Spectral Analysis in Engineering: Concepts and Case Studies
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Table of contents
- Cover
- Contentsv
- About the authorsx
- Prefacexi
- Notation and nomenclaturexii
- Chapter 1. Why understand spectral analysis?1
- 1.1 Introduction1
- 1.2 Overview3
- Chapter 2. Relationships between variables8
- 2.1 Introduction8
- 2.2 Discrete bivariate distributions9
- 2.3 Continuous bivariate distributions15
- 2.4 Linear functions of random variables27
- 2.5 Bivariate normal distribution31
- 2.6 Confidence intervals for population correlation coefficient35
- 2.7 Multivariate normal distribution36
- 2.8 Exercises36
- Chapter 3. Time varying signals39
- 3.1 Introduction39
- 3.2 Why study time series?40
- 3.3 Estimation of seasonal effects and trends41
- 3.4 Moments of a discrete random process47
- 3.5 Stationarity and ergodicity49
- 3.6 ARIMA models for discrete random processes51
- 3.7 Estimation of parameters of models for random processes62
- 3.8 Simulations73
- 3.9 Further practical examples74
- 3.10 Models for continuous time random processes83
- 3.11 Exercises87
- Chapter 4. Describing signals in terms of frequency91
- 4.1 Introduction91
- 4.2 Finite Fourier series91
- 4.3 Fourier series97
- 4.4 The Fourier transform100
- 4.5 Discrete Fourier transform105
- 4.6 Exercises108
- Chapter 5. Frequency representation of random signals109
- 5.1 Introduction109
- 5.2 Definition of the spectrum of a random process110
- 5.3 Estimation of the spectrum from the sample autocovariance function115
- 5.4 Estimation of the spectrum from the periodogram128
- 5.5 High resolution spectral estimators136
- 5.6 Exercises141
- Chapter 6. Identifying system relationships from measurements143
- 6.1 Introduction143
- 6.2 Discrete processes145
- 6.3 Linear dynamic systems148
- 6.4 Application of cross-spectral concepts150
- 6.5 Estimation of cross-spectral functions152
- 6.6 Exercises157
- Chapter 7. Some typical applications161
- 7.1 Introduction161
- 7.2 Calculating the sample autocovariance function161
- 7.3 Calculating the spectrum162
- 7.4 Calculating the response spectrum163
- 7.5 The spectrum and moving observers170
- 7.6 Calculation of significant responses173
- 7.7 Exercises179
- Chapter 8. Wave directionality monitoring184
- 8.1 Introduction184
- 8.2 Background184
- 8.3 The technical problem187
- 8.4 Reduction of the monitoring problem to a mathematical problem189
- 8.5 Application of the mathematical model192
- 8.6 The probe arrangements deployed193
- 8.7 Analysis of Loch Ness data194
- 8.8 MLM-based spectral analysis formulations197
- 8.9 Cross-spectral density simulation198
- 8.10 Simulation results and alternative probe management199
- 8.11 Final comments206
- Chapter 9. Motions of moored structures in a seaway208
- 9.1 Introduction208
- 9.2 Background209
- 9.3 Modelling moored structures211
- 9.4 Equations of motion212
- 9.5 Determination of time dependent wave force213
- 9.6 Evaluation of the quadratic transfer function (QTF)215
- 9.7 Simulation of a random sea216
- 9.8 Why the probabilistic method of simulation?218
- 9.9 Statistical analyses of the generated time series219
- 9.10 Sensitivity analysis of a moored tanker and a moored barge to integration time step221
- 9.11 Effects of wave damping on the surge motion221
- 9.12 Final comments232
- Chapter 10. Experimental measurement and time series acquisition233
- 10.1 Introduction233
- 10.2 Background233
- 10.3 Experimental facilities set-up235
- 10.4 Data collection and principles of analysis236
- 10.5 Six degrees-of-freedom SELSPOT motion analysis239
- 10.6 Data acquisition and SELSPOT calibration240
- 10.7 Practical aspects242
- 10.8 Some typical results245
- 10.9 Final comments248
- Chapter 11. Experimental evaluation of wide band active vibration controllers253
- 11.1 Introduction253
- 11.2 Background253
- 11.3 Techniques for active vibration control254
- 11.4 Why use a spectral analyser?255
- 11.5 Experimental rig255
- 11.6 Some typical results257
- 11.7 Final comments257
- Chapter 12. Hull roughness and ship resistance261
- 12.1 Introduction261
- 12.2 Background261
- 12.3 An introduction to surface metrology262
- 12.4 Process bandwidth263
- 12.5 Surface topography and fluid drag264
- 12.6 Measures of texture267
- 12.7 Filtering and filter assessment272
- 12.8 Final comments273
- Appendices274
- Appendix I: Mathematics revision274
- Appendix II: Inflows to the Font reservoir283
- Appendix III: Chi-square and F-distributions285
- Appendix IV: The sampling theorem289
- Appendix V: Wave tank data291
- Appendix VI: Sampling distribution of spectral estimators292
- References294
- Further reading299
- Index303
This text provides a thorough explanation of the underlying principles of spectral analysis and the full range of estimation techniques used in engineering. The applications of these techniques are demonstrated in numerous case studies, illustrating the approach required and the compromises to be made when solving real engineering problems. The principles outlined in these case studies are applicable over the full range of engineering disciplines and all the reader requires is an understanding of elementary calculus and basic statistics.
The realistic approach and comprehensive nature of this text will provide undergraduate engineers and physicists of all disciplines with an invaluable introduction to the subject and the detailed case studies will interest the experienced professional.
No more than a knowledge of elementary calculus, and basic statistics and probability is needed
Accessible to undergraduates at any stage of their courses
Easy and clear to follow
The realistic approach and comprehensive nature of this text will provide undergraduate engineers and physicists of all disciplines with an invaluable introduction to the subject and the detailed case studies will interest the experienced professional.
No more than a knowledge of elementary calculus, and basic statistics and probability is needed
Accessible to undergraduates at any stage of their courses
Easy and clear to follow