馬朝永，盛志鵬，胥永剛,2※，張 坤

基于自適應(yīng)頻率切片小波變換的滾動(dòng)軸承故障診斷

馬朝永1，盛志鵬1，胥永剛1,2※，張 坤1

（1. 北京工業(yè)大學(xué)先進(jìn)制造技術(shù)北京市重點(diǎn)實(shí)驗(yàn)室，北京 100124；2. 北京工業(yè)大學(xué)北京市精密測(cè)控技術(shù)與儀器工程技術(shù)研究中心，北京 100124）

頻率切片小波變換（frequency slice wavelet transform, FSWT）在汲取短時(shí)傅里葉變換和小波變換優(yōu)勢(shì)的基礎(chǔ)上引入了頻率切片函數(shù)，使傳統(tǒng)的傅里葉變換實(shí)現(xiàn)了時(shí)頻分析功能。FSWT通過(guò)對(duì)比不同頻帶處理的結(jié)果以確定最合適的中心頻率及最佳帶寬，實(shí)現(xiàn)了對(duì)信號(hào)任意頻帶及局部特征的重構(gòu)及描述，但這種方法效率很低、無(wú)自適應(yīng)性且無(wú)法保證手動(dòng)篩選出的頻段中包含所需要的故障信息。針對(duì)這個(gè)問(wèn)題，該文提出一種自適應(yīng)頻率切片小波變換（adaptive frequency slice wavelet transform, AFSWT）。首先，連續(xù)分割信號(hào)的頻譜，頻譜分割覆蓋了全頻帶且避免了手動(dòng)選取頻譜邊界的過(guò)程，均分的方式可提高計(jì)算效率。其次，引入譜負(fù)熵作為評(píng)價(jià)依據(jù)，計(jì)算每一個(gè)頻段內(nèi)信號(hào)的復(fù)雜程度以篩選可能包含周期性沖擊的循環(huán)平穩(wěn)信息。最后，選取其中譜負(fù)熵最大的頻段并將其定義為最佳的中心頻率和帶寬，重構(gòu)該頻段信號(hào)分量并包絡(luò)解調(diào)分析，實(shí)現(xiàn)故障診斷。該方法均勻分割頻譜并依據(jù)譜負(fù)熵篩選信號(hào)分量可以提高計(jì)算效率且提高篩選準(zhǔn)確率。通過(guò)模擬信號(hào)及實(shí)驗(yàn)信號(hào)證明了該方法可應(yīng)用于滾動(dòng)軸承圈故障診斷。

軸承；振動(dòng)；故障診斷；頻率切片小波變換；譜負(fù)熵；頻譜分割

0 引 言

軸承在旋轉(zhuǎn)機(jī)械中應(yīng)用十分廣泛，同時(shí)由于滾動(dòng)軸承常處于高溫差、高壓、高速運(yùn)轉(zhuǎn)等工況而極易損壞，從而導(dǎo)致耗時(shí)檢修和緊急停車(chē)等事故[1-4]。因此，檢測(cè)滾動(dòng)軸承的運(yùn)行狀態(tài)并診斷其故障非常必要[5-7]。當(dāng)滾動(dòng)軸承出現(xiàn)損傷時(shí)所采集的振動(dòng)信號(hào)常呈現(xiàn)非平穩(wěn)、調(diào)制的特征，而且不可避免地會(huì)受到工業(yè)現(xiàn)場(chǎng)強(qiáng)噪聲的干擾，識(shí)別故障特征十分困難。如何在復(fù)雜的非平穩(wěn)、調(diào)制信號(hào)中有效提取攜帶故障特征信息的成分是診斷軸承故障的關(guān)鍵[8-9]。

近年來(lái)，非平穩(wěn)信號(hào)處理方法，如短時(shí)傅里葉變換、Wigner-Ville分布、小波變換（包括連續(xù)小波變換、離散小波變換、雙樹(shù)復(fù)小波變換等）等具有堅(jiān)實(shí)的理論基礎(chǔ)，并且在機(jī)械設(shè)備故障診斷領(lǐng)域中發(fā)展迅速[10-13]。然而這些時(shí)頻分析方法需要進(jìn)行大量的前期準(zhǔn)備工作，例如需要選擇合適的窗函數(shù)或小波基函數(shù)等。因此以Huang等[14]提出的經(jīng)驗(yàn)?zāi)B(tài)分解（EMD）為代表的一系列自適應(yīng)信號(hào)分解方法出現(xiàn)并被迅速拓展[15-16]，如局部均值分解、本征時(shí)間尺度分解、局部特征尺度分解法等。這類(lèi)自適應(yīng)分解方法完全由數(shù)據(jù)驅(qū)動(dòng)并且可以將信號(hào)分解為一組模態(tài)分量。然而這些自適應(yīng)方法普遍存在模態(tài)混疊、端點(diǎn)效應(yīng)等不足。因此有學(xué)者對(duì)自適應(yīng)方法進(jìn)行了進(jìn)一步研究，Gilles等提出從頻譜提取模態(tài)信息，通過(guò)分割頻譜并構(gòu)造經(jīng)驗(yàn)小波來(lái)重構(gòu)每一個(gè)經(jīng)驗(yàn)?zāi)B(tài)。該方法一定程度避免了由時(shí)域數(shù)據(jù)驅(qū)動(dòng)產(chǎn)生的模態(tài)混疊及端點(diǎn)效應(yīng)，但不合理的頻譜分割結(jié)果會(huì)產(chǎn)生新的模態(tài)混疊及無(wú)效分量[17-18]。因此，很有必要從時(shí)域及頻域同時(shí)展現(xiàn)信號(hào)特征并提取信號(hào)分量[19-20]。

Yan等[21-22]提出一種新的時(shí)頻分析方法-頻率切片小波變換（FSWT），該方法引入頻率切片函數(shù)，使傳統(tǒng)的傅里葉變換具有了時(shí)頻分析的功能，不僅減少了小波和小波包在重構(gòu)信號(hào)時(shí)對(duì)小波基函數(shù)的依賴(lài)，而且實(shí)現(xiàn)了信號(hào)在任意頻帶的重構(gòu)及局部特征的精確描述，在各個(gè)領(lǐng)域均得到了廣泛的應(yīng)用[23]。段晨東等[24]將FSWT應(yīng)用于煉油廠齒輪箱的故障診斷之中；Liu等[25]利用FSWT提高了梁結(jié)構(gòu)損傷定位時(shí)的精度；楊仁樹(shù)等[26]將EMD與FSWT結(jié)合應(yīng)用于爆破振動(dòng)信號(hào)中，在時(shí)域上獲得了更高的時(shí)頻分辨率；王元生等[27]將去噪源分離與FSWT結(jié)合，解決了旋轉(zhuǎn)機(jī)械信號(hào)分析時(shí)產(chǎn)生的欠定盲源分離的問(wèn)題。然而上述應(yīng)用只能通過(guò)對(duì)比不同頻帶處理的結(jié)果以確定最合適的中心頻率及最佳帶寬，這種反復(fù)人為選頻分析的過(guò)程耗費(fèi)時(shí)間長(zhǎng)，效率低且難以保證準(zhǔn)確性，缺乏自適應(yīng)性，非常有必要研究一種依據(jù)信號(hào)時(shí)頻特性自適應(yīng)選頻的頻率切片小波分析方法，以拓展該方法的應(yīng)用領(lǐng)域。

為了使頻率切片小波變換的選頻過(guò)程更簡(jiǎn)便、高效，避免人為操作帶來(lái)的不確定性，本文提出了自適應(yīng)頻率切片小波變換（AFSWT），采用預(yù)定義方式將頻譜分割為若干等份代替原方法中手動(dòng)選??；利用譜負(fù)熵評(píng)估各頻段內(nèi)循環(huán)平穩(wěn)信息的強(qiáng)弱，篩選可能包含周期性沖擊成分的頻帶以重構(gòu)時(shí)頻局部分量。

1 頻率切片小波變換

1.1 頻率切片小波變換原理

常用的2個(gè)切片函數(shù)為

1.2 頻率切片小波逆變換

1.3 頻率切片小波變換選頻、重構(gòu)與不足

該方法在實(shí)際應(yīng)用中會(huì)遇到2個(gè)問(wèn)題：其一，噪聲的大小直接影響觀測(cè)頻率的選取范圍。經(jīng)驗(yàn)指定的方式難以保證結(jié)果的準(zhǔn)確性。所以很有必要引入對(duì)研究對(duì)象故障特征敏感的指標(biāo)來(lái)代替經(jīng)驗(yàn)指定法。其二，手動(dòng)選取頻段的過(guò)程耗時(shí)低效，致使該方法難以應(yīng)用于自適應(yīng)或自動(dòng)化領(lǐng)域。探索一種自適應(yīng)頻段提取法來(lái)代替手動(dòng)選頻法有重要的研究?jī)r(jià)值。本節(jié)構(gòu)造一組仿真信號(hào)模擬滾動(dòng)軸承外圈故障來(lái)展示FSWT的上述不足。

當(dāng)沖擊成分中加入調(diào)制成分和強(qiáng)噪聲后，時(shí)域波形中的周期性沖擊特征被噪聲淹沒(méi)，從時(shí)域中難以發(fā)現(xiàn)該信號(hào)中是否包含故障信息。從信號(hào)的頻譜中可以看到，5 000 Hz附近出現(xiàn)邊頻帶。根據(jù)共振解調(diào)原理，提取該頻段可獲得包含故障特征的信息。同時(shí)在該頻段右側(cè)6 000 Hz處有干擾信息。首先采用FSWT分析信號(hào)獲得時(shí)頻分布圖，如圖2所示。

圖1 仿真信號(hào)的時(shí)域波形及頻譜

圖2 FSWT時(shí)頻分布圖及經(jīng)驗(yàn)指定的故障頻段

由于信號(hào)中包含調(diào)制成分和強(qiáng)噪聲，因此FSWT時(shí)頻分布圖中難以確定所選取頻段的故障頻段。經(jīng)驗(yàn)指定法可能包含故障信息的頻段見(jiàn)圖2中的2個(gè)虛線(xiàn)框。左側(cè)頻段A有周期性幅值變化，但左右邊界難以確定；右側(cè)頻段B幅值的周期性相對(duì)較差但左右邊界比較明顯。經(jīng)驗(yàn)指定邊界的方法需要反復(fù)試驗(yàn)以尋找故障頻段，這給檢測(cè)帶來(lái)很大的工作量；如何從2個(gè)或多個(gè)頻段中篩選出可能包含故障信息的頻段需要進(jìn)一步研究。因此，自適應(yīng)確定故障頻段及引入對(duì)周期性沖擊信息敏感的指標(biāo)篩選頻段有著非常重要的研究?jī)r(jià)值。

2 自適應(yīng)的頻率切片小波變換

2.1 算法介紹

3）進(jìn)行FSWT變換，并通過(guò)iFSWT重構(gòu)頻段，獲得時(shí)域分量f()。

4）計(jì)算時(shí)域分量f()的譜負(fù)熵E，單位為bit。

6）提取f()中譜負(fù)熵最大的分量進(jìn)行包絡(luò)解調(diào)，提取故障特征。

注：圖中w11，w21，w22，w31…表示不同分解層觀測(cè)頻率的范圍。

經(jīng)驗(yàn)指定法FSWT和AFSWT流程圖如圖4所示。AFSWT方法利用FSWT重構(gòu)特性自適應(yīng)地連續(xù)分割頻帶并以譜負(fù)熵篩選出故障中心頻率和帶寬，取代了傳統(tǒng)方法手動(dòng)選取頻帶的過(guò)程，能夠更準(zhǔn)確、快速地提取故障特征。

2.2 譜負(fù)熵

旋轉(zhuǎn)機(jī)械如滾動(dòng)軸承發(fā)生故障時(shí)，振動(dòng)信號(hào)中存在非平穩(wěn)的周期性沖擊信息，其特征可簡(jiǎn)單描述為脈沖和循環(huán)平穩(wěn)。在故障診斷領(lǐng)域，信息熵可以用于衡量非平穩(wěn)沖擊成分在振動(dòng)信號(hào)中的比重?；诖?，Antoni[28-29]在譜峭度（spectral kurtosis, SK）、信息熵和包絡(luò)譜的基礎(chǔ)上擴(kuò)展并將這些概念聯(lián)系起來(lái)以捕獲時(shí)域和頻域中的周期性沖擊信息。

注：w表示FSWT選取的頻率區(qū)間，Hz；Fs表示采樣頻率，Hz。

其平均值為

當(dāng)能量流恒定時(shí)，可以得到最大譜熵，當(dāng)能量流凝聚為單個(gè)脈沖時(shí)，可以得到最小譜熵。與快速譜峭度等自適應(yīng)故障診斷方法相比，AFSWT采用信息熵替換峭度來(lái)識(shí)別沖擊成分。因此本文提出了類(lèi)似于譜峭度的信息熵：譜負(fù)熵（spectral negentropy）。其定義如下：

當(dāng)滾動(dòng)軸承發(fā)生故障時(shí)，振動(dòng)信號(hào)中包含周期性沖擊成分，該成分呈循環(huán)平穩(wěn)特性且譜負(fù)熵對(duì)此敏感。基于此，本文應(yīng)用譜負(fù)熵度量AFSWT提取的分量中包含周期性沖擊的多少。

3 仿真信號(hào)分析

由于FSWT不具備自適應(yīng)性，本文引入快速譜峭度（fast kurtogram, FK）并與自適應(yīng)頻率切片小波變換進(jìn)行對(duì)比以驗(yàn)證提出的方法的有效性。FK由Antoni在深入研究譜峭度并給出正式定義后提出，并且廣泛應(yīng)用于滾動(dòng)軸承故障診斷。采用FK處理公式（9）的仿真信號(hào)，獲得譜峭度圖，如圖5a所示。

注：Kmax為最大峭度；Level表示層；Bw為帶寬，Hz；fc為中心頻率，Hz。下同。

時(shí)域波形中的沖擊有一定的周期性，但沖擊特征不明顯，從包絡(luò)譜中能夠分辨出特征頻率及其2倍頻。該方法選取的帶寬較窄，中心頻率有偏差，可能是導(dǎo)致沖擊特征不明顯的2個(gè)因素。采用本文提出的AFSWT處理該仿真信號(hào)，獲得的快速譜負(fù)熵圖如圖6a所示。頻譜被劃分為16層，譜負(fù)熵最大的頻段位于Level 11，左起第6個(gè)頻段。其中心頻率為f=5 000 Hz，帶寬B=909 Hz，譜負(fù)熵為1.13 bit。提取該頻段的分量，獲得時(shí)域波形及包絡(luò)譜，見(jiàn)圖6c。時(shí)域波形中沖擊的周期性較明顯，包絡(luò)譜中可找到特征頻率和高倍頻，故障特征明顯。AFSWT提取的頻段的中心頻率為5 000Hz與1()的固有頻率f相等。帶寬約為快速譜峭度方法的2倍。因此該方法可找到更明顯的沖擊特征。

注：SEmax為最大譜負(fù)熵，bit；FSWT變換選取的切片函數(shù)為；尺度為k=28.85。下同。

4 實(shí)例驗(yàn)證

為了驗(yàn)證自適應(yīng)頻率切片小波變換方法的有效性，以6307型號(hào)滾動(dòng)軸承為研究對(duì)象，對(duì)軸承外圈加工凹槽模擬故障，采用西安交通大學(xué)故障診斷實(shí)驗(yàn)室的滾動(dòng)軸承試驗(yàn)臺(tái)進(jìn)行試驗(yàn)，如圖7a所示。通過(guò)杭州億恒科技有限公司的MI6008型數(shù)據(jù)采集儀、美國(guó)PCB公司的627A61型ICP加速度傳感器和筆記本電腦采集滾動(dòng)軸承的振動(dòng)信號(hào)。根據(jù)6307軸承適用的工況，設(shè)置電機(jī)轉(zhuǎn)速為1 450 r/min，采樣頻率為12 000 Hz，采樣時(shí)間20 s。經(jīng)計(jì)算，求得該軸承外圈故障特征頻率為f=74.43 Hz。

圖7 試驗(yàn)設(shè)備及信號(hào)采集結(jié)果

便于進(jìn)一步計(jì)算，截取振動(dòng)信號(hào)中轉(zhuǎn)速平穩(wěn)的8 192個(gè)點(diǎn)進(jìn)行分析，得到如圖7b的時(shí)域波形。通過(guò)傅里葉變換得到信號(hào)的頻譜圖，如圖7c所示。從時(shí)域波形中難以看出明顯的周期性沖擊現(xiàn)象，信號(hào)中包含故障的成分被強(qiáng)噪聲淹沒(méi)。從頻譜圖中也難以分辨出故障頻率。因此需要對(duì)信號(hào)進(jìn)行進(jìn)一步處理。

采用自適應(yīng)頻率切片小波變換處理該試驗(yàn)信號(hào)，結(jié)果如圖9a）所示。頻譜被劃分為16層，譜負(fù)熵最大的頻段位于Level 8，左起第4個(gè)頻段。其中心頻率為f= 2 625 Hz，帶寬B=750 Hz，譜負(fù)熵為0.89 bit。提取該頻段的分量，獲得時(shí)域波形及包絡(luò)譜，見(jiàn)圖9b和9c。

圖8 試驗(yàn)信號(hào)的快速譜峭度處理結(jié)果

提取第8層分量得到的時(shí)域波形有一定的周期性但不明顯，但是從包絡(luò)譜中可找到比較明顯的特征頻率74.71 Hz及其2～6倍頻，可以確定該軸承外圈發(fā)生故障。為了量化快速譜峭度和AFSWT方法的診斷效果，依據(jù)文獻(xiàn)[30]引入故障頻率檢測(cè)精度指標(biāo)：

根據(jù)圖8c計(jì)算快速譜峭度方法的故障頻率檢測(cè)精度為1.69/0.227=7.44，而根據(jù)圖9c計(jì)算AFSWT方法的故障頻率檢測(cè)精度為2.87/0.316=9.08，檢測(cè)精度提升了22.04%。對(duì)比2種方法的包絡(luò)譜和檢測(cè)精度可知，AFSWT方法有更多的倍頻成分和更高的檢測(cè)精度，因此本文提出的自適應(yīng)頻率切片小波變換識(shí)別沖擊特征的能力明顯優(yōu)于傳統(tǒng)的快速譜峭度。此外，傳統(tǒng)的頻率切片小波變換依次經(jīng)過(guò)計(jì)算時(shí)頻分布圖、尋找特征頻帶、反復(fù)確定觀測(cè)頻率等過(guò)程，往往需要5～10 min才能得到較為理想的診斷結(jié)果。分別運(yùn)用快速譜峭度和自適應(yīng)頻率切片小波變換方法分析本節(jié)信號(hào)，運(yùn)行過(guò)程耗時(shí)分別為25.7 s和14.7 s，自適應(yīng)頻率切片小波變換方法耗時(shí)更短，節(jié)省了42.8%的計(jì)算時(shí)間。

5 結(jié) 論

1）在滾動(dòng)軸承的故障特征提取中，傳統(tǒng)的頻率切片小波變換方法依賴(lài)人工干預(yù)確定重構(gòu)的頻帶，這種方法需要反復(fù)調(diào)整觀測(cè)頻帶的范圍，往往需要5～10 s才能提取出理想的頻帶。而經(jīng)過(guò)本文提出的自適應(yīng)頻率切片小波變換方法處理試驗(yàn)信號(hào)，耗時(shí)14.7 s，該方法通過(guò)新的頻譜分割方法改進(jìn)頻率切片小波變換，解決了手動(dòng)選取觀測(cè)頻率的自適應(yīng)性，實(shí)現(xiàn)了對(duì)振動(dòng)信號(hào)的濾波和特征分離。

2）自適應(yīng)頻率切片小波變換采用對(duì)周期性沖擊敏感的譜負(fù)熵解決了分量的選取問(wèn)題，試驗(yàn)信號(hào)的處理結(jié)果表明，該方法的故障頻率檢測(cè)精度為9.08，較快速譜峭度檢測(cè)精度提高了22.04%，且該方法得到的包絡(luò)譜包含2～6倍的特征頻率倍頻，明顯優(yōu)于包絡(luò)譜中僅有2倍頻的快速譜峭度。說(shuō)明該方法適用于滾動(dòng)軸承故障診斷。

[1] Ali Jaouher Ben, Fnaiech Nader, Saidi Lotfi, et al. Application of empirical mode decomposition and artificial neural network for automatic bearing fault diagnosis based on vibration signals[J]. Applied Acoustics, 2015, 89(3): 16－27.

[2] 王志堅(jiān)，韓振南，劉邱祖，等. 基于MED-EEMD的滾動(dòng)軸承微弱故障特征提取[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2014，30（23）：70－78. Wang Zhijian, Han Zhennan, Liu Qiuzu, et al. Weak fault diagnosis for rolling element bearing based on MED- EEMD[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2014, 30(23): 70－78. (in Chinese with English abstract)

[3] Chen Jinglong, Pan Jun, Li Zipeng, et al. Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals[J]. Renewable Energy, 2016, 89(1): 80－92.

[4] Xu Yonggang, Zhang Kun, Ma Chaoyong, et al. An improved empirical wavelet transform and its applications in rolling bearing fault diagnosis[J]. Applied Sciences, 2018, 8(12): 2352. DOI: 10.3390/app8122352

[5] 周士帥，竇東陽(yáng)，薛斌. 基于LMD和MED的滾動(dòng)軸承故障特征提取方法[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2016，32(23)：70－76.Zhou Shishuai, Dou Dongyang, Xue Bin. Fault feature extraction method for rolling element bearings based on LMD and MED[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2016, 32(23): 70－76. (in Chinese with English abstract)

[6] 陳志新，劉鑫，盧成林，等. 基于經(jīng)驗(yàn)小波變換的復(fù)雜強(qiáng)噪聲背景下弱故障檢測(cè)方法[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2016，32（20）：202－208. Chen Zhixin, Liu Xin, Lu Chenglin, et al. Weak fault detection method in complex strong noise condition based on empirical wavelet transform[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2016, 32(20): 202－208. (in Chinese with English abstract)

[7] 向家偉，崔向歡，王衍學(xué)，等. 軸承故障診斷的最優(yōu)化隨機(jī)共振方法分析[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2014，30（12）：50－55. Xiang Jiawei, Cui Xianghuan, Wang Yanxue, et al. Opti-mized stochastic resonance method for bearing fault diagnosis[J]. Transactions of the Chinese Society of Agricul-tural Engineering (Transactions of the CSAE), 2014, 30(12): 50－55. (in Chinese with English abstract)

[8] 胥永剛，孟志鵬，趙國(guó)亮，等. 基于雙樹(shù)復(fù)小波包變換能量泄漏特性分析的齒輪故障診斷[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2014，30（2）：72－77. Xu Yonggang, Meng Zhipeng, Zhao Guoliang, et al. Analysis of energy leakage characteristics of dual-tree complex wavelet packet transform and its application on gear fault diagnosis[J]. Transactions of the Chinese Society of Agricul-tural Engineering (Transactions of the CSAE), 2014, 30(2): 72－77.(in Chinese with English abstract)

[9] Xu Yonggang, Zhang Kun, Ma Chaoyong, et al. Adaptive Kurtogram and its applications in rolling bearing fault diagnosis[J]. Mechanical Systems and Signal Processing, 2019, 130(1): 87－107

[10] Wang Yi, Xu Guanghua, Liang Lin, et al. Detection of weak transient signals based on wavelet packet transform and manifold learning for rolling element bearing fault diag-nosis[J]. Mechanical Systems and Signal Processing, 2015, 54(1): 259－276.

[11] Liu Xin, Jia Yunxian, He Zeiwei, et al. Application of EMD-WVD and particle filter for gearbox fault feature extraction and remaining useful life prediction[J]. Journal of Vibroengineering, 2017, 19(3): 1793-1808.

[12] Chen Jinglong, Pan Jun, Li Zipeng, et al. Generator bearing fault diagnosis for wind turbine via empirical wavelet trans-form using measured vibration signals[J]. Renewable Energy, 2016, 89(1): 80－92.

[13] Cao Hongrui, Fan Fei, Zhou Kai, et al. Wheel-bearing fault diagnosis of trains using empirical wavelet transform[J]. Measurement, 2016, 82(1): 439－449.

[14] Huang Norden E, Shen Zheng, Long Steven R, et al, The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J]. Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903-995.

[15] Li Yongbo, Xu MinQiang, Liang Xihui, et al. Application of bandwidth EMD and adaptive multiscale morphology analysis for incipient fault diagnosis of rolling bearings[J]. IEEE Transactions on Industrial Electronics, 2017, 64(8): 6506－6517.

[16] 竇東陽(yáng)，楊建國(guó)，李麗娟，等. 基于EMD和MLEM2的滾動(dòng)軸承智能故障診斷方法[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2011，27（4）: 125－130.Dou Dongyang, Yang Jianguo, Li Lijuan, et al. Intelligent fault diagnosis method for rolling bearings based on EMD and MLEM2[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2011, 27(4): 125－130. (in Chinese with English abstract)

[17] Gilles Jér?me. Empirical wavelet transform[J]. IEEE Transactions on Signal Processing, 2013, 61(16): 3999－4010.

[18] Li Hongguang, Hu Yue, Li Fucai. Succinct and fast empirical mode decomposition[J]. Mechanical Systems and Signal Processing, 2017, 85(1): 879－895.

[19] Shi Juanjuan, Liang Ming, Dansorin Necsulescu, et al.Generalized stepwise demodulation transform and synchros-queezing for time–frequency analysis and bearing fault diagnosis[J]. Journal of Sound and Vibration, 2016, 368(1): 202－222.

[20] Liu Ruonan, Yang Boyuan, Zhang Xiaoli, et al. Time- frequency atoms-driven support vector machine method for bearings incipient fault diagnosis[J]. Mechanical Systems and Signal Processing, 2016, 75(1): 345－370.

[21] Yan Zhonghong, Miyamoto Ayaho, Jiang Zhongwei. Frequency slice wavelet transform for transient vibration response analysis[J]. Mechanical Systems & Signal Processing, 2009, 23(5): 1474－1489.

[22] Yan Zhonghong, Miyamoto Ayaho, Jiang Zhongwei, et al. An overall theoretical description of frequency slice wavelet transform[J]. Mechanical Systems & Signal Processing, 2010, 24(2): 491－507.

[23] Biswal Birendra, Mishra Sukumar. Power signal disturbance identification and classification using a modified frequency slice wavelet transform[J]. IET Generation, Transmission & Distribution, 2014, 8(2): 353-362.

[24] 段晨東，高強(qiáng). 基于時(shí)頻切片分析的故障診斷方法及應(yīng)用[J]. 振動(dòng)與沖擊，2011，30（9）：1－5. Duan Chendong, Gao Qiang. Noval fault diagnosis approach using time-frequency slice analysis and its application[J]. Journal of Vibration Engineering, 2011, 30(9): 1－5. (in Chinese with English abstract)

[25] Liu Xinglong, Jiang Zhongwei, Yan Zhonghong. Improve-ment of accuracy in damage localization using frequency slice wavelet transform[J]. Shock and Vibration, 2015, 19(4): 585－596.

[26] 楊仁樹(shù)，付曉強(qiáng)，楊國(guó)梁，等. EMD和FSWT組合方法在爆破振動(dòng)信號(hào)分析中的應(yīng)用研究[J] . 振動(dòng)與沖擊，2017，36（2）：58－64. Yang Renshu, Fu Xiaoqiang, Yang Guoliang, et al.Applic-ation of EMD and FSWT combination method in blasting vibration signal analysis[J]. Journal of Vibration Engineering, 2017, 36(2): 58－64. (in Chinese with English abstract)

[27] 王元生，任興民，鄧旺群，等. 基于DSS和FSWT的欠定信號(hào)識(shí)別方法研究[J]. 振動(dòng)與沖擊，2014，33（21）：80－84. Wang Yuansheng, Ren Xingmin, Deng Wangqun, et al. An efficient identification method for underdetermined signals based on DSS and FSWT[J]. Journal of Vibration Engine-ering, 2014, 33(21): 80－84. (in Chinese with English abstract)

[28] Antoni Jermoe. The infogram: Entropic evidence of the signature of repetitive transients[J]. Mechanical Systems & Signal Processing, 2016, 74(1): 73－94.

[29] Antoni Jermoe. Fast computation of the kurtogram for the detection of transient faults[J]. Mechanical Systems & Signal Processing, 2007, 21(1): 108－124.

[30] 馬增強(qiáng)，柳曉云，張俊甲，等. VMD和ICA聯(lián)合降噪方法在軸承故障診斷中的應(yīng)用[J]. 振動(dòng)與沖擊，2017，36（13）：201－207. Ma Zengqiang, Liu Xiaoyun, Zhang Junjia, et al. Application of VMD-ICA combined method in fault diagnosis of rolling bearings[J]. Journal of Vibration Engineering, 2017, 36(13): 201－207. (in Chinese with English abstract)

Fault diagnosis of rolling bearing based on adaptive frequency slice wavelet transform

Ma Chaoyong1, Sheng Zhipeng1, Xu Yonggang1,2※, Zhang Kun1

(1.,,, 100124,; 2.,,100124,)

In industrial production, it is necessary to detect the running state of rolling bearings and diagnose their faults. When rolling bearing is damaged, the vibration signals collected often show the characteristics of non-stationary and modulation, and will inevitably be disturbed by strong noise, so it is very difficult to identify the fault features. How to effectively extract the components carrying fault feature information from complex non-stationary and modulated signals is the key of diagnosing bearing fault. Frequency slice wavelet transform (FSWT) uses frequency slice function based on the advantages of short-time Fourier transform (STFT) and wavelet transform (WT), which makes the traditional Fourier transform realize time-frequency analysis function. The traditional fault diagnosis method based on FSWT determines the most suitable center frequency and the faulty bandwidth by comparing the results of different frequency band processing, and realizes the reconstruction and description of arbitrary frequency band and local characteristics of the signal. However, this method is inefficient, non-adaptive and can not guarantee that the frequency band screened manually contains the required fault information. Aiming at the problem that traditional methods rely on manual operation and have no self-adaptability, an adaptive frequency slice wavelet transform (AFSWT) is proposed in this paper. Firstly, the signal spectrum is segmented continuously; spectrum segmentation covers the whole frequency band and avoids the process of manual selection of spectrum boundary. The method of equalization can improve the computational efficiency. Secondly, the spectral negative entropy is introduced as the evaluation basis to calculate the complexity of the signal in each frequency band in order to screen the cyclostationary information which may contain periodic shocks. Finally, the frequency band with the largest spectral negative entropy is selected and defined as the faulty center frequency and bandwidth. The signal components in the band are reconstructed and analyzed by envelope demodulation to realize fault diagnosis. The analysis results of a simulation signal show that the AFSWT method identifies the center frequency of 5 000 Hz and the bandwidth of 909 Hz, which is very close to the ideal result. Compared with fast spectral kurtosis, AFSWT has better applicability when the central frequency of signal is located in/4,/8 and/16(is the sampling frequency). Through the test of rolling bearing test-bench, the vibration signals of rolling bearing outer ring fault are collected and analyzed. After AFSWT analysis, the characteristic frequency and its 2-6 times frequency components can be clearly found in the envelope spectrum of the results. On the other hand, AFSWT takes 14.7 seconds to process test signals. The traditional FSWT needs repeated drawing of time-frequency distribution map, determination of central frequency band and selection of observation frequency, it often takes 5-10 minutes to determine the faulty center frequency and bandwidth. The above analysis shows that AFSWT can improve the calculation efficiency and screening accuracy by uniformly dividing the spectrum of the signal and screening the signal components according to the negative entropy of the spectrum. It is suitable for fault diagnosis of rolling bearings.

bearings; vibration; fault diagnosis; frequency slice wavelet transform; spectral negative entropy; spectrum segmentation

10.11975/j.issn.1002-6819.2019.10.005

TH133.3; TH165

A

1002-6819(2019)-10-0034-08

2018-12-29

2019-02-16

國(guó)家自然科學(xué)基金（51775005，51675009）

馬朝永，副教授，博士，主要從事設(shè)備故障診斷方面研究。Email：machaoyong@bjut.edu.cn

胥永剛，副教授，博士，主要從事設(shè)備故障診斷方面研究。Email：xyg_1975@163.com

馬朝永，盛志鵬，胥永剛，張 坤. 基于自適應(yīng)頻率切片小波變換的滾動(dòng)軸承故障診斷[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2019，35(10)：34－41. doi：10.11975/j.issn.1002-6819.2019.10.005 http://www.tcsae.org

Ma Chaoyong, Sheng Zhipeng, Xu Yonggang, Zhang Kun. Fault diagnosis of rolling bearing based on adaptive frequency slice wavelet transform[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2019, 35(10): 34－41. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2019.10.005 http://www.tcsae.org