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Systems identification is a general term used to describe mathematical tools and algorithms that build dynamical models from measured data. Mastering System Identification in 100 Exercises takes readers step by step through a series of MATLAB exercises that teach how to measure and model linear dynamic systems in the presence of nonlinear distortions from a practical point of view. Each exercise is followed by a short discussion illustrating what lessons can be learned by the reader. The book, with its learn-by-doing approach, also includes: State-of-the-art system identification methods, with…mehr
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Systems identification is a general term used to describe mathematical tools and algorithms that build dynamical models from measured data. Mastering System Identification in 100 Exercises takes readers step by step through a series of MATLAB exercises that teach how to measure and model linear dynamic systems in the presence of nonlinear distortions from a practical point of view. Each exercise is followed by a short discussion illustrating what lessons can be learned by the reader.
The book, with its learn-by-doing approach, also includes:
State-of-the-art system identification methods, with both time and frequency domain system identification methods--including the pros and cons of each
Simple writing style with numerous examples and figures
Downloadable author-programmed MATLAB files for each exercise--with detailed solutions
Larger projects that serve as potential assignments
Covering both classic and recent measurement and identifying methods, this book will appeal to practicing engineers, scientists, and researchers, as well as master's and PhD students in electrical, mechanical, civil, and chemical engineering.
The book, with its learn-by-doing approach, also includes:
State-of-the-art system identification methods, with both time and frequency domain system identification methods--including the pros and cons of each
Simple writing style with numerous examples and figures
Downloadable author-programmed MATLAB files for each exercise--with detailed solutions
Larger projects that serve as potential assignments
Covering both classic and recent measurement and identifying methods, this book will appeal to practicing engineers, scientists, and researchers, as well as master's and PhD students in electrical, mechanical, civil, and chemical engineering.
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 282
- Erscheinungstermin: 26. März 2012
- Englisch
- Abmessung: 254mm x 178mm x 16mm
- Gewicht: 666g
- ISBN-13: 9780470936986
- ISBN-10: 0470936983
- Artikelnr.: 34158786
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 282
- Erscheinungstermin: 26. März 2012
- Englisch
- Abmessung: 254mm x 178mm x 16mm
- Gewicht: 666g
- ISBN-13: 9780470936986
- ISBN-10: 0470936983
- Artikelnr.: 34158786
Johan Schoukens, PhD, serves as a full-time professor in the ELEC Department at the Vrije Universiteit Brussel. He has been a Fellow of IEEE since 1997 and was the recipient of the 2003 IEEE Instrumentation and Measurement Society Distinguished Service Award. Rik Pintelon, PhD, serves as a full-time professor at the Vrije Universiteit Brussel in the ELEC Department. He has been a Fellow of IEEE since 1998 and is the recipient of the 2012 IEEE Joseph F. Keithley Award in Instrumentation and Measurement (IEEE Technical Field Award). Yves Rolain, PhD, serves as a full-time professor at the Vrije Universiteit Brussel in the ELEC department. He has been a Fellow of IEEE since 2006 and was the recipient of the 2004 IEEE Instrumentation and Measurement Society Technical Award.
Preface xiii Acknowledgments xv Abbreviations xvii 1 Identification 1
Exercise 1 .a (Least squares estimation of the value of a resistor) 2
Exercise 1 .b (Analysis of the standard deviation) 3 Exercise 2 (Study of
the asymptotic distribution of an estimate) 5 Exercise 3 (Impact of noise
on the regressor (input) measurements) 6 Exercise 4 (Importance of the
choice of the independent variable or input) 7 Exercise 5.a (combining
measurements with a varying SNR: Weighted least squares estimation) 8
Exercise 5.b (Weighted least squares estimation: A study of the variance) 9
Exercise 6 (Least squares estimation of models that are linear in the
parameters) 11 Exercise 7 (Characterizing a 2-dimensional parameter
estimate) 12 Exercise 8 (Dependence of the optimal cost function on the
distribution of the disturbing noise) 14 Exercise 9 (Identification in the
presence of outliers) 16 Exercise 10 (Influence of the number of parameters
on the model uncertainty) 18 Exercise 11 (Model selection using the AIC
criterion) 20 Exercise 12 (Noise on input and output: The instrumental
variables method applied on the resistor estimate) 23 Exercise 13 (Noise on
input and output: the errors-in-variables method) 25 2 Generation and
Analysis of Excitation Signals 29 Exercise 14 (Discretization in time:
Choice of the sampling frequency: ALIAS) 31 Exercise 15 (Windowing: Study
of the leakage effect and the frequency resolution) 31 Exercise 16
(Generate a sine wave, noninteger number of periods measured) 34 Exercise
17 (Generate a sine wave, integer number of periods measured) 34 Exercise
18 (Generate a sine wave, doubled measurement time) 35 Exercise 19.a
(Generate a sine wave using the MATLAB IFFT instruction) 37 Exercise 19.b
(Generate a sine wave using the MATLAB IFFT instruction, defining only the
first half of the spectrum) 37 Exercise 20 (Generation of a multisine with
flat amplitude spectrum) 38 Exercise 21 (The swept sine signal) 39 Exercise
22.a (Spectral analysis of a multisine signal, leakage present) 40 Exercise
22.b (Spectral analysis of a multisine signal, no leakage present) 40
Exercise 23 (Generation of a multisine with a reduced crest factor using
random phase generation) 42 Exercise 24 (Generation of a multisine with a
minimal crest factor using a crest factor minimization algorithm) 42
Exercise 25 (Generation of a maximum length binary sequence) 45 Exercise 26
(Tuning the parameters of a maximum length binary sequence) 46 Exercise 27
(Generation of excitation signals using the FDIDENT toolbox) 47 Exercise 28
(Repeated realizations of a white random noise excitation with fixed
length) 48 Exercise 29 (Repeated realizations of a white random noise
excitation with increasing length) 49 Exercise 30 (Smoothing the amplitude
spectrum of a random excitation) 49 Exercise 31 (Generation of random noise
excitations with a user-imposed power spectrum) 50 Exercise 32 (Amplitude
distribution of filtered noise) 51 Exercise 33 (Exploiting the periodic
nature of signals: Differentiation, integration, +averaging, and filtering)
52 3 FRF Measurements 55 Exercise 34 (Impulse response function
measurements) 57 Exercise 35 (Study of the sine response of a linear
system: transients and steady-state) 58 Exercise 36 (Study of a multisine
response of a linear system: transients and steady-state) 59 Exercise 37
(FRF measurement using a noise excitation and a rectangular window) 61
Exercise 38 (Revealing the nature of the leakage effect in FRF
measurements) 61 Exercise 39 (FRF measurement using a noise excitation and
a Hanning window) 64 Exercise 40 (FRF measurement using a noise excitation
and a diff window) 65 Exercise 41 (FRF measurements using a burst
excitation) 66 Exercise 42 (Impulse response function measurements in the
presence of output noise) 69 Exercise 43 (Measurement of the FRF using a
random noise sequence and a random phase multisine in the presence of
output noise) 70 Exercise 44 (Analysis of the noise errors on FRF
measurements) 71 Exercise 45 (Impact of the block (period) length on the
uncertainty) 73 Exercise 46 (FRF measurement in the presence of
input/output disturbances using a multisine excitation) 75 Exercise 47
(Measuring the FRF in the presence of input and output noise: Analysis of
the errors) 75 Exercise 48 (Measuring the FRF in the presence of input and
output noise: Impact of the block (period) length on the uncertainty) 76
Exercise 49 (Direct measurement of the FRF under feedback conditions) 78
Exercise 50 (The indirect method) 80 Exercise 51 (The local polynomial
method) 82 Exercise 52 (Estimation of the power spectrum of the disturbing
noise) 84 Exercise 53 (Measuring the FRM using multisine excitations) 85
Exercise 54 (Measuring the FRM using noise excitations) 86 Exercise 55
(Estimate the variance of the measured FRM) 88 Exercise 56 (Comparison of
the actual and theoretical variance of the estimated FRM) 88 Exercise 57
(Measuring the FRM using noise excitations and a Hanning window) 89 4
Identification of Linear Dynamic Systems 91 Exercise 58 (Identification in
the time domain) 94 Exercise 59 (Identification in the frequency domain) 96
Exercise 60 (Numerical conditioning) 97 Exercise 61 (Simulation and
one-step-ahead prediction) 99 Exercise 62 (Identify a too-simple model) 100
Exercise 63 (Sensitivity of the simulation and prediction error to model
errors) 101 Exercise 64 (Shaping the model errors in the time domain:
Prefiltering) 102 Exercise 65 (Shaping the model errors in the frequency
domain: frequency weighting) 102 Exercise 66 (One-step-ahead prediction of
a noise sequence) 105 Exercise 67 (Identification in the time domain using
parametric noise models) 108 Exercise 68 (Identification Under Feedback
Conditions Using Time Domain Methods) 109 Exercise 69 (Generating
uncertainty bounds for estimated models) 111 Exercise 70 (Study of the
behavior of the BJ model in combination with prefiltering) 113 Exercise 71
(Identification in the frequency domain using nonparametric noise models)
117 Exercise 72 (Emphasizing a frequency band) 119 Exercise 73 (Comparison
of the time and frequency domain identification under feedback) 120
Exercise 74 (Identification in the frequency domain using nonparametric
noise models and a random excitation) 122 Exercise 75 (Using the time
domain identification toolbox) 124 Exercise 76 (Using the frequency domain
identification toolbox FDIDENT) 129 5 Best Linear Approximation of
Nonlinear Systems 137 Exercise 77.a (Single sine response of a static
nonlinear system) 138 Exercise 77.b (Multisine response of a static
nonlinear system) 139 Exercise 78 (Uniform versus Pointwise Convergence)
142 Exercise 79.a (Normal operation, subharmonics, and chaos) 143 Exercise
79.b (Influence initial conditions) 146 Exercise 80 (Multisine response of
a dynamic nonlinear system) 147 Exercise 81 (Detection, quantification, and
classification of nonlinearities) 148 Exercise 82 (Influence DC values
signals on the linear approximation) 151 Exercise 83.a (Influence of rms
value and pdf on the BLA) 152 Exercise 83.b (Influence of power spectrum
coloring and pdf on the BLA) 154 Exercise 83.c (Influence of length of
impulse response of signal filter on the BLA) 156 Exercise 84.a (Comparison
of Gaussian noise and random phase multisine) 158 Exercise 84.b (Amplitude
distribution of a random phase multisine) 160 Exercise 84.c (Influence of
harmonic content multisine on BLA) 162 Exercise 85 (Influence of even and
odd nonlinearities on BLA) 165 Exercise 86 (BLA of a cascade) 167 Exercise
87.a (Predictive power BLA -- static NL system) 172 Exercise 87.b
(Properties of output residuals -- dynamic NL system) 174 Exercise 87.c
(Predictive power of BLA -- dynamic NL system) 178 6 Measuring the Best
Linear Approximation of a Nonlinear System 183 Exercise 88.a (Robust method
for noisy FRF measurements) 186 Exercise 88.b (Robust method for noisy
input/output measurements without reference signal) 190 Exercise 88.c
(Robust method for noisy input/output measurements with reference signal)
195 Exercise 89.a (Design of baseband odd and full random phase multisines
with random harmonic grid) 197 Exercise 89.b (Design of bandpass odd and
full random phase multisines with random harmonic grid) 197 Exercise 89.c
(Fast method for noisy input/output measurements -- open loop example) 203
Exercise 89.d (Fast method for noisy input/output measurements -- closed
loop example) 207 Exercise 89.e (Bias on the estimated odd and even
distortion levels) 211 Exercise 90 (Indirect method for measuring the best
linear approximation) 215 Exercise 91 (Comparison robust and fast methods)
216 Exercise 92 (Confidence intervals for the BLA) 219 Exercise 93
(Prediction of the bias contribution in the BLA) 221 Exercise 94 (True
underlying linear system) 222 Exercise 95 (Prediction of the nonlinear
distortions using random harmonic grid multisines) 225 Exercise 96 (Pros
and cons full-random and odd-random multisines) 230 7 Identification of
Parametric Models in the Presence of Nonlinear Distortions 239 Exercise 97
(Parametric estimation of the best linear approximation) 240 Exercise 98
243 Exercise 99 (Estimate a parametric model for the best linear
approximation using the Fast Method) 246 Exercise 100 (Estimating a
parametric model for the best linear approximation using the robust method)
251 References 255 Subject Index 259 Reference Index 263
Exercise 1 .a (Least squares estimation of the value of a resistor) 2
Exercise 1 .b (Analysis of the standard deviation) 3 Exercise 2 (Study of
the asymptotic distribution of an estimate) 5 Exercise 3 (Impact of noise
on the regressor (input) measurements) 6 Exercise 4 (Importance of the
choice of the independent variable or input) 7 Exercise 5.a (combining
measurements with a varying SNR: Weighted least squares estimation) 8
Exercise 5.b (Weighted least squares estimation: A study of the variance) 9
Exercise 6 (Least squares estimation of models that are linear in the
parameters) 11 Exercise 7 (Characterizing a 2-dimensional parameter
estimate) 12 Exercise 8 (Dependence of the optimal cost function on the
distribution of the disturbing noise) 14 Exercise 9 (Identification in the
presence of outliers) 16 Exercise 10 (Influence of the number of parameters
on the model uncertainty) 18 Exercise 11 (Model selection using the AIC
criterion) 20 Exercise 12 (Noise on input and output: The instrumental
variables method applied on the resistor estimate) 23 Exercise 13 (Noise on
input and output: the errors-in-variables method) 25 2 Generation and
Analysis of Excitation Signals 29 Exercise 14 (Discretization in time:
Choice of the sampling frequency: ALIAS) 31 Exercise 15 (Windowing: Study
of the leakage effect and the frequency resolution) 31 Exercise 16
(Generate a sine wave, noninteger number of periods measured) 34 Exercise
17 (Generate a sine wave, integer number of periods measured) 34 Exercise
18 (Generate a sine wave, doubled measurement time) 35 Exercise 19.a
(Generate a sine wave using the MATLAB IFFT instruction) 37 Exercise 19.b
(Generate a sine wave using the MATLAB IFFT instruction, defining only the
first half of the spectrum) 37 Exercise 20 (Generation of a multisine with
flat amplitude spectrum) 38 Exercise 21 (The swept sine signal) 39 Exercise
22.a (Spectral analysis of a multisine signal, leakage present) 40 Exercise
22.b (Spectral analysis of a multisine signal, no leakage present) 40
Exercise 23 (Generation of a multisine with a reduced crest factor using
random phase generation) 42 Exercise 24 (Generation of a multisine with a
minimal crest factor using a crest factor minimization algorithm) 42
Exercise 25 (Generation of a maximum length binary sequence) 45 Exercise 26
(Tuning the parameters of a maximum length binary sequence) 46 Exercise 27
(Generation of excitation signals using the FDIDENT toolbox) 47 Exercise 28
(Repeated realizations of a white random noise excitation with fixed
length) 48 Exercise 29 (Repeated realizations of a white random noise
excitation with increasing length) 49 Exercise 30 (Smoothing the amplitude
spectrum of a random excitation) 49 Exercise 31 (Generation of random noise
excitations with a user-imposed power spectrum) 50 Exercise 32 (Amplitude
distribution of filtered noise) 51 Exercise 33 (Exploiting the periodic
nature of signals: Differentiation, integration, +averaging, and filtering)
52 3 FRF Measurements 55 Exercise 34 (Impulse response function
measurements) 57 Exercise 35 (Study of the sine response of a linear
system: transients and steady-state) 58 Exercise 36 (Study of a multisine
response of a linear system: transients and steady-state) 59 Exercise 37
(FRF measurement using a noise excitation and a rectangular window) 61
Exercise 38 (Revealing the nature of the leakage effect in FRF
measurements) 61 Exercise 39 (FRF measurement using a noise excitation and
a Hanning window) 64 Exercise 40 (FRF measurement using a noise excitation
and a diff window) 65 Exercise 41 (FRF measurements using a burst
excitation) 66 Exercise 42 (Impulse response function measurements in the
presence of output noise) 69 Exercise 43 (Measurement of the FRF using a
random noise sequence and a random phase multisine in the presence of
output noise) 70 Exercise 44 (Analysis of the noise errors on FRF
measurements) 71 Exercise 45 (Impact of the block (period) length on the
uncertainty) 73 Exercise 46 (FRF measurement in the presence of
input/output disturbances using a multisine excitation) 75 Exercise 47
(Measuring the FRF in the presence of input and output noise: Analysis of
the errors) 75 Exercise 48 (Measuring the FRF in the presence of input and
output noise: Impact of the block (period) length on the uncertainty) 76
Exercise 49 (Direct measurement of the FRF under feedback conditions) 78
Exercise 50 (The indirect method) 80 Exercise 51 (The local polynomial
method) 82 Exercise 52 (Estimation of the power spectrum of the disturbing
noise) 84 Exercise 53 (Measuring the FRM using multisine excitations) 85
Exercise 54 (Measuring the FRM using noise excitations) 86 Exercise 55
(Estimate the variance of the measured FRM) 88 Exercise 56 (Comparison of
the actual and theoretical variance of the estimated FRM) 88 Exercise 57
(Measuring the FRM using noise excitations and a Hanning window) 89 4
Identification of Linear Dynamic Systems 91 Exercise 58 (Identification in
the time domain) 94 Exercise 59 (Identification in the frequency domain) 96
Exercise 60 (Numerical conditioning) 97 Exercise 61 (Simulation and
one-step-ahead prediction) 99 Exercise 62 (Identify a too-simple model) 100
Exercise 63 (Sensitivity of the simulation and prediction error to model
errors) 101 Exercise 64 (Shaping the model errors in the time domain:
Prefiltering) 102 Exercise 65 (Shaping the model errors in the frequency
domain: frequency weighting) 102 Exercise 66 (One-step-ahead prediction of
a noise sequence) 105 Exercise 67 (Identification in the time domain using
parametric noise models) 108 Exercise 68 (Identification Under Feedback
Conditions Using Time Domain Methods) 109 Exercise 69 (Generating
uncertainty bounds for estimated models) 111 Exercise 70 (Study of the
behavior of the BJ model in combination with prefiltering) 113 Exercise 71
(Identification in the frequency domain using nonparametric noise models)
117 Exercise 72 (Emphasizing a frequency band) 119 Exercise 73 (Comparison
of the time and frequency domain identification under feedback) 120
Exercise 74 (Identification in the frequency domain using nonparametric
noise models and a random excitation) 122 Exercise 75 (Using the time
domain identification toolbox) 124 Exercise 76 (Using the frequency domain
identification toolbox FDIDENT) 129 5 Best Linear Approximation of
Nonlinear Systems 137 Exercise 77.a (Single sine response of a static
nonlinear system) 138 Exercise 77.b (Multisine response of a static
nonlinear system) 139 Exercise 78 (Uniform versus Pointwise Convergence)
142 Exercise 79.a (Normal operation, subharmonics, and chaos) 143 Exercise
79.b (Influence initial conditions) 146 Exercise 80 (Multisine response of
a dynamic nonlinear system) 147 Exercise 81 (Detection, quantification, and
classification of nonlinearities) 148 Exercise 82 (Influence DC values
signals on the linear approximation) 151 Exercise 83.a (Influence of rms
value and pdf on the BLA) 152 Exercise 83.b (Influence of power spectrum
coloring and pdf on the BLA) 154 Exercise 83.c (Influence of length of
impulse response of signal filter on the BLA) 156 Exercise 84.a (Comparison
of Gaussian noise and random phase multisine) 158 Exercise 84.b (Amplitude
distribution of a random phase multisine) 160 Exercise 84.c (Influence of
harmonic content multisine on BLA) 162 Exercise 85 (Influence of even and
odd nonlinearities on BLA) 165 Exercise 86 (BLA of a cascade) 167 Exercise
87.a (Predictive power BLA -- static NL system) 172 Exercise 87.b
(Properties of output residuals -- dynamic NL system) 174 Exercise 87.c
(Predictive power of BLA -- dynamic NL system) 178 6 Measuring the Best
Linear Approximation of a Nonlinear System 183 Exercise 88.a (Robust method
for noisy FRF measurements) 186 Exercise 88.b (Robust method for noisy
input/output measurements without reference signal) 190 Exercise 88.c
(Robust method for noisy input/output measurements with reference signal)
195 Exercise 89.a (Design of baseband odd and full random phase multisines
with random harmonic grid) 197 Exercise 89.b (Design of bandpass odd and
full random phase multisines with random harmonic grid) 197 Exercise 89.c
(Fast method for noisy input/output measurements -- open loop example) 203
Exercise 89.d (Fast method for noisy input/output measurements -- closed
loop example) 207 Exercise 89.e (Bias on the estimated odd and even
distortion levels) 211 Exercise 90 (Indirect method for measuring the best
linear approximation) 215 Exercise 91 (Comparison robust and fast methods)
216 Exercise 92 (Confidence intervals for the BLA) 219 Exercise 93
(Prediction of the bias contribution in the BLA) 221 Exercise 94 (True
underlying linear system) 222 Exercise 95 (Prediction of the nonlinear
distortions using random harmonic grid multisines) 225 Exercise 96 (Pros
and cons full-random and odd-random multisines) 230 7 Identification of
Parametric Models in the Presence of Nonlinear Distortions 239 Exercise 97
(Parametric estimation of the best linear approximation) 240 Exercise 98
243 Exercise 99 (Estimate a parametric model for the best linear
approximation using the Fast Method) 246 Exercise 100 (Estimating a
parametric model for the best linear approximation using the robust method)
251 References 255 Subject Index 259 Reference Index 263
Preface xiii Acknowledgments xv Abbreviations xvii 1 Identification 1
Exercise 1 .a (Least squares estimation of the value of a resistor) 2
Exercise 1 .b (Analysis of the standard deviation) 3 Exercise 2 (Study of
the asymptotic distribution of an estimate) 5 Exercise 3 (Impact of noise
on the regressor (input) measurements) 6 Exercise 4 (Importance of the
choice of the independent variable or input) 7 Exercise 5.a (combining
measurements with a varying SNR: Weighted least squares estimation) 8
Exercise 5.b (Weighted least squares estimation: A study of the variance) 9
Exercise 6 (Least squares estimation of models that are linear in the
parameters) 11 Exercise 7 (Characterizing a 2-dimensional parameter
estimate) 12 Exercise 8 (Dependence of the optimal cost function on the
distribution of the disturbing noise) 14 Exercise 9 (Identification in the
presence of outliers) 16 Exercise 10 (Influence of the number of parameters
on the model uncertainty) 18 Exercise 11 (Model selection using the AIC
criterion) 20 Exercise 12 (Noise on input and output: The instrumental
variables method applied on the resistor estimate) 23 Exercise 13 (Noise on
input and output: the errors-in-variables method) 25 2 Generation and
Analysis of Excitation Signals 29 Exercise 14 (Discretization in time:
Choice of the sampling frequency: ALIAS) 31 Exercise 15 (Windowing: Study
of the leakage effect and the frequency resolution) 31 Exercise 16
(Generate a sine wave, noninteger number of periods measured) 34 Exercise
17 (Generate a sine wave, integer number of periods measured) 34 Exercise
18 (Generate a sine wave, doubled measurement time) 35 Exercise 19.a
(Generate a sine wave using the MATLAB IFFT instruction) 37 Exercise 19.b
(Generate a sine wave using the MATLAB IFFT instruction, defining only the
first half of the spectrum) 37 Exercise 20 (Generation of a multisine with
flat amplitude spectrum) 38 Exercise 21 (The swept sine signal) 39 Exercise
22.a (Spectral analysis of a multisine signal, leakage present) 40 Exercise
22.b (Spectral analysis of a multisine signal, no leakage present) 40
Exercise 23 (Generation of a multisine with a reduced crest factor using
random phase generation) 42 Exercise 24 (Generation of a multisine with a
minimal crest factor using a crest factor minimization algorithm) 42
Exercise 25 (Generation of a maximum length binary sequence) 45 Exercise 26
(Tuning the parameters of a maximum length binary sequence) 46 Exercise 27
(Generation of excitation signals using the FDIDENT toolbox) 47 Exercise 28
(Repeated realizations of a white random noise excitation with fixed
length) 48 Exercise 29 (Repeated realizations of a white random noise
excitation with increasing length) 49 Exercise 30 (Smoothing the amplitude
spectrum of a random excitation) 49 Exercise 31 (Generation of random noise
excitations with a user-imposed power spectrum) 50 Exercise 32 (Amplitude
distribution of filtered noise) 51 Exercise 33 (Exploiting the periodic
nature of signals: Differentiation, integration, +averaging, and filtering)
52 3 FRF Measurements 55 Exercise 34 (Impulse response function
measurements) 57 Exercise 35 (Study of the sine response of a linear
system: transients and steady-state) 58 Exercise 36 (Study of a multisine
response of a linear system: transients and steady-state) 59 Exercise 37
(FRF measurement using a noise excitation and a rectangular window) 61
Exercise 38 (Revealing the nature of the leakage effect in FRF
measurements) 61 Exercise 39 (FRF measurement using a noise excitation and
a Hanning window) 64 Exercise 40 (FRF measurement using a noise excitation
and a diff window) 65 Exercise 41 (FRF measurements using a burst
excitation) 66 Exercise 42 (Impulse response function measurements in the
presence of output noise) 69 Exercise 43 (Measurement of the FRF using a
random noise sequence and a random phase multisine in the presence of
output noise) 70 Exercise 44 (Analysis of the noise errors on FRF
measurements) 71 Exercise 45 (Impact of the block (period) length on the
uncertainty) 73 Exercise 46 (FRF measurement in the presence of
input/output disturbances using a multisine excitation) 75 Exercise 47
(Measuring the FRF in the presence of input and output noise: Analysis of
the errors) 75 Exercise 48 (Measuring the FRF in the presence of input and
output noise: Impact of the block (period) length on the uncertainty) 76
Exercise 49 (Direct measurement of the FRF under feedback conditions) 78
Exercise 50 (The indirect method) 80 Exercise 51 (The local polynomial
method) 82 Exercise 52 (Estimation of the power spectrum of the disturbing
noise) 84 Exercise 53 (Measuring the FRM using multisine excitations) 85
Exercise 54 (Measuring the FRM using noise excitations) 86 Exercise 55
(Estimate the variance of the measured FRM) 88 Exercise 56 (Comparison of
the actual and theoretical variance of the estimated FRM) 88 Exercise 57
(Measuring the FRM using noise excitations and a Hanning window) 89 4
Identification of Linear Dynamic Systems 91 Exercise 58 (Identification in
the time domain) 94 Exercise 59 (Identification in the frequency domain) 96
Exercise 60 (Numerical conditioning) 97 Exercise 61 (Simulation and
one-step-ahead prediction) 99 Exercise 62 (Identify a too-simple model) 100
Exercise 63 (Sensitivity of the simulation and prediction error to model
errors) 101 Exercise 64 (Shaping the model errors in the time domain:
Prefiltering) 102 Exercise 65 (Shaping the model errors in the frequency
domain: frequency weighting) 102 Exercise 66 (One-step-ahead prediction of
a noise sequence) 105 Exercise 67 (Identification in the time domain using
parametric noise models) 108 Exercise 68 (Identification Under Feedback
Conditions Using Time Domain Methods) 109 Exercise 69 (Generating
uncertainty bounds for estimated models) 111 Exercise 70 (Study of the
behavior of the BJ model in combination with prefiltering) 113 Exercise 71
(Identification in the frequency domain using nonparametric noise models)
117 Exercise 72 (Emphasizing a frequency band) 119 Exercise 73 (Comparison
of the time and frequency domain identification under feedback) 120
Exercise 74 (Identification in the frequency domain using nonparametric
noise models and a random excitation) 122 Exercise 75 (Using the time
domain identification toolbox) 124 Exercise 76 (Using the frequency domain
identification toolbox FDIDENT) 129 5 Best Linear Approximation of
Nonlinear Systems 137 Exercise 77.a (Single sine response of a static
nonlinear system) 138 Exercise 77.b (Multisine response of a static
nonlinear system) 139 Exercise 78 (Uniform versus Pointwise Convergence)
142 Exercise 79.a (Normal operation, subharmonics, and chaos) 143 Exercise
79.b (Influence initial conditions) 146 Exercise 80 (Multisine response of
a dynamic nonlinear system) 147 Exercise 81 (Detection, quantification, and
classification of nonlinearities) 148 Exercise 82 (Influence DC values
signals on the linear approximation) 151 Exercise 83.a (Influence of rms
value and pdf on the BLA) 152 Exercise 83.b (Influence of power spectrum
coloring and pdf on the BLA) 154 Exercise 83.c (Influence of length of
impulse response of signal filter on the BLA) 156 Exercise 84.a (Comparison
of Gaussian noise and random phase multisine) 158 Exercise 84.b (Amplitude
distribution of a random phase multisine) 160 Exercise 84.c (Influence of
harmonic content multisine on BLA) 162 Exercise 85 (Influence of even and
odd nonlinearities on BLA) 165 Exercise 86 (BLA of a cascade) 167 Exercise
87.a (Predictive power BLA -- static NL system) 172 Exercise 87.b
(Properties of output residuals -- dynamic NL system) 174 Exercise 87.c
(Predictive power of BLA -- dynamic NL system) 178 6 Measuring the Best
Linear Approximation of a Nonlinear System 183 Exercise 88.a (Robust method
for noisy FRF measurements) 186 Exercise 88.b (Robust method for noisy
input/output measurements without reference signal) 190 Exercise 88.c
(Robust method for noisy input/output measurements with reference signal)
195 Exercise 89.a (Design of baseband odd and full random phase multisines
with random harmonic grid) 197 Exercise 89.b (Design of bandpass odd and
full random phase multisines with random harmonic grid) 197 Exercise 89.c
(Fast method for noisy input/output measurements -- open loop example) 203
Exercise 89.d (Fast method for noisy input/output measurements -- closed
loop example) 207 Exercise 89.e (Bias on the estimated odd and even
distortion levels) 211 Exercise 90 (Indirect method for measuring the best
linear approximation) 215 Exercise 91 (Comparison robust and fast methods)
216 Exercise 92 (Confidence intervals for the BLA) 219 Exercise 93
(Prediction of the bias contribution in the BLA) 221 Exercise 94 (True
underlying linear system) 222 Exercise 95 (Prediction of the nonlinear
distortions using random harmonic grid multisines) 225 Exercise 96 (Pros
and cons full-random and odd-random multisines) 230 7 Identification of
Parametric Models in the Presence of Nonlinear Distortions 239 Exercise 97
(Parametric estimation of the best linear approximation) 240 Exercise 98
243 Exercise 99 (Estimate a parametric model for the best linear
approximation using the Fast Method) 246 Exercise 100 (Estimating a
parametric model for the best linear approximation using the robust method)
251 References 255 Subject Index 259 Reference Index 263
Exercise 1 .a (Least squares estimation of the value of a resistor) 2
Exercise 1 .b (Analysis of the standard deviation) 3 Exercise 2 (Study of
the asymptotic distribution of an estimate) 5 Exercise 3 (Impact of noise
on the regressor (input) measurements) 6 Exercise 4 (Importance of the
choice of the independent variable or input) 7 Exercise 5.a (combining
measurements with a varying SNR: Weighted least squares estimation) 8
Exercise 5.b (Weighted least squares estimation: A study of the variance) 9
Exercise 6 (Least squares estimation of models that are linear in the
parameters) 11 Exercise 7 (Characterizing a 2-dimensional parameter
estimate) 12 Exercise 8 (Dependence of the optimal cost function on the
distribution of the disturbing noise) 14 Exercise 9 (Identification in the
presence of outliers) 16 Exercise 10 (Influence of the number of parameters
on the model uncertainty) 18 Exercise 11 (Model selection using the AIC
criterion) 20 Exercise 12 (Noise on input and output: The instrumental
variables method applied on the resistor estimate) 23 Exercise 13 (Noise on
input and output: the errors-in-variables method) 25 2 Generation and
Analysis of Excitation Signals 29 Exercise 14 (Discretization in time:
Choice of the sampling frequency: ALIAS) 31 Exercise 15 (Windowing: Study
of the leakage effect and the frequency resolution) 31 Exercise 16
(Generate a sine wave, noninteger number of periods measured) 34 Exercise
17 (Generate a sine wave, integer number of periods measured) 34 Exercise
18 (Generate a sine wave, doubled measurement time) 35 Exercise 19.a
(Generate a sine wave using the MATLAB IFFT instruction) 37 Exercise 19.b
(Generate a sine wave using the MATLAB IFFT instruction, defining only the
first half of the spectrum) 37 Exercise 20 (Generation of a multisine with
flat amplitude spectrum) 38 Exercise 21 (The swept sine signal) 39 Exercise
22.a (Spectral analysis of a multisine signal, leakage present) 40 Exercise
22.b (Spectral analysis of a multisine signal, no leakage present) 40
Exercise 23 (Generation of a multisine with a reduced crest factor using
random phase generation) 42 Exercise 24 (Generation of a multisine with a
minimal crest factor using a crest factor minimization algorithm) 42
Exercise 25 (Generation of a maximum length binary sequence) 45 Exercise 26
(Tuning the parameters of a maximum length binary sequence) 46 Exercise 27
(Generation of excitation signals using the FDIDENT toolbox) 47 Exercise 28
(Repeated realizations of a white random noise excitation with fixed
length) 48 Exercise 29 (Repeated realizations of a white random noise
excitation with increasing length) 49 Exercise 30 (Smoothing the amplitude
spectrum of a random excitation) 49 Exercise 31 (Generation of random noise
excitations with a user-imposed power spectrum) 50 Exercise 32 (Amplitude
distribution of filtered noise) 51 Exercise 33 (Exploiting the periodic
nature of signals: Differentiation, integration, +averaging, and filtering)
52 3 FRF Measurements 55 Exercise 34 (Impulse response function
measurements) 57 Exercise 35 (Study of the sine response of a linear
system: transients and steady-state) 58 Exercise 36 (Study of a multisine
response of a linear system: transients and steady-state) 59 Exercise 37
(FRF measurement using a noise excitation and a rectangular window) 61
Exercise 38 (Revealing the nature of the leakage effect in FRF
measurements) 61 Exercise 39 (FRF measurement using a noise excitation and
a Hanning window) 64 Exercise 40 (FRF measurement using a noise excitation
and a diff window) 65 Exercise 41 (FRF measurements using a burst
excitation) 66 Exercise 42 (Impulse response function measurements in the
presence of output noise) 69 Exercise 43 (Measurement of the FRF using a
random noise sequence and a random phase multisine in the presence of
output noise) 70 Exercise 44 (Analysis of the noise errors on FRF
measurements) 71 Exercise 45 (Impact of the block (period) length on the
uncertainty) 73 Exercise 46 (FRF measurement in the presence of
input/output disturbances using a multisine excitation) 75 Exercise 47
(Measuring the FRF in the presence of input and output noise: Analysis of
the errors) 75 Exercise 48 (Measuring the FRF in the presence of input and
output noise: Impact of the block (period) length on the uncertainty) 76
Exercise 49 (Direct measurement of the FRF under feedback conditions) 78
Exercise 50 (The indirect method) 80 Exercise 51 (The local polynomial
method) 82 Exercise 52 (Estimation of the power spectrum of the disturbing
noise) 84 Exercise 53 (Measuring the FRM using multisine excitations) 85
Exercise 54 (Measuring the FRM using noise excitations) 86 Exercise 55
(Estimate the variance of the measured FRM) 88 Exercise 56 (Comparison of
the actual and theoretical variance of the estimated FRM) 88 Exercise 57
(Measuring the FRM using noise excitations and a Hanning window) 89 4
Identification of Linear Dynamic Systems 91 Exercise 58 (Identification in
the time domain) 94 Exercise 59 (Identification in the frequency domain) 96
Exercise 60 (Numerical conditioning) 97 Exercise 61 (Simulation and
one-step-ahead prediction) 99 Exercise 62 (Identify a too-simple model) 100
Exercise 63 (Sensitivity of the simulation and prediction error to model
errors) 101 Exercise 64 (Shaping the model errors in the time domain:
Prefiltering) 102 Exercise 65 (Shaping the model errors in the frequency
domain: frequency weighting) 102 Exercise 66 (One-step-ahead prediction of
a noise sequence) 105 Exercise 67 (Identification in the time domain using
parametric noise models) 108 Exercise 68 (Identification Under Feedback
Conditions Using Time Domain Methods) 109 Exercise 69 (Generating
uncertainty bounds for estimated models) 111 Exercise 70 (Study of the
behavior of the BJ model in combination with prefiltering) 113 Exercise 71
(Identification in the frequency domain using nonparametric noise models)
117 Exercise 72 (Emphasizing a frequency band) 119 Exercise 73 (Comparison
of the time and frequency domain identification under feedback) 120
Exercise 74 (Identification in the frequency domain using nonparametric
noise models and a random excitation) 122 Exercise 75 (Using the time
domain identification toolbox) 124 Exercise 76 (Using the frequency domain
identification toolbox FDIDENT) 129 5 Best Linear Approximation of
Nonlinear Systems 137 Exercise 77.a (Single sine response of a static
nonlinear system) 138 Exercise 77.b (Multisine response of a static
nonlinear system) 139 Exercise 78 (Uniform versus Pointwise Convergence)
142 Exercise 79.a (Normal operation, subharmonics, and chaos) 143 Exercise
79.b (Influence initial conditions) 146 Exercise 80 (Multisine response of
a dynamic nonlinear system) 147 Exercise 81 (Detection, quantification, and
classification of nonlinearities) 148 Exercise 82 (Influence DC values
signals on the linear approximation) 151 Exercise 83.a (Influence of rms
value and pdf on the BLA) 152 Exercise 83.b (Influence of power spectrum
coloring and pdf on the BLA) 154 Exercise 83.c (Influence of length of
impulse response of signal filter on the BLA) 156 Exercise 84.a (Comparison
of Gaussian noise and random phase multisine) 158 Exercise 84.b (Amplitude
distribution of a random phase multisine) 160 Exercise 84.c (Influence of
harmonic content multisine on BLA) 162 Exercise 85 (Influence of even and
odd nonlinearities on BLA) 165 Exercise 86 (BLA of a cascade) 167 Exercise
87.a (Predictive power BLA -- static NL system) 172 Exercise 87.b
(Properties of output residuals -- dynamic NL system) 174 Exercise 87.c
(Predictive power of BLA -- dynamic NL system) 178 6 Measuring the Best
Linear Approximation of a Nonlinear System 183 Exercise 88.a (Robust method
for noisy FRF measurements) 186 Exercise 88.b (Robust method for noisy
input/output measurements without reference signal) 190 Exercise 88.c
(Robust method for noisy input/output measurements with reference signal)
195 Exercise 89.a (Design of baseband odd and full random phase multisines
with random harmonic grid) 197 Exercise 89.b (Design of bandpass odd and
full random phase multisines with random harmonic grid) 197 Exercise 89.c
(Fast method for noisy input/output measurements -- open loop example) 203
Exercise 89.d (Fast method for noisy input/output measurements -- closed
loop example) 207 Exercise 89.e (Bias on the estimated odd and even
distortion levels) 211 Exercise 90 (Indirect method for measuring the best
linear approximation) 215 Exercise 91 (Comparison robust and fast methods)
216 Exercise 92 (Confidence intervals for the BLA) 219 Exercise 93
(Prediction of the bias contribution in the BLA) 221 Exercise 94 (True
underlying linear system) 222 Exercise 95 (Prediction of the nonlinear
distortions using random harmonic grid multisines) 225 Exercise 96 (Pros
and cons full-random and odd-random multisines) 230 7 Identification of
Parametric Models in the Presence of Nonlinear Distortions 239 Exercise 97
(Parametric estimation of the best linear approximation) 240 Exercise 98
243 Exercise 99 (Estimate a parametric model for the best linear
approximation using the Fast Method) 246 Exercise 100 (Estimating a
parametric model for the best linear approximation using the robust method)
251 References 255 Subject Index 259 Reference Index 263