论文部分内容阅读
摘要: 为了从滚动轴承故障振动信号中提取出冲击特征,以进行轴承故障诊断,提出基于S变换时频谱奇异值分解(SVD)的信号降噪方法。S变换是一种信号时频表示方法,适合于处理与分析非平稳的冲击特征信号。在SVD降噪过程中,数据矩阵由信号的S变换谱系数构成;奇异值序列的置零阈值位置坐标可由奇异值差分谱最前面部分峰值群的最后一个峰值点序号来确定。最后对降噪的数据矩阵进行S逆变换,获得信号的时域冲击特征。仿真研究表明,基于S变换时频谱的SVD降噪方法可以成功地从低信噪比信号中提取出周期性的冲击特征。将本方法用于处理与分析滚动轴承故障振动信号,根据所提取出的冲击特征出现频率,能够方便有效地实现轴承相关故障的诊断。关键词: 故障诊断; 滚动轴承; S变换; 奇异值分解; 冲击特征
中图分类号:TH165.3; TN911.7文献标识码: A文章编号: 10044523(2014)04062108
引言
滚动轴承广泛应用于各类旋转机械设备中,是此类机械最主要的故障来源之一。滚动轴承元件工作表面发生局部损伤时,损伤点在工作过程中会被撞击,从而产生冲击振动信号,在理想情况下,该信号中的冲击特征出现频率即为损伤点被撞击的频率,又可称为轴承故障特征频率[1]。但是,滚动轴承故障振动信号是典型的非平稳、非高斯信号,加之旋转机械设备的结构的复杂性以及工作环境的多样性,各种激励源产生的振动信号相互耦合,导致轴承故障源振动信号的冲击特征通常淹没在强背景信号与噪声中,比较难以识别。因此,若能成功提取滚动轴承故障振动信号中的冲击特征,即可方便有效地对轴承相关故障进行诊断。
针对冲击特征信号的处理,现有的方法主要是利用信号高阶统计量,如峭度、偏斜度或者峰态等,对冲击成分具有高度敏感性的特点,实现冲击特征的检测。文献[2~4]以高阶统计量为优化目标函数构造盲解卷积滤波器,检测信号中的弱冲击成分,但此方法中滤波器长度的很难确定,限制了其应用。文献[5,6]以峭度指标和互相关系数相结合的加权峭度指标为优化目标,利用随机共振检测方法提取信号冲击成分,具有一定的可行性,然而对于低信噪比的信号,加权峭度指标存在一定的局限性,且参数优化较为困难,影响检测结果。从另外一个角度考虑,可以直接对噪声混合的冲击特征信号进行降噪,从而提取出冲击成分,这种方式简单直观,针对性强。
奇异值分解(SVD)降噪方法是一种非线性滤波方法,可以有效抑制信号中的宽带随机噪声,因此,本文采用SVD对包含冲击特征的滚动轴承故障振动信号进行降噪处理。将SVD用于一维时域信号的处理与分析,关键问题之一是构造合适的数据矩阵。针对此,目前最常用的方法是由一维源信号构造Hankel矩阵,其中一维源信号可以为原始的时域信号、小波分解某一尺度的细节信号或者EMD得到的某一本征模函数等[7~10]。但具体针对冲击特征信号,特别是低信噪比的冲击特征信号,Hankel矩阵无法表征信号的冲击特征,导致SVD处理过程中,冲击特征奇异值与噪声奇异值很难区分开来,达不到冲击特征提取的目的。
S变换是一种信号时频表示方法,适合于处理与分析非平稳信号,尤其是包含冲击特征的信号。因此,本文提出一种基于S变换时频谱SVD降噪的冲击特征提取方法。先将时域冲击特征信号进行S变换,获得信号的时频谱,然后由谱系数构成数据矩阵,对其进行SVD降噪处理,最后对降噪的数据矩阵进行S逆变换,重构时域冲击特征。
第4期郭远晶,等: S变换时频谱SVD降噪的冲击特征提取方法振 动 工 程 学 报第27卷1S变换
S变换是一种将一维时域信号变换到二维时频域的信号处理方法的S变换谱SVD降噪处理,所提取出的时域冲击特征并未表现出很严格的周期性。产生这种情况的原因主要有两个:第一个是滚动轴承在实际使用过程中,当其内圈或者外圈出现较严重的故障时,滚动体触碰到故障点,必然会激发较为强烈的冲击与振动,使得轴承无法正常匀速运转,且滚动体也不是做理想的纯滚动运动;第二个是有些冲击特征强度太小而淹没在噪声中,使得其很容易随着信号的SVD去噪而丢失掉。因此,故障振动信号中的冲击特征在全局时间段上可能不具备严格的周期性,但其在局部时间段上仍可以表现出显著的周期性,只要能够检测到该周期,然后计算对应的频率,将其与轴承元件的故障特征频率相比较,就可以实现滚动轴承相关故障的诊断。
6结论
S变换是一种信号时频表示方法,具备多分辨率特性,对于信号中的高频冲击成分具有较高敏感性,满足线性叠加原理,不存在交叉项的干扰,适合于处理与分析非平稳信号,尤其是冲击特征信号。
S变换时频谱可以很好地表征信号的冲击特征,适合于作为SVD降噪处理所需的数据矩阵。而奇异值差分谱最前面部分峰值群的最后一个峰值点序号可以作为奇异值序列置零阈值σth的位置坐标,并以此方式确定阈值σth。
相对于现有的冲击特征提取方法,基于S变换时频谱SVD降噪的冲击特征提取方法是一种新方法,其简单直观、针对性强、易于实现。虽然所提取出的冲击特征不可避免会出现一定的变形和失真,但作为最重要信息的冲击特征出现频率,可以完全有效地提取出来。
将本方法应用于滚动轴承故障振动信号的处理,能够成功提取出时域冲击特征的出现频率,结合轴承元件的故障特征频率,可以实现滚动轴承相关故障的诊断。参考文献:
[1]钟秉林, 黄仁. 机械故障诊断学[M]. 北京:机械工业出版社,2006.298—301.
Zhong Binglin, Huang Ren. Introduction to Machine Fault Diagnosis [M]. Beijing: China Machine Press, 2006. 298—301.
[2]Lee J Y, Nandi A K. Blind deconvolution of impactingsignals using higherorder statistics [J]. Mechanical Systems and Signal Processing, 1998, 12(2):357—371. [3]Lee J Y, Nandi A K. Extraction of impacting signals using blind deconvolution [J]. Journal of Sound and Vibration, 2000, 232(5):945—962.
[4]王宇, 伍星, 迟毅林, 等. 基于盲解卷积和聚类的机械弱冲击声信号提取[J]. 振动工程学报, 2009,22(6):620—624.
Wang Yu, Wu Xing, Chi Yilin, et al. Weak transient impulse signal extraction based on blind deconvolution and cluster in acoustical machine diagnosis [J]. Journal of Vibration Engineering, 2009,22(6):620—624.
[5]谭继勇, 陈雪峰, 何正嘉. 冲击信号的随机共振自适应检测方法[J]. 机械工程学报, 2010,46(23):61—67.
Tan Jiyong, Chen Xuefeng, He Zhengjia. Impact signal detection method with adaptive stochastic resonance [J]. Journal of Mechanical Engineering, 2010,46(23):61—67.
[6]李继猛, 陈雪峰, 何正嘉. 采用粒子群算法的冲击信号自适应单稳态随机共振检测方法[J]. 机械工程学报, 2011,47(21) :58—63.
Li Jimeng, Chen Xuefeng, He Zhengjia. Adaptive monostable stochastic resonance based on PSO with application in impact signal detection [J]. Journal of Mechanical Engineering, 2011,47(21):58—63.
[7]张波, 李健君. 基于Hankel矩阵与奇异值分解(SVD)的滤波方法以及在飞机颤振试验数据预处理中的应用[J]. 振动与冲击, 2009, 28(2):162—166.
Zhang Bo, Li Jianjun. Denoising method based on hankel matrix and SVD and its application in flight flutter testing data preprocessing [J]. Journal of Vibration And Shock, 2009, 28(2): 162—166.
[8]赵学智, 叶邦彦, 陈统坚. 奇异值差分谱理论及其在车床主轴箱故障诊断中的应用[J]. 机械工程学报, 2010,46(1):100—108.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Difference spectrum theory of singular value and its application to the fault diagnosis of headstock of lathe[J]. Journal of Mechanical Engineering, 2010, 46(1): 100—108.
[9]赵学智, 叶邦彦, 陈统坚. 基于小波—奇异值分解差分谱的弱故障特征提取方法[J]. 机械工程学报,2012,48(7):37—48.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Extraction method of faint fault feature based on waveletSVD difference spectrum[J]. Journal of Mechanical Engineering, 2012, 48(7): 37—48.
[10]张超, 陈建军, 徐亚兰. 基于EMD分解和奇异值差分谱理论的轴承故障诊断方法[J]. 振动工程学报,2011,24(5):539—545.
Zhang Chao, Chen Jianjun, Xu Yalan. A bearing fault diagnosis method based on EMD and difference spectrum theory of singular value[J]. Journal of Vibration Engineering, 2011, 24(5): 539—545.
[11]Stockwell R G, Mansinha L, Lowe R P. Localization of the complex spectrum: the S transform [J]. IEEE Transactions on Signal Processing, 1996,44(4):998—1 001.
[12]Stockwell R G. Why use the Stransform? [J]. Fields Institute Communications, 2007, 52: 279—309.
[13]胡广书. 数字信号处理[M]. 北京:清华大学出版社, 2003. 441—445.
Hu Guangshu. Digital Signal Processing [M]. Beijing: Tsinghua University Press, 2003. 441—445. [14]Welcome to the Case Western Reserve University Bearing Data Center Website [EB/OL]. http://csegroups.case.edu./bearingdatecenter/pages/down loaddatafile.
Impact feature extracting method based on S transform timefrequency
spectrum denoised by SVD
GUO Yuanjing , WEI Yanding, ZHOU Xiaojun, FU Lei
(Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China)
Abstract: In order to extract the impact feature from rolling bearing fault vibration signal, which is significant for bearing fault diagnosis, a signal denoising method based on SVD (Singular Value Decomposition) of S transform timefrequency spectrum is proposed. S transform is a means of signal timefrequency representation and particularly suitable for processing the nonstationary signal with impact feature. During SVD denoising, the target data matrix is composed of S transform spectrum coefficients. The position of the threshold singular value, be less than or equal to which the singular value will be set zero, can be determined by the last peak index of the peak swarm in singular value difference spectrum. Finally, inverse S transform of the data matrix resulted from SVD denoising is made to reconstruct the impact feature in time domain. The simulation results show that the proposed method can successfully extract the periodic impact feature from low SNR signal. In the processing of the rolling bearing fault vibration signals, this method is able to obtain the impact feature frequency, which can be used to diagnosis relevant bearing faults effectively.Key words: fault diagnosis; rolling bearing; S transform; singular value decomposition; impact feature作者简介:郭远晶(1987—),男,博士研究生。电话:(0571)87996688;Email:gyjyn@126.com
通讯作者:魏燕定(1970—),男,教授,博士生导师。电话:(0571)87996688;Email: weiyd@zju.edu.cn
Dynamic response of reinforced concrete slab subjected
to internal blast loading
GONG Shunfeng, JIN Weiliang, HE Yong
(Institute of Structural Engineering, Zhejiang University, Hangzhou 310027, China)
Abstract: Key words: RC slab; internal blast loading; dynamic response; damage analysis; numerical simulation作者简介:龚风(1975—),男,副教授。电话:(0571)87951817608;Email: sfgong@zju.edu.cn
通讯作者:何勇(1979—),男,讲师。电话:(0571)87951817608;Email: heyong-ise@zju.edu.cn5结论
参考文献:
[1]钟秉林, 黄仁. 机械故障诊断学[M]. 北京:机械工业出版社,2006.298—301.
Zhong Binglin, Huang Ren. Introduction to Machine Fault Diagnosis [M]. Beijing: China Machine Press, 2006. 298—301. [2]Lee J Y, Nandi A K. Blind deconvolution of impactingsignals using higherorder statistics [J]. Mechanical Systems and Signal Processing, 1998, 12(2):357—371.
[3]Lee J Y, Nandi A K. Extraction of impacting signals using blind deconvolution [J]. Journal of Sound and Vibration, 2000, 232(5):945—962.
[4]王宇, 伍星, 迟毅林, 等. 基于盲解卷积和聚类的机械弱冲击声信号提取[J]. 振动工程学报, 2009,22(6):620—624.
Wang Yu, Wu Xing, Chi Yilin, et al. Weak transient impulse signal extraction based on blind deconvolution and cluster in acoustical machine diagnosis [J]. Journal of Vibration Engineering, 2009,22(6):620—624.
[5]谭继勇, 陈雪峰, 何正嘉. 冲击信号的随机共振自适应检测方法[J]. 机械工程学报, 2010,46(23):61—67.
Tan Jiyong, Chen Xuefeng, He Zhengjia. Impact Signal Detection Method with Adaptive Stochastic Resonance [J]. Journal of Mechanical Engineering, 2010,46(23):61—67.
[6]李继猛, 陈雪峰, 何正嘉. 采用粒子群算法的冲击信号自适应单稳态随机共振检测方法[J]. 机械工程学报, 2011,47(21) :58—63.
Li Jimeng, Chen Xuefeng, He Zhengjia. Adaptive Monostable Stochastic Resonance Based on PSO with Application in Impact Signal Detection [J]. Journal of Mechanical Engineering, 2011,47(21):58—63.
[7]张波, 李健君. 基于Hankel矩阵与奇异值分解(SVD)的滤波方法以及在飞机颤振试验数据预处理中的应用[J]. 振动与冲击, 2009, 28(2):162—166.
Zhang Bo, Li Jianjun. Denoising method based on hankel matrix and SVD and its application in flight flutter testing data preprocessing [J]. Journal of Vibration And Shock, 2009, 28(2): 162—166.
[8]赵学智, 叶邦彦, 陈统坚. 奇异值差分谱理论及其在车床主轴箱故障诊断中的应用[J]. 机械工程学报, 2010,46(1):100—108.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Difference spectrum theory of singular value and its application to the fault diagnosis of headstock of lathe[J]. Journal of Mechanical Engineering, 2010, 46(1): 100—108.
[9]赵学智, 叶邦彦, 陈统坚. 基于小波—奇异值分解差分谱的弱故障特征提取方法[J]. 机械工程学报,2012,48(7):37—48.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Extraction method of faint fault feature based on waveletSVD difference spectrum[J]. Journal of Mechanical Engineering, 2012, 48(7): 37—48.
[10]张超, 陈建军, 徐亚兰. 基于EMD分解和奇异值差分谱理论的轴承故障诊断方法[J]. 振动工程学报,2011,24(5):539—545.
Zhang Chao, Chen Jianjun, Xu Yalan. A bearing fault diagnosis method based on EMD and difference spectrum theory of singular value[J]. Journal of Vibration Engineering, 2011, 24(5): 539—545.
[11]Stockwell R G, Mansinha L, Lowe R P. Localization of the Complex Spectrum:The S Transform [J]. IEEE Transactions on Signal Processing, 1996,44(4):998—100 1.
[12]Stockwell R G. Why use the Stransform? [J]. Fields Institute Communications, 2007, 52: 279—309.
中图分类号:TH165.3; TN911.7文献标识码: A文章编号: 10044523(2014)04062108
引言
滚动轴承广泛应用于各类旋转机械设备中,是此类机械最主要的故障来源之一。滚动轴承元件工作表面发生局部损伤时,损伤点在工作过程中会被撞击,从而产生冲击振动信号,在理想情况下,该信号中的冲击特征出现频率即为损伤点被撞击的频率,又可称为轴承故障特征频率[1]。但是,滚动轴承故障振动信号是典型的非平稳、非高斯信号,加之旋转机械设备的结构的复杂性以及工作环境的多样性,各种激励源产生的振动信号相互耦合,导致轴承故障源振动信号的冲击特征通常淹没在强背景信号与噪声中,比较难以识别。因此,若能成功提取滚动轴承故障振动信号中的冲击特征,即可方便有效地对轴承相关故障进行诊断。
针对冲击特征信号的处理,现有的方法主要是利用信号高阶统计量,如峭度、偏斜度或者峰态等,对冲击成分具有高度敏感性的特点,实现冲击特征的检测。文献[2~4]以高阶统计量为优化目标函数构造盲解卷积滤波器,检测信号中的弱冲击成分,但此方法中滤波器长度的很难确定,限制了其应用。文献[5,6]以峭度指标和互相关系数相结合的加权峭度指标为优化目标,利用随机共振检测方法提取信号冲击成分,具有一定的可行性,然而对于低信噪比的信号,加权峭度指标存在一定的局限性,且参数优化较为困难,影响检测结果。从另外一个角度考虑,可以直接对噪声混合的冲击特征信号进行降噪,从而提取出冲击成分,这种方式简单直观,针对性强。
奇异值分解(SVD)降噪方法是一种非线性滤波方法,可以有效抑制信号中的宽带随机噪声,因此,本文采用SVD对包含冲击特征的滚动轴承故障振动信号进行降噪处理。将SVD用于一维时域信号的处理与分析,关键问题之一是构造合适的数据矩阵。针对此,目前最常用的方法是由一维源信号构造Hankel矩阵,其中一维源信号可以为原始的时域信号、小波分解某一尺度的细节信号或者EMD得到的某一本征模函数等[7~10]。但具体针对冲击特征信号,特别是低信噪比的冲击特征信号,Hankel矩阵无法表征信号的冲击特征,导致SVD处理过程中,冲击特征奇异值与噪声奇异值很难区分开来,达不到冲击特征提取的目的。
S变换是一种信号时频表示方法,适合于处理与分析非平稳信号,尤其是包含冲击特征的信号。因此,本文提出一种基于S变换时频谱SVD降噪的冲击特征提取方法。先将时域冲击特征信号进行S变换,获得信号的时频谱,然后由谱系数构成数据矩阵,对其进行SVD降噪处理,最后对降噪的数据矩阵进行S逆变换,重构时域冲击特征。
第4期郭远晶,等: S变换时频谱SVD降噪的冲击特征提取方法振 动 工 程 学 报第27卷1S变换
S变换是一种将一维时域信号变换到二维时频域的信号处理方法的S变换谱SVD降噪处理,所提取出的时域冲击特征并未表现出很严格的周期性。产生这种情况的原因主要有两个:第一个是滚动轴承在实际使用过程中,当其内圈或者外圈出现较严重的故障时,滚动体触碰到故障点,必然会激发较为强烈的冲击与振动,使得轴承无法正常匀速运转,且滚动体也不是做理想的纯滚动运动;第二个是有些冲击特征强度太小而淹没在噪声中,使得其很容易随着信号的SVD去噪而丢失掉。因此,故障振动信号中的冲击特征在全局时间段上可能不具备严格的周期性,但其在局部时间段上仍可以表现出显著的周期性,只要能够检测到该周期,然后计算对应的频率,将其与轴承元件的故障特征频率相比较,就可以实现滚动轴承相关故障的诊断。
6结论
S变换是一种信号时频表示方法,具备多分辨率特性,对于信号中的高频冲击成分具有较高敏感性,满足线性叠加原理,不存在交叉项的干扰,适合于处理与分析非平稳信号,尤其是冲击特征信号。
S变换时频谱可以很好地表征信号的冲击特征,适合于作为SVD降噪处理所需的数据矩阵。而奇异值差分谱最前面部分峰值群的最后一个峰值点序号可以作为奇异值序列置零阈值σth的位置坐标,并以此方式确定阈值σth。
相对于现有的冲击特征提取方法,基于S变换时频谱SVD降噪的冲击特征提取方法是一种新方法,其简单直观、针对性强、易于实现。虽然所提取出的冲击特征不可避免会出现一定的变形和失真,但作为最重要信息的冲击特征出现频率,可以完全有效地提取出来。
将本方法应用于滚动轴承故障振动信号的处理,能够成功提取出时域冲击特征的出现频率,结合轴承元件的故障特征频率,可以实现滚动轴承相关故障的诊断。参考文献:
[1]钟秉林, 黄仁. 机械故障诊断学[M]. 北京:机械工业出版社,2006.298—301.
Zhong Binglin, Huang Ren. Introduction to Machine Fault Diagnosis [M]. Beijing: China Machine Press, 2006. 298—301.
[2]Lee J Y, Nandi A K. Blind deconvolution of impactingsignals using higherorder statistics [J]. Mechanical Systems and Signal Processing, 1998, 12(2):357—371. [3]Lee J Y, Nandi A K. Extraction of impacting signals using blind deconvolution [J]. Journal of Sound and Vibration, 2000, 232(5):945—962.
[4]王宇, 伍星, 迟毅林, 等. 基于盲解卷积和聚类的机械弱冲击声信号提取[J]. 振动工程学报, 2009,22(6):620—624.
Wang Yu, Wu Xing, Chi Yilin, et al. Weak transient impulse signal extraction based on blind deconvolution and cluster in acoustical machine diagnosis [J]. Journal of Vibration Engineering, 2009,22(6):620—624.
[5]谭继勇, 陈雪峰, 何正嘉. 冲击信号的随机共振自适应检测方法[J]. 机械工程学报, 2010,46(23):61—67.
Tan Jiyong, Chen Xuefeng, He Zhengjia. Impact signal detection method with adaptive stochastic resonance [J]. Journal of Mechanical Engineering, 2010,46(23):61—67.
[6]李继猛, 陈雪峰, 何正嘉. 采用粒子群算法的冲击信号自适应单稳态随机共振检测方法[J]. 机械工程学报, 2011,47(21) :58—63.
Li Jimeng, Chen Xuefeng, He Zhengjia. Adaptive monostable stochastic resonance based on PSO with application in impact signal detection [J]. Journal of Mechanical Engineering, 2011,47(21):58—63.
[7]张波, 李健君. 基于Hankel矩阵与奇异值分解(SVD)的滤波方法以及在飞机颤振试验数据预处理中的应用[J]. 振动与冲击, 2009, 28(2):162—166.
Zhang Bo, Li Jianjun. Denoising method based on hankel matrix and SVD and its application in flight flutter testing data preprocessing [J]. Journal of Vibration And Shock, 2009, 28(2): 162—166.
[8]赵学智, 叶邦彦, 陈统坚. 奇异值差分谱理论及其在车床主轴箱故障诊断中的应用[J]. 机械工程学报, 2010,46(1):100—108.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Difference spectrum theory of singular value and its application to the fault diagnosis of headstock of lathe[J]. Journal of Mechanical Engineering, 2010, 46(1): 100—108.
[9]赵学智, 叶邦彦, 陈统坚. 基于小波—奇异值分解差分谱的弱故障特征提取方法[J]. 机械工程学报,2012,48(7):37—48.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Extraction method of faint fault feature based on waveletSVD difference spectrum[J]. Journal of Mechanical Engineering, 2012, 48(7): 37—48.
[10]张超, 陈建军, 徐亚兰. 基于EMD分解和奇异值差分谱理论的轴承故障诊断方法[J]. 振动工程学报,2011,24(5):539—545.
Zhang Chao, Chen Jianjun, Xu Yalan. A bearing fault diagnosis method based on EMD and difference spectrum theory of singular value[J]. Journal of Vibration Engineering, 2011, 24(5): 539—545.
[11]Stockwell R G, Mansinha L, Lowe R P. Localization of the complex spectrum: the S transform [J]. IEEE Transactions on Signal Processing, 1996,44(4):998—1 001.
[12]Stockwell R G. Why use the Stransform? [J]. Fields Institute Communications, 2007, 52: 279—309.
[13]胡广书. 数字信号处理[M]. 北京:清华大学出版社, 2003. 441—445.
Hu Guangshu. Digital Signal Processing [M]. Beijing: Tsinghua University Press, 2003. 441—445. [14]Welcome to the Case Western Reserve University Bearing Data Center Website [EB/OL]. http://csegroups.case.edu./bearingdatecenter/pages/down loaddatafile.
Impact feature extracting method based on S transform timefrequency
spectrum denoised by SVD
GUO Yuanjing , WEI Yanding, ZHOU Xiaojun, FU Lei
(Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China)
Abstract: In order to extract the impact feature from rolling bearing fault vibration signal, which is significant for bearing fault diagnosis, a signal denoising method based on SVD (Singular Value Decomposition) of S transform timefrequency spectrum is proposed. S transform is a means of signal timefrequency representation and particularly suitable for processing the nonstationary signal with impact feature. During SVD denoising, the target data matrix is composed of S transform spectrum coefficients. The position of the threshold singular value, be less than or equal to which the singular value will be set zero, can be determined by the last peak index of the peak swarm in singular value difference spectrum. Finally, inverse S transform of the data matrix resulted from SVD denoising is made to reconstruct the impact feature in time domain. The simulation results show that the proposed method can successfully extract the periodic impact feature from low SNR signal. In the processing of the rolling bearing fault vibration signals, this method is able to obtain the impact feature frequency, which can be used to diagnosis relevant bearing faults effectively.Key words: fault diagnosis; rolling bearing; S transform; singular value decomposition; impact feature作者简介:郭远晶(1987—),男,博士研究生。电话:(0571)87996688;Email:gyjyn@126.com
通讯作者:魏燕定(1970—),男,教授,博士生导师。电话:(0571)87996688;Email: weiyd@zju.edu.cn
Dynamic response of reinforced concrete slab subjected
to internal blast loading
GONG Shunfeng, JIN Weiliang, HE Yong
(Institute of Structural Engineering, Zhejiang University, Hangzhou 310027, China)
Abstract: Key words: RC slab; internal blast loading; dynamic response; damage analysis; numerical simulation作者简介:龚风(1975—),男,副教授。电话:(0571)87951817608;Email: sfgong@zju.edu.cn
通讯作者:何勇(1979—),男,讲师。电话:(0571)87951817608;Email: heyong-ise@zju.edu.cn5结论
参考文献:
[1]钟秉林, 黄仁. 机械故障诊断学[M]. 北京:机械工业出版社,2006.298—301.
Zhong Binglin, Huang Ren. Introduction to Machine Fault Diagnosis [M]. Beijing: China Machine Press, 2006. 298—301. [2]Lee J Y, Nandi A K. Blind deconvolution of impactingsignals using higherorder statistics [J]. Mechanical Systems and Signal Processing, 1998, 12(2):357—371.
[3]Lee J Y, Nandi A K. Extraction of impacting signals using blind deconvolution [J]. Journal of Sound and Vibration, 2000, 232(5):945—962.
[4]王宇, 伍星, 迟毅林, 等. 基于盲解卷积和聚类的机械弱冲击声信号提取[J]. 振动工程学报, 2009,22(6):620—624.
Wang Yu, Wu Xing, Chi Yilin, et al. Weak transient impulse signal extraction based on blind deconvolution and cluster in acoustical machine diagnosis [J]. Journal of Vibration Engineering, 2009,22(6):620—624.
[5]谭继勇, 陈雪峰, 何正嘉. 冲击信号的随机共振自适应检测方法[J]. 机械工程学报, 2010,46(23):61—67.
Tan Jiyong, Chen Xuefeng, He Zhengjia. Impact Signal Detection Method with Adaptive Stochastic Resonance [J]. Journal of Mechanical Engineering, 2010,46(23):61—67.
[6]李继猛, 陈雪峰, 何正嘉. 采用粒子群算法的冲击信号自适应单稳态随机共振检测方法[J]. 机械工程学报, 2011,47(21) :58—63.
Li Jimeng, Chen Xuefeng, He Zhengjia. Adaptive Monostable Stochastic Resonance Based on PSO with Application in Impact Signal Detection [J]. Journal of Mechanical Engineering, 2011,47(21):58—63.
[7]张波, 李健君. 基于Hankel矩阵与奇异值分解(SVD)的滤波方法以及在飞机颤振试验数据预处理中的应用[J]. 振动与冲击, 2009, 28(2):162—166.
Zhang Bo, Li Jianjun. Denoising method based on hankel matrix and SVD and its application in flight flutter testing data preprocessing [J]. Journal of Vibration And Shock, 2009, 28(2): 162—166.
[8]赵学智, 叶邦彦, 陈统坚. 奇异值差分谱理论及其在车床主轴箱故障诊断中的应用[J]. 机械工程学报, 2010,46(1):100—108.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Difference spectrum theory of singular value and its application to the fault diagnosis of headstock of lathe[J]. Journal of Mechanical Engineering, 2010, 46(1): 100—108.
[9]赵学智, 叶邦彦, 陈统坚. 基于小波—奇异值分解差分谱的弱故障特征提取方法[J]. 机械工程学报,2012,48(7):37—48.
Zhao Xuezhi, Ye Bangyan, Chen Tongjian. Extraction method of faint fault feature based on waveletSVD difference spectrum[J]. Journal of Mechanical Engineering, 2012, 48(7): 37—48.
[10]张超, 陈建军, 徐亚兰. 基于EMD分解和奇异值差分谱理论的轴承故障诊断方法[J]. 振动工程学报,2011,24(5):539—545.
Zhang Chao, Chen Jianjun, Xu Yalan. A bearing fault diagnosis method based on EMD and difference spectrum theory of singular value[J]. Journal of Vibration Engineering, 2011, 24(5): 539—545.
[11]Stockwell R G, Mansinha L, Lowe R P. Localization of the Complex Spectrum:The S Transform [J]. IEEE Transactions on Signal Processing, 1996,44(4):998—100 1.
[12]Stockwell R G. Why use the Stransform? [J]. Fields Institute Communications, 2007, 52: 279—309.