discusses the definition, algorithm and properties of generalized S transform, which is similar to the definition of fractional order S transform, constructs fractional order generalized S transform, gives the definition and algorithm of fractional order generalized S transform, and compares it with standard S transformation and generalized S transformation. This method fully absorbs the generalized S transformation and fractional order Fou. Rier transform each advantage and combine the advantages of the two. The fractional order generalized S transform can be used to analyze the nonstationary signal flexibly. The simulation results show that the fractional order generalized S transform has obvious advantages, not only can reflect the frequency structure of the signal, but also get a higher time frequency than the standard S transform and the generalized S transform. Finally, the proposed method is applied to the fault diagnosis of rolling bearings. The experimental results further verify the effectiveness of the proposed fractional order generalized S transform. The fifth chapter, combining the advantages of local mean decomposition and fractional order Fourier transform, constructs fractional order partial mean decomposition, and gives its definition and algorithm. The method of mechanical fault diagnosis based on Wigner distribution based on fractional LMD is proposed. At the same time, the proposed method is compared with the traditional Wigner distribution. The simulation and experimental results show that the fractional partial mean decomposition is superior to the traditional Wigner distribution. It can effectively eliminate its cross term, with high time-frequency resolution and low efficiency. The sixth chapter summarizes the research contents of this paper, and gives further research questions.

【学位授予单位】：南昌航空大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH17

【参考文献】