Wavelets: Theory and Applications for Manufacturing

✍ Scribed by Robert X Gao, Ruqiang Yan

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 239
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface......Page 6
Contents
......Page 12
1.1.1.1 Periodic Signal......Page 16
1.1.1.2 Transient Signal......Page 17
1.1.2 Nondeterministic Signal......Page 18
1.1.2.2 Nonstationary Signal......Page 19
1.2 Signals in Manufacturing......Page 20
1.3 Role of Signal Processing for Manufacturing......Page 26
1.4 References......Page 28
2: From Fourier Transform to Wavelet Transform: A Historical Perspective......Page 32
2.1 Fourier Transform......Page 33
2.2 Short-Time Fourier Transform......Page 36
2.3 Wavelet Transform......Page 41
2.4 References......Page 46
3: Continuous Wavelet Transform......Page 48
3.1.1 Superposition Property......Page 50
3.1.3 Covariant Under Dilation......Page 51
3.1.4 Moyal Principle......Page 52
3.2 Inverse Continuous Wavelet Transform......Page 53
3.3 Implementation of Continuous Wavelet Transform......Page 54
3.4.2 Morlet Wavelet......Page 56
3.4.3 Gaussian Wavelet......Page 57
3.4.5 Shannon Wavelet......Page 58
3.4.6 Harmonic Wavelet......Page 59
3.5.1 CWT of Sinusoidal Function......Page 60
3.5.3 CWT of Chirp Function......Page 61
3.7 References......Page 62
4.1 Discretization of Scale and Translation Parameters......Page 64
4.2.1 Multiresolution Analysis......Page 68
4.2.2 Orthogonal Wavelet Transform......Page 70
4.3 Dual-Scale Equation and Multiresolution Filters......Page 71
4.4 The Mallat Algorithm......Page 73
4.5 Commonly Used Base Wavelets......Page 75
4.5.2 Daubechies Wavelet......Page 76
4.5.3 Coiflet Wavelet......Page 77
4.5.5 Biorthogonal and Reverse Biorthogonal Wavelets......Page 78
4.6 Application of Discrete Wavelet Transform......Page 80
4.8 References......Page 83
5.1.1 Definition......Page 84
5.1.2 Wavelet Packet Property......Page 87
5.2 Recursive Algorithm......Page 88
5.3.1 Harmonic Wavelet Transform......Page 89
5.3.2 Harmonic Wavelet Packet Algorithm......Page 90
5.4.1 Time-Frequency Analysis......Page 93
5.5 Summary......Page 94
5.6 References......Page 95
6.1 Signal Enveloping Through Hilbert Transform......Page 98
6.2 Multiscale Enveloping Using Complex-Valued Wavelet......Page 101
6.3.1 Ultrasonic Pulse Differentiation for Pressure Measurement in Injection Molding......Page 102
6.3.2 Bearing Defect Diagnosis in Rotary Machine......Page 108
6.4 Summary......Page 114
6.5 References......Page 115
7.1 Generalized Signal Transformation Frame......Page 118
7.1.1 Fourier Transform in the Generalized Frame......Page 121
7.1.2 Wavelet Transform in the Generalized Frame......Page 122
7.2 Wavelet Transform with Spectral Postprocessing......Page 124
7.2.1 Fourier Transform of the Measure Function......Page 125
7.2.2 Fourier Transform of Wavelet-Extracted Data Set......Page 127
7.3 Application to Bearing Defect Diagnosis......Page 128
7.3.1 Effectiveness in Defect Feature Extraction......Page 130
7.3.2 Selection of Decomposition Level......Page 133
7.3.3 Effect of Bearing Operation Conditions......Page 135
7.5 References......Page 139
8.1 Subband Feature Extraction......Page 140
8.1.1 Energy Feature......Page 141
8.1.2 Kurtosis......Page 142
8.2 Key Feature Selection......Page 143
8.2.1 Fisher Linear Discriminant Analysis......Page 144
8.2.2 Principal Component Analysis......Page 146
8.3 Neural-Network Classifier......Page 149
8.4 Formulation of WPT-Based Defect Severity Classification......Page 151
8.5.1 Case Study I: Roller Bearing Defect Severity Evaluation......Page 152
8.5.2 Case Study II: Ball Bearing Defect Severity Evaluation......Page 157
8.7 References......Page 161
9.1 Dissimilarity Measures......Page 164
9.1.1 Relative Entropy......Page 165
9.1.3 Correlation Index......Page 166
9.1.4 Nonstationarity......Page 167
9.2 Local Discriminant Bases......Page 168
9.3 Case Study......Page 170
9.4 Application to Gearbox Defect Classification......Page 173
9.6 References......Page 177
10.1 Overview of Base Wavelet Selection......Page 180
10.1.1 Qualitative Measure......Page 181
10.1.2 Quantitative Measure......Page 183
10.2 Wavelet Selection Criteria......Page 184
10.2.1 Energy and Shannon Entropy......Page 185
10.2.2 Information Theoretic Measure......Page 187
10.3.1 Evaluation Using Real-Valued Wavelets......Page 191
10.3.2 Evaluation Using Complex-Valued Wavelets......Page 194
10.4 Base Wavelet Selection for Bearing Vibration Signal......Page 198
10.5 Summary......Page 200
10.6 References......Page 201
11.1 Overview of Wavelet Design......Page 203
11.2 Construction of an Impulse Wavelet......Page 204
11.3 Impulse Wavelet Application......Page 213
11.4 Summary......Page 217
11.5 References......Page 218
12.1 Second Generation Wavelet Transform......Page 220
12.1.1 Theoretical Basis of SGWT......Page 221
12.1.2 Illustration of SGWT in Signal Processing......Page 223
12.2.1 Theoretical Basis of Ridgelet Transform......Page 225
12.2.2 Application of the Ridgelet Transform......Page 227
12.3.1 Curvelet Transform......Page 229
12.3.2 Application of the Curvelet Transform......Page 232
12.4 Summary......Page 233
12.5References......Page 234
Index......Page 236