小波分析及其在齿轮箱故障诊断中应用研究
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摘要
作为快速发展的信号处理方法，小波变换在故障诊断等领域得到广泛应用。为了进一步提高其分析精度，提出一种小波系数校正算法。为了提高小波阈值去噪算法中阈值确定的准确性，提出一种基于系数校正的改进算法。提出一种基于内积变换和小波的特征信号分离算法以提取平稳调制和冲击调制两种分量，提高故障诊断的精度。
通过对小波滤波器特性的分析，确定出导致系数失真的原因，提出一种基于小波滤波器互补特性的小波系数校正算法，以提高系数精度。算法通过引入分离算子在隔点采样之前将卷积结果分成两部分，利用设计的转移算子将相应系数作转换后按频带进行对应相加，从而实现系数补偿校正。在理论上经过一次补偿校正能将幅值最大误差由50%降到25%。分析了补偿计算次数对于精度以及算法复杂度的影响，理论上每经过一次补偿计算最大误差降低一半。仿真结果表明经过2次、4次补偿计算，最大幅值误差分别降至10%、2%。分析了消失矩对于精度的影响，指出消失矩的增大对靠近截止频率的那些分量精度提高相对有限。对具有外圈故障的滚动轴承振动信号分析结果表明，该算法能有效增强故障特征频率分量，提高了故障诊断的准确性。
针对小波阈值去噪算法，提出一种基于小波系数校正的改进算法。该算法首先利用小波滤波器互补特性，对小波变换系数进行校正；再根据校正所得系数确定阈值，然后进行阈值去噪处理，提高阈值的准确性，从而改善小波阈值去噪算法的去噪效果。对多种信噪比的Bumps、Heavy Sine信号分别采用软、硬阈值函数进行仿真去噪处理，其结果与使用标准小波阈值去噪算法相比，改进的小波阈值去噪方法能有效保留原始信号的奇异性，信噪比最大能提高约3dB，最小提高0.2dB。工程实例也表明，改进的小波阈值去噪方法在对噪声进行抑制的同时能有效突出有用信息。
提出一种基于内积变换和小波的特征信号分离算法。算法中利用幅值调制信号和Laplace小波的实部分别作为平稳调制和冲击调制基函数，基函数的选择具有明确的物理意义。根据信号频率分布特征确定平稳调制基函数中相关参数变化范围，利用Laplace小波滤波算法确定出固有频率、阻尼参数的合理变化范围，大幅度提高了算法运算效率。根据信号与基函数之间的相关性确定基函数，从而实现信号中不同成分的分解。无噪声和有噪声(SNR=5dB)的仿真信号以及变速器振动信号分析结果都表明该算法能将信号中平稳和冲击两种调制分量较准确地提取出来。
As a fast delveloping signal processing algorithm, the wavelet transform has been widelyused in many areas such as fault diagnosis successfully. In order to improve its accuracy, anew method is presented in this paper. For improving the accuracy of the threshold in thewavelet threshold denoising algorithm, a new algorithm based on coefficients correction isproposed. An algorithm used to extract the stationary modulation component and the impactcomponent in the signal is presented to improve the accuracy of fault diagnosis.
By analyzing the characteristic of the wavelet filter, the cause of the distortion isdetermined. A new method is presented to rectify the distortion and improve the accuracy. Inthis method, a splitting operator is used to split the convolution results into two parts beforedown-sampling, which are processed by an imported transferring factor to the same frequencyband so that they can be added directly. By this, the coefficients are corrected. Theoretically,the maximum error could be reduced from50%to25%with one time compensationcalculation. The influences of the correcting times on the accuracy and the complexity of thealgorithm are analyzed. The results show that with two and four times compensationcalculations, the error is reduced to10%and2%respectively. The influence of the vanishingmoment is analyzed. The result shows that increasing the vanishing moment can effectivelyimprove the coefficient accuracy of the components far from the cutoff frequency. For thecomponents near the cutoff frequency, the effect is limited. The experiment result of thevibration signal of a roller bearing with outer ring fault shows that the proposed method caneffectively magnify the amplitude of the fault frequencies in practice.
An improved wavelet threshold denoising algorithm is proposed based on the coefficientcorrecting method. In this algorithm, the wavelet transform coefficients are corrected by usingthe complementary characteristic of wavelet filters, then the threshold is calculated and usedfor denosing. The proposed algorithm is used to process the Bumps and Heavy Sine signals ofdifferent SNR by using the soft and hard threshold functions. The results show that theimproved wavelet threshold denosing algorithm can effectively preserve the singularity of theoriginal signal. Compared with the results gotten by the standard wavelet threshold denoisingalgorithm, the maximum of the SNR is increased by3dB and the minimum is0.2dB. Theexperiment result shows that the improved method can suppress the noise and extract theuseful characteristic components effectively.
A method for extracting the characteristic signals based on the inner product and wavelet isproposed. In this algorithm, the amplitude modulation signal and the real part of the Laplace wavelet are used as the basis functions of stationary modulation and impact modulation. Thechoices of basis functions have a clear physical meaning. The parameters of the stationarymodulation basis are determined by the frequency distribution of the signal. The naturalfrequency and the damping parameters are determined by using the Laplace wavelet filteringalgorithm. By doing this, the operation efficiency of the algorithm can be greatly improved.By determined the base functions according to the correlation between the signal and the basisfunctions, the signal is decomposed into different parts. The result of two kinds of simulationsignals and the transmission vibration signal show the algorithm can extract the twomodulation signals accurately.
通过对小波滤波器特性的分析，确定出导致系数失真的原因，提出一种基于小波滤波器互补特性的小波系数校正算法，以提高系数精度。算法通过引入分离算子在隔点采样之前将卷积结果分成两部分，利用设计的转移算子将相应系数作转换后按频带进行对应相加，从而实现系数补偿校正。在理论上经过一次补偿校正能将幅值最大误差由50%降到25%。分析了补偿计算次数对于精度以及算法复杂度的影响，理论上每经过一次补偿计算最大误差降低一半。仿真结果表明经过2次、4次补偿计算，最大幅值误差分别降至10%、2%。分析了消失矩对于精度的影响，指出消失矩的增大对靠近截止频率的那些分量精度提高相对有限。对具有外圈故障的滚动轴承振动信号分析结果表明，该算法能有效增强故障特征频率分量，提高了故障诊断的准确性。
针对小波阈值去噪算法，提出一种基于小波系数校正的改进算法。该算法首先利用小波滤波器互补特性，对小波变换系数进行校正；再根据校正所得系数确定阈值，然后进行阈值去噪处理，提高阈值的准确性，从而改善小波阈值去噪算法的去噪效果。对多种信噪比的Bumps、Heavy Sine信号分别采用软、硬阈值函数进行仿真去噪处理，其结果与使用标准小波阈值去噪算法相比，改进的小波阈值去噪方法能有效保留原始信号的奇异性，信噪比最大能提高约3dB，最小提高0.2dB。工程实例也表明，改进的小波阈值去噪方法在对噪声进行抑制的同时能有效突出有用信息。
提出一种基于内积变换和小波的特征信号分离算法。算法中利用幅值调制信号和Laplace小波的实部分别作为平稳调制和冲击调制基函数，基函数的选择具有明确的物理意义。根据信号频率分布特征确定平稳调制基函数中相关参数变化范围，利用Laplace小波滤波算法确定出固有频率、阻尼参数的合理变化范围，大幅度提高了算法运算效率。根据信号与基函数之间的相关性确定基函数，从而实现信号中不同成分的分解。无噪声和有噪声(SNR=5dB)的仿真信号以及变速器振动信号分析结果都表明该算法能将信号中平稳和冲击两种调制分量较准确地提取出来。
As a fast delveloping signal processing algorithm, the wavelet transform has been widelyused in many areas such as fault diagnosis successfully. In order to improve its accuracy, anew method is presented in this paper. For improving the accuracy of the threshold in thewavelet threshold denoising algorithm, a new algorithm based on coefficients correction isproposed. An algorithm used to extract the stationary modulation component and the impactcomponent in the signal is presented to improve the accuracy of fault diagnosis.
By analyzing the characteristic of the wavelet filter, the cause of the distortion isdetermined. A new method is presented to rectify the distortion and improve the accuracy. Inthis method, a splitting operator is used to split the convolution results into two parts beforedown-sampling, which are processed by an imported transferring factor to the same frequencyband so that they can be added directly. By this, the coefficients are corrected. Theoretically,the maximum error could be reduced from50%to25%with one time compensationcalculation. The influences of the correcting times on the accuracy and the complexity of thealgorithm are analyzed. The results show that with two and four times compensationcalculations, the error is reduced to10%and2%respectively. The influence of the vanishingmoment is analyzed. The result shows that increasing the vanishing moment can effectivelyimprove the coefficient accuracy of the components far from the cutoff frequency. For thecomponents near the cutoff frequency, the effect is limited. The experiment result of thevibration signal of a roller bearing with outer ring fault shows that the proposed method caneffectively magnify the amplitude of the fault frequencies in practice.
An improved wavelet threshold denoising algorithm is proposed based on the coefficientcorrecting method. In this algorithm, the wavelet transform coefficients are corrected by usingthe complementary characteristic of wavelet filters, then the threshold is calculated and usedfor denosing. The proposed algorithm is used to process the Bumps and Heavy Sine signals ofdifferent SNR by using the soft and hard threshold functions. The results show that theimproved wavelet threshold denosing algorithm can effectively preserve the singularity of theoriginal signal. Compared with the results gotten by the standard wavelet threshold denoisingalgorithm, the maximum of the SNR is increased by3dB and the minimum is0.2dB. Theexperiment result shows that the improved method can suppress the noise and extract theuseful characteristic components effectively.
A method for extracting the characteristic signals based on the inner product and wavelet isproposed. In this algorithm, the amplitude modulation signal and the real part of the Laplace wavelet are used as the basis functions of stationary modulation and impact modulation. Thechoices of basis functions have a clear physical meaning. The parameters of the stationarymodulation basis are determined by the frequency distribution of the signal. The naturalfrequency and the damping parameters are determined by using the Laplace wavelet filteringalgorithm. By doing this, the operation efficiency of the algorithm can be greatly improved.By determined the base functions according to the correlation between the signal and the basisfunctions, the signal is decomposed into different parts. The result of two kinds of simulationsignals and the transmission vibration signal show the algorithm can extract the twomodulation signals accurately.
引文
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