Condition Monitoring with Vibration Signals, First by Asoke Nandi, Hosameldin Ahmed

Condition Monitoring with Vibration Signals

Compressive Sampling and Learning Algorithms for Rotating Machines

Hosameldin Ahmed and Asoke K. Nandi

Brunel University London
UK

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Preface

As an essential element of most engineering processes in many critical functions of industries, rotating machine condition monitoring is a key technique for ensuring the efficiency and quality of any product. Machine condition monitoring is a process of monitoring machine health conditions. It is incorporated into various sensitive applications of rotating machines, e.g. wind turbines, oil and gas, aerospace and defence, automotive, marine, etc. The increased level of complexity of modern rotating machines requires more effective and efficient condition monitoring techniques. For that reason, a growing body of literature has resulted from research and development efforts by many research groups around the world. These publications have made a direct impact on current and future developments in machine condition monitoring. However, there is no collection of works, including previous and recently developed methods, devoted to the field of condition monitoring for rotating machines using vibration signals. As this field is still developing, such a book cannot be definitive or complete. But this book attempts to bring together many techniques in one place, and outlines the complete guide from the basics of rotating machines to the generation of knowledge using vibration signals. It provides an introduction to rotating machines and the vibration signals produced from them at a level that can be easily understood by readers such as postgraduate students, researchers, and practicing engineers. The introduction introduces those readers to the basic knowledge needed to appreciate the specific applications of the methods in this book.

Based on the stages of the machine condition monitoring framework, and with the aim of designing effective techniques for detecting and classifying faults in rotating machines, a major part of the book covers various feature‐extraction, feature‐selection, and feature‐classification methods as well as their applications to machine vibration datasets. Moreover, this book presents the latest methods, including machine learning and compressive sampling. These offer significant improvements in accuracy with reduced computational costs. It is important for these to be made available to all researchers as well as practitioners and new people coming into this field, to help improve safety, reliability, and performance. Although this is not intended to be a textbook, examples and case studies using vibration data are given throughout the book to show the use and application of the included methods in monitoring the condition of rotating machines.

The layout of the book is as follows:

Chapter 1 offers an introduction to machine condition monitoring and its application in condition‐based maintenance. The chapter explains the importance of machine condition monitoring and its use in various rotating machine applications, machine maintenance approaches, and machine condition monitoring techniques that can be used to identify machine health conditions.

Chapter 2 is concerned with the principles of rotating machine vibration and acquisition techniques. The first part of this chapter is a presentation of the basics of vibration, vibration signals produced by rotating machines, and types of vibration signals. The second part is concerned with vibration data acquisition techniques and highlights the advantages and limitations of vibration signals.

Chapter 3 introduces signal processing in the time domain by giving an explanation of mathematical and statistical functions and other advanced techniques that can be used to extract basic signal information from time‐indexed raw vibration signals that can sufficiently represent machine health conditions.

Chapter 4 presents signal processing in the frequency domain, which has the ability to extract information based on frequency characteristics that are not easy to observe in the time domain. The first part describes the Fourier transform, the most commonly used signal‐transformation technique, which allows one to transform the time domain signal to the frequency domain. In addition, this chapter gives an explanation of different techniques that can be used to extract various frequency spectrum features that can more efficiently represent machine health conditions.

Chapter 5 introduces signal processing in the time‐frequency domain and gives an explanation of several techniques that can be used to examine time‐frequency characteristics of time‐indexed series signals, which can be figured more effectively than the Fourier transform and its corresponding frequency spectrum features.

Chapter 6 is concerned with vibration‐based machine condition monitoring using machine learning algorithms. The first part of this chapter gives an overview of the vibration‐based machine condition monitoring process, and describes fault detection, the problem diagnosis framework, and types of learning that can be applied to vibration data. The second part defines the main problems of learning from vibration data for the purpose of fault diagnosis and describes techniques to prepare vibration data for analysis to overcome the aforementioned problems.

Chapter 7 presents common, appropriate methods for linear subspace learning that can be used to reduce a large amount of collected vibration data to a few dimensions without significant loss of information.

Chapter 8 introduces common, suitable methods for nonlinear subspace learning that can be used to reduce a large amount of collected vibration data to a reduced amount without loss of information.

Chapter 9 introduces generally applicable methods that can be used to select the most important features that can effectively represent the original features. Also, it provides an explanation of feature ranking and feature subset selection techniques.

Chapter 10 is concerned with the basic theory of the diagnosis tool decision tree, its data structure, the ensemble model that combines decision trees into a decision forest model, and their applications in diagnosing machine faults.

Chapter 11 is devoted to a description of two probabilistic models for classification: (i) the hidden Markov model (HMM) as a probabilistic generative model, and (ii) the logistic regression model and generalised logistic regression model, also called multinomial logistic regression or multiple logistic regression, as probabilistic discriminative models, and their applications in diagnosing machine faults.

Chapter 12 begins with a discussion of the basic principles of the learning method known as artificial neural networks (ANNs). Then, the chapter describes three different types of ANNs (i.e. multi‐layer perceptron, radial basis function network, and Kohonen network), which can be used for fault classification. In addition, the applications of these methods in diagnosing machine faults are described.

Chapter 13 presents the support vector machine (SVM) classifier, by giving a brief description of the basic idea of the SVM model for binary classification problems. Then, the chapter explains the multiclass SVM approach and the different techniques that can be used for multiclass SVMs. Examples of their applications in diagnosing machine faults are provided.

Chapter 14 describes recent trends of deep learning in the field of machine condition monitoring and provides an explanation of commonly used techniques and examples of their applications in diagnosing machine faults.

Chapter 15 provides an overview of the efficacy of the classification algorithms introduced in this book. This chapter describes different validation techniques that can be used to validate the efficacy of classification algorithms in terms of classification results.

Chapter 16 presents new feature‐learning frameworks based on compressive sampling and subspace learning techniques for machine condition monitoring. The chapter starts with a concise exposition of the basic theory of compressive sampling and shows how to perform compressive sampling for sparse frequency representations and sparse time‐frequency representations. Then, the chapter presents an overview of compressive sampling in machine condition monitoring. The second part of the chapter describes three frameworks based on compressive sampling and presents different method implementation based on these frameworks. In the third part, two case studies and applications of these methods to different classes of machine health conditions are considered.

Chapter 17 presents an original framework combining compressive sampling and a deep neural network based on a sparse autoencoder. Overcomplete features with a different number of hidden layers in the deep neural network are considered in the application of this method to different classes of machine health conditions, using the same two case studies as Chapter 16.

Chapter 18 provides conclusions and recommendations for the application of the different methods studied in this book. These will benefit practitioners and researchers involved in the field of vibration‐based machine condition monitoring.

This book is up‐to‐date and covers many techniques used for machine condition monitoring, including recently developed methods. In addition, this book will provide new methods, including machine learning and compressive sampling, which cover various topics of current research interest. Additional to the material provided in the book, publicly accessible software for most of the introduced techniques in this book and links to publicly available vibration datasets are provided in the appendix.

A work of this magnitude will unfortunately contain errors and omissions. We would like to take this opportunity to apologise unreservedly for all such indiscretions in advance. We would welcome comments and corrections; please send them by email to a.k.nandi@ieee.org or by any other means.

February 2019

Hosameldin Ahmed and Asoke K. Nandi

London, UK

About the Authors

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Hosameldin Ahmed received the degree of B.Sc. (Hons.) in Engineering Technology, specialisation in Electronic Engineering, from the Faculty of Science and Technology University of Gezira, Sudan, in 1999 and M.Sc. degree in Computer Engineering and Networks from the University of Gezira, Sudan, in 2010. He has recently received the Ph.D. degree in Electronic and Computer Engineering at Brunel University London, UK. Since 2014, he has been working with his supervisor, Professor Asoke. K. Nandi, in the area of machine condition monitoring. Their collaboration has made several contributions to the advancement of vibration based machine condition monitoring using compressive sampling and modern machine learning algorithms. His work has been published in high‐quality journals and international conferences. His research interests lie in the areas of signal processing, compressive sampling, and machine learning with application to vibration‐based machine condition monitoring.

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Asoke K. Nandi received the degree of Ph.D. in Physics from the University of Cambridge (Trinity College), Cambridge, UK. He has held academic positions in several universities, including Oxford, Imperial College London, Strathclyde, and Liverpool as well as the Finland Distinguished Professorship in Jyvaskyla (Finland). In 2013, he moved to Brunel University London, to become the Chair and Head of Electronic and Computer Engineering. Professor Nandi is a Distinguished Visiting Professor at Tongji University (China) and an Adjunct Professor at the University of Calgary (Canada).

In 1983, Professor Nandi jointly discovered the three fundamental particles known as W+, W, and Z0, providing the evidence for the unification of the electromagnetic and weak forces, for which the Nobel Committee for Physics in 1984 awarded the prize to his two team leaders for their decisive contributions. His current research interests lie in the areas of signal processing and machine learning, with applications to communications, gene expression data, functional magnetic resonance data, machine condition monitoring, and biomedical data. He has made many fundamental theoretical and algorithmic contributions to many aspects of signal processing and machine learning. He has much expertise in ‘Big Data’, dealing with heterogeneous data, and extracting information from multiple datasets obtained in different laboratories and at different times. Professor Nandi has authored over 590 technical publications, including 240 journal papers, as well as 4 books: Automatic Modulation Classification: Principles, Algorithms and Applications (Wiley, 2015), Integrative Cluster Analysis in Bioinformatics (Wiley, 2015), Blind Estimation Using Higher‐Order Statistics (Springer, 1999), and Automatic Modulation Recognition of Communications Signals (Springer, 1996). The h‐index of his publications is 73 (Google Scholar) and the ERDOS number is 2.

Professor Nandi is a Fellow of the Royal Academy of Engineering (UK) and of seven other institutions. Among the many awards he has received are the Institute of Electrical and Electronics Engineers (USA) Heinrich Hertz Award in 2012; the Glory of Bengal Award for his outstanding achievements in scientific research in 2010; award from the Society for Machinery Failure Prevention Technology, a division of the Vibration Institute (USA) in 2000; the Water Arbitration Prize of the Institution of Mechanical Engineers (UK) in 1999; and the Mountbatten Premium of the Institution of Electrical Engineers (UK) in 1998. Professor Nandi is an IEEE Distinguished Lecturer (2018–2019).

List of Abbreviations

AANNAuto‐associative neural network
ACOAnt colony optimisation
ADCAnalog to digital converter
AEAcoustic emission
AFSAArtificial fish swarm algorithm
AIArtificial intelligence
AICAkaike's information criterion
AIDAutomatic interaction detector
AMAmplitude modulation
ANCAdaptive noise cancellation
ANFISAdaptive neuro‐fuzzy inference system
ANNArtificial neural network
ANNCAdaptive nearest neighbour classifier
ARAutoregressive
ARIMAAutoregressive integrated moving average
ARMAAutoregressive moving average
ART2Adaptive resonance theory‐2
AUCArea under a ROC curve
BFDFBearing fundamental defect frequency
BPFIBearing pass frequency of inner race
BPFOBearing pass frequency of outer race
BPNNBackpropagation neural network
BSBinary search
BSFBall spin frequency
BSSBlind source separation
CAEContractive autoencoder
CARTClassification and regression tree
CBLSTMConvolutional bi‐directional long short‐term memory
CBMCondition‐based maintenance
CBRCase‐based reasoning
CCACanonical correlation analysis
CDFCharacteristics defect frequency
CFCrest factor
CFTContinuous Fourier transform
CHAIDChi‐square automatic integration detector
Chi‐2Chi‐squared
cICAConstraint‐independent component analysis
CLFClearance factor
CMCondition monitoring
CMFCombined mode function
CMFEComposite multiscale fuzzy entropy
CNNConvolutional neural network
CoSaMPCompressive sampling matching pursuit
CS‐Chi‐2Compressive sampling and Chi‐square feature selection algorithm
CS‐CMDSCompressive sampling and classical multidimensional scaling
CS‐CPDCCompressive sampling and correlated principal and discriminant components
CS‐FRCompressive sampling and feature ranking
CS‐FSCompressive sampling and Fisher score
CS‐GSNCompressive sampling and GMST, SPE, and neighbourhood component analysis
CS‐KLDACompressive sampling and kernel linear discriminant analysis algorithm
CS‐KPCACompressive sampling and kernel principal component analysis method
CS‐LDACompressive sampling and linear discriminant analysis method
CS‐LSCompressive sampling and Laplacian score
CS‐LSLCompressive sampling and linear subspace learning
CS‐NLSLCompressive sampling and nonlinear subspace learning
CS‐PCACompressive sampling and principal component analysis
CS‐PCCCompressive sampling and Pearson correlation coefficients
CS‐Relief‐FCompressive sampling and Relief‐F algorithm
CS‐SAE‐DNNCompressive sampling and sparse autoencoder‐based deep neural network
CS‐SPECompressive sampling and stochastic proximity embedding
CVMCross‐validation method
CWTContinuous wavelet transform
DAGDirect acyclic graph
DBNDeep belief network
DDMADiscrete diffusion maps analysis
DFADetrended‐fluctuation analysis
DFTDiscrete Fourier transform
DIFSDifference signal
DMDiffusion map
DNNDeep neural network
DPCADynamic principal component analysis
DRFFDeep random forest fusion
DTDecision tree
DTCWPTDual‐tree complex wavelet packet transform
DWTDiscrete wavelet transform
EBPError backpropagation
EDAEEnsemble deep autoencoder
EEMDEnsemble empirical mode decomposition
ELMExtreme learning machine
ELUExponential linear unit
EMAExponential moving average
EMDEmpirical mode decomposition
ENTEntropy
EPGSElectrical power generation and storage
EPSOEnhanced particle swarm optimisation
ESVMEnsemble support vector machine
FC‐WTAFully connected winner‐take‐all autoencoder
FDAFisher discriminant analysis
FDKFrequency domain kurtosis
FFNNFeedforward neural network
FFTFast Fourier transform
FHMMFactorial hidden Markov model
FIRFinite impulse response
FKNNFuzzy k‐nearest neighbour
FMFrequency modulation
FMMFuzzy min‐max
FRFeature ranking
FsSampling frequency
FSFisher score
FSVMFuzzy support vector machine
FTFFundamental train frequency
GAGenetic algorithm
GMMGaussian mixture model
GMSTGeodesic minimal spanning tree
GPGenetic programming
GRGain ratio
GRUGated recurrent unit
HEHierarchical entropy
HFDHigher‐frequency domain
HHTHilbert‐Huang transform
HISTHistogram
HLLEHessian‐based local linear embedding
HMMHidden Markov model
HOCHigher‐order cumulant
HOMHigher‐order moment
HOSHigher‐order statistics
HTHilbert transform
ICAIndependent component analysis
ICDSVMInter‐cluster distance support vector machine
ID3Iterative Dichotomiser 3
I‐ESLLEIncremental enhanced supervised locally linear embedding
IFImpulse factor
IGInformation gain
IGAImmune genetic algorithm
IIRInfinite impulse response
IMFIntrinsic mode function
IMFEImproved multiscale fuzzy entropy
IMPEImproved multiscale permutation entropy
ISBMImproved slope‐based method
ISOMAPIsometric feature mapping
KAKernel Adatron
KCCAKernel canonical correlation analysis
KFCMKernel fuzzy c‐means
KICAKernel independent component analysis
K‐LKullback–Leibler divergence
KLDAKernel linear discriminant analysis
KNNKohonen neural network
k‐NNk‐nearest neighbours
KPCAKernel principal component analysis
KURTKurtosis
LBLower bound
LCNLocal connection network
LDALinear discriminant analysis
LELaplacian eigenmap
LhLikelihood
LLELocal linear embedding
LMDLocal mean decomposition
LOOCVLeave‐one‐out cross‐validation
LPPLocality preserving projection
LRLogistic regression
LRCLogistic regression classifier
LSLaplacian score
LSLLinear subspace learning
LSSVMLeast‐square support vector machine
LTSALocal tangent space alignment
LTSMLong short‐term memory
MAMoving average
MCCVMonte Carlo cross‐validation
MCEMinimum classification error
MCMMachine condition monitoring
MDSMultidimensional scaling
MEDMinimum entropy deconvolution
MEISVMMultivariable ensemble‐based incremental support vector machine
MFMargin factor
MFBModulated filter‐bank structure
MFDMulti‐scale fractal dimension
MFEMulti‐scale fuzzy entropy
MHDMultilayer hybrid denoising
MIMutual information
MLPMultilayer perceptron
MLRMultinomial logistic regression
MLRCMultinomial logistic regression classifier
MMVMultiple measurement vectors
MRAMultiresolution analysis
MRFMarkov random field
MSEMultiscale entropy
MSEMean square error
MVUMaximum variance unfolding
NCANeighbourhood component analysis
NILESNonlinear estimation by iterative least square
NIPALSNonlinear iterative partial least squares
NLSLNonlinear subspace learning
NNNeural network
NnlNormal negative log‐likelihood
NNRNearest neighbour rule
NSAENormalised sparse autoencoder
NRSNeighbourhood rough set
O&MOperation and maintenance
OLSOrdinary least squares
OMPOrthogonal matching pursuit
ONPEOrthogonal preserving embedding
ORDWTOvercomplete rational dilation discrete wavelet transform
ORTOrthogonal criterion
OSFCMOptimal supervised fuzzy C‐means clustering
OSLLTSAOrthogonal supervised local tangent space alignment analysis
PCAPrincipal component analysis
PCCPearson correlation coefficient
PCHIPiecewise cubic Hermite interpolation
PDFProbability density function
PFProduct function
PHMPrognostic and health management
PLSPartial least squares
PLS‐PMPartial least squares path modelling
PLS‐RPartial least squares regression
PNNProbabilistic neural network
p–pPeak to peak
PReLUParametric rectified linear unit
PSOParticle swarm optimisation
PSVMProximal support vector machine
PWVDPseudo Wigner‐Ville distribution
QPQuadratic programming
QPSP‐LSSVMQuantum behaved particle optimisation‐least square support vector machine
RBFRadial basis function
RBMRestricted Boltzmann machine
RCMFERefined composite multi‐scale fuzzy entropy
ReLURectified linear unit
RESResidual signal
RFRandom forest
RFERecursive feature elimination
RIPRestricted isometry property
RLReinforcement learning
RMSRoot mean square
RMSERoot mean square error
RNNRecurrent neural network
ROCReceiver operating characteristic
RPMRevolutions per minute
RSARescaled range analysis
RSGWPTRedundant second‐generation wavelet packet transform
RULRemaining useful life
RVMRelevance vector machine
SAESparse autoencoder
S‐ANCSelf‐adaptive noise cancellation
SBFSSequential backward floating selection
SBSSequential backward selection
SCADASupervisory control and data acquisition system
SCGScale conjugate gradient
SDAStacked denoising autoencoder
SDESemidefinite embedding
SDOFSingle degree of freedom
SDPSemidefinite programming
SELTSASupervised extended local tangent space alignment
SFShape factor
SFFSSequential forward floating selection
SFSSequential forward selection
SGWDSecond generation wavelet denoising
SIDLShift‐invariant dictionary learning
SILTSASupervised incremental local tangent space alignment
SKSkewness
SKSpectral kurtosis
S‐LLEStatistical local linear embedding
SLLTASupervised learning local tangent space alignment
SMSammon mapping
SMOSequential minimal optimisation
SMVSingle measurement vector
SNRSignal‐to‐noise ratio
SOMSelf‐organising map
SPSubspace pursuit
SpaEIADSparse extraction of impulse by adaptive dictionary
SPEStochastic proximity embedding
SPWVDSmoothed pseudo Wigner‐Ville distribution
SSCSlope sign change
STDStandard deviation
STEStandard error
STFTShort‐time Fourier transform
STGSSteam turbine‐generators
StOMPStagewise orthogonal matching pursuit
SU‐LSTMStacked unidirectional long short‐term memory
SVDSingular value decomposition
SVDDSupport vector domain description
SVMSupport vector machine
SVRSupport vector regression
SWSVMShannon wavelet support vector machine
TAWSTime average wavelet spectrum
TBMTime‐based maintenance
TDIDTTop‐down induction on decision trees
TEOTeager energy operator
TSATime synchronous average
UBUpper bound
VKFVold‐Kalman filter
VMDVariational mode decomposition
VPMCDVariable predictive model‐based class discrimination
VRVariance
WAWillison amplitude
WDWigner distribution
WFEWaveform entropy
WKLFDAWavelet kernel function and local Fisher discriminant analysis
WLWavelength
WPAWavelet packet analysis
WPEWavelet packet energy
WPTWavelet packet transform
WSNWireless sensor network
WSVMWave support vector machine
WTWavelet transform
WTDWavelet thresholding denoising
WVDWigner‐Ville distribution
ZCZero crossing

Part I
Introduction