滾動軸承缺陷振動建模及沖擊特征提取*

李祥陽，陳萬強（西安航空學院陜西省泵類裝備工程研究中心 西安，710077）

滾動軸承缺陷振動建模及沖擊特征提取*

李祥陽，陳萬強
（西安航空學院陜西省泵類裝備工程研究中心 西安，710077）

以SKF6205-2RS深溝球軸承為研究對象，運用Hertzian接觸理論、彈性力學及滾動軸承幾何學，建立了可預測滾動軸承不同損傷位置和程度的狀態模型，并通過Runge-Kutta數值方法獲取了系統響應。計算結果表明：徑向負荷作用下，模型對內圈、外圈、鋼球局部損傷所激勵的頻率及其諧波成分可進行良好預測；闡述不同狀態下軸承振動規律，論證連續Haar小波變換周期性；利用連續Haar小波變換在時間-尺度域上所特有的周期性結合自相關消噪，提出了一種滾動軸承早期損傷特征提取的自相關連續Haar小波方法。診斷實例證明，這種方法能夠有效消除信號的噪聲，提取信號的弱沖擊成分。

滾動軸承；預測模型；連續Haar小波；自相關消噪；弱沖擊成分

引 言

航空發動機和航空燃氣渦輪機等重大裝備的核心技術問題之一就是軸承，它對整個飛機制造業的發展水平有著舉足輕重的作用。對滾動軸承進行狀態評估可以提高裝備的可靠性，實現由“事后維修”到“預知維修”的轉變，提高飛機設備的管理水平，保證產品質量；同時又為航空軸承可靠性增長設計和服役性能控制奠定了方法基礎［1-2］。預測模型是一種有效的工具，它可以幫助深入理解產生損傷的機理，還可以用來檢驗各種評估方法的實效性。文獻［3-4］從數字信號角度出發，用周期性脈沖序列來模擬單點和多點損傷對軸承的沖擊激勵，并給出了軸承損傷響應模型，在研究軸承載荷分布基礎上采用脈沖序列模擬瞬態沖擊力。文獻［5］提出了一種數學模型，用來描述當軸承通過損傷點時內部軸承力的變化，并且采用VB編制了載荷影響及譜圖分析程序。文獻［6］分析了外負荷和損傷位置對振動行為的影響，確定了外載荷作用下振動的周期性與力傳遞的途徑。文獻［7］論證了滾動軸承局部損傷信號的統計量具有近似循環平穩性，指出由于離心力、陀螺力矩和潤滑形態的影響，會導致接觸角的不斷變化和軸承部件的相對滑動，從嚴格意義上講，軸承損傷信號是非平穩信號，但仍然可以將其視為近似循環平穩信號。文獻［8-9］研究了球軸承的自然振動，拾取了外圈的徑向、軸向的振動，對拾取信號進行FFT譜分析和模態分析，導出了外圈自然振動表達式、平面內自然振動頻率表達式和平面外自然振動頻率表達式，分析了3種振動頻率公式的精度。研究了單個和多個缺陷對應的沖擊響應特點，給出了損傷頻率的計算公式，但并沒有在時、頻域進行分析，只是認為損傷對軸承的沖擊可以用矩形波、三角波和半余弦波等脈沖序列來描述。以上研究從動力學響應的角度進行統計模擬，沒有涉及軸承本身的建模問題。文獻［10］提出考慮接觸-變形域的軸承仿真模型，討論了故障位置對振動的影響。文獻［11］采用兩自由度方程模擬了內、外圈和滾動體故障，分析了軸承周期、準周期和混沌運動。文獻［12］用有限元法研究了不平衡力作用下損傷軸承的動特性。

筆者對已有的狀態模型作了改進。在Fukata二自由度方程［13］基礎上引入了套圈-鋼球-支座的振動耦合作用，綜合考慮了局部損傷的位置和程度，建立了可預測不同損傷位置和損傷程度的滾動軸承狀態分析模型，揭示了不同狀態下的振動規律。要獲得軸承服役的準確信息，信號處理至關重要。FFT變換通過構造不同類型的濾波器來滿足消噪的需要，卻無法消除遍布于整個頻域范圍內的噪聲。應用匹配濾波器時，如果輸入信號的信噪比較低，濾波器將輸出多峰，造成特征失效［14］。筆者在對預測響應信號處理的基礎上，分析了連續Haar小波所特有的時間-尺度周期性，指出這種特性可以充分展示滾動軸承損傷振動信號中的周期性沖擊成分。已有的小波技術在軸承信號處理中的應用往往從基函數相似性匹配的角度出發，筆者進一步發掘小波基函數在滾動軸承振動信號中的應用。結合自相關預處理，提出了一種自相關連續Haar小波變換方法用來識別軸承早期損傷模式。理論和實踐證明，這種方法能夠有效消除損傷信號中的干擾，使得在消除干擾信號的同時保留信號中的弱沖擊成分。

1 滾動軸承預測模型

滾動軸承受載接觸時，鋼球與滾道之間將發生非線性彈性變形，由Hertzian理論，點接觸彈性恢復力［15］為

其中：δ為彈性趨近量；K為總接觸剛度系數。

內外圈分別為Ki，Ko，由以下兩式求的

其中：∑-ρ為接觸點的曲率和；γ*為變形系數，其值的計算參見文獻［15］。

圖1為滾動軸承坐標示意圖，第i個鋼球-套圈接觸變形δi為內圈在x，y方向位移（xs，ys），鋼球位置角θi和游隙c的函數

圖1 滾動軸承示意圖Fig.1 The reference axes of the rolling bearing

設（xb，yb）為鋼球的坐標，由于振動傳遞作用，考慮到鋼球自身的振動，局部接觸變形為

其中：θi為軸承第i個鋼球的位置角。

其中：ωc為軸承公轉速度即保持器轉速；N為鋼球個數。

設軸的轉速為ω，則，其中：Db為鋼球直徑；Dp為軸承節圓直徑。

同理，設（xo，yo）為支座處的運動坐標，接觸變形就可表示為

圖2為內圈-鋼球-支座振動耦合作用示意圖。根據Lagrange方程，動力學方程為

其中：ms，mb，mo分別為內圈與軸的質量、鋼球質量、外圈與支座質量；cs為軸承內阻尼；ko，co為支座剛度與阻尼。

圖2 滾動軸承振動系統坐標圖Fig.2 The reference axes of the rolling bearing vibration system

2 局部損傷模型及響應分析

2.1 軸承損傷建模

軸承長期服役由于交互應力作用會出現疲勞剝落等局部損傷，在損傷接觸域θd中，載荷作用會激發短時沖擊，沖擊可以表示為

對內圈處的局部損傷誘發振動可表示為

設kd為動荷系數，其大小與損傷類型、形狀及尺寸等因素有關，通過調整kd的值可以模擬不同損傷程度；ε為載荷分配系數；β為外圈局部損傷角位置，根據文獻［15］則有

內圈接觸角為

外圈處局部損傷誘發沖擊序列可表示為

滾動體自轉時損傷處會與內、外圈作用而激發兩個序列，同內、外圈作用時產生的脈沖大小不同，表達式為

軸承外圈與支座固定，因此外圈接觸角為

2.2 軸承預測響應分析

上述軸承損傷建模方法可以根據設計參數預測各種損傷信號，表現在模型上相當于把式（5），（7）中的游隙c增加損傷激勵沖擊序列，使得

鋼球損傷總的振動沖擊序列為

軸承診斷首要的任務是根據軸承損傷信號的特點選擇可行的處理方法。預測模型從動力學角度描述了軸承損傷的內在涵義，這對時序方法的選擇十分有益。以SKF6205-2RS深溝球軸承為研究對象進行算例分析，有關參數為：轉軸質量ms=5.5 kg，軸承阻尼cs=877.6 Ns/m，內圈直徑為25.001 mm，外圈直徑為51.998 mm，厚度為0.5906 mm，鋼球直徑Db= 7.94 mm，節圓直徑Dp=39.039 mm，支座質量mo= 12.638 kg，支座阻尼co=1796 Ns/m，支座剛度ko= 12.3×106N/m，軸承游隙e=0.1um，鋼球個數N= 9，轉速為1796 r/min，徑向載荷Fx=650 N，Fy= 500 N，軸承為普通軸承鋼制。式（8）非線性很強，難以得到解析解，通過Runge-Kutta數值方法獲取系統響應。

軸承從正常演化為異常，在波形和譜圖上會顯示一定的規律。圖3對應正常狀態軸承的振動，顯然從波形中看不出沖擊成分，這時軸承的振動主要由轉頻fs和變柔度振動頻率［13］及其諧波組成。這是因為在徑向載荷的作用下，各鋼球的受力情況是不一樣的，隨著鋼球上的某一點的運動位置不同受力情況亦不一樣。隨著鋼球相對于徑向載荷作用線的移動，軸承剛度以數倍于鋼球沿靜止套圈轉動的頻率呈周期性變化。文獻［13］研究證明，當轉速遠離臨界轉速時，軸承振動頻率表現為變柔度振動頻率振動和它的諧波。

圖3 正常狀態波形與譜圖Fig.3 Waveform and spectrum of normal signal

以外圈為例進行損傷模擬，圖4為模擬信號波形和功率譜圖。與正常狀態相比，其特點是時域為一系列有一定時間間隔的周期性沖擊波形，循環周期T=1/fo與損傷頻率相對應，這是由于損傷接觸產生沖擊能量所致。譜圖主要為轉頻fs，損傷特征頻率fo=0.5 N 1-d/D（）

pfs=105.8 Hz及其高次諧波與調制成分。在承受來自鋼球方向的接觸載荷作用下，軸承支座處產生彎曲變形，并與滾動體一起旋轉而產生振動。Fukata二自由度方程實質上描述了轉軸處的運動，缺乏式（8）耦合效應，因此振動頻率表現為低頻成分，反映不出損傷的循環周期沖擊與鋼球-支座振動的高頻調制。圖4中，因為沖擊能量較弱，低頻處譜線被軸承其他振動成分壓制。同時，損傷接觸區產生的脈沖沖擊力受到載荷分布的調制，沖擊響應為一種單邊振蕩衰減波形，是局部化的，通過圖5可以明顯看出特征頻率的各次諧波。

圖4 外圈損傷信號波形與譜圖Fig.4 Waveform and spectrum of outer ring damage signal

圖5 外圈損傷信號包絡譜圖Fig.5 Envelope spectrum of outer ring damage signal

3 自相關Haar小波原理

使用與信號波形最相似的基函數對信號分解，提取隱含異常特征是特征波形混合基分解的精髓［16］。小波函數中Haar小波在支撐域上是單位矩形波，標準的Haar小波為

Haar小波在時域中不連續，且為方形波，如圖6所示。連續Haar小波特有的時間（平移）和尺度的周期性可以充分展示信號中的周期性沖擊成分及其特點，用這種小波來分析由滾動軸承局部損傷而誘發的周期性沖擊振動有著其他小波不具備的特定優勢。

圖6 Haar小波波形Fig.6 Waveform of Haar wavelet

3.1 連續Haar小波變換周期性

與二進離散小波相比，連續小波具有以下兩個方面的優勢［14］：a.連續小波變換的分割是使窗長按尺度減低方向逐漸減少的，在尺度劃分上比二進小波更加精細，信息冗余度高，對時間-尺度特性體現更加直觀，適合瞬態成分檢測；b.二進小波要求基函數正交并且不具有“時不變”特性，對不確定時刻信號檢測時，則要求小波的時不變性。對于標準Haar小波，幅值變化最大倍數為2，設軸承損傷信號為s（ t），因此s（ t）的Haar小波變換在時間b上是以T為周期，在尺度j上以2T為周期的［17］，即

其中：n為自然數。

圖7為損傷信號局部放大圖，可以清晰看出周期性沖擊分量和軸承阻尼作用使沖擊波形衰減。可見，對一個固定的尺度，當Haar小波沿時間移動整周期時，內積是不變的，形成了時間上的周期性。同理，尺度整周期變化時由于整周期部分的內積互相抵消，總的內積仍保持不變，從而形成了尺度上的周期性。對損傷信號連續Haar小波變換正是利用時間-尺度上的周期性，將滾動軸承周期沖擊衰減模式提取出來。

圖7 損傷信號時間周期性表示Fig.7 Time periodic expression of damage signal

3.2 連續Haar小波自相關分析及應用

診斷實踐表明，滾動軸承正常信號峭度值約為3，近似為高斯信號。除了軸承自身轉頻和變柔度振動外，還有許多隨機性干擾，有效去除可以大幅提高診斷的準確性［14-16］。利用Haar小波變換提取周期性沖擊成分，利用自相關消噪可以預除噪聲干擾，兩者結合可對軸承早期損傷進行精確識別。

時間序列（）s t按時間平均計算的各態歷經隨機過程的自相關函數［1］為

s（ t），Rs（τ）中包含損傷信息，由于噪聲與噪聲之間的不相關性會隨著時間延遲而很快衰減為0，并且不需要任何關于信號與噪聲的譜分布和概率分布的先驗知識。

自相關連續Haar小波處理流程如圖8所示，對圖4外圈損傷信號加強噪聲干擾來模擬軸承早期損傷，圖9為波形和譜圖。可見，沖擊成分被大量噪聲掩蓋，直接進行譜分析難以提取出特征譜線。將信號進行連續Haar小波變換，如圖10所示。可以看出，兩圖中均有等間隔的脈沖成分，但是噪聲干擾使圖10（a）分辨率不高，自相關處理后圖10（b）的等間隔沖擊成分顯示清晰，周期約為0.009 5 s與損傷頻率一致。為了譜分析的需要，需要計算尺度與頻率的對應關系［16］

圖8 連續自相關Haar小波流程圖Fig.8 The flow of autocorrelation-Continuous Haar wavelet

圖9 模擬信號波形與譜圖Fig.9 Waveform and spectrum of simulation signal

圖10 模擬信號Haar小波時間-尺度圖Fig.10 Haar wavelet time-scale map of simulation signal

其中：fj為尺度j對應的頻率；fc為小波的中心頻率；δt為采樣周期。

選擇沖擊特征明顯的尺度進行包絡譜分析如圖11所示。轉頻fs=ω/2π=29.5 Hz以及損傷頻率與其高次諧波清晰可辨。可見，自相關連續Haar小波變換在提取淹沒在強大背景噪聲中的微弱周期性沖擊成分是有效的，且Haar小波形式簡單，運算方便，非常適合于基于圖像的在線監測系統。

4 實 驗

實驗數據來源于美國凱斯西儲大學軸承研究中心［18］。該中心提供了深溝球軸承正常與內外圈、鋼球損傷的實驗數據，并設置了軸承的不同損傷程度以供研究者使用。實驗裝置如圖12所示，實驗軸承支承電動機轉軸，電動機風扇端和驅動端的軸承座上方各放置一個加速度傳感器來采集軸承的振動加速度信號。分析的為6205-2RS JEM SKF深溝球軸承，轉速為1 772 r/min，采樣頻率為12 k Hz，結構參數見文獻［18］。圖13為軸承早期損傷信號的時域波形。由于在確定尺度下連續Haar小波整周期移動的內積不變，對不同的信號連續Haar小波沿一個周期移動內積變化不同，因此導致不同信號在其時間-尺度圖上具有不同的特征。圖14為各種狀態的自相關連續Haar小波時間-尺度圖。可以看到，各種狀態在圖形中得到了明顯區分，正常情況主要表現為諧波形式；損傷狀態下均有等間隔的沖擊產生，其余信號成分的能量在圖形上產生了發散。這樣利用連續Haar小波所特有的時間-尺度周期性加之自相關消噪就可以分離弱沖擊。

圖11 自相關連續Haar小波處理后譜圖Fig.11 Spectrum of autocorrelation-continuous Haar wavelet processing

當滾動軸承在轉速為1 772 r/min時，鋼球內外圈損傷頻率分別為139.205，159.928和105.871 Hz。從圖15可以看出，表征鋼球輕微故障的特征信息已被完全淹沒在振動信號中，即使145.9 Hz附近都沒有明顯的譜峰，自相關連續Haar小波處理后選擇相應尺度譜分析可以清楚地觀察到軸承鋼球損傷特征頻率139.2 Hz。利用自相關連續Haar小波對內、外圈損傷進行識別［19-20］，如圖16，17所示。可見，特征頻率非常明顯，譜峰突出，與實際損傷類型相符。

圖12 實驗裝置Fig.12 Experimental apparatus

圖13 典型型號時域波形Fig.13 Typical time domain waveform

圖14 實驗信號自相關連續Haar小波時間-尺度圖Fig.14 Haar wavelet time-scale map of test signal

5 案例分析

滾動軸承的服役性能是復雜工況下運動行為的綜合體現，貫穿于設計、制造、裝調和服役整個壽命周期。出廠前的全壽命周期實驗是軸承企業掌握軸承服役行為的重要途徑。ABLT-1A型全壽命軸承實驗機可以測試到軸承從正常到失效的全壽命周期振動信號，實驗現場如圖18所示。ABLT-1A型試驗機一次能實驗4個軸承，4個測試軸承都為6309深溝球軸承，實驗機轉速為3 kr/min，振動信號由探針傳感器直接接觸軸承外圈測量，采樣頻率為32 k Hz。

圖15 鋼球損傷頻譜Fig.15 Spectrum of the ball damage signal

圖16 內圈損傷頻譜Fig.16 Spectrum of the inner ring damage signal

圖17 外圈損傷頻譜Fig.17 Spectrum of the outer ring damage signal

圖19（a）為監測到的振動信號。由于測試過程中噪聲很大，因此監測到的振動信號雜亂無章，沖擊特征信號基本被完全淹沒，得不到有用的失效信息。經自相關-連續Haar小波消噪后，大量噪聲被剔除，可以觀察到多個明顯的沖擊且具有一定周期，如圖19（b）和（c）所示。對濾波后的信號進行包絡譜分析，譜圖中特征頻率及其倍頻分量突出，這與外圈故障頻率相吻合，因此可以認定實驗軸承的外圈已經損傷，結果與現場實際情況相吻合。

圖18 實驗現場Fig.18 Experimental site

圖19 使用提取方法測得信號的消噪結果Fig.19 De-noising measured results of signal using the extraction method

6 結 論

1）在已有的二自由度方程基礎上建立了滾動軸承局部損傷的預測模型，該模型可預測不同狀態下軸承振動響應。分析了預測響應及其規律，指出滾動軸承正常信號是由轉頻和變柔度振動頻率及其諧波組成，沒有沖擊特征；損傷振動信號本質上為循環的周期性脈沖序列，是損傷特征頻率及其高次諧波的組合和調制。

2）論證了連續Haar小波變換在時間-尺度上的周期性，運用這種特定優勢有效提取了滾動軸承周期性沖擊模式。在基函數相似匹配的基礎上揭示了小波選擇深層次的理論，豐富了小波選擇的思路。

3）沖擊振蕩信號在時間-尺度域的圖形特征便于在諧波干擾下突出沖擊成分。自相關處理不需要任何關于信號與噪聲的譜分布和概率分布的先驗知識，就能高效去除噪聲，用于信號預處理，增強了連續Haar小波時間-尺度圖的沖擊特征。實踐表明，該方法在滾動軸承弱沖擊提取方面有較好的應用前景。

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Abstract A cone-shaped MDOF-USM（multi-degree-of-freedom ultrasonic motor）is designed for research and application.The single-foot drive mode is adopted on the stator.A four-quadrant piezoelectric stack is employed as the exciting element to generate two-dimensional linear motion，and its movement mechanism is analyzed.The parametric model of the MDOF-USM is set up in ANSYS，and the finite element model is imported into the Optimus（a multi-disciplinary optimization software）.Optimization results indicate that the design requirements of the MDOF-USM are fulfilled.Finally，a MDOF-USM is successfully manufactured and applied to an x-y platform.

Keywords ultrasonic motors；multi-degree of freedom；optimal design；Optimus；x-y platform

Abstract To provide a real loading environment for structural design，product life estimation and health assessment，it is important to correctly identify the dynamic load and its position.In this paper，the fre-

quency domain method is used to study dynamic load position determination，and an equivalent load error method based on the vibration characteristic of the linear elastic system is proposed.This method constructs an object function with equivalent load error values at the same location from different measuring points.The actual position is where the equivalent load error is the smallest.Simulation on the tablet is perfect with both single point drive and double points one，and the method is still valid when noise is added.It provides the basis for complex structures and the determination of multiple loading locations.The experimental verification on a simply supported beam shows that this method can correctly identify the dynamic load location，is not sensitive to noise，and has good prospects for engineering applications.

Keywords load identification；position determination；equivalent load；frequency domain method

Abstract The floor of a car body experiences an abnormal vibration when a metro accelerates and brakes，which significantly deteriorates riding comfort.Theoretical analysis and field experiments are conducted to study this abnormal vibration，with resolution promoted and validation measurements.The short-time Fourier transform（STFT）time-frequency method is applied to tested data.It shows that the excitation of the abnormal floor vibration comes from the twice frequency of motor rotation.A mathematical model consisting of the motor shaft and gear rotor connected by a coupler is built to study the rotary dynamics of the traction system of the railroad vehicle＇s powered bogie.Analysis illustrates that the dynamics in the traction system experience a shaft misalignment between the motor shaft and gear rotor.The output torque of the gear rotor is obtained and shows that this misalignment can result in even frequencies oscillation of motor shaft rotation with the twice frequency dominated.The measurement is explained by the analysis，and it is shown that the abnormal vibration can be alleviated by eliminating this misalignment.Validation measurements are conducted after eliminating the misalignment and show that the twice frequency vibration of motor rotation dropp significantly，which reduces the root mean square and amplitude of acceleration of the car body floor by 41％and 53％，respectively.The measurements agree with the theoretical analysis，and a high level of riding comfort is obtained.

Keywords metro；car body；coupler；misalignment

Abstract The dispersion and multimode nature of a guided wave makes the analysis and identification of guided wave echoes complex.This paper proposes an echo identification method based on the frequency domain phase tracking.First，the frequency domain phase of the analyzed signals is extracted and normalized to the referenced signals of the direct propagation wave-packet.Then，the normalized values are pres-ented in an order spectrum.Finally，the location and recognition of each echo is determined with the analysis of the propagation path in the propagation medium.Simulation analysis and experimental results demonstrate the applicability and effectiveness of the proposed method.

Keywords Ultrasonic guided waves；dispersion characteristic；phase shift tracking；echo identification

Abstract Aiming at the end effect and mode mixing of empirical mode decomposition（EMD）in practical applications，an improved EMD method consisting of the following techniques is proposedafter analyzing several solutions.First，short signals are extended with genetic support vector regression，then an ensemble EMD combined with an alternative envelope for the sifting procedure is employed to process the extended signals.The simulation results of two nonlinear and one simulated fault signals，as well as comparisons with other EMD methods，verify the capability of the proposed method to alleviatethe end effect and mode mixing.Applying the proposed method and envelope analysis to fault diagnosis of the ball bearing with an inner raceway defect，the results demonstrate the superiority of the method in extracting fault characteristic information for engineering applications.

Keywords empirical mode decomposition；end effect；genetic support vector regression；mode mixing；envelope fitting；fault diagnosis

Abstract Variable predictive model based class discrimination（VPMCD）is a pattern recognition method that utilizes the inner relations among characteristic values extracted from the original data.In this paper，VPMCD and independent component analysis（ICA）are combined with the correlation coefficient in order to diagnosis the rolling bearing fault.First，the ICA is used to analyze vibration signals with different fault categories，and the independent components are extracted from each category.Second，the correlation coefficients are extracted from the samples and independent components of each category.The sum of the absolute values of the correlation coefficients is used as a characteristic value.Finally，the VPMCD classifier is used to recognize and classify the faults.The experimental results show that this method can be effectively applied to rolling bearing fault diagnosis.

Keywords variable predictive model based class discriminate；independent component analysis；correlation coefficient；rolling bearing；fault diagnosis

Abstract In the fault diagnosis of a hydro-turbine generating unit（HGU），kernel clustering is a valid non-supervised learning method.In order to solve the problems of kernel parameter selection and cluster center calculation，a novel electromagnetism-like artificial bee colony weighted kernel clustering（EAWKC）is proposed.First，after considering the influence of different symptoms，the data is weighted，and the clustering model is built based on the kernel Xie-Beni clustering index.Then，the electromagnetism-like artificial bee colony（ELABC）method is proposed and introduced in order to solve the objective function to realize the synchronized optimization of the clustering center，symptom weight and kernel parameter.The classification accuracy of EAWKC is checked by three of the UCI testing data sets and the HGU fault samples，and compared with the traditional method.The experimental results show that EAWKC has higher accuracy and can effectively complete the fault diagnosis.

Keywords hydroelectric generating unit；fault diagnosis；mercer kernel；weighted kernel clustering；electromagnetism-like artificial bee colony（ELABC）

Abstract In order to diagnose the abnormal noise of a certain type of diesel generating set，a new method of empirical mode decomposition（EMD）and Hilbert transform is proposed to analyze the non-stationary vibration signals of the generator main bearing，which can effectively extract the time-frequency characteristics of main bearing vibration signals.Comprehensive analyses are made based on the signals of diesel generating set noise，generator main bearing vibration and shaft system torsional vibration.The diagnostic results show that the torsional vibration amplitude values of the shaft system are too high，with diesel engine excitation causing the relative motion of pin coupling rubber parts surfaces.This procedure can produce dry friction force，which leads to the intermittent abnormal vibration noise of the shaft system.This method has reference value for the abnormal vibration noise diagnosis caused by friction of the rotary shaft system components.

Keywords vibration noise；empirical mode decomposition（EMD）；Hilbert transform；time-frequency characteristic；diagnosis

Abstract A novel method is proposed for finite element model updating and structural damage identification.The second generation wavelet is used as a platform for the multi-resolution representation of the updating information.This method reduces the uncertainty of the model updating process.At the lower level of resolution，the updating curve of stiffness is represented by a limited number of scaling and wavelet coefficients，which are realized with the generic algorithm（GA）.The complex finite element model is simplified by matching a number of modal parameters for easy manipulation in the updating process.Then，damage identification is carried out based on the simplified model.An example of a box girder with variable cross-sections is given for varying sectional properties to show the effectiveness of the proposed method.The results indicate that the proposed method is stable against variations in crack depth and changes in the number of concentrated cracks.The method is also suitable for the identification of multiple groups of cracks.

Keywords model updating；damage identification；multi-resolution analysis；wavelet

Abstract The rotor inter-turn short circuit fault is one of the main electrical faults of turbo-generators.It can cause the unbalanced electromagnetic force to act on the rotor，leading to rotor vibration and even greatly affecting the security of the generator and power system.The accurate calculation of the electromagnetic force is significant for the stability of the generator and power system.By establishing the generator finite element model，the operation of the generator under a rotor winding short-circuit fault is simulated.The changes of magnetic field lines and air-gap field density are analyzed for the impacts of short position，short circuit number of turns and excitation current on the electromagnetic force.The equivalent magnetic flux method and the magnetomotive force superposition method are compared and come up with some improvements for the equivalent magnetic flux method.The calculation results of the unbalanced electromagnetic force by the two methods are compared with the results of the finite element method，and reasons for the difference are pointed out.

Keywords rotor inter-turn short circuit fault；unbalanced electromagnetic force；the finite element method；the equivalent magnetic flux method；the magnetomotive force superposition method

Abstract In order to analyze the multi-component and multi-modulation characteristics of a gearbox fault signal，an optimal wavelet demodulation method based on singular value decomposition（SVD）is proposed.In this method，Morlet wavelet transform is used as an adaptive band-pass filter to extract the impact component in the geabox vibration signal.The minimum Shannon entropy is used as the wavelet timescale resolution index to optimize the Morlet wavelet parameters.Based on SVD，the optimal wavelet coefficient is utilized to determine the parameters.The new method can extract transient information better，reduce noise，effectively extract the signal period，and assure the validity of the fault feature recognition.The experimental results show that the proposed method can more accurately and effectively extract the fault characteristic hidden in the gearbox vibration signal.

Keywords singular value decomposition；continuous wavelet transform；parameter selection；feature extraction

Abstract Shaft orbit recognition is an important approach for the vibration state judgment of steam turbines.Extracting the features of shaft orbit images is not an easy task，and the traditional feature extraction methods are not perfect in comprehensiveness，accuracy and stability.In order to overcome these problems，a feature extraction method based on imitating human eyes is proposed for the steam turbine.This method imitates human eyes to extract the most important information of the image structure，boundary and region，and realizes the shape characterization comprehensively and accurately through full integration of the information.Three intelligent classification methods are used to test the effectiveness of the proposed method，and the experimental results prove that this feature extraction method for steam turbine is simple，efficient and accurate.

Keywords steam turbine；shaft orbit；condition monitoring；feature extraction；imitating human eyes

Abstract This paper presents a neural sliding mode control method for the mechanical arm with a non-singular inversion terminal in order to realize the trajectory tracking of a multi-joint robot arm with external

interference and modeling errors.First，an inversion-sliding-mode controller with a non-singular terminal sliding surface is designed based on the inversion method and the principle of sliding mode control.Then，the radial basis function（RBF）neural network adaptive law is designed against the uncertainty in the inversion sliding mode control system due to its modeling errors and external interference.The upper bound of this uncertainty is estimated online.Finally，the stability of the control system is proved using the Lyapunov Theorem.Simulation analysis and experimental results show that the proposed method can not only eliminate the chattering phenomenon in the system，but also improve its tracking performance and robustness.

Keywords inversion of control；neural network；sliding mode control；non-singular terminal

Abstract In environmental shaker testing applications，sigma clipping of the shaker drive signal is used to protect the test system.However，the clipped signal spectrum will no longer correspond exactly to the given power spectral density（PSD）.This may cause reduced vibration test reliability and even the wrong results，especially for modal tests.Both the power spectrum equalization control algorithm and PID control strategy are presented in order to compensate for the difference between certain spectra and the clipped specification.The results show that，in the case of Gaussian random signals，the two methods show almost the same compensation effect in terms of minimum error and iterative steps.For non-Gaussian random signals，however，the PID control strategy obtained fewer iterative steps and minor errors.

Keywords clipping；Gaussian signal；Non-Gaussian signal；power spectrum equalization；PID control

Abstract It is of great importance to useany prior information effectively and reasonably in the evaluation of small samples.Therefore，a new testability evaluation method based on mixed Beta prior distribution is presented，while considering both the credibility and the importance of prior information as well as the testability evaluation of complex equipment in small samples.The results show that，according to classical methods using small binomial samples，the lowerconfidence limits of product testability are conservative.Most of the measurements for the credibility of the prior information are based on data.The evaluation results are aggressive due to the missing sources of prior information.Thus，the conclusion is reasonable，and this method is promising for engineering applications.

Keywords testability evaluation；small sample；credibility；importance；mixed Beta distribution

Abstract In the processing of fault vibration signals，an improved CBI-LMD（cubic B-spline interpolation local mean decomposition）method based on self-adaptive waveform matching and an orthogonality criterion is proposed to combat the low decomposition accuracy of the cubic spline interpolation-based local mean decomposition（CSI-LMD）method.First，the raw vibration signal is extended with a self-adaptive waveform matching technique.Next，instead of CSI，the CBI is used to calculate the local means and envelope functions.Finally，the orthogonality criterion is used to set a stopping criterion for the product function.Simulation and experimental results show that the proposed method can effectively extract more accurate feature information in less time than CSI-LMD.

Keywords local mean decomposition；cubic B-spline interpolation；orthogonality criterion；fault rotor；vibration analysis

Abstract Aiming at the multi-functional properties of Pb-based lanthanumdoped zirconate titanates（PZT）sensors in concrete for structural health monitoring，which enable the sensors to simultaneously receive signals with different functions，a method for extracting the signals for variant purposes in the multi-functional PZT sensors is proposed.Because there is a difference in frequency ranges from different function signals，the vibration signal related to the overall structure performance and the acoustic emission signal associated with local damages are acquired based on the Mallat algorithm.The correctness of the extracted signals is verified by comparing with those from accelerometers and acoustic emission sensors.In addition，the proposed method is applied to the seismic damage experiment of a reinforced concrete frame-shear structure.The experimental results show that the vibration signal acquired by the proposed method can abstract the frequency of the structure.Meanwhile，the acoustic emission signal abstracted from PZT sensors can monitor the released energy caused by local damage.It can be concluded that the vibration signals and acoustic emission signals can be extracted using the proposed method，and the evaluation of the overall dynamic performance and local damage can be realized.

Keywords PZT sensors；wavelet analysis；acoustic emission；vibration test

Abstract Based on wavelet packet analysis and wavelet packet energy，the sum square of the wavelet packet energy change rate（WPERSS）damage index is proposed.The wavelet packet is applied to extract the damage index from both healthy and damaged structures for damage detection.A simply supported beam example is simulated in different damage and noise conditions.In addition，a double pylon cablestayed bridge model is tested in three damage conditions.The results are analyzed and prove the effectiveness of the WPERSS damage index.

Keywords wavelet packet；damage detection；damage index；sum square of energy change rate

Abstract To improve the impeller milling efficiency，the zero-order analytical method to construct the milling stability lobe diagram is investigated，which is used to determine parameter optimization of the FV520B material milling.The appropriate number of revolutions and the cutting depth processing can be selected，and the chatter occurrence can be avoided.By using this method，the required accuracy and surface quality for the workpiece can be achieved，and tool safety and machine reliability can be maintained.Through experimental data analysis，the parameters to construct the lobe diagram can be obtained.Different testing points in the constructed lobes are used to verify the method＇s correctness.This method has great significance in the actual impeller manufacturing process.

Keywords milling chatter；stability lobes；modal analysis；FV520B

Abstract A method for realizing tool wear condition monitoring using multi-feature of the cutting sound is presented.Based on empirical mode decomposition and Hilbert transformation theories，the cutting sound signal is analyzed.The energies of intrinsic modes and Hilbert spectrum in different frequency ranges are extracted as candidatefeatures of the monitoring signal.To solve the feature selection problem，the sup-port vector machine is selected as the classifier，and the multiple population genetic algorithm is used to optimize its input features.Then，the interference features are eliminated from the candidate features.After the classifier parameters are also optimized with the multiple population genetic algorithm，the test samples are classified with the optimized classifier，and the performances of the classifiers before and after optimization are compared.The results show that the performance of the optimized classifier is significantly improved，and the method can be used effectively for identification of the tool wear condition.

Keywords empirical mode decomposition；Hilbert transformation；cutting sound；support vector machine；multiple population genetic algorithm

Abstract The mode shape functions of the elastic beams with concentrated mass and stiffness and their frequency equations under typical boundary conditions are derived with Laplace transform.Using these equations，the inherent characteristics of a cantilever beam with a spring and lumped mass are obtained.Then，its modal parameters are recognized using the NEx T-ERA（eigen system realization algorithm based on the natural excitation technique）method.The analytic and experimental results show that modal parameters change with the stiffness and location of the mass and spring.

Keywords elastic beams；concentrated masses；lumped springs；NEx T-ERA；modal identification

Abstract The dynamic responses of a light-weight，high-speedplanar parallel robot are studied based on elastodynamics and experiments.First，according to the geometric and inertial nonlinearities of the mechanism，a set of linear ordinary differential equations of motion is built，and the dynamic responses of two typical configurations are analyzed.Second，an experimental setup that includes the test-bed mechanism of a 3-RRR light-weight parallel robot and a control system is developed.Finally，the experimentally measured residual vibrations of the manipulator are compared with the numerical results.It turns out that the experimental results agree with the numerical ones at configuration two，but differ at configuration one，where the experimentally measured dynamic response is self-excited vibrationand the simulation result is damped vibration.This shows that the robot has different dynamic responses at different configurations.

Keywords planar parallel robot；high-speed；elasto-dynamic；residual vibration

Abstract In order to effectively minimize the harmful vibration caused by rotor unbalance and to monitor the balance state in real time，an embedded on-line automatic balance system for a magnetic balancer is designed based on a modular design concept.First，an embedded controller is constructed using the combination of digital signal processing（DSP）and field-programmable gate array（FPGA）.At the same time，a mathematical model of an adaptive control algorithm is established based on the traditional influence coefficient method.Multithreaded balance control software and a user interface are developed using C and C# language，respectively.Lastly，the experiment is conducted on a domestic electric spindle to verify the function of the whole system.The experimental results show that the unbalance-induced vibration can decrease by 43％at 3 000 r/min.

Keywords rotor unbalance；online automatic balance；embedded control system；adaptive control；digital signal processing

Abstract While the existing de-noising algorithm requires prior knowledge of vibration signals，a new adaptive de-noising algorithm is proposed based on sparse coding and dictionary learning（DLSDF）.Depending on the essential attribute of different signals，the optimal dictionary of data-driving is learned from the raw data.The orthogonal matching pursuit algorithmworks out the sparsest coefficients.Then，the de-noised signal is reconstructed using sparse coding and the optimal dictionary.Simulation and experimental results show that the algorithm based on sparse coding and dictionary learning is adaptive，and denoising is stronger than the existing one.

Keywords dictionary learning；sparse coding；adaptive de-nosing；vibration signal

Abstract Multiscale entropy has begun to play an increasingly important role in the analysis of non-sta-tionary and nonlinear vibration signals.Changes in the sample entropy of different scales can reflect changes in the transformer windings of different runnings.In this paper，a novel feature extraction is proposed，and a new and effective feature parameter is provided to efficiently and quantitatively describe faulty signals of the transformer winding.The results of analyzing the experimental data of the winding vibration show that compared to sample entropy，multiscale entropy can efficiently realize the feature extraction of faulty signals.Therefore，it is feasible to introduce the effective feature parameter into the use of transformer winding vibration signal analysis.

Keywords multiscale entropy；transformer winding；vibration signal；feature extraction；effective feature parameter

Abstract To analyze milling chatter stability lobes and surface location error with worn tools，the cutting force coefficients under different worn conditions are identified using the full-discrete method.The stable critical cutting depth of the milling system increases after normal wear，and gradually declines as the work piece surface hardness increases.Then，the difference in the critical cutting depth between the normal wear tool and the wear free tool flank gradually becomes small.In addition，surface location error appears in some stable regions.Experimental results prove that the theoretical model can effectively optimize machining parameters with varying wear loss of the milling cutter.

Keywords milling cutter wear；full-discrete method；chatter stability lobes；surface location error

Abstract This paper proposes a method based on singular value decomposition technology in order to solve the hard target penetration overload signals de-noising problem.First，the signal reconstruction submatrix is established based on the principle of stability of the main singular components.Second，the″dominant of the former K singular values energy″rule is used to extract the effective order of singular value.Penetration signals are then decomposed based on the previous steps.Finally，the signal is reconstructed using the extracted effective singular values.Experiments show that the proposed method can effectively eliminate the vibration and noise hiding in the penetration process.The proposed method can get a better signal to noise ratio than when using the wavelet transform，as well as the exact penetration depths of the experiments.Ultimately，the proposed method is a feasible new method on penetration fuse signals processing.

Keywords penetration overload signals；singular value decomposition；signal reconstruction；signal to noise ratio

Abstract A method for flood discharge structure in the time domain is proposed in order to identify the operating modal parameters of high dams.First，useful information of the vibration signals is obtained by filtering the white noise and flow fluctuating noise using the wavelet threshold empirical mode decomposition filtering method.Then，the natural frequency and damping ratio of the system are identified using Hilbert-Huang transform（H HT）.Finally，the modal orders and operating modal parameters of the flood discharge structure are determined using the singular entropy increment theory.Simulation results show that this method has strong robustness and superior precision，and can effectively avoid frequency confounding.Its successful use on the No.5 overflow section of the Three Gorges gravity dam provides the basis of the safe operation and online dynamic non-destruction monitoring of the high dam flood discharge structure.

Keywords flood discharge excitation；operating modal；parameter identification；wavelet threshold-empirical mode decomposition filtering；Hilbert-Huang transform

Abstract The state models of the SKF6205-2RS deep groove ball bearing are set to predict the location and degree of its damage based on the Hertzian contact deformation theory，elastic theory and the geometry of the rolling bearing.Next，the system response is obtained using the Runge-Kutta numerical method.The calculation results prove that the frequency and harmonic components of the local damages of the inner ring，outer ring and ball under radial loads are well predicted.Moreover，the bearing vibration laws under different conditions are introduced to prove the periodicity of the continuous Haar wavelet transform.Finally，an autocorrelation continuous Haar wavelet method is proposed for early damage signals exacting of rolling bearings.The proposed approach is successfully applied to noise reduction and weak impulse feature extraction of bearing signals.

Keywords rolling bearing；prediction model；continuous Haar wavelet；autocorrelation denoising；weak impulse component

Advance in Electrokinetic Phenomena and Theory

Guo Wanlin1，2，Fei Wenwen1，2
（1.State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）
（2.Key Laboratory for Intelligent Nano Materials and Devices of the MOE，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

Electrokinetic phenomena are a family of dynamic phenomena that occur commonly in the interfaces of solids and ionic liquids.All the electrokinetic phenomena originate from the same source of the electrical double layer formed at the interface，and are widely used in areas such as separation of mass and protein，purification of water，detection of molecules and particles and gene sequencing.A brief historical review of the discovery of electrokinetic phenomena is firstly given here，and the development of the electrical double layer theory is described in details.The important classical electrokinetic phenomena are introduced.Especially，the newly discovered electrokinetic phenomena in graphene are introduced and compared with the classical phenomena.The review is aimed to deepen our understanding of the physical mechanisms of electrokinetic phenomena and enhance their applications.

electrokinetic phenomena；solid/liquid interfaces；electrical double layer；graphene

Optimization of a Multi-degree of Freedom Ultrasonic Motor and Its Application on a x-y Platform

Zhu Hua，Wu Wencai，Liu Weidong，Pan Song
（State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

The Equivalent Load Error Method of Dynamic Load Position Determination

Jiang Qi1，2，Zhang Fang1，2，Jiang Jinhui1，2，Zhu Dechun1，2，Xu Jing1，2，Pu Yuxue1，2
（1.State Key Laboratory for Strength and Vibration of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）
（2.Institute of Vibration Engineering Research，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

Car Body Vibration Analysis Subject to Coupling Misalignment in Traction System of Metro Vehicle

Shi Huailong，Wang Jianbin，Dai Huanyun，Wu Pingbo
（Traction Power Skate Key Laboratory，Southwest Jiaotong University Chengdu，610031，China）

Echo Identification of Phase Shift Tracking for Ultrasonic Guided Waves

Bo Lin，Liu Xiaofeng，Fu Libin
（The State Key Laboratory of Mechanical Transmission，Chongqing University Chongqing，400044，China）

Applications of Improved Empirical Mode Decomposition in Machinery Fault Diagnosis

Ma Wenpeng1，2，Zhang Junhong1，3，Ma Liang1，3，Liu Yu1，Jia Xiaojie1
（1.State Key Laboratory of Engines，Tianjin University Tianjin，300072，China）
（2.School of Mechanical Engineering，Tianjin University of Technology Tianjin，300384，China）
（3.Renai College，Tianjin University Tianjin，301636，China）

The Rolling Bearing Fault Diagnosis Method Based on Correlation Coefficient of Independent Component Analysis and VPMCD

Cheng Junsheng，Ma Xingwei，Yang Yu
（State Key Laboratory of Advanced Design and Manufacture for Vehicle Body，Hunan University Changsha，410082，China）

Fault Diagnosis for Hydroelectric Generator Unit Based
on Electromagnetism-Like Artificial Bee Colony Weighted Kernel Clustering

Xiao Han1，2，Fu Junfang1，Cai Daquan1，Zhou Jianzhong2，Xiao Jian2，Fu Wenlong2
（1.Henan Electric Power Survey and Design Institute Zhengzhou，450000，China）
（2.School of Hydropower and Information Engineering，Huazhong University of Science and Technology Wuhan，430074，China）

Abnormal Vibration Noise Diagnosis for Rubber Pin Coupling of Diesel Generating Set

Wen Huabing，Peng Zilong，Meng Fanlin
（School of Energy and Power Engineering，Jiangsu University of Science and Technology Zhenjiang，212003，China）

Finite Element Model Updating and Damage Identification Based on the Second Generation Wavelet Analysis

Zhang Xin，Liu Yang，Gao Danying
（School of Civil Engineering，Zhengzhou University Zhengzhou，450001，China）

Contrast of Calculation Method for Unbalanced Electromagnetic Force Under Rotor Inter-Turn Short Circuit Faults

Wan Shuting，Dou Longjiang，Zhang Yu，Zhang Chengjie，Zhou Guowei
（Department of Mechanical Engineering，North China Electric Power University Baoding，071003，China）

The Feature Extraction Method of Non-Stationary Vibration Signal Based on SVD-Complex Analytical Wavelet Demodulation

Zhao Ling1，Liu Xiaofeng2，Lou Lu1
（1.The College of Information Science and Engineering，Chongqing Jiaotong University Chongqing，400074，China）
（2.The State Key Laboratory of Mechanical Transmission，Chongqing University Chongqing，400044，China）

A Shaft Orbit Identification Method Imitating Human Eyes for Steam Turbine

Chen Xiaoyue1，2，Zhou Jianzhong2，Xiao Jian2，Fu Wenlong2，Zhang Weibo2，
Xia Xin2，Li Chaoshun2，Zhang Yongchuan2
（1.School of Electrical and Electronic Engineering，East China Jiaotong University Nanchang，330013，China）
（2.College of Hydropower and Information Engineering，Huazhong University of Science and Technology Wuhan，430074，China）

Manipulator Inversion of Non-Singular Terminal Neural Sliding Mode Control

Jia Yuqin1，2，Hu Xiaoxiong2
（1.Department of Mining Engineering，Lüliang University Lüliang，033001，China）
（2.School of Mechanical Engineering，Taiyuan University of Science and Technology Taiyuan，030024，China）

Power Spectral Density Compensation Algorithm for Signal Clipping in Vibration Test

Yan Lutao，Yang Zhipeng，Gao Fei，Liu Jie
（Beijing Institute of Structure and Environment Engineering Beijing，100076，China）

Evaluation of Complex Equipment Testability Based on Mixed Prior Distribution

Zhang Xishan1，Huang Kaoli2，Yan Pengcheng2，Lian Guangyao2，Wang Shaoguang2
（1.Four Department，Ordnance Engineering College Shijiazhuang，050003，China）
（2.One Research Room，Ordnance Technological Research Institute Shijiazhuang，050003，China）

Vibration Analysis of Fault Rotor Based on the Improved Local Mean Decomposition

Deng Linfeng，Zhao Rongzhen，Jin Wuyin
（School of Mechanical and Electronical Engineering，Lanzhou University of Technology Lanzhou，730050，China）

The Analysis and Application of Multi-functional PZT Sensors for Health Monitoring of Concrete Structures

Li Xu1，Huo Linsheng1，Li Hongnan1，Bai Fenglong2
（1.Faculty of Infrastructure Engineering，Dalian University of Technology Dalian，116023，China）
（2.Dalian Building Scientific Research＆amp；Design Stock Co.，LTD Dalian，116021，China）

Wavelet Packet Energy Based Damage Detection Index for Bridge

Zhu Jinsong1，2，Sun Yadan1
（1.School of Civil Engineering，Tianjin University Tianjin，300072，China）
（2.The Ministry of Education Key Laboratory of Coast Civil Structure Safety，Tianjin University Tianjin，300072，China）

Milling Stability Lobe Diagram Construction on FV520B Stainless Steel and Experimental Testing Investigation

Li Hongkun，Zhao Pengshi，Li Jingzhong，Dong Lei
（School of Mechanical Engineering，Dalian University of Technology Dalian，116023，China）

Tool Wear Condition Monitoring Based on Cutting Sound Signal and Optimized SVM

Zhang Kaifeng1，2，Yuan Huiqun1，Nie Peng2
（1.School of Mechanical Engineering＆amp；Automation，Northeastern University Shenyang，110819，China）
（2.School of Mechanical＆amp；Electrical Engineering，Shenyang Aerospace University Shenyang，110136，China）

Analytical Study and Modal Identification Experiment on Free Vibration of Beams Carrying Concentrated Masses and Springs

Wang Zhuang1，2，Hong Ming2，Xu Junchen2，Cui Hongyu2
（1.China Ship Development and Design Center Wuhan，430064，China）
（2.School of Naval Architecture Engineering，Dalian University of Technology Dalian，116024，China）

Dynamic Analysis and Experiment of High-Speed Planar Parallel Robots

Gao Mingwang1，Zhang Xianmin2
（1.School of Mechanical Engineering，Shandong University of Technology Zibo，255049，China）
（2.School of Mechanical and Automotive Engineering，South China University of Technology Guangzhou，510641，China）

Development and Validation of Embedded Control System for Rotor Online Automatic Balance

Fan Hongwei1，2，Jing Minqing1，Zhi Jingjuan1，Xin Wenhui3，Li Meng1，Liu Heng1
（1.School of Mechanical Engineering，Xi＇an Jiaotong University Xi＇an，710049，China）
（2.School of Mechanical Engineering，Xi＇an University of Science and Technology Xi＇an，710054，China）
（3.School of Mechanical and Precision Instrument Engineering，Xi＇an University of Technology Xi＇an，710048，China）

Adaptive De-noising for Vibration Signal Based on Dictionary Learning and Sparse Coding

Guo Liang1，Yao Lei2，Gao Hongli1，Huang Haifeng1，Zhang Xiaochen1
（1.School of Mechanical Engineering，Southwest Jiaotong University Chengdu，610031，China）
（2.Air-Breathing Hypersonic Technology Research Center，China Aerodynamics Research and Development Center Mianyang，621000，China）

Feature Research of Vibration Signal of Power Transformer Using Multiscale Entropy

Li Li1，Zhu Yongli2，Song Yaqi1
（1.School of Control and Computer Engineering，North China Electric Power University Baoding，071003，China）
（2.State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources，North China Electric Power University Beijing，102206，China）

The Influence of Wear Loss of Milling Cutter on Milling Stability and Surface Location Error

Wu Shi，Liu Xianli，Song Shenggang，Qu Da
（School of Mechanical and Power Engineering，Harbin University of Science and Technology Harbin，150080，China）

Research of the Penetration Overload Signals De-noising Method Based on Singular Value Decomposition

Zhao Haifeng1，2，3，Zhang Ya1，Li Shizhong1，Guo Yan1，2
（1.Faculty of Mechanical and Electrical Engineering，North University of China Taiyuan，030051，China）
（2.School of Mechatronics，Nanjing College of Information Technology Nanjing，210023，China）
（3.Department of Mechanical Engineering，University of Ottawa Ottawa，K1N 6N5，Canada）

Research on Operating Modal Parameter Identification for High Dam Discharge Structure Based on the Hilbert-Huang Transform

Zhang Jianwei，Zhu Lianghuan，Jiang Qi，Zhao Yu，Guo Jia
（College of Water Conservancy，North China University of Water Conservancy and Electric Power Zhengzhou，450011，China）

Vibration Modeling of Rolling Bearing Defect and Impulse Feature Extraction

Li Xiangyang，Chen Wanqiang
（Pump Equipment Engineering Research Center of Shaanxi Province，Xi＇an Aeronautical College Xi＇an，710077，China）

TB17；TH133.3

10.16450/j.cnki.issn.1004-6801.2015.04.030

李祥陽，男，1972年10月生，講師。主要研究方向為機械設計及理論。曾發表《Rolling bearing fault diagnosis based on physical model and one-class support vector machine》（《ISRN Mechanical Engineering》2014，No.4）等論文。

E-mail：lxygyl@163.com

*科技部創新基金資助項目（13C26216105730）；陜西省自然科學基礎研究計劃資助項目（2014JM2-5069）

2014-12-03；

2015-03-01