Index. baseline-free damage detection, 188, bifurcation, 263, 282

Transcription

1 Index Airworthiness Assurance Non-Destructive Inspection Validation Centre, 28 acoustic emissions, 28, 32, 158, 312, 410 Akaike information criterion (AIC), 233, 340, 433 aliasing, 519 anomaly detection, see statistical modelling, novelty detection applications aerospace structures, airframes, 4 composite fuel tanks, 27, 32 jet engines, 4, 28, 32 protective coatings, 28 repair bonds, 28 rotorcraft, 25 6 space shuttle, 3, 5 orbiter body flap, 27 shuttle modal inspection system, 25 7 thermal protection system, 26 7 space station, 25, 27 unmanned aerial vehicles, 28, 67 9, 448 9, civil infrastructure bridges, 32 7, 87 97, 104 8, 447, 452, 462, 464 high-rise building, 462 nuclear power plant structures, 463 nuclear reactors, 21 offshore oil platforms, 21 5, 195 pressure vessels, 1 railroad wheels, 17 rails, 1 reciprocating machinery, 1, 20 rotating machinery, 1, 17 21, 445, 461, 463 bearings, 19 20, 265 gearbox, 12, 20, 446 ships, 407 9, autocorrelation function, see signal processing, autocorrelation function averaging ensemble averaging, 488 of spectra, time averaging, 488 baseline-free damage detection, 188, bifurcation, 263, 282 case studies Alamosa Canyon bridge, 104 8, 235 6, 252 9, 406 7, 410, concrete column, 92 7, , 196, 233 4, 264 5, DOF system, , 162, 195 6, , 206, 208 9, 211, , Gnat aircraft, , 372 4, 382 4, I-40 bridge, 87 92, 196, , , 214, 217, 245, 251 2, 405 simulated building structure, , 176 8, 197 8, 238, , 254, 256, , , 425 8, Chaos (deterministic), 119 chaotic attractor, 282 characteristic equation, 614 classification, see statistical modelling, group classification coherence function, 536 Structural Health Monitoring: A Machine Learning Perspective, First Edition. Charles R. Farrar and Keith Worden John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.

2 624 Index combat asset readiness, 4 complexity, condition monitoring (CM), rotating machinery, 1, 15, 17, 37 confusion matrix, 374 convolution theorem, 504 correlation test, 266 cradle-to-grave system state awareness, 476 cross-correlation function, see signal processing, cross-correlation function curse of dimensionality, 299, 309 damage chipped gear teeth, 18, 246 corrosion, 22, 28, 34, 59 crack, 6, 22, 28, 52, 101, 245, 455, debonding, 28, 32, 447, 474 debris impact (foreign object impact), 27 8, 447 defects, 5, 295, 440 definition of, 4 7, 440 delamination (composites), 28, 32, 52, 122 3, 246, 447, 474 earthquake, 3, 13, 33, 462 failure, 5, 295, 441, 461 fastener failure, 28 fatigue (cracks), 22, 28, 37, 49, 88, 245, 279, fibre breakage (composites), 28, 447, 474 flutter, 449, 468, 474 galling, 27 loose bearings, 246 loose connections, 246, 410 matrix microcracking (composites), 28, 447, 474 moisture intrusion, 28 prestressing force, 34 scour, 7, 34 shaft misalignment, 18 yielding, 28, 247 seismic, see earthquake damage prognosis (DP), 1 2, 399, damage-tolerant design philosophy, 441 data acquisition, 9 10, aerospace structures, bridges, 34 5 offshore oil platforms, 24 rotating machinery, data cleansing, 9, 11 data compression, 9, 11 data fusion, 9, 11, 163 data normalisation, 9 11, 25, 163, intelligent feature selection, look-up table, machine learning approaches auto-associative neural networks, 422 3, cointegration, factor analysis, 423, Mahalanobis squared-distance, 306, principal component analysis (minor components), , singular value decomposition, standardisation, 415 data to decision process, 298 decision boundary, 304, 306 8, 316 decision region, 304 decision tree, 308 degree-of-freedom, 594 delta function (Dirac), 500, 604 discriminant analysis, 316 functions, 306, 316 kernel, 317 Duhamel s integral, 533 eigenvalue problem, 614 excitation ambient traffic, 35, 47, waves, 21, 24, 35 wind, 35 impact coin, 30 hammer, 34, 106 tap, 17 shaker electrodynamic, 30, 35, 57, 93, 101, 110, 410 hydraulic, 35, 57, 91 piezoelectric (PZT), 75 6 tensioned cable, 35 expectation, see probability, expectation extreme value statistics, fundamental theorem, 150 limit distributions, 150 parent distribution, 148 features aerospace structures, 31 2 arrival time (reflected waves), 185

3 Index 625 attenuation, 185 attractor correlation dimension, 281 autocorrelation function, 165 average local attractor variance ratio (ALAVR), baseline subtraction, 186 bridges, 35 6 coherence function, 169, cross-correlation function, 165, cross-spectral density function, 167 decay measures, definition, 12, 161 dimension, 162 duration (acoustic emission), 183 feature extraction, 12, 161, 298 feature selection, 9, 161 frequency response function (FRF), 168, 251 6, harmonic distortion, harmonics, 18, 20, 49, 279, 444, 458 Hilbert transform distortion, Holder exponent, , 458 impedance, impulse response function, 168 load-dependent Ritz vectors, Lyapunov exponent, 280 modal properties damping, 90 modal flexibility, mode shape curvature, mode shapes, 24, 30, 36, 90, 162, complex, 197 unit-mass-normalised, 197 modal strain energy, 36, , 443 resonance frequencies, 21, 24, 30, 36, 90, 192 7, 405 7, 453 uniform load surface (flexibility shape), 36, measured area under the rectified signal envelope (acoustic emissions), 183 metric, 163, 187, coordinate modal assurance criteria (COMAC), 201 correlation coefficient, 189 modal assurance criteria (MAC), 199 root-mean-square deviation, 189 Yuen function, model parameters model updating, 36, , 442, 445 constraints, direct solution, eigenstructure assignment, hybrid methods, 231 objective (cost) function modal force error, 220 perturbation matrix, 220 optimal matrix update, sensitivity-based update, nonlinear time series models nonlinear autoregressive with exogenous inputs (NARX), 274 nonlinear autoregressive moving average with exogenous inputs (NARMAX), 275 stiffness matrix indices, 219 time series models autoregressive (AR), 232 4, 271 3, autoregressive with exogenous inputs (ARX), 273 4, linearity check, nonlinearity, 18, 249 power spectral density function, 166, 187 probability density function, reciprocity check, residuals, 271 3, , 458 restoring force surface, ring down count (acoustic emissions), 183 rotating machinery, sensitivity, 195 sidebands, 279, 444 signal statistics crest factor, 19, 173, 177 K-factor, 173, 177 kurtosis, 19 20, 173, 177, 445 mean, mean-square, 173, 175 peak amplitude, 19, 172 3, 183 root-mean-squared amplitude, 19, 173, 175 shock pulse counting, 19 skewness, 17, 176 standard deviation, 173, 175, temporal moments, time-reversal property, 187 time series prediction errors, transmissibility, 445 types model parameters, 161, 191 predictive errors, 161 waveforms, 161, 164,

4 626 Index feature selection, see also features, 458 genetic algorithms for, 389 information content entropy, 238, mutual information, 238 optimisation, 239 robustness, 239 sensitivity, 195, filters, analogue, 564 anti-aliasing, 564 band-pass, 571 band-stop, 571 bilinear transform, 573 Butterworth, definition of, 572 example of design, 576 general design of, combination of, 578 digital, 564 frequency warping, 573, 575 high-pass, 569 introduction to, 564 low-pass, 565 pulse transfer function of, 569 flexibility matrix, 215 Fourier, analysis, 597 inversion theorem, 498 series (exponential), 496 series (phase form), 496 series (sine cosine),.489 transform, 497 convolution theorem, 504 definition, 498 discrete, 512 fast, of a periodic function, 501 of a pulse/impulse, 502 of derivatives and integrals, 509 Parseval s theorem for, 506 short-time, 543 frequency response function, see signal processing, frequency response function fundamental axioms, 14, 82, 194, 258, 429, Gaussian distribution, 130, 330 multivariate, 135 univariate, 131 genetic algorithms, Gibb phenomenon, 494 Hanning window, 526 harmonic probing, 511, 568 health and usage monitoring (HUMS), rotorcraft, 1 2, 25 6, 28, 463 Heaviside (step) function, 500 hyperparameters, 143, 312 hypothesis testing, 300 impedance method (measurements), 75 6, , 445, impulse response, 511, integrated condition assessment system, 463 Kronecker delta, 492 leakage, 525 machine learning, 8, algorithms, 9 auto-associative neural network (nonlinear principal component analysis), 422 3, 425 8, 442 cointegration, 431 6, 447 factor analysis, 163, 423, 425 8, 447 negative selection, 442 Sammon mapping, 163, 442 hyper parameters, 143 neural network classifier, 20 supervised learning, 9, 12, 37, 296, 303, , 444, 447 support vector machine, 20 unsupervised learning, 9, 12, 297, , 444, 447 Mahalanobis distance, see statistics, Mahalanobis squared-distance maintenance specific items, 462 maintenance strategies condition-based, 4, 34 reliability centred, 28 run-to-failure, 4 time-based, 4 margins assessment (seismic), 463 mean, see statistics, mean models finite element, 9, 24, 36, , 442, 445, 452 time series, 24, 166, 232 4, 271 4,

5 Index 627 autoregressive (AR), 339, 356, 585 autoregressive moving-average (ARMA), 586 moving-average (MA), 585, 605 monitoring loads, 25 predictive, 13 protective, 13 usage, 4, 25, 461 neural networks, artificial auto-associative, biological motivation, 361 cross-validation, validation set, 370 generalisation in, 370, overfitting, 370 Hopfield network, 367 Kohonen network, 375 learning in, 363 backpropagation, 369 Hebbian learning, 364 memory, 363 multilayer perceptron (MLP), 327, , 373 1ofM strategy, 374 neuron, 361 biological, 362 McCulloch Pitts, 363, 365 perceptron, 366 training of, 326 nondestructive evaluation (NDE) 1, 13 acoustic, 13 eddy-current, 13 magnetic, 13 radiography (X-ray), 13, 27 thermal field (thermography), 13, 28, 59 ultrasonic, 13, 27, 451 nondestructive testing, see nondestructive evaluation normal distribution, see Gaussian distribution normal operating condition, 297 novelty detection, see statistical modelling, novelty detection Nyquist frequency, 514, 516, 607 operational evaluation, 9 10, aerospace structures, 28 9 bridges, 34, offshore oil platforms, 21 rotating machinery, 18 wind turbine, 51 2 orthogonality relation, 491, 515 outlier, 128, 139 analysis, , exclusive, inclusive, 141 multivariate, 141 thresholds, 141, univariate, 140 discordancy, 139, 142 Paris Erdogan law, Parseval s theorem, 506 pattern recognition neural, 8 statistical, 8 syntactic, 8 Poincare map, 282 power spectral density, see signal processing, power spectral density principal component analysis, see statistical modelling, dimension reduction principle of indifference, 301 principle of reciprocity, see also features, reciprocity check, 609, 614 principle of superposition, 595, 597, 606 probabilistic risk assessment (seismic), 463 probability Bayes theorem (inferencing), 135, 474 Bernoulli trial, 148 central limit theorem, 131 conditional, 134 confidence interval, correlation, 133, 163, 276 cumulative distribution function, 138 empirical, 139, 151, 349 definition of, density estimation, 140, 144, 309 nonparametric histogram, 140, 143 kernel function, 143 kernel method, 143, 177, 330 least-squares cross-validation, 145, 318, 331, 333 smoothing parameter, 144, 318, 330, 333 parametric, 142 distribution Bernoulli, 149 Frechet, 148, 150

6 628 Index probability (Continued ) Gumbel, 148, 150 log-normal, 132 normal (Gaussian), 130 Rayleigh, 131 Weibull, 132, 150 of detection, 302, 358 event, 121 expectation (expected value), frequentist, 120, 135 Gaussian plotting paper, 140 histogram, 139, 143 independence, 122 joint probability distribution function, 133, 467 likelihood, 136 likelihood ratio, 301 marginal distributions, 133 mean, arithmetic, 127 mutually exclusive events, 121 parameter estimation differential evolution, 154 least-squares probability relative error, 154 method of moments, 154 posterior probability, 136, 305 prior probability, 136 probability density function, 124, 454, 457, 471, 474 probability paper, random variables, 122 continuous, 122 discrete, 122 sample space, 121 statistical fluctuation, 126 tests for Gaussianity, 139 total probability theorem, 137 prognosis, see damage prognosis random, 119 random variables, see probability, random variables RAPTOR telescopes, 354 receiver operating characteristics (ROC) curve, 302, reciprocity, 192 regression, see statistical modelling, regression analysis resonant ultrasound spectroscopy, 196 Rytter hierarchy, 296, 361 safe-life design philosophy, 441 safety specific items, 462 sensing active/passive, 75 global, 13 local, 13 multiscale, 14 sensing systems components, 60 fail-safe, 71 fusion,79 82 high-explosives radio telemetry system, 74 optimisation, 71, 78 9 power,77 properties, signal conditioning, 77 8 wired,60 61 wireless, 61 3 sensors accelerometers force balance, 34 piezoelectric, 18, 24, 30, 34, 57, 90, 95, 100, 102, 106, 110, 445, 453 anemometers, 34 calibration, 481 definition, 480 eddy current, 19 electrochemical (for corrosion), 35 force transducer, 57, 91, 102 laser vibrometer, 30, 59 linear variable differential transducers (LVDT), 57 load cell, see force transducer microelectromechanical systems (MEMS), 57 8 piezoelectric (PZT) transducer (also PZT patches, PZT sensor actuator), 61, 68, 247, 429, 441, 447 robots, smart, 57, 63 strain gauges electric resistance, 30, 34, 57 fibre optic, 30, 34, 57 vibrating wire, 34 thermocouples, 34 thermometers, 107 velocity transducers, 18 signal classification of, definition, 119, 479

7 Index 629 deterministic, 119 ergodic, 488 probabilistic, 119 random, 119 stationary, 488 time series, 119 transient, 484 signal processing, AC coupling, 91, 105 autocorrelation function, 165, 532 cepstrum, 20 coherence, 90, 95, 100 cross-correlation function, 165, 532 cross-power spectra, 90, 95, 100, 105, 167 Fourier transform (Fourier spectra), 90, 163, 456, 600 frequency response function, 27, 92, 95, 100, 105, 163, 511, 535, 600 accelerance or inertance form of, 603, 619 Bode plot of, 600, 602, mobility form of, 602, 619 Nyquist plot of, 602 receptance form of, 602, 619 Hanning window, 91, 95 Hilbert transform, 182, 186, power spectral density (power spectra), 90, 95, 105, 163, 167, 454, 532 transmissibility (spectrum), 90, 110, 445, 449 sampling frequency, 605 sampling interval, 605 wavelet transform, 20, 268 9, continuous, 545 discrete, application to compression, 562 application to detection of discontinuities, 561 computation, 561 level decomposition, 557 introduction to, 540 mother wavelet, 540, 554 Daubechies, 556 Haar, 555 Morlet, 546 orthogonal, 552 scale parameter, 545 scaling functions, 554 translation parameter, 545 singular value decomposition, 157, spectrogram, 544 spectrum simple example, 495 standard deviation, see statistics, standard deviation standards, 21 2 stationarity, 488 statistical learning theory, 371, statistical modelling, 9, Bayesian classification, 20 curse of dimensionality, 154, 446 dimension reduction principal component analysis (PCA), 156 8, 163, 314, 325 scores, 156 simple projection, 156 extreme value statistics, , false-negative, 13, 301 false-positive, 13, 301 group classification, or classification, 12, 299, 309, 364, 444 kth nearest neighbour, 20, 312 maximum likelihood method, 143, 310 Monte Carlo method (analysis), 142, 469, 471, 474 novelty detection, 12, 32, 137, , 297, 299, , 364, 441, 444, 449 outlier analysis, see outlier probability density function, 9, 124, 454, 457, 471, 474 regression analysis or regression, 12, 299, 309, 364, , 444, 465 sequential hypothesis test, 21 sequential probability ratio test, 32 statistical quality control, see statistical process control statistical pattern recognition paradigm, 7 13, statistical process control (SPC), 1 2, , control charts, 338, 388 CUSUM chart, 344 exponentially weighted moving-average (EWMA) chart, 345 Hotelling or Shewhart, 346 S chart, 344 X-bar chart, X chart, 339 control limits, 338

8 630 Index statistical process control (SPC) (Continued ) multivariate (MSPC), 343 multivariate CUSUM chart, 347 multivariate EWMA chart, 347 statistics, 120 arithmetic mean, 127 chi-squared statistic, 141 covariance, 133 covariance (matrix), 133 4, 141, 157, 423 4, 449 deviation statistic, 141 discordant, 139 exclusive/inclusive, 141 independence, 122 interquartile range, 146 kurtosis, 130 Mahalanobis squared-distance, 141, 322, 356, 424 7, 429, 441, 447, 449 mean, 127 median, mode, 127 moments, 128 multivariate, order statistic, outlier, 139 robust, 127 sample statistics, 141 skewness, 130 standard deviation, 127 standardised variable, 138, 158 variance, 128 9, 157 stiffness matrix, 215 stochastic (signal), 119 stochastic process, 486 independent, identically distributed (i.i.d), 486 stress intensity factor, 469 structural dynamics (linear), damped natural frequency, 596 damping, 595 constant, 595 critical, 596 matrix, 610, 617 proportional or Rayleigh, 610, 617 ratio, 596 generalised forces, 618 generalised or normal coordinates, 616 mass generalised, 615 matrix, 609 normalisation, 616 modal, see also features, modal properties analysis, 613 constants or residues, 619 coordinates, 610, 616 dampings, 611 masses, 610 matrix, 615 stiffnesses, 610 resonance frequency, 599 steady-state response, 598, 606 stiffness constant, 594 generalised, 615 matrix, 609 transient response, 596, 606 undamped natural frequency, 595 structural health monitoring (SHM), 1 data-based, 9, 465 forward problem, inverse problem, 9, 194 law-base, see physics-based model-based, see inverse problem physics-based, 9 structural risk minimisation, 375 subspace algorithms, 621 supervised learning, see machine learning, supervised learning support vector machines, 377 for classification, for regression, kernel functions, system continuous-time, deterministic, 597 discrete-time, gain, 598 multi degree-of-freedom, 595, phase, 598 single degree-of-freedom, 595 system identification, introduction to, 583 parameter estimation for, 584, least-squares, 587 parameter uncertainty, 589 training training data, 8 9, 142, 155, 300, 303, 315, 375, 405, 446 transducer, 480 transmissibility (function), 324, 331, 372

9 Index 631 type I error, 301, type II error, 301, unsupervised learning, see machine learning, unsupervised learning Vapnik Chervonenkis (VC) dimension, 376 variability environmental ice build-up, 409 marine growth, 21 moisture (water ingress, rain), 47, 50, 406 radiation, 406 sea states, 406 temperature, 29, 47, 50, 56, 101, 405 7, 410, , 433 6, 447 turbulence, 29, 406 wind, 50, 56, 406 operational manoeuvres, 29, 47, 60 mass, 29, 47, 60 speed, 29, 47, 56, 60 traffic, 34, 50, 56, 60, 90, 101, 406 variance, see statistics, variance verification and validation, 467 waveform Random, 110 wavelets, see signal processing, wavelet transform wave propagation damage localisation, 188 guided wave, 185, 410, 441, 445 Lamb wave, 185, , 433 6, 441 4, 447, 452 pitch-catch, 28, 185 pulse-echo, 28, 185 time-reversal property, 187, 444 white noise, 533 window effect on Fourier transform, 506 function, 507 Hanning, 526 Harris test, 527