本文方法具體步驟如下:1)原始信號(hào)X重構(gòu)得到Hankel矩陣,求出N個(gè)奇異值σi;2)對(duì)每個(gè)奇異值σi重構(gòu)得到N個(gè)分量信號(hào)Pi;3)計(jì)算分量信號(hào)Pi與原始信號(hào)X的邊緣概率分布及聯(lián)合概率分布,得出各分量信號(hào)的互信息,并求取各分量信號(hào)對(duì)原始信號(hào)的貢獻(xiàn)率;4)計(jì)算各分量信號(hào)Pi的互信息差分譜,根據(jù)最大突變峰值ki選取有效分量,即選取有效奇異值個(gè)數(shù);5)將選取的k個(gè)有效奇異值σi對(duì)應(yīng)的分量信號(hào)Pi移頻變尺度處理,使其滿足小參數(shù)要求;6)將移頻變尺度處理后的分量信號(hào)Pi輸入到隨機(jī)共振系統(tǒng),利用蟻群算法自適應(yīng)優(yōu)化隨機(jī)共振的2個(gè)參數(shù)a和b,得到k個(gè)被增強(qiáng)的有效分量信號(hào);7)計(jì)算k個(gè)有效分量信號(hào)的均值,最終提取微弱故障特征。
4 自適應(yīng)選取仿真信號(hào)的奇異值及特征提取
為了驗(yàn)證所提方法的有效性,仿真一個(gè)周期信號(hào)[31],采樣頻率為10 KHz,特征頻率是100 Hz,采樣時(shí)間是0.3 s,如圖1a所示。為了模仿強(qiáng)背景噪聲下的軸承故障信號(hào),向周期信號(hào)加入標(biāo)準(zhǔn)差為0.5的高斯白噪聲,如圖1b所示。

圖1 仿真信號(hào)時(shí)域波形和頻譜圖Fig.1 Time domain waveform and spectrum of simulation signal
由于周期信號(hào)被強(qiáng)噪聲所淹沒,在圖1c頻譜中不能獲取周期信號(hào)的特征頻率,因此,采用奇異值分解降噪,構(gòu)建行列式為1 700×30的Hankel矩陣,得到30個(gè)從大到小依次排列的奇異值,如圖2a所示。為了獲取強(qiáng)噪聲背景下的有效奇異值,將所有奇異值重構(gòu)得到30個(gè)分量信號(hào),根據(jù)式(8)得出30個(gè)分量信號(hào)的互信息,如圖2b所示。從圖2b中可知,每個(gè)分量信號(hào)互信息不同,而各分量信號(hào)互信息與所有分量信號(hào)互信息的百分比以貢獻(xiàn)率衡量,由此得出各分量信號(hào)對(duì)原始信號(hào)的貢獻(xiàn)率,如表1所示。

圖2 互信息差分譜選取的有效奇異值Fig.2 Difference spectra of mutual information select effective singular value

表1 奇異值重構(gòu)的分量信號(hào)對(duì)原始信號(hào)的貢獻(xiàn)率Table 1 Contribution rate of singular value reconstruction component signal to raw signal
由圖2a可知,序列號(hào)4具有較大奇異值,但對(duì)原始信號(hào)的貢獻(xiàn)率最小僅為0.7%;同理,序列號(hào)14也具有較大奇異值,但對(duì)原始信號(hào)的貢獻(xiàn)率為2.0%,與其他奇異值對(duì)原始信號(hào)的貢獻(xiàn)率相比數(shù)值較小,根據(jù)互信息差分譜選取有效奇異值的方法,在序列號(hào)3處突變最大,因此選取前3個(gè)奇異值為有用信號(hào),即得到3個(gè)有效奇異值,說明序列號(hào)4和14雖然具有較大奇異值,但并非有用信號(hào),即奇異值大不一定包含有用信息,在強(qiáng)噪聲背景下可能為噪聲干擾。根據(jù)選取的前3個(gè)奇異值分別重構(gòu)分量信號(hào),每個(gè)分量信號(hào)的頻譜圖,如圖3a所示。

圖3 自適應(yīng)選取的分量信號(hào)頻譜Fig.3 Spectrum of adaptive selected component signal
由圖3a可知,分量信號(hào)P1和P2高頻段頻率比較明顯,但特征頻率不在其范圍內(nèi),而分量信號(hào)P3在低頻段有明顯頻率,但無法識(shí)別目標(biāo)頻率,說明對(duì)于強(qiáng)背景噪聲下的微弱故障特征,僅SVD降噪難以提取出特征頻率,因此,將3個(gè)有效分量信號(hào)分別輸入到隨機(jī)共振,首先采用移頻變尺度處理,由于目標(biāo)頻率是100 Hz,載波頻率是1 000 Hz,因此設(shè)定高通濾波器的通過頻率和截止頻率是分別是90和85 Hz,調(diào)制頻率為85 Hz,變尺度壓縮率是400,則預(yù)處理后的目標(biāo)頻率被壓縮為0.0751,滿足小參數(shù)要求,利用蟻群算法在0<α<10,0
從圖3b可知,有效分量信號(hào)自適應(yīng)隨機(jī)共振處理后,強(qiáng)背景噪聲下的周期信號(hào)特征頻率被明顯增強(qiáng),但每個(gè)有效分量隨機(jī)共振的最大譜峰頻率不同,P1、P2分量信號(hào)的最大譜峰頻率為100 Hz,P3分量信號(hào)的最大譜峰頻率為96.67 Hz,由于故障特征頻率被載波信號(hào)所調(diào)制,在頻譜中表現(xiàn)為以載波頻率為中心,以故障特征頻率為邊帶的一個(gè)共振頻帶,因此不能根據(jù)P1和P2判斷故障頻率,只能判斷是否存在共振頻帶,另外,有效分量信號(hào)的最大譜峰頻率并不都是目標(biāo)頻率,因此,將3個(gè)有效分量信號(hào)統(tǒng)計(jì)學(xué)平均得出最終頻譜圖,如圖4所示。

圖4 統(tǒng)計(jì)學(xué)平均的頻譜圖Fig.4 Spectra of statistical average
由圖4可知,通過統(tǒng)計(jì)學(xué)平均后部分噪聲被過濾,噪聲減少意味著干擾減少,從而要提取的故障特征頻率100 Hz被明顯凸顯出來,幅值為0.106 9,與周期信號(hào)的特征頻率完全相同,從而驗(yàn)證了所提方法的有效性。
5 試驗(yàn)驗(yàn)證
試驗(yàn)中采用Spectra Quest公司生產(chǎn)的機(jī)械設(shè)備故障綜合試驗(yàn)臺(tái),如圖5所示。信號(hào)則由IOtech公司生產(chǎn)的Zonic Book/618E 型數(shù)據(jù)動(dòng)態(tài)系統(tǒng)采集,該設(shè)備由8個(gè)信號(hào)輸出通道,幅值精度可達(dá)±0.5 dB,試驗(yàn)中采用ER-10k滾動(dòng)軸承作為故障軸承,其幾何尺寸D=33.5,d=7.939 5 mm,α=0°, Z=8,采樣頻率為2 560 Hz,轉(zhuǎn)速為3 060 r/min,根據(jù)振動(dòng)理論分析可知,軸承外圈的特征頻率是155.664 Hz,原始信號(hào)的時(shí)域和頻譜圖如圖6所示。

圖5 機(jī)械設(shè)備綜合故障試驗(yàn)臺(tái)Fig.5 Comprehensive failure test of mechanical equipment
由圖6a原始信號(hào)時(shí)域波形可知,由于軸承外圈故障頻率被強(qiáng)背景噪聲所淹沒信噪比極低,看不出任何故障特征,而在頻譜圖6b中有明顯的轉(zhuǎn)頻50.52 Hz以及轉(zhuǎn)頻的4~9倍頻,但無法看到155.664 Hz的故障頻率,為了提取微弱故障特征,利用本文所提出的方法檢測(cè)軸承外圈故障,將原始信號(hào)構(gòu)建行列式為1 700×20的Hankel矩陣,得出20個(gè)奇異值序列,如圖7a所示。

圖6 原始信號(hào)的時(shí)域波形和頻譜Fig.6 Time domain waveform and spectrum of raw signal

圖7 互信息差分譜選取有效奇異值Fig.7 Difference spectra of mutual information selecting effective singular value
通過重構(gòu)奇異值獲取20個(gè)分量信號(hào),利用式(8)求取各分量信號(hào)的互信息,如圖7b所示。由圖7b可知,每個(gè)分量信號(hào)互信息不同,序列號(hào)11和15具有相對(duì)較大的奇異值,但貢獻(xiàn)率較小,由表2可知,其值分別為3.8%和3.3%,且序列號(hào)15的互信息達(dá)到最小,而根據(jù)互信息差分譜選取有效奇異值的方法,在序列號(hào)10處出現(xiàn)最大突變,因此選取前10個(gè)分量信號(hào)為有效分量,即選取前10個(gè)奇異值為有效奇異值,而序列號(hào)11和15并非有效奇異值,從而通過試驗(yàn)驗(yàn)證奇異值較大不一定為有效奇異值,有可能為噪聲信息。根據(jù)選取的前10個(gè)有效奇異值重構(gòu)得到分量信號(hào),隨機(jī)選取不同貢獻(xiàn)率的分量信號(hào),即序號(hào)為2、3、6、8和10的分量信號(hào)作為分析樣本,對(duì)其頻譜分析,如圖8所示。

表2 軸承外圈信號(hào)奇異值重構(gòu)的分量信號(hào)對(duì)原始信號(hào)的貢獻(xiàn)率Table 2 Contribution rate of component signal by singular value reconstruction to raw signal for bearing inner ring

圖8 P2,P3,P6,P8,P10分量信號(hào)頻譜圖Fig.8 Spectrum of P2, P3, P6, P8, P10component signal
由圖8可知,各分量信號(hào)噪聲有所降低,但仍難以提取故障特征,同樣說明在信噪比極低情況下僅奇異值分解無法提取故障特征,因此將選取的5個(gè)有效分量樣本信號(hào)自適應(yīng)隨機(jī)共振。由于軸承外圈的故障特征頻率是155.664 Hz,首先采用移頻變尺度處理,設(shè)定高通濾波器的通過頻率和截止頻率分別是是154和150 Hz,調(diào)制頻率為150 Hz,變尺度壓縮率是400,則預(yù)處理后的目標(biāo)頻率被壓縮為0.014 16,滿足小參數(shù)要求,利用蟻群算法在0<α<10,0

圖9 P2,P3,P6,P8,P10分量信號(hào)自適應(yīng)隨機(jī)共振頻譜圖Fig.9 Spectra of P2, P3, P6, P8, P10component signal adaptive stochastic resonance
由圖9可知,強(qiáng)背景噪聲中的微弱故障特征被明顯增強(qiáng), P2,P6,P8,P10分量信號(hào)自適應(yīng)隨機(jī)共振的最大譜峰頻率接近于故障頻率155.664 Hz,但最大譜峰頻率大小不同,P3分量信號(hào)自適應(yīng)隨機(jī)共振的最大譜峰頻率為161.9 Hz,與特征頻率155.664 Hz相差較大,不能真實(shí)反映軸承的外圈故障,因此將各有效分量信號(hào)合成并統(tǒng)計(jì)學(xué)平均得出最終的頻譜圖,如圖10所示。

圖10 統(tǒng)計(jì)學(xué)平均頻域圖Fig.10 Spectra of statistical average
由圖10可知,最大譜峰頻率是155.5 Hz,與隨機(jī)選取分量信號(hào)自適應(yīng)隨機(jī)共振的最大譜峰頻率相比,統(tǒng)計(jì)學(xué)平均的最大譜峰頻率辨識(shí)度更高,更接近于軸承外圈故障頻率155.664 Hz,因此,利用統(tǒng)計(jì)學(xué)平均隨機(jī)共振比單個(gè)分量信號(hào)的隨機(jī)共振效果更優(yōu),更接近于特征頻率,從而通過試驗(yàn)再次驗(yàn)證了所提方法的有效性。
6 結(jié) 論
提出了自適應(yīng)奇異值分解的隨機(jī)共振微弱故障特征提取方法,可有效提取強(qiáng)背景噪聲下的微弱故障特征。
1)通過構(gòu)造互信息差分譜,提出了一種有效奇異值選擇方法。該方法考慮分量信號(hào)與原始信號(hào)的貢獻(xiàn)率,一方面防止了有用信號(hào)的剔除;另一方面實(shí)現(xiàn)了自適應(yīng)選取,有效避免人為選擇的主觀性。另外,利用互信息差分譜,在仿真和軸承外圈信號(hào)中分別得出在序列號(hào)3和序列號(hào)10發(fā)生突變,因此,可分別選取3個(gè)和10個(gè)有效奇異值。
2)由于強(qiáng)背景噪聲的存在,較大的奇異值可能有較小的互信息,但并非是有效奇異值,說明奇異值較大不一定包含有用信息,有可能是噪聲干擾,因此有效奇異值的選擇不應(yīng)以奇異值的大小作為判定依據(jù)。
3)由于強(qiáng)背景噪聲下信噪比極低,僅通過奇異值分解不能提取微弱故障特征,而利用隨機(jī)共振提取分量信號(hào)的故障特征,最大譜峰頻率大小不同,本文將兩者結(jié)合,不僅克服了強(qiáng)背景噪聲下有效奇異值的選取困難,而且能夠更好的增強(qiáng)微弱故障特征,通過仿真和軸承外圈試驗(yàn)有效提取出100和155.5 Hz的微弱故障特征,從而得出該方法提取效果優(yōu)于單純的奇異值分解和隨機(jī)共振方法。
該研究可廣泛應(yīng)用于強(qiáng)噪聲背景下的軸承故障診斷,可對(duì)農(nóng)業(yè)機(jī)械及大功率、高轉(zhuǎn)速設(shè)備的軸承故障診斷提供參考。
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Extracting weak fault characteristics with adaptive singular value decomposition and stochastic resonance
Li Zhixing1,2, Shi Boqiang1※
(1. School of Mechanical Engineering, University of Science & Technology Beijing, Beijing 100083, China; 2. School of Mechanical Engineering, University of Science & Technology Inner Mongolia, Baotou 014000, China)
Bearings are the important component of agricultural machinery and equipment, whose failure may seriously endanger the healthy operation of equipment and even lead to bodily injury. So the fault diagnosis of agricultural machinery and equipment gains more and more attention. Using the vibration signal to extract the fault characteristics is the most common method, but it is difficult to extract the weak fault characteristics in strong background noise. Therefore, the extraction of weak fault characteristics with very low SNR (signal-to-noise ratio) under strong background noise becomes the key to the fault diagnosis of agricultural machinery bearings. There are 2 general methods for weak feature extraction under weak background noise. One method is to extract weak faults from the perspective of suppressing or eliminating noise. The other one is not to eliminate noise but using noise to improve the SNR to extract the weak fault characteristics, such as stochastic resonance (SR) theory. Compared to the traditional noise reduction method, SR makes use of noise energy transfer to weak signal, so the weak fault characteristics are enhanced while some of the noises are weakened. Because of the excellent features of extracting weak fault characteristics in strong background noise, SR has become a hot topic for many scholars in recent years. In this paper, the weak fault characteristics extraction method of SR based on adaptive SVD (singular value decomposition) was proposed. In the method, firstly, the original signal was decomposed by singular value and reconstructed to obtain the component signal; the difference spectrum of mutual information was constructed, the mutual information of each component signal and the original signal was weighed, and the number of valid singular values was selected adaptively, in order to overcome the problem of existing methods including human subjective choice or only considering the size of singular values and other deficiencies. Using the mutual information difference spectrum, 3 and 10 effective singular values were obtained in the simulation signal and bearing outer ring signal, respectively. Secondly, the adaptive SR was performed for the component signal corresponding to the selected effective singular value which enhances weak fault characteristics. Finally, the enhanced component signals were statistically averaged to extract the weak fault characteristics. In this paper, constructing the mutual information differential spectrum, and considering the mutual information of the component signal and the original signal, on the one hand, it avoids the elimination of the useful signals; on the other hand, the adaptive selection is realized which avoids the subjectivity of the artificial selection. In addition, due to the presence of strong background noise, the larger singular value may have smaller mutual information, but it is not valid singular value. It indicates that large singular value does not necessarily contain useful information, and there may be noise interference. Hence, the selection of effective singular values should not be based on the size of the singular value. The above analysis shows that it is difficult to extract the weak fault characteristics by SVD in strong background noise. We combine the 2 methods to process the effective component signal selected by mutual information difference spectrum in SR, and the maximum spectral frequency of each component is obtained. The statistical average is used to achieve noise filtering in order to highlight the characteristics of weak fault frequency. The results of simulation and bearing outer ring test show that, the proposed method is superior to the SVD and SR method. The method can effectively extract 100 and 155.5 Hz weak fault characteristics respectively for simulation signal and bearing outer ring signal. The proposed method can be applied not only to the fault diagnosis of bearing in strong noise background, but also to provide reference for bearing fault diagnosis of agricultural machinery and equipment.
vibrations; agricultural machinery; fault detection; singular value decomposition; difference spectrum of mutual information; weak characteristic
10.11975/j.issn.1002-6819.2017.11.008
TN911.72
A
1002-6819(2017)-11-0060-08
李志星,石博強(qiáng). 自適應(yīng)奇異值分解的隨機(jī)共振提取微弱故障特征[J]. 農(nóng)業(yè)工程學(xué)報(bào),2017,33(11):60-67.
10.11975/j.issn.1002-6819.2017.11.008 http://www.tcsae.org
Li Zhixing, Shi Boqiang. Extracting weak fault characteristics with adaptive singular value decomposition and stochastic resonance[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(11): 60-67. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2017.11.008 http://www.tcsae.org
2016-12-13
2017-05-10
國家自然科學(xué)基金資助項(xiàng)目(51075029)
李志星,男(漢族),河北衡水人,博士生,講師,主要從事機(jī)械設(shè)備故障診斷的研究。北京 北京科技大學(xué)機(jī)械工程學(xué)院,100083。
Email:onyxlzx@126.com
※通信作者:石博強(qiáng),男(漢族),河北唐山人,教授,博士生導(dǎo)師,主要從事機(jī)械設(shè)備故障診斷、機(jī)械可靠性研究。北京 北京科技大學(xué)機(jī)械工程學(xué)院,100083。Email:shiboqiang@ustb.edu.cn