Wavelets : Theory and Applications for Manufacturing

Wavelets: Theory and Applications for Manufacturing presents a systematic yet easily accessible description of the fundamentals of wavelet transform and its applications in manufacturing. Given the widespread utilization of machine tools in modern manufacturing and the increasing need for minimizing unexpected machine down-time to ensure reliable, economical, and high quality production, it is of critical importance to continually advance the science base for machine condition monitoring, fault diagnosis, and remaining service life prognosis. The adaptive, multi-resolution capability of the wavelet transform has made it a powerful mathematical tool for accomplishing such goals. In addition, this volume also: •Provides a historical overview of the evolution of signal processing techniques, from the Fourier transform to wavelet transform •Introduces the fundamental mathematics for understanding what wavelet transform is and does, and how to apply it to problems typically encountered in manufacturing •Discusses the integration of wavelet transforms with other techniques, such as signal enveloping and neural networks, for enhanced machine defect detection and severity classification •Demonstrates how to select an appropriate base wavelet or custom design a wavelet for optimal performance in signal analysis Focusing on wavelet transform as a tool specifically applied to and designed for manufacturing, Wavelets: Theory and Applications for Manufacturing presents material appropriate for both academic researchers and practicing engineers working in the field of manufacturing. 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 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. "Wavelets: Theory and Applications for Manufacturing presents a systematic yet easily accessible description of the fundamentals of wavelet transform and its applications in manufacturing. Given the widespread utilization of machine tools in modern manufacturing and the increasing need for minimizing unexpected machine down-time to ensure reliable, economical, and high quality production, it is of critical importance to continually advance the science base for machine condition monitoring, fault diagnosis, and remaining service life prognosis. The adaptive, multi-resolution capability of the wavelet transform has made it a powerful mathematical tool for accomplishing such goals"--Page 4 of cover