Rolling elementbearingfaultdiagnosisusingwavelettransform

Rolling element bearing fault diagnosis using wavelet transform

P.K.Kankar,Satish C.Sharma,S.P.Harsha n

Vibration and Noise Control Laboratory,Mechanical and Industrial Engineering Department,Indian Institute of Technology Roorkee,Roorkee 247667,India

a r t i c l e i n f o

Article history:

Received 16August 2010Received in revised form 13January 2011

Accepted 21January 2011Communicated by J.Zhang

Available online 21March 2011Keywords:Wavelets

Support vector machine (SVM)

Learning vector quantization (LVQ)Self-organizing maps (SOM)Shannon Entropy

a b s t r a c t

This paper is focused on fault diagnosis of ball bearings having localized defects (spalls)on the various bearing components using wavelet-based feature extraction.The statistical features required for the training and testing of arti?cial intelligence techniques are calculated by the implementation of a wavelet based methodology developed using Minimum Shannon Entropy Criterion .Seven different base wavelets are considered for the study and Complex Morlet wavelet is selected based on minimum Shannon Entropy Criterion to extract statistical features from wavelet coef?cients of raw vibration signals.In the methodology,?rstly a wavelet theory based feature extraction methodology is developed that demonstrates the information of fault from the raw signals and then the potential of various arti?cial intelligence techniques to predict the type of defect in bearings is investigated.Three arti?cial intelligence techniques are used for faults classi?cations,out of which two are supervised machine learning techniques i.e.support vector machine,learning vector quantization and other one is an unsupervised machine learning technique i.e.self-organizing maps.The fault classi?cation results show that the support vector machine identi?ed the fault categories of rolling element bearing more accurately and has a better diagnosis performance as compared to the learning vector quantization and self-organizing maps.

&2011Elsevier B.V.All rights reserved.

1.Introduction

Rolling element bearings are essential parts of rotating machinery from small hand held devices to heavy duty industrial systems and are primary cause of breakdowns in machines.A machine can be seriously damaged if faults occur in bearings during service.The importance of early detection of defects in bearings has led to continuous efforts due to the fact that unpredictable occurrence of damage may cause disastrous failure.In order to ensure the normal operation of industry fault diag-nosis of bearings is essential.Fault diagnosis of rolling element bearings using vibration signature analysis is the most commonly used to prevent breakdowns in machinery.

Fault diagnosis is a type of classi?cation problem,and arti?cial intelligence techniques based classi?ers can be effectively used to classify normal and faulty machine conditions.A machine fault classi?cation problem consists of two main steps.First step is feature extraction from raw vibration signals to extract some features that demonstrate the information of fault from the raw signals and second step is to use these extracted features for fault diagnosis using various arti?cial intelligence techniques like

arti?cial neural networks,support vector machines,etc.To analyze vibration signals and extract features,different techni-ques such as time domain [1–5],frequency domain [6–8]and time–frequency domain [9–18]are extensively used.The complex and non-stationary vibration signals with a large amount of noise make the bearing faults very dif?cult to detect by conventional time domain and frequency domain analysis,which assumes that the analyzed signal to be strictly periodic.Recently,wavelet transform,which is a time–frequency domain analysis method,has been widely used for fault diagnosis of rolling element bearings.It has the local characteristic of time-domain as well as frequency domain and its time–frequency window is change-able.In the processing of non-stationary signals it presents better performance than the traditional Fourier analysis.

Samantha and Al.-Balushi [4]have presented a procedure for fault diagnosis of rolling element bearings through arti?cial neural network (ANN).The characteristic features of time-domain vibration signals of the rotating machinery with normal and defective bearings have been used as inputs to the ANN.Kankar et al.[5]have conducted a comparative experimental study for the effectiveness of ANN and SVM in fault diagnosis of ball bearings and concluded that the classi?cation accuracy for SVM is better than of ANN.Nikolaou and Antoniadis [10]have used wavelet packet transform to identify the nature of rolling element bearing faults.The wavelet packet transform is used for the analysis of vibration signals resulting from bearings with

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journal homepage:https://www.wendangku.net/doc/3b1532601.html,/locate/neucom

Neurocomputing

0925-2312/$-see front matter &2011Elsevier B.V.All rights reserved.doi:10.1016/j.neucom.2011.01.021

n

Corresponding author.Tel.:t911332286602.

E-mail addresses:pavankankar@https://www.wendangku.net/doc/3b1532601.html, (P.K.Kankar),

sshmefme@iitr.ernet.in (S.C.Sharma),spharsha@https://www.wendangku.net/doc/3b1532601.html, (S.P.Harsha).Neurocomputing 74(2011)1638–1645

localized defects.Prabhakar et al.[11]and Purushotham et al.[12] have used discrete wavelet transform for detection of bearing race faults.The effectiveness of wavelet-based features for fault diagnosis of gears using support vector machines(SVM)and proximal support vector machines(PSVM)has been revealed by Saravanan et al.[13].Methods for intelligent fault diagnosis of rotating machinery based on wavelet packet transform(WPT), empirical mode decomposition(EMD),dimensionless parameters, a distance evaluation technique and radial basis function(RBF) network are proposed by Lei et al.[14].

Ra?ee et al.[15]have developed a procedure which experi-mentally recognizes gears and bearings faults of a typical gearbox system using a multi-layer perceptron neural network.Ra?ee and Tse[16]have presented a time–frequency-based feature recogni-tion system for gear fault diagnosis using autocorrelation of continuous wavelet coef?cients(CWC).It has been shown that the size of vibration signals can be reduced with minimal loss of signi?cant frequency content.Ra?ee et al.[17]have further proposed a technique for selecting mother wavelet function using an intelligent fault diagnosis system.The type of gear failures of a complex gearbox system are identi?ed using genetic algorithm and arti?cial neural networks.Ra?ee et al.[18]have shown that the Daubechies44wavelet is the most effective for both faulty gears and bearings.

An extensive comparative study concerning the performance of SVM against sixteen other popular classi?ers,using twenty-one different data sets,is carried out by Meyer et al.[19].The results verify that SVM classi?ers rank at the very top among these classi?ers,although there are cases for which other classi?ers gave lower error rates[19].Based on the comparison and recommendation of previous studies,authors have employed SVM and LVQ for bearing faults classi?cation[19,20].LVQ is a supervised machine learning technique and it is special case of ANN.In many situations,it is not easy to collect training data set because of routine maintenance and periodically repairs.To solve this problem,authors have also used self-organizing maps(SOM) because unlike SVM and ANN,SOM-based approach has the practical advantage of learning and producing fault classi?cations without any supervision.

In order to extract the fault feature of signals more effectively, an appropriate wavelet-base function should be selected.Pre-sently,in mechanical fault diagnosis,Daubechies and Morlet wavelets are mostly applied to extract the fault feature[9–18]. In present work,a methodology is proposed based on Minimum Shannon Entropy Criterion for selection of most appropriate wavelet and to determine scale corresponding to characteristic defect frequency.Seven different wavelets are considered each with27sub-signals i.e.128scales.In order to select the best base wavelet for rolling element bearings fault diagnosis,Shannon Entropy for each wavelet is calculated.Statistical features are calculated from wavelet coef?cients and fed as input to machine learning techniques SVM,LVQ and SOM.The useful features can be extracted from the original data and high dimensional of original data can be reduced by removing irrelevant features with the use of proposed methodology.Hence,the classi?er can achieve a higher accuracy.

2.Machine learning techniques

Machine learning is an approach of using examples(data)to synthesize programs.In the particular case when the examples are input/output pairs,it is called Supervised Learning.In a case, where there are no output values and the learning task is to gain some understanding of the process that generated the data, this type of learning is said to be unsupervised.In the present study,the two supervised machine learning techniques i.e.SVM and LVQ are considered and the unsupervised machine learning technique like SOM is considered.Pattern recognition and classi?cation using machine learning techniques are described in Ref.[21].

2.1.Self-organizing maps

Self-organizing maps are special class of ANN and are based on competitive learning.In self-organizing maps,the neurons are placed at the nodes of a lattice that is usually one or two dimensional.The neurons become selectively tuned to various input patterns or classes of input patterns in the course of a competitive learning process.The location of neuron is so tuned (winning neurons)that it becomes ordered with respect to each other in such a way that a meaningful co-ordinate system for different input features is created over the lattice.

A SOM is therefore characterized by the formation of a topographic map of the input patterns in which the spatial locations of the neurons in the lattice are indicative of intrinsic statistical features contained in the input patterns,hence self-organizing map.

2.2.Support vector machine

Support vector machine is a supervised machine learning method based on the statistical learning theory.It is a useful method for classi?cation and regression in small-sample cases such as fault diagnosis.In this method,a boundary is placed between the two different classes and orients it,in such a way that the margin is maximized,which results in the least general-ization error.The nearest data points that have been used to de?ne the margin are called Support Vectors.This is implemented by reducing it to a convex optimization problem:minimizing a quadratic function under linear inequality constraints[22].A training sample set{(x i,y i)};i?1to N is considered,where N is total number of samples.The hyperplane f(x)?0that separates the given data can be obtained as a solution to the following optimization problem:

Minimize

1

2

:w:2tC

X N

i?1

x ie1TSubject to

y iew T x itbTZ1àx i

x i Z0,i?1,2,...,N

(

e2T

where C is a constant representing error penalty.Rewriting the above optimization problem in terms of Lagrange multipliers, leads to the following problem:

Maximize WelT?

X N

i?1

l ià

1X N

i,j?1

y i y j l i l jex i:x jTe3TSubject to

0r l i r C

X N

i?1

l i y i?0,i?1,2,...,N

8

>><

>>:e4T

The Sequential Minimal Optimization(SMO)algorithm gives an ef?cient way of solving the dual problem arising from the deriva-tion of the SVM.SMO decomposes the overall quadratic program-ming problem into quadratic programming sub-problems.

2.3.Learning vector quantization

Learning vector quantization[21]is a supervised machine learning technique in which the structure of the input space is

P.K.Kankar et al./Neurocomputing74(2011)1638–16451639

exploited so that the size of the input data can be reduced which results in less computational time.LVQ is based on vector quantization in which an input space is divided into number of distinct regions and for each region a reconstruction vector is de?ned.When a new vector is presented to the quantizer,the region in which the vector lies is ?rst determined,and is then represented by the reproduction vector for that region.The collection of possible reproduction vectors is called the code book of quantizer,and its members are called code words.

The SOM algorithm provides an approximate method for computing the Voronoi vectors in unsupervised manner,with the approximation being speci?ed by the synaptic weight vectors of the neurons in the feature map.Therefore we can say that ?rstly SOM can be employed for the computation of the feature map and secondly LVQ is applied which provides a mechanism for the ?nal tuning of a feature map.Hence LVQ is said to be supervised version of SOM.

3.Experimental setup

The problem of predicting the degradation of working condi-tions of bearings before they reach the alarm or failure threshold

is extremely important in industries to fully utilize the machine production capacity and to reduce the plant downtime.In the present study,an experimental test rig is used and vibration response for healthy bearing and bearing with faults are obtained.The rig is connected to a data acquisition system through proper instrumentation.Data acquisition and analysis system consists of VibraQuest software and data acquisition hardware.VibraQuest software is designed in Lab VIEW for quick data acquisition,review,and storage.Hardware consists of 16analog input channels,for simultaneous sampling.PCI bus ensures high-speed data acquisition (102.4k samples/s).A remote optical sensor with a visible red LED light source is used to measure rotor speed.Piezo-electric accelerometers (IMI 603C01)are used for picking up the vibration signals from various stations on the rig.These accelerometers are having measurement range as 7490m/s 2.Table 1shows dimensions of the ball bearings taken for the study.Piezo-electric accelerometers are used for picking up the vibra-tion signals from various stations on the rig.

As a ?rst step,the machine was run with healthy bearing to establish the base-line data.Then data are collected for different fault conditions.Various faults considered in bearing components are as

shown in Fig.1.A variety of faults on bearings are simulated on the rig at different rotor speed i.e.250,500,1000,1500and 2000rpm.Following ?ve bearing conditions are considered for the study:1.Healthy bearings (HB).

2.Bearing with spall on inner race (SIR).

3.Bearing with spall on outer race (SOR).

4.Bearing with spall on ball (BFB).

5.

Combined bearing component defects (CBD).

4.Minimum Shannon Entropy Criterion (MEC)

Total of seven different wavelets have been considered for the present study.An appropriate wavelet is the base wavelet which minimizes the Shannon Entropy of the corresponding wavelet coef?cients.The Shannon Entropy of wavelet coef?cients is given as S entropy en T?à

X m i ?1

p i log 2p i

e5T

where p i is the energy probability distribution of the wavelet coef?cients,de?ned as

p i ?

9C n ,i 9

2

E en Te6Twith P m i ?1p i ?1,and in the case of p i ?0for some i ,the value of p i log 2p i is taken as zero.

The following steps explain the methodology developed for selecting a base wavelet based on the ‘‘Minimum Shannon Entropy Criterion’’for the vibration signals under study:

(1)Total 150vibration signals are obtained by considering

healthy and faulty bearing conditions.

(2)To convert the complex vibration signals into simpli?ed

signals with more resolution in time and frequency domain,these raw signals are divided into 27sub-signals i.e.128scales in seventh level of decomposition.

(3)For healthy and faulty bearings,continuous wavelet coef?-cients (CWC)of vibration signals are calculated using seven different mother wavelets in which three from real valued as Daubechies 44,Meyer,Coi?et,Symlet wavelets and other three are complex valued as complex Gaussian,Complex Morlet and Shannon wavelets.

(4)The Shannon Entropy of CWC is calculated for each of 30

segmented signals at different rotor speed 250,500,1000,1500and 2000rpm and loading conditions using healthy and faulty bearings.The average of the Shannon Entropy in the 30segmented signals is calculated for ?ve bearing conditions i.e.BFB,SIR,CBD,HB and SOR.

(5)Sum of the mentioned average of the ?ve bearing conditions

is determined for each scale (27).

(6)The total Shannon Entropy for each wavelet is calculated by

adding ‘‘sum of the mentioned average’’of all the scales as shown in Table 2.

Table 1

Parameters of bearing.Parameter

Value Outer race diameter 28.262mm Inner race diameter 18.738mm Ball diameter 4.762mm Ball number 8

Radial clearance

10m m

Spall

Spall

Fig.1.Bearing components with faults induced in them.(a)Spall on outer race,(b)spall on inner race and (c)ball with spall.

P.K.Kankar et al./Neurocomputing 74(2011)1638–1645

1640

(7)The wavelet having minimum Shannon Entropy is considered

for fault diagnosis of rolling element bearing.

The?owchart for above mentioned methodology is shown in Fig.2.Shannon Entropy calculated for Complex Morlet wavelet is found minimum.Hence,Complex Morlet wavelet is considered to extract features for fault diagnosis.

For healthy and faulty bearings,Fig.3shows the plots between Shannon Entropy and scale number at rotor speed2000rpm with no loader using Complex Morlet wavelet.Entropy plots for faults in ball, inner race and outer race are as shown in Fig.3(a),(b)and(e), respectively.From this,it is concluded that fault in inner race gives minimum entropy as compare to fault in ball or outer race,which indicates that inner race defect has more effect on machine vibra-tions.While for combined bearing component defects,Fig.3(c)shows that Shannon Entropy value is less.For healthy bearing,it is observed that Shannon Entropy value is more as compare to bearing containing some faults as shown in Fig.3(d).Fig.3clearly indicates that Minimum Shannon Entropy Criterion applied in this study can be effectively used for fault diagnosis of rotor bearing system.

5.Feature extraction

Complex Morlet wavelet is selected as the best base wavelet among the other wavelets considered from the proposed methodol-ogy.The CWC of all the150signals with Complex Morlet as a base wavelet are calculated at seventh level of decomposition(27scales).

When applying wavelet transform to a signal,if the Shannon Entropy measure of a particular scale is minimum then we can say that a major defect frequency component exists in the scale.In the present study out of27scales considered,the scale having the minimum Shannon Entropy is selected,and the statistical features of the CWC corresponding to the selected scale are calculated.

Root mean square(RMS)value,crest factor,kurtosis,skewness, standard deviation,etc.are the most commonly used statistical measures used for fault diagnosis of rolling element bearings. Statistical moments like kurtosis,skewness and standard deviation are descriptors of the shape of the amplitude distribution of vibration data collected from a bearing,and have some advantages over traditional time and frequency analysis,such as its lower sensitivity to the variations of load and speed,the analysis of the condition monitoring results is easy and convenient,and no precious history of the bearing life is required for assessing the bearing condition[23]. When selecting certain normalized statistical moments to monitor the bearing condition,we usually need to consider two most essential characteristics,i.e.sensitivity and robustness.By rectifying the signal,Honarvar and Martin[23]compared the third moment, skewness,of the recti?ed data to kurtosis,and found that this third moment has better characteristics than kurtosis.In present paper,

Table2

Comparison of parameters for wavelet selection.

Wavelet type Shannon Entropy

Daubechies4421.43

Meyer21.59

Coi?et39.49

Symlet28.88

Complex Gaussian40.03

Shannon21.26

Complex Morlet19.79

Fig.2.Flowchart for wavelet selection criteria.

P.K.Kankar et al./Neurocomputing74(2011)1638–16451641

authors’use statistical moments like kurtosis,skewness and standard deviation as features to effectively indicate early faults occurring in rolling element bearing.The statistical features that are considered in the present study are:

(1)Kurtosis :a statistical measure used to describe the distribu-tion of observed data around the mean.Kurtosis is de?ned as the degree to which a statistical frequency curve is peaked.

Kurtosis ?

n en t1Ten à1Ten à2Ten à3TX x j àx s 4(

)

à

3en à1T2

en à2Ten à3T

e7T

(2)Skewness :skewness characterizes the degree of asymmetry of

a distribution around its mean.Skewness can come in the form of negative or positive skewness.

Skewness ?n

X x j àx 3e8T

(3)Standard deviation :standard deviation is measure of energy

content in the vibration signal.

Standard deviation ?

????????????????????????????????n P x 2àeP x T

2n en à1Ts e9TThese statistical features are fed as input to the arti?cial intelligence techniques for faults classi?cation.The following

steps give an overview of the methodology presented in this

study for bearing faults diagnosis:

(1)In this study,healthy bearings,bearing with spall in outer

race,inner race,ball and bearing with combined compo-nent defects are considered.Vibration signals in time domain are obtained both in horizontal and vertical directions for each bearing condition at different rotor speed 250,500,1000,1500and 2000rpm under loader and no loader condition.

(2)Continuous wavelet coef?cients of the vibration signals are

calculated at the seventh level of decomposition (27scales for each sample).These coef?cients are calculated for all seven mother wavelets,considered in this study.

(3)Shannon Entropy of CWC can be calculated thereafter.

(4)Complex Morlet wavelet is considered for the fault diagnosis

among the seven mother wavelets based on minimum Shan-non Entropy Criterion.

(5)Statistical features like kurtosis,skewness and standard

deviation are calculated from the wavelet coef?cients corresponding to scales having the minimum Shannon Entropy.

These statistical features are fed as input to the machine learning algorithms SVM,LVQ and SOM for faults classi?-

cation.

Fig.3.Plots between Shannon Entropy and scale number at rotor speed 2000rpm with no loader using Complex Morlet wavelet.(a)Bearing with spall on ball,(b)bearing with spall on inner race,(c)combined bearing component defects,(d)healthy bearings and (e)bearing with spall on outer race.

P.K.Kankar et al./Neurocomputing 74(2011)1638–1645

1642

6.Results and discussions

In the present study,classi?cation of bearing faults is carried out using SVM,LVQ and SOM.The number of code book vectors ?xed before the training of the LVQ algorithm is 20.Out of this 20code book vectors the class distribution among the ?ve different fault classes is given in Table 3.Four different code book vectors are selected by the LVQ algorithm to represent each of BFB and SIR cases and this corresponds to 20%each.Whereas 2(10%),7(35%),3(15%)for CBD,HB,SOR,respectively.The class distribu-tion among the ?ve different bearing cases for SOM is given in Table 4.

The results on a test set in a multi-class prediction are displayed as a two dimensional confusion matrix with a row and column for each class [24].Each matrix element shows the number of test examples for which the actual class is the row and the predicted class is the column.A sample training/testing vector is shown in Table 5.Total 75instances and 8features are used for the study including statistical features for each of the horizontal and vertical response,number of loader and rotor speed used.Tables 6–8show the test results as confusion matrices for each of the two techniques i.e.SVM,LVQ and SOM.Total 75numbers of

instances are obtained in which 15cases are considered with each of BFB,SIR,CBD,HB and SOR,respectively.SVM has correctly predicted all instances for BFB,SIR,CBD,HB and SOR,respectively,as shown in Table 6.From Table 7,it is inferred that LVQ has correctly predicted 12,12,15,14and 14instances,while Table 8

Table 3

Class distribution for LVQ.S.no.Type of bearing No.of code book vectors 1BFB 4(20%)2SIR 4(20%)3CBD 2(10%)4HB 7(35%)5

SOR

3(15%)

Table 4

Class distribution for SOM.S.no.Type of bearing %Class 1BFB 10(21%)2SIR 9(19%)3CBD 8(17%)4HB 10(21%)5

SOR

11(23%)

Table 5

Sample input vector for SVM,LVQ and SOM.

Features

Horizontal response Vertical response Loader

Speed

Class

Kurtosis

Skewness Standard deviation Kurtosis Skewness Standard deviation Amplitude of features

10.83371 2.2199120.0002244.70497 4.7533330.00070201000BFB 11.07509 2.3281350.00218922.66564 3.3985470.00197501500BFB 6.465513 1.501720.00054316.52251 2.7511540.0044402000BFB 5.105068 1.2510129.59E à0554.83589 4.19490.00011811000SIR 6.461471 1.540270.000284 5.805013 1.4649650.00021711500SIR 11.52051 2.0970720.0002497.707975 1.7417950.00037112000SIR 11.93591 2.4104870.0001987.281817 1.7352770.00020911000CBD 4.630504 1.2101620.00019313.42329 2.3758810.00046711500CBD 5.553487 1.4008720.00034810.68352 2.1910450.00118312000CBD 7.704414 1.5198890.000105 6.478991 1.5785420.00039921000HB 6.118728 1.4805160.000204 4.864674 1.2546690.00020521500HB 4.282953 1.0938930.000264 5.511267 1.365930.00029722000HB 14.40096 2.5583410.000231.59812 4.549730.00126821000SOR 6.202332 1.4471550.00024625.01716 3.5081820.0056821500SOR 5.107758

1.28273

0.000466

8.521063

2.24933

0.030608

2

2000

SOR

Table 6

Confusion matrix for SVM.BFB SIR CBD HB SOR Classi?ed as 150000BFB 015000SIR 001500CBD 000150HB 0

15

SOR

Table 9

Evaluation of the success of numeric prediction.Parameters

SVM LVQ

SOM

Correctly classi?ed instances 75(100%)67(89.3333%)56(74.6667%)Incorrectly classi?ed instances Nil 8(10.6667%)19(25.3333%)Total number of instances

75

75

75

Table 8

Confusion matrix for SOM.BFB SIR CBD HB SOR Classi?ed as 130002BFB 310011SIR 101202CBD 31083HB 0

1

1

13

SOR

Table 7

Confusion matrix for LVQ.BFB SIR CBD HB SOR Classi?ed as 120102BFB 012120SIR 001500CBD 000141HB 0

1

14

SOR

P.K.Kankar et al./Neurocomputing 74(2011)1638–16451643

shows that SOM has classi?ed13,10,12,8and13instances. Table9shows accuracy associated with each technique for faults classi?cation.For this study,classi?cation accuracy shows that SVM is a better classi?er than LVQ and SOM.The prediction performance of SVM is coming out to be superior mainly due to its good generalization capability,which is also reported by Meyer et al.[19].The correctly classi?ed instances for SVM,LVQ and SOM are100%,89.3333%and74.6667%,respectively.To show the ef?ciency of the selected features and the methodology,a comparison between the current work and some published literatures has been shown in Table10.In this table,comparison has been made on the basis of the objects used,defects consid-ered for the study,techniques used for vibration signature analysis,features considered,classi?er used and the classi?er ef?ciencies in each paper.7.Conclusion

Aiming at the characteristics of the vibration signal of rolling bearing with fault,the Complex Morlet wavelet is selected based on Minimum Shannon Entropy Criterion to extract the fault feature in this paper.Ra?ee et al.[18]have also shown that among a wide variety of mother wavelets,Complex Morlet wavelet have satisfactory performances for both bearing and gear fault identi?cation,which is veri?ed by obtained results.This study presents a methodology for detection of bearing faults by classifying them using three arti?cial intelligence techniques.The responses observed for different fault condition of bearing shows that minimum Shannon Entropy is obtained for bearings with inner race fault.The results of faults classi?cation with SVM(100%)are superior to LVQ and SOM.LVQ being the supervised version of SOM the classi?cation accuracy

Table10

A compressive study between the present work and some recent publications.

References Objects Defects considered Techniques used

for vibration

signature

analysis Features

considered

Classi?er used Classi?er

ef?ciencies

Paya et al.[9]Bearings and

gears Defects on inner race of bearing

and gear tooth irregularity.

Daubechies410wavelet

numbers

indicating both

time and

frequency and

their10

corresponding

amplitudes

Arti?cial neural

networks

96%

Nikolaou and Antoniadis[10]Rolling element

bearings

Inner race and outer race fault Daubechies12Mean and

standard deviation

of wavelet packet

coef?cients

NA NA

Prabhakar et al.[11]Rolling element

bearings

One scratch mark each on inner

race(on the track)and outer

race(on the track),two scratch

marks on outer race(1801apart

on the track),one scratch mark

on each of inner race and outer

race(on the track)

Daubechies4RMS,Kurtosis NA NA

Purushotham et al.[12]Rolling element

bearings

Single and multiple point

defects on inner race,outer

race,ball fault and combination

of these faults

Daubechies Mel Frequency

Complex

Cepstrum(MFCC)

coef?cients

Hidden Markov

model classi?ers

Best ef?ciency

obtained as99%

Saravanan et al.[13]Gears Gear tooth breakage,gear with

crack at root and with face wear

Morlet wavelet Statistical features

namely,standard

error,sample

variance,kurtosis

and minimum

value

Support vector

machines(SVM)

and proximal

support vector

machines(PSVM)

Best ef?ciency

obtained as

100%

Ra?ee et al.[15]Gears and

bearings Three different fault conditions

on gears(slight-worn,medium-

worn and broken tooth),faulty

bearings

Daubechies4

(wavelet packet)

Standard

deviation of

wavelet packet

coef?cients

Arti?cial neural

networks

Best ef?ciency

obtained as

100%

Ra?ee et al.[18]Gears and

bearings Ball,cage,inner race,outer race

defects on bearings and three

different fault conditions on

gears(slight-worn,medium-

worn and broken tooth)

324mother

wavelets from

various wavelet

families like Haar,

Daubechies,

Coi?et,Morlet,etc.

Variance,standard

deviation,kurtosis

and4th central

moment of CWC-

SVS

Arti?cial neural

networks

Recommended

that the best

ef?ciency can be

achieved using

db44for gear

and bearing

fault diagnosis

Present work Rolling element

bearings Spall in inner race,outer race,

rolling element and combined

component defects

Daubechies44,

Meyer,Coi?et5,

Symlet2,Gaussian,

Complex Morlet

and Shannon

wavelets

Statistical features

namely,kurtosis,

skewness and

standard deviation

from wavelet

coef?cients

corresponding to

scale maximizing

energy to Shannon

Entropy ratio

Support vector

machines,

arti?cial neural

networks,self-

organizing maps

The best

ef?ciency

obtained using

complex Morlet

wavelet and

SVM classi?er as

100% P.K.Kankar et al./Neurocomputing74(2011)1638–1645

1644

obtained89.3333%,which is better than SOM(74.6667%).The results show the potential application of these arti?cial intelligence techni-ques for developing effective maintenance strategies to prevent catastrophic failure and reduce operating cost.

Acknowledgement

This work was?nancially supported by the Department of Science and Technology,Government of India[Grant number DST/457/MID]. References

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Mr.P.K.Kankar has done his B.E.(Mechanical Engi-

neering),M.E.(Manufacturing System Engineering)

and pursuing Ph.D.(Vibration).His research areas are

machine design,vibration,controls and non-linear

dynamics.He has published more than10papers in

various refereed

journals.

Prof.Satish C.Sharma has done his B.E.(Mechanical

Engineering),M.E.(Machine Design)and Ph.D.(Tribol-

ogy).His research areas are machine design,tribology

and measurement.He has published more than70

papers in various refereed

journals.

Dr.S.P.Harsha has done his B.E.(Mechanical Engineer-

ing),M.E.(Machine Design)and Ph.D.(Vibration).His

research areas are machine design,vibration,controls

and non-linear dynamics.He has published more than

60papers in various refereed journals.

P.K.Kankar et al./Neurocomputing74(2011)1638–16451645

rollinginthedeep歌词

路漫漫其修远兮，吾将上下而求索- 百度文库Rolling In The Deep There's a fire starting in my heart 胸中燃起怒火 Reaching a fever pitch and it's bringing me out the dark 狂热救赎我于黑暗 Finally, I can see you crystal clear 终于看清本性 Go ahead and sell me out and I'll lay your sheet bare. 继续背叛而我亦将不再留恋 See how I leave, with every piece of you 看我如何将你撕碎 Don't underestimate the things that I will do 请别低估我的能耐 There's a fire starting in my heart 我胸中升起的怒火 Reaching a fever pitch and it's bringing me out the dark 熊熊燃烧驱走黑暗 The scars of your love, remind me of us 爱之伤疤疼痛于心 They keep me thinking that we almost had it all 让我回想曾经的拥有 The scars of your love, they leave me breathless 爱之伤疤令人窒息 I can't help feeling 思绪万千不能自已 We could have had it all 我们本应幸福Rolling in the deep 如今却在深渊中翻滚 You had my heart inside of your hands 你将我的心捏在手里 And you played it to the beat 玩弄于股掌之间 Baby I have no story to be told 宝贝我已无话可说 But I've heard one of you and I'm gonna make your head burn 可我亦知你愁肠百结 Think of me in the depths of your despair 在绝望深处想着我 Making a home down there, as mine sure won't be shared 纠结着吧，老娘不再与你同甘共苦 The scars of your love, remind me of us 爱之伤疤疼痛于心 They keep me thinking that we almost had it all 让我回想曾经的拥有 The scars of your love, they leave me breathless 爱之伤疤令人窒息 I can't help feeling 思绪万千不能自已 We could have had it all 我们本应幸福 Rolling in the deep 如今却在深渊中翻滚 You had my heart inside of your hands

Rolling in the deep(中文发音对照)

Rolling in the deep肉铃音则地谱 There's a fire starting in my heart, 贼而子额FAI而司大婷音买哈特 Reaching a fever pitch and it's bringing me out the dark 瑞驰英额飞唔儿皮尺案的一次布瑞英米奥特则大可 Finally, I can see you crystal clear. Fai呢里，爱看细有克瑞斯头科利尔 Go ahead and sell me out and I'll lay your ship bare. 勾阿?的案的赛哦米奥特案的爱哦累幼儿谁谱?耳 See how I leave, with every piece of you 细好唉礼物，维斯爱吴瑞劈死奥夫有 Don't underestimate the things that I will do. 懂特安德尔瑞斯四蹄梅特则丝印死在特唉唯有读 There's a fire starting in my heart, 贼而子额FAI而司大婷音买哈特 Reaching a fever pitch and it's bringing me out the dark 瑞驰英额飞唔儿皮尺案的一次布瑞英米奥特则大可 The scars of your love, remind me of us. 则死卡死奥夫幼儿辣舞，瑞慢的米奥夫阿斯 They keep me thinking that we almost had it all 贼?谱米丝印刻印在特为哦某斯特?得特傲 The scars of your love, they leave me breathless 则死卡死奥夫幼儿辣舞，贼礼物米布瑞斯里斯 I can't help feeling... 唉康特还奥普非零 We could have had it all... (you're gonna wish you, never had met me)... 为苦的还无?得特傲（有啊够那为石油，乃武还的麦特米） Rolling in the Deep (Tears are gonna fall, rolling in the deep) 肉铃音则地谱（提而死啊够那佛，肉铃音则地谱） Y ou had my heart... (you're gonna wish you)... Inside of your hand (Never had met me) 有还得买哈特（有啊够那为石油）因赛的奥夫幼儿??（乃武还的麦特米）And you played it... (Tears are gonna fall)... To the beat (Rolling in the deep) 案的有普雷的伊特（提而死啊够那佛）图则比特（肉铃音则地谱） Baby I have no story to be told, 北鼻唉还无no 四道瑞图比投的 But I've heard one of you and I'm gonna make your head burn. 巴特爱屋赫尔德午安奥夫有案的爱慕够那没课幼儿?得伯儿恩 Think of me in the depths of your despair.

rollinginthedeep谐音歌词

rolling in the deep谐音歌词 There's a fire starting in my heart, 贼而死啊 FAI而司大婷音买哈特 Reaching a fever pitch and it's bringing me out the dark 瑞驰Ing 额飞我皮尺案的一次布瑞ING 米奥特则大可 Finally, I can see you crystal clear. 烦NOU里，爱看 sei 有克瑞斯头科利尔 Go ahead and sell me out and I'll lay your ship bare. 勾阿海的案的赛哦米奥特案的爱哦来幼儿谁谱拜耳 See how I leave, with every piece of you SEI 好唉礼物，维斯爱吴瑞劈死奥夫有 Don't underestimate the things that I will do. 懂特安德尔RUAI四蹄梅特则丝印死在特唉唯有读 There's a fire starting in my heart, 贼而死啊 FAI而司大婷音买哈特 Reaching a fever pitch and it's bringing me out the dark 瑞驰Ing 啊飞我皮尺案的一次布瑞ING 米奥特则大可 The scars of your love, remind me of us. 则死盖尔死奥夫幼儿辣舞，瑞慢的米奥夫阿斯 They keep me thinking that we almost had it all 贼 KEI谱米丝印刻印在特为哦某斯特还得伊特傲 The scars of your love, they leave me breathless 则死盖尔死奥夫幼儿辣舞，贼礼物米布瑞斯里斯 I can't help feeling... 唉康特还奥普非零 We could have had it all... (you're gonna wish you, never had met me)... 为苦的还无还得伊特傲（有啊够那为石油，乃武还的麦特米） Rolling in the Deep (Tears are gonna fall, rolling in the deep) 揉林音则地谱（提而死啊够那佛，揉林音则地谱） You had my heart... (you're gonna wish you)... Inside of your hand (Never had met me) 有还得买哈特（有啊够那为石油）因赛的奥夫幼儿汗的（乃武还的麦特米）And you played it... (Tears are gonna fall)... To the beat (Rolling in the deep) 案的有普雷的伊特（提而死啊够那佛）图则比特（揉林音则地谱） Baby I have no story to be told, 北鼻唉还无 nou 四道瑞图比投的 But I've heard one of you and I'm gonna make your head burn. 巴特爱屋赫尔德午安奥夫有案的爱慕够那没课幼儿还得伯儿恩 Think of me in the depths of your despair. SIN可奥夫米音则带普斯奥夫幼儿第四百二 Making a home down there, as mine sure won't be shared. 没刻印啊后母当贼而，爱死迈恩说儿翁特比晒儿的 The scars of your love, remind me of us.

roling in the deep中英文翻译对照

roling in the deep There's a fire starting in my heart 胸中燃起怒火 Reaching a fever pitch and it's bringing me out the dark 狂热救赎我于黑暗 Finally, I can see you crystal clear 终于看清本性 Go ahead and sell me out and I'll lay your sheet bare. 继续背叛而我亦将不再留恋 See how I leave, with every piece of you 看我如何将你撕碎 Don't underestimate the things that I will do 请别低估我的能耐 There's a fire starting in my heart 我胸中升起的怒火 Reaching a fever pitch and it's bringing me out the dark 熊熊燃烧驱走黑暗 The scars of your love, remind me of us 爱之伤疤疼痛于心 They keep me thinking that we almost had it all 让我回想曾经的拥有 The scars of your love, they leave me breathless 爱之伤疤令人窒息 I can't help feeling 思绪万千不能自已 We could have had it all 我们本应幸福 Rolling in the deep 如今却在深渊中翻滚 You had my heart inside of your hands 你将我的心捏在手里 And you played it to the beat 玩弄于股掌之间 Baby I have no story to be told

rolling in the deep 歌词及翻译

There's a fire starting in my heart 我怒火中烧 Reaching a fever pitch and it's bringing me out the dark 熊熊烈焰带我走出黑暗 Finally, I can see you crystal clear 最终我将你看得一清二楚 Go ahead and sell me out and I'll lay your ship bare 去吧出卖我我会让你一无所有See how I'll leave with every piece of you 看我怎么离你而去带走你的一切 Don't underestimate the things that I will do 不要低估我将来的所作所为 There's a fire starting in my heart 我怒火中烧 Reaching a fever pitch and it's bring me out the dark 熊熊烈焰带我走出黑暗 The scars of your love remind me of us 你的爱情伤痕让我想起了我们曾经的甜蜜They keep me thinking that we almost had it all 它们总在提醒我我们几乎拥有了一切

The scars of your love, they leave me breathless 你的爱情伤痕让我窒息 I can't help feeling 我不禁心生感触 We could have had it all 我们本该拥有一切 (You're gonna wish you never had met me) （你会祈祷要是从未遇见我该有多好）Rolling in the deep 内心深处爱恨交织 (Tears are gonna fall, rolling in the deep) （眼泪快要掉下来，内心深处爱恨交织）You had my heart inside your hand 你俘虏了我的芳心 (You're gonna wish you never had met me) （你会祈祷要是从未遇见我该有多好）And you played it to the beat 但是你玩弄它伴着每一次心跳 (Tears are gonna fall, rolling in the deep) （眼泪快要掉下来，内心深处爱恨交织）Baby, I have no story to be told 宝贝我没有故事可讲

《Rolling,in,The,Deep》中文歌词

《Rolling，in，The，Deep》中文歌词 There'safirestartinginmyheart 我怒火中烧 Reachingafeverpitchandit'sbringingmeoutthedark 熊熊烈焰带我走出黑暗 Finally,Icanseeyoucrystalclear 最终我将你看得一清二楚 GoaheadandsellmeoutandI'lllayyourshipbare 去吧出卖我我会让你一无所有 SeehowI'llleavewitheverypieceofyou 看我怎么离你而去带走你的一切 Don'tunderestimatethethingsthatIwilldo 不要低估我将来的所作所为 There'safirestartinginmyheart

我怒火中烧 Reachingafeverpitchandit'sbringmeoutthedark 熊熊烈焰带我走出黑暗 Thescarsofyourloveremindmeofus 你的爱情伤痕让我想起了我们曾经的甜蜜 Theykeepmethinkingthatwealmosthaditall 它们总在提醒我我们几乎拥有了一切 Thescarsofyourlove,theyleavemebreathless 你的爱情伤痕让我窒息 Ican'thelpfeeling 我不禁心生感触 Wecouldhavehaditall 我们本该拥有一切 (You'regonnawishyouneverhadmetme) (你会祈祷要是从未遇见我该有多好)

Rollinginthedeep 内心深处爱恨交织 (Tearsaregonnafall,rollinginthedeep) (眼泪快要掉下来，内心深处爱恨交织) Youhadmyheartinsideyourhand 你俘虏了我的芳心 (You'regonnawishyouneverhadmetme) (你会祈祷要是从未遇见我该有多好) Andyouplayedittothebeat 但是你玩弄它伴着每一次心跳 (Tearsaregonnafall,rollinginthedeep) (眼泪快要掉下来，内心深处爱恨交织) Baby,Ihavenostorytobetold 宝贝我没有故事可讲 ButI'veheardoneonyouandI'mgonnamakeyourheadburn

Roll in the deep

Roll in the deep There's a fire starting in my heart 我怒火中烧 Reaching a fever pitch and it's bringing me out the dark 熊熊烈焰带我走出黑暗 Finally, I can see you crystal clear 最终我将你看得一清二楚 Go ahead and sell me out and I'll lay your ship bare 去吧出卖我我会让你一无所有 See how I'll leave with every piece of you 看我怎么离你而去带走你的一切Don't underestimate the things that I will do 不要低估我将来的所作所为 There's a fire starting in my heart 我怒火中烧 Reaching a fever pitch and it's bring me out the dark 熊熊烈焰带我走出黑暗 The scars of your love remind me of us 你的爱情伤痕让我想起了我们曾经的甜蜜 They keep me thinking that we almost had it all 它们总在提醒我我们几乎拥有了一切 The scars of your love, they leave me breathless 你的爱情伤痕让我窒息 I can't help feeling 我不禁心生感触 We could have had it all 我们本该拥有一切 (You're gonna wish you never had met me) （你会祈祷要是从未遇见我该有多好） Rolling in the deep 内心深处爱恨交织 (Tears are gonna fall, rolling in the deep) （眼泪快要掉下来，内心深处爱恨交织） You had my heart inside your hand 你俘虏了我的芳心 (You're gonna wish you never had met me) （你会祈祷要是从未遇见我该有多好） And you played it to the beat 但是你玩弄它伴着每一次心跳 (Tears are gonna fall, rolling in the deep) （眼泪快要掉下来，内心深处爱恨交织） Baby, I have no story to be told 宝贝我没有故事可讲 But I've heard one on you and I'm gonna make your head burn 但是我听说了一件有关你的事情我会让你焦头烂额 Think of me in the depths of your despair 在绝望的深渊中想起我

Roling in the deep

Roling in the deep -Adele 歌词及翻译 Rolling In the Deep -- Adele 滑向深处 There's a fire starting in my heart, 我心中燃起了火焰 Reaching a fever pitch and it's bringing me out the dark 那温度驱走了黑暗 Finally, I can see you crystal clear. 我终于看得清你 Go ahead and sell me out and I'll lay your ship bare. 放弃自己的全部赤裸的留在你的心中 See how I leave, with every piece of you 我会一片一片把你剥离我的记忆 Don't underestimate the things that I will do. 不要以为我真的不会这么做 There's a fire starting in my heart, 心中燃起了火焰 Reaching a fever pitch and it's bringing me out the dark 那温度驱走了黑暗 The scars of your love, remind me of us. 害怕爱你让我更清晰的了解你我 They keep me thinking that we almost had it all 让我觉得总是有一步之遥 The scars of your love, they leave me breath less 害怕爱你让我无法呼吸 I can't help feeling... 我无法阻止自己的思绪 We could have had it all... (you're gonna wish you, never had met me)... 我们本应幸福（你会祈祷你从未遇见我） Rolling in the Deep (Tears are gonna fall, rolling in the deep) 在内心的深处辗转（流下的泪水在心中反侧） Your had my heart... (you're gonna wish you)... Inside of your hand (Never had met me) 你拥有我的心（你会希望）在你的手掌上（从未遇见我） And you played it... (Tears are gonna fall)... To the beat (Rolling in the deep) 你却没有珍惜（泪水滑下）没有留恋（滑向内心深处） Baby I have no story to be told,

ROLLING IN THE DEEP吉他谱

ROLLING IN THE DEEP by, Adele CAPO 3 Am(Palm Mute) / / / / / / / / / / / / / / / / Am E There's a fire starting in my heart, G E G Reaching a fever pitch and it's bringing me out the dark Am E Finally, I can see you crystal clear. G E G Go ahead and sell me out and I'll lay your ship bare. Am E See how I leave, with every piece of you G E G Don't underestimate the things that I will do. Am E There's a fire starting in my heart, G E G Reaching a fever pitch and it's bringing me out the dark F G The scars of your love, remind me of us. Em F They keep me thinking that we almost had it all F G The scars of your love, they leave me breathless Em E I can't help feeling... E Am G We could have had it all... (I wish you, never had met me)... F(hold) G Rolling in the Deep (Tears are gonna fall, rolling in the deep) Am G Your had my heart... (I wish you)... Inside of your hand (Never had met me) F(hold) G

rollinginthedeep的歌词

rollinginthedeep的歌词There's a fire starting in my heart 胸中燃起怒火 Reaching a fever pitch and it's bringing me out the dark 狂热救赎我于黑暗 Finally, I can see you crystal clear 终于看清本性 Go ahead and sell me out and I'll lay your sheet bare. 继续背叛而我亦将不再留恋 See how I leave, with every piece of you 看我如何将你撕碎 Don't underestimate the things that I will do 请别低估我的能耐 There's a fire starting in my heart 我胸中升起的怒火 Reaching a fever pitch and it's bringing me out the dark 熊熊燃烧驱走黑暗 The scars of your love, remind me of us 爱之伤疤疼痛于心 They keep me thinking that we almost had it all 让我回想曾经的拥有 The scars of your love, they leave me breathless 爱之伤疤令人窒息 I can't help feeling 思绪万千不能自已 We could have had it all 我们本应幸福 Rolling in the deep 如今却在深渊中翻滚 You had my heart inside of your hands 你将我的心捏在手里 And you played it to the beat 玩弄于股掌之间

rolling in the deep 歌词 中英对照

Rolling In the Deep – Adele There's a fire starting in my heart, 我心中燃起了火焰 Reaching a fever pitch and it's bringing me out the dark 达到狂热的程度，将我带出了黑暗。 Finally, I can see you crystal clear. 最后，我终于看清了你。 Go ahead and sell me out and I'll lay your ship bare. (你)出卖了我，离开我。而我也将彻底把你忘记。 See how I leave, with every piece of you 看我会如何离开你的点点滴滴 Don't underestimate the things that I will do. 不要看轻我将要做的事情。 There's a fire starting in my heart, 心中燃起了火焰 Reaching a fever pitch and it's bringing me out the dark 那温度驱走了黑暗 The scars of your love remind me of us. 你的爱留下的伤痕，提醒着我我们的曾经 They keep me thinking that we almost had it all 它一直让我认为我们几乎拥有了那一切幸福。 The scars of your love, they leave me breathless 你的爱留下的伤痕，让我无法呼吸 I can't help feeling... 我无法阻止我的感觉 We could have had it all... 我们本应幸福的 Rolling in the Deep 思绪翻滚 Your had my heart Inside of your hand 曾经我的心放在你的手心， And you played it. To the beat 你玩弄它，让它伤痕累累。 Baby I have no story to be told, 宝贝，我没有什么故事要说 But I've heard one of you and I'm gonna make your head burn. 可我听到一个你的故事——我将让你的头脑崩溃 Think of me in the depths of your despair. 在绝望的深处想着我

英文歌曲中英对照Rolling in the Deep 在灵魂深处翻滚

Rolling in the Deep 在灵魂深处翻滚 There's a fire starting in my heart. Reaching a fever pitch it's bringing me out the dark 一团火焰在我心中熊熊燃烧，狂热的温度带我走出黑暗 Finally I can see you crystal clear. Go head and sell me out and I'll lay your shit bare 我终于看透你了，继续出卖我吧，小心我揭你老底 See how I'll leave with every piece of you. Don't underestimate the things that I will do 等着瞧我离去后让你体无完肤，别低估我将来的所作所为 There's a fire starting in my heart. Reaching a fever pitch and it's bring me out the dark 一团火焰在我心中熊熊燃烧，狂热的温度让我远离黑暗 The scars of your love remind me of us. They keep me thinking that we almost had it all 你爱情的伤疤让我回忆起了你我的当初，让我想起我们几乎可以拥有一切 The scars of your love they leave me breathless. I can't help feeling we could have had it all.Rolling in the deep 你爱情的伤疤让我无法呼吸，让我不禁心生感触，我们本来可以拥有一切，内心深处爱恨交织 You had my heart inside of your hand and you played it to the beat 你把我的真心拿在手上，你百般玩弄，我无法忍受 Baby I have no story to be told. But I've heard one of you and I'm gonna make your head burn 我已无话可说，但我听说你倒有一个，我要让你焦头烂额 Think of me in the depths of your despair. Making a home down there as mine sure won't be shared 让你想起我，当你深陷绝望时，在那建立自己的家园与世隔绝 The scars of your love remind me of us. They keep me thinking that we almost had it all 你爱情的伤疤让我回忆起了当初，它一直提醒着我我们曾几乎拥有一切 The scars of your love they leave me breathless. I can't help feeling we could have had it all.Rolling in the deep 你爱情的伤疤让我无法呼吸，让我不禁感到我们本来可以拥有一切，内心深处爱恨交织You had my heart inside of your hand and you played it to the beat 你把我的真心拿在手上，你百般玩弄，令我心碎 We could have had it all. Rolling in the deep 我们本来可以拥有一切，泪水只能流淌在心底 You had my heart inside of your hand but you played it with the beat 你把我的真心拿在手上，但你百般玩弄，伴随着每次心跳

rollinginthedeep歌词

Roll the Dice（掷骰子) Sometimes you wonder 有时候你会期望 what if you could rewrite the moment 如果重新来过会怎么样 Sometimes you figure out 有时候去发现其实 there's another luck in imperfection 不完美才是完美的真相 Sometimes you've been hurt 有时候难免要受伤 then you learn to think about and feel more 却收获了感悟的力量 Sometimes you've been bored 有时候你也厌倦了 with the life you hate 生活本来的模样 always be amazed 要一直好奇啊 always take a risk 要不断冒险啊 always keep the pace in a lifetime game 要在生活这场游戏里前进的自如漂亮 1,2,3,4,5,6, life is rolling the dice,babe 人生的骰子不停地转啊 you can not imagine what would happen in a second 谁能猜得透下一秒是哪一面朝上 1,2,3,4,5,6 life is rolling the dice,babe 人生的骰子不停地转啊 while you're lost in the dark,close your eyes, 迷失在黑暗里就把眼睛闭上 you'll find the lights shine in the other side 我们总会发现彼岸之光 （重复） Sometimes you wonder 有时候你会期望 what if you could rewrite the moment 如果重新来过会怎么样 Sometimes you figure out 有时候去发现其实 there's another luck in imperfection 不完美才是完美的真相

Rolling in the deep翻译

Rolling in the deep 爱情漩涡 There's a fire starting in my heart 心，躁动，如火Reaching a fever pitch and it's bringing me out the dark 让我狂，黑暗远去Finally, I can see you crystal clear 终于我看清Go ahead and sell me out and I'll lay your ship bare 你的背叛，就让它继续吧 我有我的做法，你将一无所有See how I'll leave with every piece of you 看我离你而去，不必挽留Don't underestimate the things that I will do 我有我的做法，永远不要低估There's a fire starting in my heart 我心如火Reaching a fever pitch and it's bring me out the dark 让我狂，逃离黑暗The scars of your love remind me of us 你给我的爱满是伤痕，不禁想起They keep me thinking that we almost had it all 一切都只是即将拥有The scars of your love, they leave me breathless 你给我的爱满是伤痕，不忍呼吸 I can't help feeling 不禁感触We could have had it all 我们本该拥有Rolling in the deep 爱情漩涡将我困住You had my heart inside your hand 我心已为你所俘And you played it to the beat 丢掉的珍惜，反被玩弄 一次，又一次…Baby, I have no story to be told Baby，我没有故事But I've heard one on you and I'm gonna make your head burn 你的故事， 我有听过，你的意志，由我掌握Think of me in the depths of your despair 绝望中忆起Making a home down there as mine sure won't be shared 我给的迁就，这次不会再有 The scars of your love remind me of us 你给我的爱满是伤痕，不禁想起They keep me thinking that we almost had it all 一切都只是即将拥有The scars of your love, they leave me breathless 你给我的爱满是伤痕，不忍呼吸 I can't help feeling 不禁感触We could have had it all 我们本该拥有Rolling in the deep 深深无奈，苦苦纠结You had my heart inside your hand 我的心已为你所俘And you played it to the beat 丢掉的珍惜，反被玩弄 一次，又一次…We could have had it all 我们本该拥有Rolling in the deep 深深无奈，苦苦纠结You had my heart inside your hand 我的心已为你所俘But you played it with a beating 丢掉的珍惜，反被玩弄 一次，又一次…Throw your soul through every open door 抛弃灵魂

Rolling In The Deep(中英文对照歌词)

Adele(歌手) 中英文对照歌词 声明;翻译参照网上,仅供学习交流，任何用于商业目的的行为，触犯原作者版权的，与本人无关！ 可用歌词制作工具直接制作双语歌词 歌词正文： Rolling In The Deep 爱恨交织 There's a fire starting in my heart 我满腔怒火 Reaching a fever pitch and it's bring me out of the dark 熊熊燃烧的烈火带我远离黑暗 Finally I can see you crystal clear 终于我看透了你 Go ahead and sell me out and I'll lay your ship bare 来吧背叛我吧我会令你一无所有 See how I'll leave with every piece of you 看我如何带走你所有的一切 Don't underestimate The things that I will do 千万不要低估我的能耐 There's a fire starting in my heart 我满腔怒火 Reaching a fever pitch and it's bring me out of the dark 熊熊燃烧的烈火带我远离黑暗 The scars of your love remind me of us 你的爱情疤痕让我想起我们 They keep me thinking that we almost had it all 往事历历在目我们似乎拥有一切 The scars of your love,they leave me breashless 你的爱情疤痕让我无法呼吸

rollinginthedeep的歌词

遗憾- 许美静 别再说是谁的错 让一切成灰 除非放下心中的负累一切难以挽回 你总爱让往事跟随 怕过去白费 你总以为要体会人生就要多爱几回 与其让你在我怀中枯萎宁愿你犯错后悔 让你飞向梦中的世界留我独自伤悲 与其让你在我爱中憔悴宁愿你受伤流泪 莫非要你尝尽了苦悲才懂真情可贵 别再说是谁的错 让一切成灰 除非放下心中的负累一切难以挽回 你总爱让往事跟随 怕过去白费 你总以为要体会人生就要多爱几回 与其让你在我怀中枯萎宁愿你犯错后悔 让你飞向梦中的世界留我独自伤悲 与其让你在我爱中憔悴宁愿你受伤流泪 莫非要你尝尽了苦悲才懂真情可贵 与其让你在我怀中枯萎宁愿你犯错后悔 让你飞向梦中的世界留我独自伤悲 与其让你在我爱中憔悴宁愿你受伤流泪 莫非要你尝尽了苦悲

才懂真情可贵 莫非要你尝尽了苦悲 才懂真情可贵 才懂真情可贵 Apologize歌词 歌手：Timbaland 歌曲：Apologize I'm holding on your rope 我紧紧握住你给的希望 Got me ten feet off the ground 它让我双脚悬空 I'm hearing what you say but I just can't make a sound 听懂了你的言意我却只能绝望沉默 You tell me that you need me 爱我要我曾是你山盟海誓 Then you go and cut me down, but wait 伤心于你的离去我却只能空虚等待 You tell me that you're sorry 不说你的歉意是那么苍白无力 Didn't think I'd turn around, and say... 可你不会想到我要重新向你致意 It's too late to apologize, it's too late 你说的对不起已是太迟，真的太迟 I said it's too late to apologize, it's too late 我说过现在已是太迟，真的太迟 I'd take another chance, take a fall 我想我还会努力，宁愿再次被你伤害 Take a shot for you 也再给你一次让我接受你的机会 And I need you like a heart needs a beat 我需要你就像我的心要跳动得一次又一次 But it's nothing new