摘要
振动信号的特征提取一直是设备状态监测及故障诊断领域的研究前沿，特别是大型复杂装备系统早期故障、微弱故障及多源复合故障的非线性非平稳信号特征提取问题存在着更大的困难，已成为该领域最具挑战性的研究热点。基于对频率内涵本质的重新考察和认识，本文提出了广义局部频率新概念，深入开展了适于非线性非平稳信号故障特征提取方法研究，并成功应用于往复压缩机组多源冲击振动故障特征的提取。该研究对信号频谱及时频分析理论发展具有重要科学意义，对具有非线性非平稳信号特点的其它工程领域的特征提取也具有广泛的应用前景。
在频谱及时频分析方法中广泛应用的全局频率（即周期的倒数）与瞬时频率（即相位的导数）概念，分别在描述信号的整体概貌及局部细节特征方面发挥了重要作用。然而，它们在表征非线性非平稳信号特征方面仍然存在局限性，为此，本文提出了广义局部频率新概念及其定义，通过构造广义局部频率的频域和时频域表达方法，使其兼容全局频率和瞬时频率优势的同时，克服了全局频率概念只对周期信号才具有物理意义而无法描述频率及幅值随时间变化非周期信号特征的缺陷，弥补了瞬时频率只对窄带信号才能给出合理物理解释而损失众多大尺度频率信息的不足。此外，通过仿真实例，对广义局部频率概念的适用性进行验证，表明了广义局部频率定义的准确性。
以短时Fourier变换、小波变换、Wigner-Ville分布、Chirplet变换、EMD及LMD等为基础的时频分析方法，在旋转机械的典型故障诊断过程中发挥着非常有效的作用。但是，随着故障诊断领域向着大型复杂装备系统的延伸，振动信号表现出较强的非线性、非平稳及非高斯等复杂特性，时频分布变得非常复杂，频带与故障激励之间缺乏映射关系，许多频率成分物理意义不明确，难以提取出足以识别故障的有用特征信息。为此，本文提出了基于自适应波形分解的广义局部频率时频分析方法，实现了多分量非平稳信号的广义局部频率时频特征提取，摆脱了现有时频分析方法依赖先验知识将信号按基函数展开思想的束缚，具有良好的自适应性。此外，为了减少噪声对非平稳信号时频分析的影响，提出了将自适应波形分解与互信息法相融合的降噪技术，通过仿真实例对比，验证了其有效性。
功率谱图出现连续谱峰及噪声背景等现象往往作为辨识系统处于混沌状态的重要依据。但是，功率谱是以平稳假设为前提，在分析具有非平稳性的非线性时间序列时存在明显缺陷。为此，本文提出了基于广义局部频率的频域分析方法，以Duffing系统为对象，揭示了系统演化过程中的频域分岔现象，克服了功率谱分析时产生的虚假频率信息，有效表征了不同系统状态下非线性时间序列频域结构特点及分布规律。另外，通过基于自适应波形分解的广义局部频率解调分析，发现了混沌时间序列具有频率调制特性及频率调制的相似性特征。
广义局部频率频域和时频域特征量虽然能够准确形象地描述非线性非平稳信号本质信息，但其特征值受噪声及样本选取的影响，不同信号特征量级差别较大，分析结果的可比性、可重复性及稳定性较差。为了弥补这方面的不足，本文应用Lempel-Ziv复杂度方法，定量分析了广义局部频率时频特征的复杂性，揭示出的信号时频结构相对于时域结构更加简洁、物理意义更加明确，更能够准确辨识各信号特征类型。通过对滚动轴承振动信号的实例分析，进一步验证了广义局部频率时频特征提取及其复杂测度分析的有效性。
往复压缩机组多源冲击振动信号表现出较强的非线性非平稳特征，现有时频分析方法难以提取出足以识别故障的特征信息，在本文理论研究基础上，应用广义局部频率谱分析与时频分析方法，有效揭示了气阀不同状态下振动信号的整体概貌统计特征及局部细节时变特征，为往复压缩机组气阀故障诊断提供了更加丰富及意义明确的特征依据。另外，应用Lempel-Ziv复杂度方法对气阀信号的时域与时频域特征进行复杂测度分析，结果表明气阀信号的广义局部频率时频特征结构相比于时域结构更加简洁，在一定程度上降低了噪声带来的随机性干扰，更能够有效表征不同气阀状态的非线性关系，并分别给出了其LZC特征的定量参考标准，为往复压缩机气阀故障诊断提供了参考依据。
Feature extraction of vibration signal has always been the frontier in conditionmonitoring and fault diagnosis of equipment. Particularly, there exist greatdifficulties in feature extraction of nonlinear nonstationary signal of early fault, weakfault and multiple faults for large and complex equipment. It has become the mostchallenging problem in the field. Based on the re-examining and re-understanding offrequency, a novel concept of general local frequency is proposed. The research onfault feature extraction of nonlinear nonstationary signal is investigated andsuccessfully applied to the multi-source impact vibration signal of reciprocatingcompressor. This study has important scientific significance in development ofspectrum analysis and time-frequency analysis. It also has broad application prospectin other nonlinear nonstationary engineering fields.
The concept of global frequency (i.e., the reciprocal of periodic) andinstantaneous frequency (i.e. the derivative of phase) has been widely used inspectrum analysis and time-frequency analysis respectively. They play an importantrole in describing the overview and detail of signals. However, there are also somelimitations in feature extraction of nonlinear nonstationary signal. To solve thisproblem, a novel concept of general local frequency is proposed, which presentsboth the advantage of global frequency and instantaneous frequency according to theexpression in frequency domain and time-frequency domain. It not only overcomethe limitation of global frequency which is meaningful for period signal and can notdescribe the non-period signal with varying frequency and amplitude, but also solvethe problem of instantaneous frequency which is defined for narrow-band signal andlack of many large-scale frequency information. In addition, some simulations aretaken as example to verify the applicability of general local frequency, whichdemonstrate the accuracy of general local frequency.
Time-frequency analysis techniques, such as short time Fourier transform, wavelet transform Wigner-Ville distribution, chirplet transform, empirical modeldecomposition and local mean decomposition, have been played an effective role infault diagnosis of rotating machinery. However, with the extension of fault diagnosistoward large and complex equipment, whose vibration signal presents complexcharacteristics of nonlinearity, nonstationarity and non-Gaussian. Its time-frequencydistribution will become very complicated. Between the frequency band and faultfeature is lack of mapping. The physical meaning of some frequency components isnot clear, and it is difficult to extract useful feature information. To solve thisproblem, a novel time-frequency analysis method of general local frequency basedon adaptive waveform decomposition is presented for extracting the time-frequencyfeatures of multi-component nonstationary signal. The proposed method has gottenrid of the thought that signal is composed by seriers of basis function which rely onsome priori knowledge, and it still has a well self-adaptive. In addition, a fusionnoise reduction technology based on adaptive waveform decomposition and mutualinformation is investigated and the simulation results verify its effectiveness.
The phenomenon that power spectrum contains the continuous peaks and noisebackground is often an important basis for recognizing system in chaotic state.However, the power spectrum is based on the stationary assumption, which is noteffective in analyzing the nonlinear nonstationary time series. Therefore, a novelfrequency domain analysis method based on general local frequency is proposed.The Duffing system is taken as example, the bifurcation phenomenon in frequencydomain of Duffing system is investigated. The method not only can over come thefalse frequency information generated by the power spectrum, but also caneffectively describe the structure and distribution of nonlinear signal in frequencydomain. In addition, the modulation characteristic and modulation similarity ofchaos time series are found by general local frequency analysis based on adaptivewaveform decomposition.
Although the essential information of nonlinear nonstationary signals can be described by the features in frequency-domain and time-frequency domain ofgeneral local frequency, their values are seriously influenced by noise and sampleselection. There are great differences in magnitude order for various signals. Thecomparability, repeatability and stability of results are poor. In order to compensatethese deficiencies, the Lempel-Ziv complexity is applied to analyze thetime-frequency complexity of general local frequency. Comparing the time domainanalysis, the structure of time-frequency is simpler, the physical meaning is moreclearly and the type of signal is identified more accurately. Vibration signals ofrolling bearing are taken as examples, and the effectiveness of complexity analysisof time-frequency feature extracted by general local frequency is verified.
Multiple source impact signals of reciprocating compressor present typicalnonlinear nonstationary characteristics. It is difficult to extract feature informationby existing time-frequency analysis methods. According to the theoretical research inthis paper, the method of spectrum analysis and time-frequency analysis based ongeneral local frequency is applied to describe the overview and detail of vibrationsignals for gas valve in different states, which can supply more rich and meaningfulfeatures for fault diagnosis of reciprocating compressor. In addition, the Lempel-Zivcomplexity is also applied to feature analysis in time domain and time-frequencydomain of gas valve signal. The results indicate that the structure of time-frequencyis simpler than time domain structure, and the proposed method can reduce theinterference of randomness brought by noise in some extent. So it is more effectivelyin describing the nonlinear relationship of gas valve in different states. In addition,the standard of LZC feature for gas valve in different states is given, which can beused as the auxiliary reference of fault diagnosis for reciprocating compressor.
引文
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