振动信号的包络解调分析方法研究及应用
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摘要
本文以机械故障振动信号的包络解调方法为研究对象,在分别回顾现有包络解调方法的原理、特点及存在的问题基础上(如Hilbert变换、广义检波滤波、能量算子以及基于循环平稳和经验模态分解的解调方法等),运用解析小波变换、S变换和随机共振理论,着重研究了周期或几乎周期调制信号的包络解调新方法,期望所提出的方法具有良好的抗噪声能力。
解析小波是复小波,由于其实部和虚部可构成Hilbert变换对,因此常用于故障振动信号的包络提取,其中的Morlet小波最常用。在阐述了解析小波频谱为一实值函数是其实部和虚部构成Hilbert变换对的一个充分条件后,论证了“这类解析小波变换系数的实部和虚部同样构成Hilbert变换对”的结论。由此直接推知,谐波小波、谐波组合小波也属于这类解析小波,其对信号的变换可用于提取信号的包络。在这些基础上,提出了一种基于谐波组合小波变换的周期调制信号的包络解调方法,该方法通过谐波组合小波变换简便地实现了信号梳状滤波和包络解调的统一。由于它基于信号的梳状滤波,显然比基于带通滤波的包络解调方法(包括Morlet小波方法)具有更好的抗噪声能力,可得到简明的解调谱特征。
S变换是同时具有连续小波变换和短时傅里叶变换特征的一种新的时频局域分析方法。它与一个特定的连续Morlet小波变换有着内在联系,是对该Morlet小波变换结果的相位校正。基于窄带调幅信号的S变换时频谱的切片是该信号包络的事实,提出用奇异值分解的周期性检测方法,在S变换时频谱中检测周期调幅信号的特征频率,并对含有周期或几乎周期分量的切片(即包络)用奇异值分解提取该分量,从而实现周期调幅信号的包络解调分析。由于奇异值分解的周期或几乎周期分量检测方法在抗噪声能力上优于频谱和自相关函数分析,又该方法从含有干扰分量的切片中直接提纯周期调幅信号的包络,因此它适用于强噪声干扰下周期调幅信号的包络解调分析。
随机共振在微弱信号的增强放大和检测方面有着独特的优势。结合双稳系统随机共振效应和常用的包络解调方法,提出了增强放大微弱的低频调制信号,在解调谱中识别低频调制频率的方法。通过调节计算步长和双稳系统形状参数,成功实现了直接增强放大弱的低频调制信号,而不是高频载波信号。为获得较好的随机共振效果,采用自动搜索确定最佳计算步长和双稳系统形状参数的策略。由仿真和实测的弱周期调制信号分析可知,所提出方法对于低频周期调制信号的解调谱分析效果明显优于FFT谱分析和常用解调方法。
以上所提出的周期或几乎周期调制信号的包络解调新方法,通过信号仿真以及用于齿轮和滚动轴承故障实测振动信号的分析,证实了它们的有效性,以及某些独特的优越性。有理由相信,它们在齿轮和滚动轴承故障诊断方面有着良好的应用前景。
This academic dissertation has devoted its research subject to demodulation or enveloping based methods of mechanical faults vibration signals. Some existing methods, such as the Hilbert transform, gerneralized demodulating-filtering, energy operator, cyclostationary and empirical mode decomposition based methods, were briefly reviewed for their principles, features and disadvantages. Analytic wavelet transforms, S- transform and the stochastic resonance effect were explored in the dissertation to develop new demodulation methods for cycle-modulating signals, which are expected to have good noiseproof properties.
Analytic wavelets are complex wavelets, whose real part and imaginary part can constitute an Hilbert transform pair, and usually used to extract the signal envelope. The Morlet wavelet is the most familiar one amongst them. A sufficient condition for a analytic wavelet to be an Hilbert transform pair is presented, that is the analytic wavelet with real valued frequency representation. For this group of analytic wavelets, the conclusion that the real part and imaginary part of their transform coefficients also constitute an Hilbert transform pair was perfectly deduced. Upon these discussions, a straightforward deduction is that Harmonic wavelets and combined Harmonic wavelets also belong to above mentioned analytic wavelets. They can also be used to the envelope-demodulation of mechanical faults vibration signals. Combined Harmonic wavelets were proposed to design a comb-filter and a envelope-demodulator for a specified cycle-modulating signal. This technique integrates comb-filtering and envelope-demodulating, and can obtain a clear and noiseproof envelope spectrum, compared to the band-pass filtering based demodulation techniques.
S-transform is a new time-frequency analysis method, and simultaneously has good features of continuous wavelet transform and short-time Fourier transform. It has a interrelation with a concrete continuous Morlet wavelet transform, is a phase correction of the Morlet wavelet transform. The fact that the slice of S-transform time-frequency spectrum could be the envelope of the amplitude-modulated signal is employed to detect and extract a periodical amplitude-modulating signal and its envelope, combing with a robust method for periodicity detection and characterization of irregular cyclical series in term of embedded periodic components. This periodicity detection method is based on singular value decomposition (SVD), and has the advantage over the spectrum analysis and autocorrelation function analysis in detecting periodic components embedded in stronger noises. Using simulated signals and the faulty bearing vibration signals, the proposed envelope-demodulation method was proven to be noiseproof.
The stochastic resonance effect has particular advantages on enhancing and detecting weak signals. Enhancement and extraction of the weak low-frequency amplitude-modulated signals were studied using the combination of the stochastic resonance (SR) and the common envelope demodulation analysis. The SR effect of the signal was realized only for the low-frequency amplitude-modulating signal, not for high-frequency carrier signal, by using the step-changed numerical algorithm and the adjustment of the bistable system parameters. An automatic searching strategy for optimal the algorithm step and the bistable system parameters was adopted in order to achieve the maximum SR effect. The effectiveness of the proposed method was demonstrated on both simulated signals and real vibration signals of a low-speed and heavy-duty gearbox. It was proven to be superior to the spectrum analysis and the common envelope-demodulation analysis.
The proposed envelope-demodulation methods in this dissertation have be demonstrated on their effectiveness and superiority to the common envelope-demodulation methods. It's worth reling that they would have a promising application for the fault diagnosis of the gear and rolling element bearings.
解析小波是复小波,由于其实部和虚部可构成Hilbert变换对,因此常用于故障振动信号的包络提取,其中的Morlet小波最常用。在阐述了解析小波频谱为一实值函数是其实部和虚部构成Hilbert变换对的一个充分条件后,论证了“这类解析小波变换系数的实部和虚部同样构成Hilbert变换对”的结论。由此直接推知,谐波小波、谐波组合小波也属于这类解析小波,其对信号的变换可用于提取信号的包络。在这些基础上,提出了一种基于谐波组合小波变换的周期调制信号的包络解调方法,该方法通过谐波组合小波变换简便地实现了信号梳状滤波和包络解调的统一。由于它基于信号的梳状滤波,显然比基于带通滤波的包络解调方法(包括Morlet小波方法)具有更好的抗噪声能力,可得到简明的解调谱特征。
S变换是同时具有连续小波变换和短时傅里叶变换特征的一种新的时频局域分析方法。它与一个特定的连续Morlet小波变换有着内在联系,是对该Morlet小波变换结果的相位校正。基于窄带调幅信号的S变换时频谱的切片是该信号包络的事实,提出用奇异值分解的周期性检测方法,在S变换时频谱中检测周期调幅信号的特征频率,并对含有周期或几乎周期分量的切片(即包络)用奇异值分解提取该分量,从而实现周期调幅信号的包络解调分析。由于奇异值分解的周期或几乎周期分量检测方法在抗噪声能力上优于频谱和自相关函数分析,又该方法从含有干扰分量的切片中直接提纯周期调幅信号的包络,因此它适用于强噪声干扰下周期调幅信号的包络解调分析。
随机共振在微弱信号的增强放大和检测方面有着独特的优势。结合双稳系统随机共振效应和常用的包络解调方法,提出了增强放大微弱的低频调制信号,在解调谱中识别低频调制频率的方法。通过调节计算步长和双稳系统形状参数,成功实现了直接增强放大弱的低频调制信号,而不是高频载波信号。为获得较好的随机共振效果,采用自动搜索确定最佳计算步长和双稳系统形状参数的策略。由仿真和实测的弱周期调制信号分析可知,所提出方法对于低频周期调制信号的解调谱分析效果明显优于FFT谱分析和常用解调方法。
以上所提出的周期或几乎周期调制信号的包络解调新方法,通过信号仿真以及用于齿轮和滚动轴承故障实测振动信号的分析,证实了它们的有效性,以及某些独特的优越性。有理由相信,它们在齿轮和滚动轴承故障诊断方面有着良好的应用前景。
This academic dissertation has devoted its research subject to demodulation or enveloping based methods of mechanical faults vibration signals. Some existing methods, such as the Hilbert transform, gerneralized demodulating-filtering, energy operator, cyclostationary and empirical mode decomposition based methods, were briefly reviewed for their principles, features and disadvantages. Analytic wavelet transforms, S- transform and the stochastic resonance effect were explored in the dissertation to develop new demodulation methods for cycle-modulating signals, which are expected to have good noiseproof properties.
Analytic wavelets are complex wavelets, whose real part and imaginary part can constitute an Hilbert transform pair, and usually used to extract the signal envelope. The Morlet wavelet is the most familiar one amongst them. A sufficient condition for a analytic wavelet to be an Hilbert transform pair is presented, that is the analytic wavelet with real valued frequency representation. For this group of analytic wavelets, the conclusion that the real part and imaginary part of their transform coefficients also constitute an Hilbert transform pair was perfectly deduced. Upon these discussions, a straightforward deduction is that Harmonic wavelets and combined Harmonic wavelets also belong to above mentioned analytic wavelets. They can also be used to the envelope-demodulation of mechanical faults vibration signals. Combined Harmonic wavelets were proposed to design a comb-filter and a envelope-demodulator for a specified cycle-modulating signal. This technique integrates comb-filtering and envelope-demodulating, and can obtain a clear and noiseproof envelope spectrum, compared to the band-pass filtering based demodulation techniques.
S-transform is a new time-frequency analysis method, and simultaneously has good features of continuous wavelet transform and short-time Fourier transform. It has a interrelation with a concrete continuous Morlet wavelet transform, is a phase correction of the Morlet wavelet transform. The fact that the slice of S-transform time-frequency spectrum could be the envelope of the amplitude-modulated signal is employed to detect and extract a periodical amplitude-modulating signal and its envelope, combing with a robust method for periodicity detection and characterization of irregular cyclical series in term of embedded periodic components. This periodicity detection method is based on singular value decomposition (SVD), and has the advantage over the spectrum analysis and autocorrelation function analysis in detecting periodic components embedded in stronger noises. Using simulated signals and the faulty bearing vibration signals, the proposed envelope-demodulation method was proven to be noiseproof.
The stochastic resonance effect has particular advantages on enhancing and detecting weak signals. Enhancement and extraction of the weak low-frequency amplitude-modulated signals were studied using the combination of the stochastic resonance (SR) and the common envelope demodulation analysis. The SR effect of the signal was realized only for the low-frequency amplitude-modulating signal, not for high-frequency carrier signal, by using the step-changed numerical algorithm and the adjustment of the bistable system parameters. An automatic searching strategy for optimal the algorithm step and the bistable system parameters was adopted in order to achieve the maximum SR effect. The effectiveness of the proposed method was demonstrated on both simulated signals and real vibration signals of a low-speed and heavy-duty gearbox. It was proven to be superior to the spectrum analysis and the common envelope-demodulation analysis.
The proposed envelope-demodulation methods in this dissertation have be demonstrated on their effectiveness and superiority to the common envelope-demodulation methods. It's worth reling that they would have a promising application for the fault diagnosis of the gear and rolling element bearings.
引文
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