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This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics.
Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems.

This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization

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CONTENTS
Preface = ⅴ
1 Introduction = 1
2 Modeling = 3
 2.1 Introduction = 3
 2.2 Model building approaches = 5
 2.3 Mathematical models = 9
  2.3.1 Static models = 9
  2.3.2 Dynamic continuous models = 10
  2.3.3 Dynamic discrete models = 14
 2.4 Index of a DAE = 16
 2.5 Examples = 18
 2.6 Bond graphs = 24
  2.6.1 Variables = 24
  2.6.2 Bonds = 25
  2.6.3 Bond graph elements = 28
  2.6.4 Causalify = 29
 2.7 Comparison circuits, bond graphs and block diagrams = 31
 2.8 Examples = 34
 2.9 Summary = 39
 2.10 References = 39
 2.11 Problems = 40
3 Black - box model representations = 43
 3.1 Introduction = 43
 3.2 Discrete-time systems = 46
 3.3 Impulse response and transfer function = 47
 3.4 Disturbances = 49
  3.4.1 Statistics and stochastics = 49
  3.4.2 Discrete white noise = 55
 3.5 Time - domain representations = 56
  3.5.1 Finite Impulse Response model = 57
  3.5.2 Auto - Regressive with eXogenous input model = 57
  3.5.3 Auto - Regressive Moving Average with eXogenous input model = 58
  3.5.4 Output Error model = 58
  3.5.5 Box - Jenkins model = 58
  3.5.6 Summary = 59
 3.6 Frequency - domain representations = 60
  3.6.1 Frequency Function = 60
  3.6.2 Signal spectrum = 61
  3.6.3 Transformation of spectra = 64
 3.7 Examples : calculation of stochastic quantities = 65
  3.7.1 Covariance function of a MA process = 65
  3.7.2 Covariance function of an AR process = 67
  3.7.3 Approximation of mean and covariance = 68
 3.8 Summary = 69
 3.9 References = 70
 3.10 Problems = 70
4 Nonparametric identification = 73
 4.1 Time domain identification by correlation analysis = 73
 4.2 Frequency response analysis = 75
 4.3 Frequency response analysis by the correlation method = 76
 4.4 Fourier analysis : the Empirical Transfer Function Estimate = 77
  4.4.1 Fourier analysis = 77
  4.4.2 Empirical Transfer Function Estimate (ETFE) = 79
  4.4.3 Smoothing of the ETFE = 83
 4.5 Persistence of Excitation = 85
 4.6 Summary = 86
 4.7 References = 87
 4.8 Problems = 88
5 Parametric identification = 89
 5.1 Prediction error methods = 89
 5.2 Prediction models = 90
  5.2.1 One - step ahead prediction = 90
  5.2.2 Prediction model for the FIR structure = 93
  5.2.3 Prediction model for the ARX structure = 93
  5.2.4 Prediction model for the ARMAX structure = 94
  5.2.5 Prediction model for the OE structure = 95
 5.3 Least Squares method = 95
  5.3.1 Linear Least Squares = 96
  5.3.2 Pseudo - Linear Least Squares = 97
  5.3.3 Example = 97
 5.4 Analysis of the linear LS estimate = 98
 5.5 Convergence and consistency = 100
 5.6 Approximate identification = 102
  5.6.1 Fixed noise model = 103
  5.6.2 General noise model = 104
  5.6.3 Filtered prediction errors = 104
  5.6.4 Example = 106
 5.7 Summary = 107
 5.8 References = 108
 5.9 Problems = 109
6 Identification in practice = 111
 6.1 Experiment design = 111
  6.1.1 Input design = 112
  6.1.2 Sampling frequency = 113
  6.1.3 Data preprocessing = 114
  6.1.4 Prediction error prefilter = 114
 6.2 Model structure selection = 114
  6.2.1 Determination of the model order = 115
  6.2.2 Estimation of dead time = 116
 6.3 Model validation = 118
  6.3.1 Residual analysis = 118
  6.3.2 Other validation techniques = 121
 6.4 Summary = 122
 6.5 References = 123
 6.6 Problems = 123
7 Simulation = 125
 7.1 Introduction = 125
 7.2 Simulation tools = 127
  7.2.1 Simulation hardware = 127
  7.2.2 Simulation software = 130
 7.3 Numerical solution of differential equations = 133
  7.3.1 Introduction = 133
  7.3.2 Numerical integration = 136
  7.3.3 Examples = 147
 7.4 Conversion from parallel to series = 148
 7.5 Solving stiff ODEs and DAEs = 152
  7.5.1 BDF methods = 153
  7.5.2 Error analysis of a BDF method = 154
  7.5.3 Propagation of the truncation error = 155
  7.5.4 Newton iteration = 157
  7.5.5 Numerical problems of higher index DAE = 157
 7.6 Applications = 158
  7.6.1 Parameter estimation = 158
  7.6.2 Controller design = 159
 7.7 Summary = 160
 7.8 References = 161
 7.9 Problems = 161
8 Optimization = 163
 8.1 Introduction = 163
 8.2 Convergence = 167
 8.3 Determination of step size s_i = 167
 8.4 Determination of search direction d_i = 170
  8.4.1 Direct search methods = 170
  8.4.2 Gradient methods = 172
  8.4.3 Conjugate-gradient methods = 173
  8.4.4 Example = 175
  8.4.5 Comparison search methods = 177
 8.5 Least Squares Problem = 178
 8.6 Optimization with constraints = 180
  8.6.1 Elimination = 181
  8.6.2 Lagrange multipliers = 182
  8.6.3 Gradient - projection method = 182
  8.6.4 Reduced - gradient method = 184
  8.6.5 Penalty function = 185
 8.7 Summary = 186
 8.8 References = 187
 8.9 Problems = 187
 Literature = 189
Index = 192