Fault Diagnosis and Prognostics Based on Cognitive Computing and Geometric Space Transformation

Preface
Acknowledgments
Contents
Chapter 1: Introduction
	1.1 Overview of Fault Diagnosis and Prognosis Technology
		1.1.1 Background
		1.1.2 Basic Concepts
		1.1.3 Technological Progress
		1.1.4 Problems and Insights
	1.2 Overview of Cognitive Computing
		1.2.1 Cognitive Computing
		1.2.2 Deep Learning
		1.2.3 Visual Cognition
		1.2.4 Compressed Sensing
	1.3 Overview of Geometric Space Transformation and Morphology Recognition
		1.3.1 Differential Manifold Theory
		1.3.2 Geometric Space Transformation Techniques
		1.3.3 Geometrical Morphology Recognition
	1.4 Overview of the Book
	References
Chapter 2: Fault Diagnosis and Prognosis Based on Deep Learning and Transfer Learning
	2.1 Introduction
	2.2 Deep Learning
		2.2.1 Basic Ideas and Principles of Deep Learning
		2.2.2 Common Deep Learning Methods
		2.2.3 Application of Deep Learning
	2.3 Transfer Learning Technology
		2.3.1 Basic Ideas and Principles of Transfer Learning
		2.3.2 Classification of Transfer Learning Methods
		2.3.3 Applications of Transfer Learning
	2.4 Fault Diagnosis of Rotating Machinery Based on Deep Learning Classifier
		2.4.1 Feature Self-Learning
		2.4.2 Deep Learning Classification Technology Based on SAE
		2.4.3 Deep Learning Classification Technology Based on SDA
		2.4.4 Case Analysis
	2.5 Adaptive Fault Detection of Control System Based on Deep Learning Regressor
		2.5.1 Deep Learning Regression Technology Based on Model Averaging
		2.5.2 Adaptive Fault Detection of Control System Based on Model Average Deep Learning
		2.5.3 Case Analysis
	2.6 Health Assessment of Electromechanical Equipment Based on Deep Learning of Multilayer Feature Fusion
		2.6.1 Health Assessment Technology Based on Deep Learning of Multilayer Feature Fusion
		2.6.2 Case Analysis
	2.7 Fault Diagnosis of Similar Devices Based on Transfer Learning
		2.7.1 Shared Feature Learning Technology of Auxiliary Training Data and Target Training Data
		2.7.2 Research on the Fault Diagnosis Strategy Based on TrAdaBoost Sample Screening
		2.7.3 Fault Diagnosis of Similar Devices Based on Shared Feature Learning and TrAdaBoost
		2.7.4 Case Analysis
	2.8 Residual Life Prediction of Similar Devices Based on Transfer Learning
		2.8.1 Residual Life Prediction of Similar Engines Based on Transfer Learning
		2.8.2 Residual Life Prediction of Multi-Formula Lithium Battery Based on Transfer Learning
		2.8.3 Case Analysis
	2.9 Summary
	References
Chapter 3: Fault Diagnosis and Evaluation Based on Visual Cognitive Computing
	3.1 Introduction
	3.2 Basic Characteristics of Visual Cognition
		3.2.1 Visual Invariance
			3.2.1.1 Global Visual Invariant Features
			3.2.1.2 Local Visual Invariant Features
		3.2.2 Visual MSC
		3.2.3 Visual Multichannel Characteristics
	3.3 Equivalent Graphical Representation of Fault Signals
		3.3.1 Equivalent Graphical Representation Based on the Bispectrum
			3.3.1.1 Definition and Properties of the Bispectrum
			3.3.1.2 Bispectrum Estimation Based on the Non-parametric Method
			3.3.1.3 Bispectrum Analysis Based on Simulation Signals
				Simulation Analysis of Bispectrum Anti-Noise Performance
				Bispectrum Analysis Based on Bearing Simulation Signal
		3.3.2 Equivalent Graphical Representation Based on Recurrence Plots
			3.3.2.1 Construction Principle of Recurrence Plots
			3.3.2.2 Recurrence Plot Analysis Based on Simulated Signals
				Uniform Structure
				Periodic Structure
				Drift Structure
				Mutant Structure
		3.3.3 Equivalent Graphical Representation Based on Time Series Arrangement
	3.4 Fault Diagnosis Under Variable Working Conditions Based on Visual Invariance and MSC
		3.4.1 Scale-Invariant Feature Transform (SIFT)
			3.4.1.1 Construct a Scale Space
				Construct a Gaussian Pyramid
				Construct the DOG Pyramid
			3.4.1.2 Extreme Point Detection in Scale Space
			3.4.1.3 Precise Location of Key Points
			3.4.1.4 Orientation Assignment of Key Points
			3.4.1.5 Generation of Feature Point Descriptors
		3.4.2 Speeded Up Robust Feature (SURF)
			3.4.2.1 SURF Detection
				Integral Image
				Approximate Hessian Matrix
				Scale Space Construction
				Location of Interest Points
					Determine the Extreme Point Candidates
					Eliminate Unstable Points
			3.4.2.2 SURF Descriptor
				Determination of the Main Orientation of Feature Points
				Feature Extraction and Diagnosis of Hydraulic Pump Based on SIFT
				Feature Extraction and Diagnosis of Hydraulic Pump Based on SURF
				Performance Analysis and Comparison of Centrifugal Pump Fault Diagnosis
					Equivalent Graphical Representation of the Centrifugal Pump Vibration Signal Based on Bispectrum
					Feature Extraction and Diagnosis of Centrifugal Pump Based on SIFT
					Feature Extraction and Diagnosis of Centrifugal Pump Based on SURF
					Comparison Between Fault Diagnosis Based on Visual Invariance of a Centrifugal Pump and Traditional Methods
		3.4.3 Fault Diagnosis Under Variable Working Conditions Based on SURF and Manifold Sensing
			3.4.3.1 Analysis and Comparison of Equivalent Graphical Representations of Bispectrum Technology and Recurrence Plot Under Var...
			3.4.3.2 Constructing Manifold Space Based on Isometric Mapping
			3.4.3.3 Fault Diagnosis Method under Variable Working Conditions Based on SURF and Isometric Mapping
		3.4.4 Case Analysis
			3.4.4.1 Equivalent Graphical Representation of Vibration Signals Based on the Recurrence Plot
			3.4.4.2 Visual Invariant Feature Extraction Based on Surf and Isometric Mapping
			3.4.4.3 Rolling Bearing Fault Recognition Under Variable Working Conditions
	3.5 Health Assessment Based on Visual MCC and MSC
		3.5.1 Contourlet Transform (CT)
			3.5.1.1 LP Decomposition
			3.5.1.2 DFB
			3.5.1.3 Contourlet Transform (CT)
		3.5.2 Nonsubsampled Contourlet Transform (NSCT)
			3.5.2.1 Nonsubsampled Pyramid Filter Bank (NSPFB)
			3.5.2.2 Nonsubsampled Directional Filter Bank (NSDFB)
			3.5.2.3 Nonsubsampled Contourlet Transform (NSCT)
		3.5.3 Health Assessment Based on NSCT and Manifold Sensing
			3.5.3.1 Feature Reduction and Distance Measurement Based on Visual MSC
			3.5.3.2 Health Assessment Method Based on NSCT and LE
				Equivalent Graphical Representation Based on Time Series Arrangement
				Performance Degradation Feature Extraction Based on NSCT
				Manifold Space Construction Based on LE
				Performance State Deviation Measurement Based on Geodesic Distance
				Calculating the Health Degree of Electromechanical Products
		3.5.4 Case Analysis
			3.5.4.1 Lithium Battery Test Data
			3.5.4.2 Equivalent Image Conversion of Current/Voltage Data Based on Time Series Arrangement
			3.5.4.3 Image Feature Extraction Based on NSCT and LE
			3.5.4.4 Lithium Ion Battery Capacity Estimation Based on Geodesic Distance
			3.5.4.5 Performance State Estimation of Lithium Ion Batteries
	3.6 Summary
	References
Chapter 4: Fault Diagnosis Based on Compressed Sensing
	4.1 Introduction
	4.2 Compressed Sampling, Reconstruction and Noise Reduction Technology of Monitoring Data
		4.2.1 Compressed Sampling and Reconstruction Method of Monitoring Data Based on Compressed Sensing
			4.2.1.1 Compressed Sensing Mathematical Model
			4.2.1.2 Dictionary Matrix Construction
			4.2.1.3 Measurement Matrix Design
			4.2.1.4 Reconstruction Algorithm Design
		4.2.2 Noise Reduction Method of Monitoring Data Based on Compressed Sensing
			4.2.2.1 Basic Principles of Noise Reduction
			4.2.2.2 Noise Reduction Simulation Analysis
			4.2.2.3 Influence Analysis of Key Parameters
		4.2.3 Improved Compressed Data Reconstruction Method Based on Ensemble Dictionary
			4.2.3.1 Selection of Sub-Dictionary Matrix Based on Information Expression Accuracy
			4.2.3.2 Normalization and Cascading of Dictionaries
			4.2.3.3 Selective Ensemble of Dictionaries
		4.2.4 Adaptive Based StMOP and Noise Reduction of Compressed Data
			4.2.4.1 Principle of the StOMP Algorithm
			4.2.4.2 Vibration Signal Noise Reduction Method Based on StOMP
			4.2.4.3 Vibration Signal Reconstruction and Noise Reduction Algorithm Based on Improved StOMP
		4.2.5 Case Analysis
			4.2.5.1 Compression and Reconstruction of the Vibration Signal of the Hydraulic Pump
			4.2.5.2 Compression and Reconstruction of Battery Monitoring Data
	4.3 Equipment Diagnosis Technology Based on Compressed Domain Information
		4.3.1 Fault Diagnosis Technology Based on Hybrid Compressed Sampling
		4.3.2 Equipment Fault Diagnosis Based on Two-Stage Compression Learning
		4.3.3 Fault Diagnosis of Rotating Machinery Under Multiple Working Conditions Based on Reconstruction Matching
			4.3.3.1 Original Signal Compression and Reference Matrix Construction
			4.3.3.2 Selection of Similarity Measurement Index
			4.3.3.3 Calculation of ACV
		4.3.4 Fault Diagnosis Based on Multisignal Collaborative Compression
		4.3.5 Case Analysis
			4.3.5.1 Bearing Fault Diagnosis Based on Hybrid Compressed Sampling
				Fault Diagnosis Based on Compressed Data
				Reconstruction of Compressed Signals
			4.3.5.2 Fault Diagnosis of Hydraulic Pump Based on Two-Stage Compression Learning
			4.3.5.3 Bearing Fault Diagnosis under Disturbed Working Conditions Based on Reconstruction Matching
				Bearing Fault Diagnosis Under Disturbed Working Conditions
					Construction and Compression of Reference Matrix
					Calculation of ACV
					Fault Diagnosis and Reconstruction Evaluation
				Vibration Signal Reconstruction Example
			4.3.5.4 Collaborative Compression Diagnosis of Aileron Actuator Based on Reconstruction Matching
	4.4 Summary
	References
Chapter 5: Fault Diagnosis and Evaluation Based on Differential Geometry
	5.1 Introduction
	5.2 Research on Nonlinear Data Test and Preprocessing
		5.2.1 Surrogate Data Method
			5.2.1.1 Null Hypothesis
			5.2.1.2 Generation of Surrogate Data
			5.2.1.3 Test Statistics
			5.2.1.4 Statistical Test Method
		5.2.2 Phase Space Reconstruction Method
			5.2.2.1 Determination of Embedded Dimensionality
			5.2.2.2 Determination of Delay Time
		5.2.3 Intrinsic Dimensionality Calculation and Improved Method
	5.3 Local Projection Nonlinear Noise Reduction Technique Based on Neighborhood Distribution Information Constraints
		5.3.1 Principles of LP Denoising Method
			5.3.1.1 The Principles of LP Denoising
			5.3.1.2 The Processes of LP Denoising
			5.3.1.3 Analysis of the LP Denoising Characteristics
		5.3.2 Neighborhood Radius Selection Based on EMD Noise Estimation
		5.3.3 Determination of Noise Subspace Based on Neighborhood Distribution Information Constraints
		5.3.4 Case Analysis
			5.3.4.1 Simulation Analysis
			5.3.4.2 Noise Reduction Test of Double Row Bearing Signal
	5.4 Feature Extraction Technique Based on Manifold Learning and SVD
		5.4.1 Manifold Learning Method
		5.4.2 Feature Extraction Based on LTSA and SVD
		5.4.3 Case Analysis
	5.5 Health Assessment Technology Based on Manifold Distance-Taguchi Method
		5.5.1 Basic Ideas and Processes
		5.5.2 Manifold Distance
			5.5.2.1 Definition of Manifold Distance
			5.5.2.2 Path Optimization Algorithm
		5.5.3 Feature Optimization Based on Taguchi Method
			5.5.3.1 Two-Level Orthogonal Table Design
			5.5.3.2 SNR Analysis
		5.5.4 Health Assessment Based on GMM
			5.5.4.1 The Definition of GMM
			5.5.4.2 Estimation of Model Parameters
			5.5.4.3 Health Degree Assessment
		5.5.5 Case Analysis
			5.5.5.1 Calculate the Manifold Distance
			5.5.5.2 Feature Optimization Based on Taguchi Method
			5.5.5.3 Health Degree Calculation Based on GMM
	5.6 Health Assessment Technology Based on Cumulative Geodesic Distance (CGD)
		5.6.1 Basic Ideas and Processes
		5.6.2 Construction of Intrinsic Manifolds Based on LE
		5.6.3 Manifold Cumulative Geodesic Distance
		5.6.4 Case Analysis
			5.6.4.1 Geometrical Feature Extraction of Lithium Battery Feature Data
			5.6.4.2 LE Method: Constructing Intrinsic Manifolds
	5.7 Fault Diagnosis Technology Based on Information Geometry and Support Vector Machine
		5.7.1 Information Geometric SVM
			5.7.1.1 Information Geometry
			5.7.1.2 Geometric Structure Analysis of SVM Kernel Function
			5.7.1.3 Optimization of Kernel Function Structure Based on Information Geometry
			5.7.1.4 Implementation Process of IG-SVM
		5.7.2 Fault Diagnosis Based on Information Geometry Support Vector Machine
		5.7.3 Case Analysis
			5.7.3.1 Sample Preparation and Feature Extraction under Disturbed Working Conditions
			5.7.3.2 Experimental Analysis of IG-SVC Fault Classification under Disturbed Working Condition
	5.8 Summary
	References
Chapter 6: Performance Degradation Prediction and Assessment Based on Geometric Space Transformation and Morphology Recognition
	6.1 Introduction
	6.2 Enlightenment and Geometric Concepts of Performance Degradation Prediction in a Health Manifold Space
		6.2.1 Concepts Related to Classical Physics and Mathematics
			6.2.1.1 Manifold Learning
			6.2.1.2 Geodesic Lines and Geodesic Distances on a Manifold Space
			6.2.1.3 Orthogonal Transformation
			6.2.1.4 Affine Transformation
			6.2.1.5 Projection Transformation
			6.2.1.6 Embedding Submanifolds
			6.2.1.7 Spacetime
			6.2.1.8 Euclidean Metric
			6.2.1.9 Euclidean Space
			6.2.1.10 Metric and Lorentzian
			6.2.1.11 Minkowski Spacetime
			6.2.1.12 High-Dimensional Background Manifold Space (DBMS)
		6.2.2 Conjectures of the Background Manifold Space of Performance Degradation: Minkowski Spacetime
			6.2.2.1 Combination of Minkowski Spacetime and Special Relativity
			6.2.2.2 Inspirations from the Combination of Minkowski Spacetime and Special Relativity
				Health State Space Diagram
				World Line and Lifetime Curve
				Proper Time-Coordinate Time and Operating Time-Storage Time
				Line Elements in Minkowski Spacetime and Health State Spacetime
				Length of a Lifetime Curve in the Spacetime Diagram
				Slope of the Lifetime Curve and the Ideal Lifetime Curve in the Spacetime Diagram
				Variable Degradation Processes on the Health State Space Diagram
		6.2.3 Basic Concepts of Performance Degradation Prediction in the Health Manifold Space
			6.2.3.1 Performance Degradation Prediction
			6.2.3.2 Evolutionary Trajectory of Performance Degradation
			6.2.3.3 Health Manifold
			6.2.3.4 Neighborhood Geodesic Distance
			6.2.3.5 Construction of Lifetime Curve and Spacetime Diagram
			6.2.3.6 Numerical Case of Spacetime Diagram
	6.3 Intrinsic Dimensionality Estimation of a Health Manifold
		6.3.1 M-SVD for Intrinsic Dimensionality Estimation of a Health Manifold
			6.3.1.1 Linear Manifold SVD Methods
			6.3.1.2 Intrinsic Dimensionality Estimation of Noisy Nonlinear Manifold Space Based on M-SVD
		6.3.2 Intrinsic Dimensionality Estimation of a Health Manifold Based on the K-Nearest Neighbor Graph
			6.3.2.1 Any Random Point in Riemannian Manifold Space
			6.3.2.2 k-NN Geodesic Distance Approximation
			6.3.2.3 Intrinsic Dimensionality Estimation of a Health Manifold
		6.3.3 Intrinsic Dimensionality Estimation of a Health Manifold Based on Packing Numbers
	6.4 The Dimensionality Determination of a High-Dimensional Background Manifold Space
		6.4.1 Measuring Methods of the Principal Coordinate Information Cost (PCIC)
		6.4.2 Method Based on Global Optimization of Local Geometric Information and Measurement of Principal Coordinate Information C...
	6.5 Mappings from a High-Dimensional Manifold Space to a Low-Dimensional Health Manifold Space
		6.5.1 Health Manifold Space Construction Based on Isometric Mapping
			6.5.1.1 Select the Neighborhood and Construct the Neighborhood Relation Graph
			6.5.1.2 Calculate the Shortest Path Between Any Two Arbitrary Points in the Original Data Set
			6.5.1.3 Construct d-Dimensional Embedding
		6.5.2 Construction of a Health Manifold Space Based on LE
			6.5.2.1 General Description of LE
			6.5.2.2 Theory of LE
		6.5.3 Construction of a Health Manifold Space Based on MLLEP
			6.5.3.1 Proposal of Problems
			6.5.3.2 Ideas for Solving Problems
			6.5.3.3 Health Manifold Construction Algorithm Targeting at Fully Truncated Data
	6.6 Performance Degradation Prediction in a Health Manifold Space Under Variable Working Conditions
		6.6.1 Health Manifolds and Performance Degradation Trajectory in a High-Dimensional Background Manifold Space
			6.6.1.1 Determination of the Intrinsic Dimensionality of a Health Manifold and the Dimensionality of a Background Space
			6.6.1.2 Health Manifold Construction and Degradation Trajectory
		6.6.2 Affine Transformations and Establishment of Affine Relations
		6.6.3 Construction of Health State Space Diagrams Based on Sample Population and Individual Information
		6.6.4 Case Analysis
			6.6.4.1 Test Equipment and Data Composition
			6.6.4.2 Extraction and Description of High-Dimensional Performance Degradation Features of Lithium Batteries
			6.6.4.3 Determination of the Dimensionality of Health Manifold and Background Manifold Space for Lithium Batteries
				Determination of the Dimensionality of Health Manifold Space
				Determination of the Dimensionality of Background Manifold Space
			6.6.4.4 Construction of a Health Manifold Based on LE
			6.6.4.5 Affine Transformations and Construction of Health State Space Diagrams Under Different Working Conditions
				Analysis of Health Manifold Performance Trajectory of Lithium Batteries Under Different Working Conditions
				Affine Transformation and Optimization of the Health Manifold Under Different Working Conditions
				Construction of Health State Space Diagrams of Lithium Batteries Under Different Working Conditions
			6.6.4.6 Lifetime Curve Tracking and Prediction of li-Ion Battery Based on Particle Filter
				Effect Analysis of the Global Construction Algorithm for Health Manifold
				Battery #18 Lifetime Curve Prediction
				Results and Discussions
					Qualitative Analysis of Test Results
					Quantitative Analysis of Test Results
					Performance Degradation Prediction and Life Prediction of Lithium Batteries
					Deficiency of PF in this Case
	6.7 Performance Degradation Prediction with Fully Truncated Data in the Health Manifold Space
		6.7.1 Manifold Structure of Truncated Data in a High-Dimensional Background Manifold Space
			6.7.1.1 Visual Qualitative Analysis
			6.7.1.2 Quantitative Analysis
		6.7.2 Recognition and Prediction of Cumulative Geodesic Line in a Health Manifold Space
		6.7.3 Geometric Method for Performance Degradation Prediction Based on Intelligent Product Limit Estimator
			6.7.3.1 Feed Forward Neural Network
			6.7.3.2 Survival Probability Estimation Based on the Intelligent Product Limit Estimator (iPLE)
				Construction of the Training Parameter Set for Full Life Cycle Data
				Construction of the Training Parameter Set for Truncated Data
		6.7.4 Case Analysis
			6.7.4.1 Geometric Method for Performance Degradation Prediction of Truncated Data Objects in a Health Manifold Space
				Experimental Apparatus and Data Description
				Analysis of Performance Degradation Features and Data Truncation with Fully Truncated Data
				Construction of High-Dimensional Manifold Space with Fully Truncated Data Based on MLLEP
				Performance Degradation Prediction of Fully Truncated Data Objects Based on MLLEP
			6.7.4.2 Performance Degradation Prediction Based on Intelligent Product Limit Estimator (iPLE): Combination of Geometric and N...
				Survival Probability Calculation Based on iPLE Method
					Construction of Full Life Cycle Data Samples (Obtained by Fitting and Prediction)
					Construction of Truncated Data Samples
				Construction of FFNN Network
					Structure of FFNN Model
					Construction of Training and Test Samples of FFNN Prediction Model
				Prediction Training and Testing Based on iPLE
	6.8 Performance Degradation Assessment Based on Geometric Figures and Morphology Recognition
		6.8.1 Dynamic Time Warping: Advantages and Disadvantages
		6.8.2 Fast Similarity Search Under Time Warping Distance
			6.8.2.1 Computation of Lower Bounding Distance Using a Dynamic Programming Approach
			6.8.2.2 Early Stoppage to Exclude Useless Warping Paths
			6.8.2.3 Refinement of LBS
		6.8.3 Fast Dynamic Spatial Time Warping Method
		6.8.4 Case Analysis
			6.8.4.1 DSTW Simulation Tests
				Translation Tests for Straight and Curve Lines
				Rotation Tests for Straight and Curve Lines
			6.8.4.2 Estimation of Li-Ion Battery Capacity
	6.9 Summary
	References