周期能量與優(yōu)化LMD結(jié)合的軸承故障診斷方法*

熊邦書，　李　龍，　李新民，　莫　燕

(1.南昌航空大學(xué)無(wú)損檢測(cè)技術(shù)教育部重點(diǎn)實(shí)驗(yàn)室　南昌，330063) (2.中國(guó)直升機(jī)設(shè)計(jì)研究所直升機(jī)旋翼動(dòng)力學(xué)國(guó)防科技重點(diǎn)實(shí)驗(yàn)室　景德鎮(zhèn)，333001)

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周期能量與優(yōu)化LMD結(jié)合的軸承故障診斷方法*

熊邦書1，李龍1，李新民2，莫燕1

(1.南昌航空大學(xué)無(wú)損檢測(cè)技術(shù)教育部重點(diǎn)實(shí)驗(yàn)室南昌，330063) (2.中國(guó)直升機(jī)設(shè)計(jì)研究所直升機(jī)旋翼動(dòng)力學(xué)國(guó)防科技重點(diǎn)實(shí)驗(yàn)室景德鎮(zhèn)，333001)

摘要為了提高軸承故障診斷準(zhǔn)確率，縮短神經(jīng)網(wǎng)絡(luò)訓(xùn)練時(shí)間，將周期能量特征和優(yōu)化的局域均值分解(local mean decomposition,簡(jiǎn)稱LMD)特征結(jié)合，提出了一種新的軸承故障診斷方法。首先，采用形態(tài)濾波法對(duì)振動(dòng)信號(hào)去噪；其次，以軸承一個(gè)旋轉(zhuǎn)周期采樣點(diǎn)數(shù)為標(biāo)準(zhǔn)，對(duì)振動(dòng)信號(hào)進(jìn)行截取，提取周期能量特征和LMD特征；然后，對(duì)提取的特征進(jìn)行u律壓擴(kuò)和滑動(dòng)平均優(yōu)化處理；最后，設(shè)計(jì)兩個(gè)同精度神經(jīng)網(wǎng)絡(luò)，采用經(jīng)優(yōu)化和未優(yōu)化的特征對(duì)設(shè)計(jì)好的RBF神經(jīng)網(wǎng)絡(luò)進(jìn)行訓(xùn)練，用訓(xùn)練好的神經(jīng)網(wǎng)絡(luò)進(jìn)行故障診斷。實(shí)驗(yàn)結(jié)果表明，神經(jīng)網(wǎng)絡(luò)收斂迭代次數(shù)減少了50次，診斷正確率提高了10%，提高了軸承故障診斷正確率，縮短了神經(jīng)網(wǎng)絡(luò)訓(xùn)練時(shí)間。

關(guān)鍵詞u律壓擴(kuò)； 滑動(dòng)平均； 故障診斷； 局域均值分解

引言

滾動(dòng)軸承廣泛應(yīng)用于各類機(jī)械設(shè)備的傳動(dòng)系動(dòng)中，它的缺陷和損傷影響整臺(tái)設(shè)備安全運(yùn)行，因此對(duì)其故障診斷方法研究具有重要意義。特征提取是故障診斷的關(guān)鍵環(huán)節(jié)之一，對(duì)于滾動(dòng)軸承，特征提取方法很多，可分為時(shí)域、頻域和時(shí)頻域等方法。由于軸承振動(dòng)信號(hào)的非平穩(wěn)非線性特點(diǎn)，目前時(shí)頻域特征提取方法被廣泛應(yīng)用，常見(jiàn)的時(shí)頻域方法主要有Winger分布、短時(shí)傅里葉變換、小波變換和LMD方法等。Winger分布對(duì)多信號(hào)分量分析時(shí)會(huì)產(chǎn)生交叉項(xiàng)[1]，短時(shí)傅里葉變換窗口是固定不變的[2]，小波變換雖然有可變的窗口，但其分解過(guò)程仍是基于頻率的線性分解[3]，對(duì)于非線性非平穩(wěn)特點(diǎn)的信號(hào)難以提取到理想的故障特征。LMD方法[4]雖然已經(jīng)應(yīng)用于軸承故障診斷方法中，但其提取的各類故障特征間存在間隔不均衡和特征值波動(dòng)現(xiàn)象，影響故障診斷準(zhǔn)確率和神經(jīng)網(wǎng)絡(luò)訓(xùn)練時(shí)間。根據(jù)軸承故障信號(hào)特點(diǎn)，筆者提出了周期能量特征和優(yōu)化LMD特征相結(jié)合的軸承故障診斷方法。

1周期能量特征提取方法

1.1周期能量特征

周期能量特征是指以振動(dòng)信號(hào)一個(gè)周期采樣點(diǎn)數(shù)為標(biāo)準(zhǔn)，對(duì)振動(dòng)信號(hào)進(jìn)行截取，計(jì)算截取信號(hào)能量，即周期能量特征。

設(shè)振動(dòng)信號(hào)為{xi}(i=1,2,…,n)，采樣頻率為fs，傳動(dòng)軸的轉(zhuǎn)動(dòng)速率為Vr。

采樣間隔為

(1)

旋轉(zhuǎn)頻率為

(2)

傳動(dòng)軸的轉(zhuǎn)動(dòng)周期為

(3)

一個(gè)周期采樣點(diǎn)數(shù)

(4)

能量計(jì)算公式為

(5)

由式(4)和(5)可得到周期能量特征提取公式為

(6)

其中：m為第m個(gè)周期；N為一個(gè)周期采樣點(diǎn)數(shù)。

1.2周期能量特征歸一化

在故障識(shí)別過(guò)程中，為提高傳遞函數(shù)的靈敏度，需對(duì)周期能量特征進(jìn)行歸一化處理，將其處理到0～1范圍內(nèi)。

周期能量特征歸一化公式為

(7)

1.3周期能量特征優(yōu)化處理

1.3.1u律壓擴(kuò)處理

經(jīng)歸一化后，各類故障特征間存在間隔不均衡現(xiàn)象，影響診斷正確率和神經(jīng)網(wǎng)絡(luò)收斂速度，筆者采用u律壓擴(kuò)方法[5]，對(duì)各類故障特征間間隔進(jìn)行調(diào)整。u律壓擴(kuò)公式為

(8)

其中：x為歸一化輸入；y為u律壓擴(kuò)輸出；u為壓擴(kuò)參數(shù)，表示壓擴(kuò)程度。

不同u值壓擴(kuò)特性如圖1所示。

圖1　u律壓擴(kuò)曲線Fig.1　The u-law compression-expansion curve

由圖1知，u=0時(shí)，壓擴(kuò)曲線是一條通過(guò)原點(diǎn)的直線，故沒(méi)有壓擴(kuò)效果，小特征值得不到改善；u值越大壓擴(kuò)效果越明顯。

1.3.2滑動(dòng)平均處理

由于各類故障的特征值存在波動(dòng)現(xiàn)象，影響故障特征的有效性，筆者采用三點(diǎn)滑動(dòng)平均處理方法，消除各類故障特征值出現(xiàn)的波動(dòng)現(xiàn)象。三點(diǎn)滑動(dòng)平均公式為

(9)

2優(yōu)化的LMD特征提取方法

2.1LMD方法

對(duì)信號(hào)x(t)進(jìn)行LMD分解[6]，分解過(guò)程如下。

1) 用ni(i=1,2,…,λ)表示信號(hào)x(t)中的所有局部極值點(diǎn)，計(jì)算ni和ni+1的和，以及ni和ni+1相減的絕對(duì)值，再分別除以2，可得到mi和ai

(10)

(11)

2) 用直線將所有相鄰mi連接起來(lái)。

3) 用滑動(dòng)平均方法進(jìn)行平滑處理，可得到局部均值函數(shù)m11(t)；用同樣的方法可得到包絡(luò)估計(jì)函數(shù)a11(t)。

4) 將局部均值函數(shù)m11(t)從原始信號(hào)x(t)中分離出來(lái)，得

(12)

5) 用h11(t)除以包絡(luò)估記函數(shù)a11(t)進(jìn)行解調(diào)，得

(13)

其中：a12(t)為s11(t)的包絡(luò)估計(jì)函數(shù)。

如果a12(t)≠1，就用s11(t)替代原始信號(hào)，對(duì)其重復(fù)上述過(guò)程，直至s1n(t)的包絡(luò)估計(jì)函數(shù)a1(n+1)(t)滿足a1(n+1)(t)=1時(shí)，迭代終止。在實(shí)際工程中，一般情況下，設(shè)定一個(gè)不影響分解效果的變動(dòng)量Δ，當(dāng)包絡(luò)估計(jì)函數(shù)滿足1-Δ≤a1n≤1+Δ時(shí)，迭代終止。

6) 將迭代過(guò)程中得到的全部包絡(luò)估計(jì)函數(shù)相乘可得到包絡(luò)信號(hào)

(14)

7) 將包絡(luò)信號(hào)a1(t)和純調(diào)頻信號(hào)s1n(t)相乘得到原始信號(hào)的第1個(gè)PF分量

(15)

8) 從給定信號(hào)x(t)中減去PF1(t)，可得到信號(hào)u1(t)，即

(16)

9) 將信號(hào)u1(t)作為原始數(shù)據(jù)重復(fù)上述步驟，循環(huán)k次，直到uk(t)的極值點(diǎn)個(gè)數(shù)不大于l個(gè)時(shí)停止，得到殘余項(xiàng)R。

這樣給定的原始信號(hào)x(t)通過(guò)上述步驟被分解成k個(gè)PF分量和R之和，即

(17)

2.2LMD特征提取及歸一化

當(dāng)軸承發(fā)生故障時(shí)，故障振動(dòng)信號(hào)與正常振動(dòng)信號(hào)相比，相同頻帶內(nèi)信號(hào)的能量有較大差別，在信號(hào)各個(gè)頻率成分的能量中包含著豐富的故障信息，從而以分解后PF分量信號(hào)能量作為特征，可以有效提取軸承的各類故障特征。因此由式(5)能量計(jì)算公式對(duì)式(17)中的k個(gè)PF分量求取能量，可得到LMD特征向量T為

(18)

令

(19)

特征向量歸一化公式為

(20)

2.3LMD特征優(yōu)化處理

對(duì)各類故障振動(dòng)信號(hào)進(jìn)行LMD特征提取，可得到若干個(gè)PF分量特征，但各PF分量的各類故障特征間存在間隔不均衡和特征值波動(dòng)現(xiàn)象，嚴(yán)重影響了各PF分量故障特征的有效性。為了提高各PF分量故障特征的有效性，需利用特征壓擴(kuò)和滑動(dòng)平均方法對(duì)各類故障特征間存在的間隔不均衡和特征值波動(dòng)現(xiàn)象進(jìn)行優(yōu)化處理。

關(guān)于LMD特征的壓擴(kuò)和滑動(dòng)平均處理，在這里引用周期能量特征優(yōu)化處理小節(jié)的u律壓擴(kuò)公式(8)和滑動(dòng)平均公式(9)，對(duì)LMD特征進(jìn)行優(yōu)化處理。

3提取實(shí)例分析

筆者采用美國(guó)凱斯西儲(chǔ)大學(xué)電氣工程與計(jì)算機(jī)科學(xué)系軸承實(shí)驗(yàn)數(shù)據(jù)[7]進(jìn)行實(shí)例分析，傳動(dòng)軸端的軸承為6205-2RS SKF型深溝滾珠軸承，軸承的鋼球直徑為8 mm，球組節(jié)圓直徑為40 mm,鋼球數(shù)目為9個(gè)，接觸角為0°，由功率為1.47 kW的電動(dòng)機(jī)、電器控制裝置、測(cè)力計(jì)和傳感器構(gòu)成實(shí)驗(yàn)平臺(tái)。采樣頻率fs=12 kHz，傳動(dòng)軸轉(zhuǎn)速Vr=1 797 r/min，則由式(2)可得到旋轉(zhuǎn)頻率fr=29.95 Hz，再由式(4)可得到一個(gè)周期采樣點(diǎn)數(shù)N=400.67，取N=400。

3.1周期能量特征實(shí)例分析

3.1.1周期能量特征提取

首先，以一個(gè)周期采樣點(diǎn)數(shù)N=400為標(biāo)準(zhǔn)，對(duì)經(jīng)過(guò)形態(tài)濾波[7]處理的軸承內(nèi)圈故障、外圈故障、滾珠故障和正常這四路振動(dòng)信號(hào)分別截取50段，一個(gè)周期一段；其次，由式(6)計(jì)算截取信號(hào)的周期能量特征，再由周期能量歸一化公式(7)進(jìn)行歸一化處理，可得到經(jīng)歸一化后的內(nèi)圈故障周期能量特征T1,T2,…,T50、外圈故障周期能量特征T1,T2,…,T50、滾珠故障周期能量特征T1,T2,…,T50和正常振動(dòng)信號(hào)周期能量特征T1,T2,…,T50；最后，以周期為橫坐標(biāo)，各類故障的周期能量特征值為縱坐標(biāo)，則各類故障的周期能量特征如圖2所示。

圖2　周期能量特征圖Fig.2　Period-energy feature

由圖2可看出，各類故障的周期能量特征值處于不同范圍，但內(nèi)圈故障、滾珠故障和正常振動(dòng)信號(hào)的周期能量特征間間隔微小，各類故障周期能量特征間存在間隔不均衡和特征值波動(dòng)現(xiàn)象。

3.1.2周期能量特征優(yōu)化

為了消除各類故障周期能量特征間的間隔不均衡現(xiàn)象，采用式(8)u律壓擴(kuò)公式，對(duì)圖2中各類故障周期能量特征間間隔不均衡現(xiàn)象進(jìn)行壓擴(kuò)處理，經(jīng)大量實(shí)驗(yàn)，壓擴(kuò)參數(shù)u=200時(shí)壓擴(kuò)效果較好。針對(duì)各類故障周期能量特征出現(xiàn)的波動(dòng)現(xiàn)象，采用式(9)滑動(dòng)平均公式，對(duì)圖2中各類故障特征出現(xiàn)的波動(dòng)現(xiàn)象進(jìn)行平滑處理。經(jīng)u律壓擴(kuò)和滑動(dòng)平均優(yōu)化處理后的周期能量特征如圖3所示。

圖3　優(yōu)化后的周期能量特征圖Fig.3　Optimized period-energy feature

對(duì)比圖2和圖3可看出，經(jīng)優(yōu)化后，各類故障周期能量特征間，間隔不均衡和特征值波動(dòng)現(xiàn)象被消除，突顯了各類故障與其特征的一一對(duì)應(yīng)效果。

3.2優(yōu)化的LMD特征提取實(shí)例分析

3.2.1LMD特征提取

以滾動(dòng)軸承一個(gè)轉(zhuǎn)動(dòng)周期內(nèi)采樣點(diǎn)數(shù)N=400為標(biāo)準(zhǔn)，對(duì)經(jīng)過(guò)形態(tài)濾波[7]處理的內(nèi)圈故障、外圈故障、滾珠故障和正常四路振動(dòng)信號(hào)分別截取50個(gè)周期(一個(gè)周期一段)，再分別進(jìn)行LMD分解，取其前3個(gè)PF分量[8]對(duì)其進(jìn)行特征提取，可得到經(jīng)歸一化后的內(nèi)圈故障特征T1',T2',…,T50'、外圈故障特征T1',T2',…,T50'、滾珠故障特征T1',T2',…,T50'和正常振動(dòng)信號(hào)特征T1',T2',…,T50'。

以周期為橫坐標(biāo)，與其對(duì)應(yīng)的各類故障前3個(gè)PF分量的特征值為縱坐標(biāo)，則每個(gè)PF分量的特征如圖4所示。

圖4　各PF分量特征Fig.4　Feature of each PF component

從圖4可看出，PF1，PF2和PF3分量外圈故障、內(nèi)圈故障、滾珠故障和正常振動(dòng)信號(hào)的特征間存在間隔不均衡和特征值波動(dòng)現(xiàn)象。

3.2.2LMD特征優(yōu)化

為了消除4種狀態(tài)間PF1，PF2和PF3特征間隔不均衡現(xiàn)象，采用式(8)u律壓擴(kuò)公式，對(duì)圖4中各PF分量特征進(jìn)行壓擴(kuò)處理，經(jīng)大量實(shí)驗(yàn)，u=200時(shí)壓擴(kuò)效果較好。針對(duì)各PF分量特征存在的波動(dòng)現(xiàn)象，采用式(9)滑動(dòng)平均公式，對(duì)圖4中各類故障特征進(jìn)行平滑處理。經(jīng)u律壓擴(kuò)和滑動(dòng)平均優(yōu)化處理后的各PF分量特征如圖5所示。

對(duì)比圖4和圖5可看出，經(jīng)u律壓擴(kuò)和滑動(dòng)平均優(yōu)化處理后，各PF分量的各類故障特征明顯優(yōu)于未經(jīng)優(yōu)化處理的故障特征，提高了各類故障特征的有效性。

圖5　經(jīng)優(yōu)化處理的各PF分量特征Fig.5　Optimized feature of each PF component

4應(yīng)用實(shí)例

為了驗(yàn)證筆者方法的有效性，仍采用美國(guó)凱斯西儲(chǔ)大學(xué)電氣工程與計(jì)算機(jī)科學(xué)系軸承實(shí)驗(yàn)數(shù)據(jù)，提取60組周期能量特征和LMD特征,其中內(nèi)圈故障、外圈故障、滾珠故障和正常振動(dòng)信號(hào)特征各15組。設(shè)計(jì)一個(gè)四輸入、四輸出、分布密度為0.3和訓(xùn)練目標(biāo)誤差為1×10-7的RBF神經(jīng)網(wǎng)絡(luò)[9-10]。 在60組特征中，取前40組(每種故障10組)作為訓(xùn)練樣本，其余20組(每種故障5組)作為測(cè)試樣本進(jìn)行實(shí)驗(yàn)。

將周期能量和LMD特征非優(yōu)化和優(yōu)化后進(jìn)行對(duì)比實(shí)驗(yàn)，采用非優(yōu)化的特征值對(duì)RBF神經(jīng)網(wǎng)絡(luò)進(jìn)行訓(xùn)練，迭代100次達(dá)到目標(biāo)精度，而采用優(yōu)化后的特征值進(jìn)行訓(xùn)練，迭代50次達(dá)到目標(biāo)精度，說(shuō)明優(yōu)化的故障特征加快了RBF神經(jīng)網(wǎng)絡(luò)訓(xùn)練的速度。

為驗(yàn)證故障特征優(yōu)化對(duì)提高故障診斷正確率的效果，分別用20組非優(yōu)化和優(yōu)化后的故障特征作為測(cè)試樣本進(jìn)行測(cè)試實(shí)驗(yàn)，非優(yōu)化特征進(jìn)行故障診斷的結(jié)果如表1所示，優(yōu)化特征進(jìn)行故障診斷的結(jié)果如表2所示。對(duì)比表1和表2知，20組未經(jīng)優(yōu)化測(cè)試樣本有2組診斷錯(cuò)誤(在表中以黑體標(biāo)注)，而經(jīng)過(guò)優(yōu)化的20組測(cè)試樣本未出現(xiàn)診斷錯(cuò)誤，證明筆者方法提高了軸承故障診斷正確率。

表1　未經(jīng)優(yōu)化處理特征測(cè)試結(jié)果

Tab.1　The test result of unoptimized feature

狀態(tài)序號(hào)RBF神經(jīng)網(wǎng)絡(luò)輸入輸出未經(jīng)優(yōu)化處理特征輸入診斷結(jié)果輸出期望目標(biāo)正常10.0098,0.6597,0.0707,0.02950.8990,0.0044,0.0002,-0.003620.0093,0.7321,0.1035,0.39910.9930,-0.0125,-0.0005,0.019930.0117,0.4818,0.0235,0.06310.8949,0.1130,0.0025,-0.010440.0064,1.0625,0.0952,0.07240.7895,0.0615,-0.0592,0.822950.0108,0.6220,0.0795,0.02521.0138,-0.0194,-0.0007,0.0063(1,0,0,0)內(nèi)圈故障10.1635,0.0353,0.0028,0.0004-0.0016,1.0065,-0.0005,-0.004420.1451,0.0412,0.0041,0.00110.0045,0.9566,-0.0008,0.039730.1834,0.0319,0.0030,0.0004-0.0167,1.0392,0.0028,-0.025440.1564,0.0365,0.0026,0.00060.0021,0.9832,-0.0009,0.015750.1632,0.0347,0.0024,0.0006-0.0037,0.9894,-0.0005,0.0048(0,1,0,0)外圈故障10.8682,0.0056,0.0000,0.0000-0.0007,0.0055,1.0001,-0.004920.7342,0.0066,0.0001,0.00000.0016,0.0191,0.9899,-0.010730.9060,0.0053,0.0000,0.00000.0003,-0.0028,0.9983,0.003240.8844,0.0055,0.0000,0.0000-0.0003,0.0012,0.9986,-0.000550.8033,0.0061,0.0000,0.0000-0.0005,0.0252,1.0023,-0.0269(0,0,1,0)滾珠故障10.0213,0.2606,0.0120,0.00910.1910,0.0737,0.7334,0.001920.0553,0.0942,0.0040,0.00170.0151,0.1635,0.0031,0.818330.0406,0.1309,0.0071,0.0010-0.0120,0.0225,0.0007,0.988840.0429,0.1236,0.0055,0.0020-0.0081,0.0397,0.0010,0.967450.0390,0.2324,0.0166,0.00650.1074,-0.0502,0.0007,0.9421(0,0,0,1)

表2　經(jīng)優(yōu)化處理特征測(cè)試結(jié)果

Tab.2　The test result of the optimized feature

狀態(tài)序號(hào)RBF神經(jīng)網(wǎng)絡(luò)輸入輸出經(jīng)優(yōu)化預(yù)處理特征輸入診斷結(jié)果輸出期望目標(biāo)正常10.1505,0.9078,0.5518,0.53121.0002,-0.0005,-0.0000,0.000320.1560,0.9079,0.5195,0.57651.0002,0.0002,-0.0001,-0.000330.1424,0.9231,0.5201,0.54700.9999,0.0002,-0.0000,-0.000040.1479,0.9260,0.5362,0.51571.0000,0.0004,0.0002,-0.000650.1444,0.9185,0.5463,0.54290.9919,0.0026,0.0022,0.0033(1,0,0,0)內(nèi)圈故障10.6747,0.3360,0.1188,0.03370.0001,0.9994,0.0001,0.000520.6854,0.3321,0.1184,0.0325-0.0000,1.0006,-0.0002,-0.000430.6829,0.3286,0.1113,0.0299-0.0002,0.9995,0.0005,0.000140.6896,0.3273,0.1063,0.0279-0.0004,0.9976,0.0019,0.001050.6836,0.3263,0.1062,0.0260-0.0006,0.9959,0.0029,0.0017(0,1,0,0)外圈故障10.9627,0.1006,0.0027,0.00150.0000,0.0022,0.9984,-0.000620.9681,0.0995,0.0025,0.0013-0.0000,0.0009,0.9994,-0.000230.9691,0.0980,0.0021,0.00110.0000,0.0003,0.9998,-0.000140.9744,0.0987,0.0021,0.0010-0.0000,0.0000,0.9999,0.000150.9671,0.1010,0.0025,0.0009-0.0000,0.0013,0.9990,-0.0003(0,0,1,0)滾珠故障10.4412,0.5969,0.1902,0.12590.0000,-0.0003,0.0001,1.000220.4347,0.5762,0.1840,0.09620.0006,-0.0036,0.0002,1.002830.4716,0.5830,0.1965,0.0944-0.0005,0.0127,-0.0017,0.989540.4288,0.6047,0.2140,0.11120.0002,0.0015,0.0000,0.998350.4267,0.6085,0.2019,0.11150.0000,0.0001,0.0002,0.9997(0,0,0,1)

5結(jié)束語(yǔ)

筆者給出振動(dòng)信號(hào)周期能量特征的定義和計(jì)算方法，對(duì)周期能量進(jìn)行歸一化，提高了不同故障間特征的可比性；進(jìn)行u律壓擴(kuò)處理，調(diào)整不同故障間特征的間隔；進(jìn)行滑動(dòng)平均處理，消除不同故障間特征的波動(dòng)。同理，對(duì)LMD特征進(jìn)行壓擴(kuò)和滑動(dòng)平均處理優(yōu)化，消除了不同故障間各PF分量特征存在間隔不均衡和特征波動(dòng)現(xiàn)象。在此基礎(chǔ)上，將周期能量特征和優(yōu)化的LMD特征相結(jié)合，提出了一種新的軸承故障診斷方法。經(jīng)應(yīng)用實(shí)例驗(yàn)證，該方法提高了神經(jīng)網(wǎng)絡(luò)的訓(xùn)練收斂速度和軸承故障診斷正確率，驗(yàn)證了方法的有效性和可行性。

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E-mail: xiongbs@126.com

doi:10.16450/j.cnki.issn.1004-6801.2016.02.027

收稿日期：2014-04-03；修回日期：2014-12-26

中圖分類號(hào)TH165.3

第一作者簡(jiǎn)介：熊邦書，男，1968年5月生，博士、教授、碩士生導(dǎo)師。主要研究方向?yàn)橹鄙龣C(jī)故障診斷、圖像處理及應(yīng)用。曾發(fā)表《小波包降噪與LMD相結(jié)合的滾動(dòng)軸承故障診斷方法》(《振動(dòng)與沖擊》2012年第31卷第18期)等論文。

*航空科學(xué)基金資助項(xiàng)目(2010ZD56009)；江西省教育廳科技資助項(xiàng)目(GJJ14519)