外文翻譯----整體經(jīng)驗(yàn)?zāi)Ｊ椒纸猓╡emd）的改進(jìn)

1、<p><b>　　附 錄</b></p><p>　　附錄A 外文資料翻譯</p><p>　　Machanical Systerms and Signal Processing 13 (2010)</p><p>　　Performance enhancement of ensemble empirical mode deco

2、mposition</p><p><b>　　Abstract</b></p><p>　　Ensemble empirical mode decomposition (EEMD) is a newly developed method aimed at eliminating mode mixing present in the original empirica

3、l mode decomposition (EMD). To evaluate the performance of this new method, this paper investigates the effect of two parameters pertinent to EEMD: the amplitude of added white noise and the number of ensemble trials. A

4、test signal with mode mixing that mimics realistic bearing vibration signals measured on a bearing test bed was developed to enable quantitati</p><p>　　1. Introduction</p><p>　　In recent years,

5、time–frequency and time-scale analysis techniques such as short time Fourier transform (STFT) [1] and wavelet transform [2, 3] have been increasingly investigated for non-stationary and/or nonlinear signal processing in

6、machine health diagnosis. These techniques, while having shown to be successful in various applications, are non-adaptive in nature. As a result, once the window type or a base wavelet has been chosen, the analysis funct

7、ion remains the same during the subsequent </p><p>　　This paper investigates the effect of two parameters – the amplitude of added noise and the number of ensemble trials – on the performance of the EEMD met

8、hod. After introducing the theoretical background of the EEMD process, a simulated signal that presents the mode mixing phenomenon is developed to facilitate quantitative evaluation of the two parameters. Furthermore, it

9、 is proposed to replace white noise with noise of finite bandwidth for the EEMD process to improve computational efficiency. S</p><p>　　2. Modified EEMD method</p><p>　　While the EEMD method sol

10、ves the problem of mode mixing, the large number of ensemble trails presents a high computational load. Improving the computational efficiency of EEMD is thus desired. The purpose of adding white noise is to facilitate t

11、hat components in different scales of the signal are properly projected onto scales of reference established by the white noise [21]. This means the low frequency part of the added white noise will affect the decompositi

12、on results of the EEMD process (i.e</p><p>　　To evaluate the effectiveness of the modified EEMD (MEEMD) method, Fourier transform is first performed on the signal to gain an overview of its frequency spectru

13、m. As shown in Fig. 9, the high frequency component of the signal is located in the region of approximately 1300–2000Hz. Accordingly, noise with a finite bandwidth of [0–2,000] Hz is chosen to be added into the signal fo

14、r EEMD decomposition. Fig. 10 illustrates how the decomposition results have varied with the number of ensemble trials</p><p>　　3. Experimental evaluation </p><p>　　To evaluate the effectiveness

15、 of the modified EEMD method for non-stationary signal analysis, vibration signals were collected from a bearing test system (Fig. 21). The system consists of a DC motor (Lesson C16D34FT18), two supporting pillow blocks

16、(SKF209-112), a testing bearing with supporting housing, a hydraulic cylinder (Miller 4Z644B), a hydraulic pump (Enerpac P392), and an optical encoder for bearing speed measurement. The hydraulic cylinder applies variabl

17、e load to the bearing in the ra</p><p>　　Fig. 22 illustrates vibration signals measured from two identical bearings: one without any seeded defect (i.e. bearing is ‘‘healthy’’) and the other with a seeded de

18、fect (i.e. bearing is ‘‘defective’’). The traditional EMD method is first applied to the two vibration signals, and the result is shown in Fig. 23, where a comparison of the extracted IMFs between the healthy (Fig. 23 (l

19、eft)) and defective bearing (Fig. 23 (right)) is contrasted. In Fig. 24, their corresponding HHT spectrum is shown</p><p>　　To evaluate the computational cost, both the original EEMD and the modified EEMD me

20、thods are run in the MATLAB environment on a laptop computer, which has a 2.4 GHz dual-core CPU and 2GB RAM. It took the original EEMD method approximately 100 s to complete the task, whereas for the MEEMD method, it was

21、 60 s. This demonstrates that the MEEMD method is not only effective in eliminating mode mixing, but also computationally more efficient than the original EEMD method. </p><p>　　To systematically evaluate th

22、e computational efficiency of the MEEMD method, experimental data obtained from defective bearings with seeded defects of 1, 0.5, and 0.1 inch diameter on the outer and inner raceways were analyzed. The bearings are test

23、ed under different rotating speeds (600, 1200, and 2100 rpm, respectively) in the experiment. In Figs. 28and 29, the computational times of the original EEMD and modified EEMD methods are compared with each other. Furthe

24、r details are listed in Tables </p><p>　　4. Conclusion </p><p>　　The ensemble empirical mode decomposition method has been investigated for signal decomposition. Two parameters that affect the p

25、erformance of the EEMD method: the amplitude of the added noise and the number of ensemble trials, have been systematically investigated using a simulated signal. Based on the analysis, a modified EEMD method, termed MEE

26、MD, has been proposed. This method uses band-limited noise instead of white noise to facilitate the EEMD computation process, thus improving its comput</p><p><b>　　譯 文</b></p><p>　　

27、《機(jī)械工程和信號(hào)處理》2010年第10期</p><p>　　整體經(jīng)驗(yàn)?zāi)Ｊ椒纸猓‥EMD）的改進(jìn)</p><p><b>　　摘 要</b></p><p>　　整體經(jīng)驗(yàn)?zāi)Ｊ椒纸猓‥EMD）是一種新開發(fā)的方法，旨在消除原經(jīng)驗(yàn)?zāi)Ｊ椒纸猓‥MD）存在的模式混合問題。為了評(píng)估這種新方法的性能，本文著重探討與EEMD性能有關(guān)的倆個(gè)參數(shù)：加性白噪聲的幅度

28、和整體試驗(yàn)的數(shù)量。在軸承試驗(yàn)平臺(tái)上測得的模擬仿真軸承振動(dòng)的具有模式混合的信號(hào)使得對(duì)EEMD的定量評(píng)價(jià)成為可能，同時(shí)還對(duì)如何針對(duì)軸承信號(hào)分解來合適地選擇這倆個(gè)參數(shù)提供了指導(dǎo)。隨后，改良后的EEMD（MEEMD）方法提出了如何減少EEMD原方法的計(jì)算成本，以及提高其性能。用在一個(gè)實(shí)驗(yàn)軸承試驗(yàn)床上測量的振動(dòng)數(shù)據(jù)進(jìn)行數(shù)值計(jì)算以及對(duì)系統(tǒng)的研究，證實(shí)了改進(jìn)后的EEMD方法對(duì)于軸承缺陷的診斷具有有效性及高效性。</p><p>

29、;<b>　　第1章 介紹</b></p><p>　　近年來，時(shí)間頻率和時(shí)間尺度分析技術(shù)例如短時(shí)傅里葉變換（STFT）和小波變換，已越來越多被研究用于機(jī)械故障診斷中非平穩(wěn)或非線性信號(hào)處理診斷。這些技術(shù)，在各種應(yīng)用中已被證明是成功的，并且具有非自適應(yīng)性質(zhì)。因此，一旦窗口類型或基小波已被選定，分析功能仍然相同，在隨后的信號(hào)分解過程中，分析功能仍然保持相同。相比之下，希爾伯特 - 黃變換（HHT

30、），分解成一組固有模態(tài)函數(shù)（貨幣基金組織）通過經(jīng)驗(yàn)?zāi)Ｊ椒纸猓‥MD）的過程將信號(hào)分解成一組固有模態(tài)函數(shù)（本征模式分解），因此，只涉及信號(hào)分析本身，而不是要求一個(gè)信號(hào)分析功能，這是令人費(fèi)解的。因此，它提出了一個(gè)數(shù)據(jù)驅(qū)動(dòng)的方法來處理信號(hào)的非平穩(wěn)性或非線性。</p><p>　　HHT的技術(shù)已經(jīng)應(yīng)用到各個(gè)領(lǐng)域，如機(jī)械健康監(jiān)測和結(jié)構(gòu)損傷檢測，信號(hào)的過濾、降噪以及生物工程，然而在EMD過程一直存在的問題是模式混合，這會(huì)導(dǎo)致

31、信號(hào)出現(xiàn)間斷。為了提高EMD方法，總體經(jīng)驗(yàn)?zāi)Ｊ椒纸夥ǎ‥EMD）最近已被提出來，以消除模式混合。從本質(zhì)上講，EEMD運(yùn)用原EEMD的方法將混合白噪聲信號(hào)的原始信號(hào)重復(fù)分解為一系列本征模式分量，并且在這個(gè)重復(fù)的過程中將相應(yīng)的本征模式分量作為最終的EEMD分解的結(jié)果。</p><p>　　本文探討兩個(gè)參數(shù)即噪聲幅度的增加和整體試驗(yàn)的數(shù)量對(duì)于EEMD方法性能的影響。在介紹了EEMD過程的理論背景后，模擬一個(gè)具有信號(hào)混合

32、現(xiàn)象的模擬信號(hào)來促進(jìn)對(duì)這倆個(gè)參數(shù)的定量評(píng)價(jià)。此外，在EEMD過程中，建議有帶線寬的噪聲來取代白噪聲以提高計(jì)算效率。隨后，對(duì)模擬軸承振動(dòng)信號(hào)的數(shù)值評(píng)價(jià)和軸承試驗(yàn)臺(tái)測得信號(hào)的實(shí)驗(yàn)研究都驗(yàn)證了改進(jìn)后的EEMD方法在軸承缺陷診斷方面的有效性。EMD和EEMD與原方法的比較表明，改良后的EEMD（MEEMD）方法更有效，計(jì)算效率更高，適合應(yīng)用于旋轉(zhuǎn)機(jī)械的健康診斷。</p><p>　　第2章 改進(jìn)的總體平均經(jīng)驗(yàn)?zāi)Ｊ椒纸夥椒?/p>

33、</p><p>　　EEMD方法雖然解決了混合模式的問題，但大量的集成創(chuàng)新產(chǎn)生了很高的計(jì)算負(fù)荷。因此，提高的EEMD計(jì)算效率是理想的。加入白噪聲的目的是為了方便在不同尺度的信號(hào)下將分量正確投射到由白色噪聲信號(hào)建立的參考尺度。這意味著所加白噪聲的低頻部分將會(huì)影響EEMD分解過程（即本征模式分解過程中減少模式混合）的結(jié)果，只要它涵蓋了感興趣的信號(hào)的頻率范圍。在分解過程中，所加白噪聲信號(hào)的高頻部分對(duì)結(jié)果無影響。這就意

34、味著可以通過將白噪聲替換為被分解的帶限噪聲來提高EEMD的計(jì)算效率。這種替換將會(huì)有效的減少需要用來獲得有意義的本證模式分量整體實(shí)驗(yàn)的次數(shù)。技術(shù)上來講，帶限噪聲信號(hào)可通過低通濾波白噪聲信號(hào)來獲取，伴隨著將感興趣信號(hào)的截止頻率作為上限。</p><p>　　要評(píng)估改良EEMD（MEEMD）方法的有效性，傅立葉變換是首先被用來推薦作為獲得信號(hào)頻譜概述的方法。正如圖9所示，信號(hào)的高頻成分坐落在約1300-2000赫茲的地

35、區(qū)。因此，0-2000赫茲的有限帶寬信號(hào)被選擇添加到作為EEMD分解用的信號(hào)。圖10說明，隨著整體實(shí)驗(yàn)次數(shù)的不同，分解結(jié)果是怎樣變化的。圖11顯示了IMF1和分量x2(t)在信號(hào)上的相關(guān)性。相比而言，使用原來的EEMD方法取得圖8所示的結(jié)果，圖10是使用修改后的EEMD方法獲得的結(jié)果，可以看出，使用修改后的方法，高頻分量可以很容易地在70整體試驗(yàn)后在IMF1中確定，而不是以前需要100試驗(yàn)。這意味著節(jié)省了30%的計(jì)算量。圖11顯示的結(jié)果

36、看出，對(duì)于70次的整體實(shí)驗(yàn)，提取的IMF2和高頻分量之間的相關(guān)系數(shù)達(dá)到了0.95。</p><p><b>　　第3章 試驗(yàn)評(píng)價(jià)</b></p><p>　　為了評(píng)估修改后EEMD方法分析非平穩(wěn)信號(hào)的有效性，于軸承測試系統(tǒng)采集振動(dòng)信號(hào)（圖21）。該系統(tǒng)由直流電動(dòng)機(jī)（(Lesson C16D34FT18），兩個(gè)支撐枕塊（SKF209-112），液壓缸（米勒4Z644B）

37、，液壓泵（ENERPAC P392），用于軸承轉(zhuǎn)速測量的光電編碼器。在徑向，液壓缸為軸承提供了變載荷。加速度計(jì)（帶寬1 Hz到30 kHz）從兩個(gè)測試軸承測量振動(dòng)，其中一個(gè)種子缺陷軸承帶有缺陷（整個(gè)外圈滾道有0.27毫米的溝）。設(shè)置采樣頻率為100千赫，試驗(yàn)軸承的轉(zhuǎn)速為2100每分，徑向預(yù)緊力為200磅每平方英寸。</p><p>　　圖22顯示了倆個(gè)相同軸承的振動(dòng)信號(hào)：：一個(gè)沒有任何種子缺陷

38、（即軸承是“健康”），一個(gè)有缺陷（即軸承是“不健康”的）。傳統(tǒng)的EMD方法首次應(yīng)用于兩個(gè)振動(dòng)信號(hào)，結(jié)果如圖 23所示，將健康的軸承和有缺陷的軸承的本征模式分量進(jìn)行了對(duì)比，其相應(yīng)的HHT頻譜在圖24顯示?？梢钥闯觯】递S承（圖24（a）），沒有明顯的周期信號(hào)被識(shí)別，而在缺陷軸承的HHT頻譜中，一個(gè)時(shí)間間隔為8毫秒的周期信號(hào)明顯顯示出來。這樣的結(jié)果來源于滾動(dòng)體和滾到缺陷定期相互作用的結(jié)果?？梢钥闯?，在圖 24的HHT的光

39、譜中，高頻率分量和中頻分量沒有明確的相互分離，低頻分量混合在一起，這就表明混合模式是存在的。然后將EEMD原始的方法應(yīng)用到相同的振動(dòng)信號(hào)，提取的本征分量示于圖25（左為健康軸承，右為有缺陷軸承），其相應(yīng)的HHT譜如圖26所示。比較圖 24（b）所示結(jié)果，可以看出，在圖26（b）中，中、高頻率成分清楚分開。 對(duì)于有缺陷的軸承，8毫秒的周期信號(hào)被識(shí)別。此外，低頻成分不再混在一起。當(dāng)將MEEMD的方法應(yīng)用于振動(dòng)信號(hào)，振動(dòng)信

40、號(hào)的頻率范圍第一次被估計(jì)用來確定被添加的用來促進(jìn)EEMD過程的噪聲信號(hào)的合適帶寬。隨后，這樣的帶限噪聲</p><p>　　為了評(píng)估計(jì)算成本，原EEMD和修改后的EEMD方法在同一臺(tái)擁有2.4 GHz的雙核CPU和2GB RAM的筆記本電腦的 MATLAB環(huán)境下運(yùn)行，對(duì)于原始的EEMD方法，花費(fèi)了約100秒來完成全部工作，而對(duì)于MEEMD,才花費(fèi)約60秒。這表明，MEEMD方法不僅能有效地消除模式混合，

41、也比原來的EEMD方法更高效。</p><p>　　要系統(tǒng)評(píng)估MEEMD方法的計(jì)算效率，將從內(nèi)部和外部滾道缺陷分別為1、0.5、0.1英寸的軸承上獲得的數(shù)據(jù)進(jìn)行了分析。軸承在不同的旋轉(zhuǎn)速度（600，1200和2100RPM）下進(jìn)行測試測試。傳統(tǒng)的EEMD和改進(jìn)后的EEMD的計(jì)算時(shí)間的對(duì)比在圖28和圖29中已顯示，更進(jìn)一步的數(shù)據(jù)列于表格3和4中?？梢钥闯?，基于運(yùn)行環(huán)境，計(jì)算效率提高了30%到45%。這就意味著改進(jìn)后

42、的EEMD方法可以廣泛應(yīng)用于原EEMD檢測軸承故障領(lǐng)域來提高效率。</p><p><b>　　第4章 結(jié)論</b></p><p>　　整體經(jīng)驗(yàn)?zāi)Ｊ椒纸庑盘?hào)的方法已被研究用于信號(hào)分解，兩個(gè)參數(shù)影響EEMD方法的性能：噪聲增加的幅度和整體實(shí)驗(yàn)的數(shù)量，這已經(jīng)用模擬信號(hào)進(jìn)行了系統(tǒng)研究。根據(jù)分析，修改后的EEMD方法，即MEEMD，已經(jīng)被提出來了。這種方法使用帶限噪聲來代替