Spectral Analysis in Engineering, Concepts and Case Studies

Front Cover......Page 1
Spectral Analysis in Engineering Concepts and Cases......Page 4
Copyright Page......Page 5
Contents......Page 6
About the authors......Page 11
Preface......Page 12
Notation and nomenclature......Page 13
1.1 Introduction......Page 14
1.2 Overview......Page 16
2.1 Introduction......Page 21
2.2 Discrete bivariate distributions......Page 22
2.3 Continuous bivariate distributions......Page 28
2.4 Linear functions of random variables......Page 40
2.5 Bivariate normal distribution......Page 44
2.6 Confidence intervals for population correlation coefficient......Page 48
2.8 Exercises......Page 49
3.1 Introduction......Page 52
3.2 Why study time series?......Page 53
3.3 Estimation of seasonal effects and trends......Page 54
3.4 Moments of a discrete random process......Page 60
3.5 Stationarity and ergodicity......Page 62
3.6 ARIMA models for discrete random processes......Page 64
3.7 Estimation of parameters of models for random processes......Page 75
3.8 Simulations......Page 86
3.9 Further practical examples......Page 87
3.10 Models for continuous time random processes......Page 96
3.11 Exercises......Page 100
4.2 Finite Fourier series......Page 104
4.3 Fourier series......Page 110
4.4 The Fourier transform......Page 113
4.5 Discrete Fourier transform......Page 118
4.6 Exercises......Page 121
5.1 Introduction......Page 122
5.2 Definition of the spectrum of a random process......Page 123
5.3 Estimation of the spectrum from the sample autocovariance function......Page 128
5.4 Estimation of the spectrum from the periodogram......Page 141
5.5 High resolution spectral estimators......Page 149
5.6 Exercises......Page 154
6.1 Introduction......Page 156
6.2 Discrete processes......Page 158
6.3 Linear dynamic systems......Page 161
6.4 Application of cross-spectral concepts......Page 163
6.5 Estimation of cross-spectral functions......Page 165
6.6 Exercises......Page 170
7.2 Calculating the sample autocovariance function......Page 174
7.3 Calculating the spectrum......Page 175
7.4 Calculating the response spectrum......Page 176
7.5 The spectrum and moving observers......Page 183
7.6 Calculation of significant responses......Page 186
7.7 Exercises......Page 192
8.2 Background......Page 197
8.3 The technical problem......Page 200
8.4 Reduction of the monitoring problem to a mathematical problem......Page 202
8.5 Application of the mathematical model......Page 205
8.6 The probe arrangements deployed......Page 206
8.7 Analysis of Loch Ness data......Page 207
8.8 MLM-based spectral analysis formulations......Page 210
8.9 Cross-spectral density simulation......Page 211
8.10 Simulation results and alternative probe management......Page 212
8.11 Final comments......Page 219
9.1 Introduction......Page 221
9.2 Background......Page 222
9.3 Modelling moored structures......Page 224
9.4 Equations of motion......Page 225
9.5 Determination of time dependent wave force......Page 226
9.6 Evaluation of the quadratic transfer function (QTF)......Page 228
9.7 Simulation of a random sea......Page 229
9.8 Why the probabilistic method of simulation?......Page 231
9.9 Statistical analyses of the generated time series......Page 232
9.11 Effects of wave damping on the surge motion......Page 234
9.12 Final comments......Page 245
10.2 Background......Page 246
10.3 Experimental facilities set-up......Page 248
10.4 Data collection and principles of analysis......Page 249
10.5 Six degrees-of-freedom SELSPOT motion analysis......Page 252
10.6 Data acquisition and SELSPOT calibration......Page 253
10.7 Practical aspects......Page 255
10.8 Some typical results......Page 258
10.9 Final comments......Page 261
11.2 Background......Page 266
11.3 Techniques for active vibration control......Page 267
11.5 Experimental rig......Page 268
11.7 Final comments......Page 270
12.2 Background......Page 274
12.3 An introduction to surface metrology......Page 275
12.4 Process bandwidth......Page 276
12.5 Surface topography and fluid drag......Page 277
12.6 Measures of texture......Page 280
12.7 Filtering and filter assessment......Page 285
12.8 Final comments......Page 286
Appendix I: Mathematics revision......Page 287
Appendix II: Inflows to the Font reservoir......Page 296
Appendix III: Chi-square and F-distributions......Page 298
Appendix IV: The sampling theorem......Page 302
Appendix V: Wave tank data......Page 304
Appendix VI: Sampling distribution of spectral estimators......Page 305
References......Page 307
Further reading......Page 312
Index......Page 316