Gao / Yan Wavelets

Theory and Applications for Manufacturing
1. Auflage 2010
ISBN: 978-1-4419-1545-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 224 Seiten

Wavelets: Theory and Applications for Manufacturing presents a systematic description of the fundamentals of wavelet transform and its applications. Given the widespread utilization of rotating machines in modern manufacturing and the increasing need for condition-based, as opposed to fix-interval, intelligent maintenance to minimize machine down time and ensure reliable production, it is of critical importance to advance the science base of signal processing in manufacturing. This volume also deals with condition monitoring and health diagnosis of rotating machine components and systems, such as bearings, spindles, and gearboxes, while also: -Providing a comprehensive survey on wavelets specifically related to problems encountered in manufacturing -Discussing the integration of wavelet transforms with other soft computing techniques such as fuzzy logic, for machine defect and severity classification -Showing how to custom design wavelets for improved performance in signal analysis Focusing on wavelet transform as a tool specifically applied and designed for applications in manufacturing, Wavelets: Theory and Applications for Manufacturing presents material appropriate for both academic researchers and practicing engineers working in the field of manufacturing.

Autoren/Hrsg.

Gao, Robert X

Yan, Ruqiang

Inhaltsverzeichnis

1;Wavelets;3
1.1;Preface;5
1.2;Contents;11
1.3;Chapter 1: Signals and Signal Processing in Manufacturing;15
1.3.1;1.1 Classification of Signals;15
1.3.1.1;1.1.1 Deterministic Signal;15
1.3.1.1.1;1.1.1.1 Periodic Signal;15
1.3.1.1.2;1.1.1.2 Transient Signal;16
1.3.1.2;1.1.2 Nondeterministic Signal;17
1.3.1.2.1;1.1.2.1 Stationary Signal;18
1.3.1.2.2;1.1.2.2 Nonstationary Signal;18
1.3.2;1.2 Signals in Manufacturing;19
1.3.3;1.3 Role of Signal Processing for Manufacturing;25
1.3.4;1.4References;27
1.4;Chapter 2: From Fourier Transform to Wavelet Transform: A Historical Perspective;30
1.4.1;2.1 Fourier Transform;31
1.4.2;2.2 Short-Time Fourier Transform;34
1.4.3;2.3 Wavelet Transform;39
1.4.4;2.4References;44
1.5;Chapter 3: Continuous Wavelet Transform;46
1.5.1;3.1 Properties of Continuous Wavelet Transform;48
1.5.1.1;3.1.1 Superposition Property;48
1.5.1.2;3.1.2 Covariant Under Translation;49
1.5.1.3;3.1.3 Covariant Under Dilation;49
1.5.1.4;3.1.4 Moyal Principle;50
1.5.2;3.2 Inverse Continuous Wavelet Transform;51
1.5.3;3.3 Implementation of Continuous Wavelet Transform;52
1.5.4;3.4 Some Commonly Used Wavelets;54
1.5.4.1;3.4.1 Mexican Hat Wavelets;54
1.5.4.2;3.4.2 Morlet Wavelet;54
1.5.4.3;3.4.3 Gaussian Wavelet;55
1.5.4.4;3.4.4 Frequency B-Spline Wavelet;56
1.5.4.5;3.4.5 Shannon Wavelet;56
1.5.4.6;3.4.6 Harmonic Wavelet;57
1.5.5;3.5 CWT of Representative Signals;58
1.5.5.1;3.5.1 CWT of Sinusoidal Function;58
1.5.5.2;3.5.2 CWT of Gaussian Pulse Function;59
1.5.5.3;3.5.3 CWT of Chirp Function;59
1.5.6;3.6 Summary;60
1.5.7;3.7References;60
1.6;Chapter 4: Discrete Wavelet Transform;62
1.6.1;4.1 Discretization of Scale and Translation Parameters;62
1.6.2;4.2 Multiresolution Analysis and Orthogonal Wavelet Transform;66
1.6.2.1;4.2.1 Multiresolution Analysis;66
1.6.2.2;4.2.2 Orthogonal Wavelet Transform;68
1.6.3;4.3 Dual-Scale Equation and Multiresolution Filters;69
1.6.4;4.4 The Mallat Algorithm;71
1.6.5;4.5 Commonly Used Base Wavelets;73
1.6.5.1;4.5.1 Haar Wavelet;74
1.6.5.2;4.5.2 Daubechies Wavelet;74
1.6.5.3;4.5.3 Coiflet Wavelet;75
1.6.5.4;4.5.4 Symlet Wavelet;76
1.6.5.5;4.5.5 Biorthogonal and Reverse Biorthogonal Wavelets;76
1.6.5.6;4.5.6 Meyer Wavelet;78
1.6.6;4.6 Application of Discrete Wavelet Transform;78
1.6.7;4.7 Summary;81
1.6.8;4.8References;81
1.7;Chapter 5: Wavelet Packet Transform;82
1.7.1;5.1 Theoretical Basis of Wavelet Packet;82
1.7.1.1;5.1.1 Definition;82
1.7.1.2;5.1.2 Wavelet Packet Property;85
1.7.1.2.1;5.1.2.1 Shift Orthogonality;85
1.7.1.2.2;5.1.2.2 Orthogonal Relationship between $$\bi u_{2n}^{\bi(\,j)} (t)$$ and $$\bi u_{2n + 1}^{(\,j)} (t)$$;86
1.7.2;5.2 Recursive Algorithm;86
1.7.3;5.3 FFT-Based Harmonic Wavelet Packet Transform;87
1.7.3.1;5.3.1 Harmonic Wavelet Transform;87
1.7.3.2;5.3.2 Harmonic Wavelet Packet Algorithm;88
1.7.4;5.4 Application of Wavelet Packet Transform;91
1.7.4.1;5.4.1 Time-Frequency Analysis;91
1.7.4.2;5.4.2 Wavelet Packet for Denoising;92
1.7.5;5.5 Summary;92
1.7.6;5.6References;93
1.8;Chapter 6: Wavelet-Based Multiscale Enveloping;95
1.8.1;6.1 Signal Enveloping Through Hilbert Transform;95
1.8.2;6.2 Multiscale Enveloping Using Complex-Valued Wavelet;98
1.8.3;6.3 Application of Multiscale Enveloping;99
1.8.3.1;6.3.1 Ultrasonic Pulse Differentiation for Pressure Measurement in Injection Molding;99
1.8.3.1.1;6.3.1.1 Simulation;102
1.8.3.1.2;6.3.1.2 Experimental Study;103
1.8.3.2;6.3.2 Bearing Defect Diagnosis in Rotary Machine;105
1.8.3.2.1;6.3.2.1 Numerical Simulation Using the MuSEnS Algorithm;107
1.8.3.2.2;6.3.2.2 Case Study;109
1.8.4;6.4 Summary;111
1.8.5;6.5References;112
1.9;Chapter 7: Wavelet Integrated with Fourier Transform: A Unified Technique;114
1.9.1;7.1 Generalized Signal Transformation Frame;114
1.9.1.1;7.1.1 Fourier Transform in the Generalized Frame;117
1.9.1.2;7.1.2 Wavelet Transform in the Generalized Frame;118
1.9.2;7.2 Wavelet Transform with Spectral Postprocessing;120
1.9.2.1;7.2.1 Fourier Transform of the Measure Function;121
1.9.2.2;7.2.2 Fourier Transform of Wavelet-Extracted Data Set;123
1.9.3;7.3 Application to Bearing Defect Diagnosis;124
1.9.3.1;7.3.1 Effectiveness in Defect Feature Extraction;126
1.9.3.2;7.3.2 Selection of Decomposition Level;129
1.9.3.3;7.3.3 Effect of Bearing Operation Conditions;131
1.9.3.3.1;7.3.3.1 Variation of Radial Load;131
1.9.3.3.2;7.3.3.2 Variation of Axial Load;131
1.9.3.3.3;7.3.3.3 Variation of Rotational Speed;131
1.9.4;7.4 Summary;135
1.9.5;7.5References;135
1.10;Chapter 8: Wavelet Packet-Transform for Defect Severity Classification;136
1.10.1;8.1 Subband Feature Extraction;136
1.10.1.1;8.1.1 Energy Feature;137
1.10.1.2;8.1.2 Kurtosis;138
1.10.2;8.2 Key Feature Selection;139
1.10.2.1;8.2.1 Fisher Linear Discriminant Analysis;140
1.10.2.2;8.2.2 Principal Component Analysis;142
1.10.3;8.3 Neural-Network Classifier;145
1.10.4;8.4 Formulation of WPT-Based Defect Severity Classification;147
1.10.5;8.5 Case Studies;148
1.10.5.1;8.5.1 Case Study I: Roller Bearing Defect Severity Evaluation;148
1.10.5.2;8.5.2 Case Study II: Ball Bearing Defect Severity Evaluation;153
1.10.6;8.6 Summary;157
1.10.7;8.7References;157
1.11;Chapter 9: Local Discriminant Bases for Signal Classification;159
1.11.1;9.1 Dissimilarity Measures;159
1.11.1.1;9.1.1 Relative Entropy;160
1.11.1.2;9.1.2 Energy Difference;161
1.11.1.3;9.1.3 Correlation Index;161
1.11.1.4;9.1.4 Nonstationarity;162
1.11.2;9.2 Local Discriminant Bases;163
1.11.3;9.3 Case Study;165
1.11.4;9.4 Application to Gearbox Defect Classification;168
1.11.5;9.5 Summary;172
1.11.6;9.6References;172
1.12;Chapter 10: Selection of Base Wavelet;174
1.12.1;10.1 Overview of Base Wavelet Selection;174
1.12.1.1;10.1.1 Qualitative Measure;175
1.12.1.2;10.1.2 Quantitative Measure;177
1.12.2;10.2 Wavelet Selection Criteria;178
1.12.2.1;10.2.1 Energy and Shannon Entropy;179
1.12.2.2;10.2.2 Information Theoretic Measure;181
1.12.2.2.1;10.2.2.1 Joint Entropy;181
1.12.2.2.2;10.2.2.2 Conditional Entropy;181
1.12.2.2.3;10.2.2.3 Mutual Information;182
1.12.2.2.4;10.2.2.4 Relative Entropy;184
1.12.3;10.3 Numerical Study on Base Wavelet Selection;185
1.12.3.1;10.3.1 Evaluation Using Real-Valued Wavelets;185
1.12.3.2;10.3.2 Evaluation Using Complex-Valued Wavelets;188
1.12.4;10.4 Base Wavelet Selection for Bearing Vibration Signal;192
1.12.5;10.5 Summary;194
1.12.6;10.6References;195
1.13;Chapter 11: Designing Your Own Wavelet;197
1.13.1;11.1 Overview of Wavelet Design;197
1.13.2;11.2 Construction of an Impulse Wavelet;198
1.13.3;11.3 Impulse Wavelet Application;206
1.13.4;11.4 Summary;210
1.13.5;11.5References;211
1.14;Chapter 12: Beyond Wavelets;212
1.14.1;12.1 Second Generation Wavelet Transform;212
1.14.1.1;12.1.1 Theoretical Basis of SGWT;213
1.14.1.2;12.1.2 Illustration of SGWT in Signal Processing;215
1.14.2;12.2 Ridgelet Transform;217
1.14.2.1;12.2.1 Theoretical Basis of Ridgelet Transform;217
1.14.2.2;12.2.2 Application of the Ridgelet Transform;219
1.14.3;12.3 Curvelet Transform;221
1.14.3.1;12.3.1 Curvelet Transform;221
1.14.3.2;12.3.2 Application of the Curvelet Transform;224
1.14.4;12.4 Summary;225
1.14.5;12.5References;226
1.15;Index;228