Maths for engineers Books

Book SynopsisExplore the diverse electrical engineering application of polymer composite materials with this in-depth collection edited by leaders in the field Polymer Composites for Electrical Engineering delivers a comprehensive exploration of the fundamental principles, state-of-the-art research, and future challenges of polymer composites. Written from the perspective of electrical engineering applications, like electrical and thermal energy storage, high temperature applications, fire retardance, power cables, electric stress control, and others, the book covers all major application branches of these widely used materials. Rather than focus on polymer composite materials themselves, the distinguished editors have chosen to collect contributions from industry leaders in the area of real and practical electrical engineering applications of polymer composites. The book?s relevance will only increase as advanced polymer composites receive more attention and interest iTable of ContentsAbout the Author xi Preface to the Fourth Edition xiii 1 Introduction 1 The Case for Imprecision 2 A Historical Perspective 4 The Utility of Fuzzy Systems 7 Limitations of Fuzzy Systems 9 The Illusion: Ignoring Uncertainty and Accuracy 11 Uncertainty and Information 13 Fuzzy Sets and Membership 14 Chance versus Fuzziness 17 Intuition of Uncertainty: Fuzzy versus Probability 19 Sets as Points in Hypercubes 21 Summary 23 References 23 Problems 24 2 Classical Sets and Fuzzy Sets 27 Classical Sets 28 Fuzzy Sets 36 Summary 45 References 46 Problems 46 3 Classical Relations and Fuzzy Relations 51 Cartesian Product 52 Crisp Relations 53 Fuzzy Relations 58 Tolerance and Equivalence Relations 67 Fuzzy Tolerance and Equivalence Relations 70 Value Assignments 72 Other Forms of the Composition Operation 76 Summary 77 References 77 Problems 77 4 Properties of Membership Functions, Fuzzification, and Defuzzification 84 Features of the Membership Function 85 Various Forms 87 Fuzzification 88 Defuzzification to Crisp Sets 90 λ-Cuts for Fuzzy Relations 92 Defuzzification to Scalars 93 Summary 102 References 103 Problems 104 5 Logic and Fuzzy Systems 107 Part I: Logic 107 Classical Logic 108 Fuzzy Logic 122 Part II: Fuzzy Systems 132 Summary 151 References 153 Problems 154 6 Historical Methods of Developing Membership Functions 163 Membership Value Assignments 164 Intuition 164 Inference 165 Rank Ordering 167 Neural Networks 168 Genetic Algorithms 179 Inductive Reasoning 188 Summary 195 References 196 Problems 197 7 Automated Methods for Fuzzy Systems 201 Definitions 202 Batch Least Squares Algorithm 205 Recursive Least Squares Algorithm 210 Gradient Method 213 Clustering Method 218 Learning from Examples 221 Modified Learning from Examples 224 Summary 233 References 235 Problems 235 8 Fuzzy Systems Simulation 237 Fuzzy Relational Equations 242 Nonlinear Simulation Using Fuzzy Systems 243 Fuzzy Associative Memories (FAMs) 246 Summary 257 References 258 Problems 259 9 Decision Making with Fuzzy Information 265 Fuzzy Synthetic Evaluation 267 Fuzzy Ordering 269 Nontransitive Ranking 272 Preference and Consensus 275 Multiobjective Decision Making 279 Fuzzy Bayesian Decision Method 285 Decision Making under Fuzzy States and Fuzzy Actions 295 Summary 309 References 310 Problems 311 10 Fuzzy Classification and Pattern Recognition 323 Fuzzy Classification 324 Classification by Equivalence Relations 324 Cluster Analysis 332 Cluster Validity 332 c-Means Clustering 333 Hard c-Means (HCM) 333 Fuzzy c-Means (FCM) 343 Classification Metric 351 Hardening the Fuzzy c-Partition 354 Similarity Relations from Clustering 356 Fuzzy Pattern Recognition 357 Single-Sample Identification 357 Multifeature Pattern Recognition 365 Summary 378 References 379 Problems 380 11 Fuzzy Control Systems 388 Control System Design Problem 390 Examples of Fuzzy Control System Design 393 Fuzzy Engineering Process Control 404 Fuzzy Statistical Process Control 417 Industrial Applications 431 Summary 434 References 437 Problems 438 12 Applications of Fuzzy Systems Using Miscellaneous Models 455 Fuzzy Optimization 455 Fuzzy Cognitive Mapping 462 Agent-Based Models 477 Fuzzy Arithmetic and the Extension Principle 481 Fuzzy Algebra 487 Data Fusion 491 Summary 498 References 498 Problems 500 13 Monotone Measures: Belief, Plausibility, Probability, and Possibility 505 Monotone Measures 506 Belief and Plausibility 507 Evidence Theory 512 Probability Measures 515 Possibility and Necessity Measures 517 Possibility Distributions as Fuzzy Sets 525 Possibility Distributions Derived from Empirical Intervals 528 Summary 548 References 549 Problems 550 Index 554

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Book SynopsisA problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals.Table of ContentsList of Figures xvii List of Tables xxiii Preface xxv List of Abbreviations xxix How to Use the Book xxxi About the Companion Website xxxiii Prerequisites xxxv Why are there so many matrixes in this book? xxxvii 1 Manipulations on Matrixes 1 1.1 Matrix Properties 1 1.1.1 Elementary Operations 2 1.2 Eigen-Decomposition 6 1.3 Eigenvectors in Everyday Life 9 1.3.1 Conversations in a Noisy Restaurant 9 1.3.2 Power Control in a Cellular System 12 1.3.3 Price Equilibrium in the Economy 14 1.4 Derivative Rules 15 1.4.1 Derivative with respect to x 16 1.4.2 Derivative with respect to x 17 1.4.3 Derivative with respect to the Matrix X 18 1.5 Quadratic Forms 19 1.6 Diagonalization of a Quadratic Form 20 1.7 Rayleigh Quotient 21 1.8 Basics of Optimization 22 1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23 1.8.2 Quadratic Function with Multiple Linear Constraints 23 Appendix A: Arithmetic vs. Geometric Mean 24 2 Linear Algebraic Systems 27 2.1 Problem Definition and Vector Spaces 27 2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29 2.2 Rotations 31 2.3 Projection Matrixes and Data-Filtering 33 2.3.1 Projections and Commercial FM Radio 34 2.4 Singular Value Decomposition (SVD) and Subspaces 34 2.4.1 How to Choose the Rank of Afor Gaussian Model? 35 2.5 QR and Cholesky Factorization 36 2.6 Power Method for Leading Eigenvectors 38 2.7 Least Squares Solution of Overdetermined Linear Equations 39 2.8 Efficient Implementation of the LS Solution 41 2.9 Iterative Methods 42 3 Random Variables in Brief 45 3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45 3.2 Convexity and Jensen Inequality 49 3.3 Uncorrelatedness and Statistical Independence 49 3.4 Real-Valued Gaussian Random Variables 51 3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54 3.6 Conditional pdf in Additive Noise Model 56 3.7 Complex Gaussian Random Variables 56 3.7.1 Single Complex Gaussian Random Variable 56 3.7.2 Circular Complex Gaussian Random Variable 57 3.7.3 Multivariate Complex Gaussian Random Variables 58 3.8 Sum of Square of Gaussians: Chi-Square 59 3.9 Order Statistics for N rvs 60 4 Random Processes and Linear Systems 63 4.1 Moment Characterizations and Stationarity 64 4.2 Random Processes and Linear Systems 66 4.3 Complex-Valued Random Processes 68 4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69 4.4.1 Stability of LTI Systems 70 4.4.2 Rational PSD 71 4.4.3 Paley–Wiener Theorem 72 4.5 Gaussian Random Process (Discrete-Time) 73 4.6 Measuring Moments in Stochastic Processes 75 Appendix A: Transforms for Continuous-Time Signals 76 Appendix B: Transforms for Discrete-Time Signals 79 5 Models and Applications 83 5.1 Linear Regression Model 84 5.2 Linear Filtering Model 86 5.2.1 Block-Wise Circular Convolution 88 5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89 5.2.3 Identification and Deconvolution 90 5.3 MIMO systems and Interference Models 91 5.3.1 DSL System 92 5.3.2 MIMO in Wireless Communication 92 5.4 Sinusoidal Signal 97 5.5 Irregular Sampling and Interpolation 97 5.5.1 Sampling With Jitter 100 5.6 Wavefield Sensing System 101 6 Estimation Theory 105 6.1 Historical Notes 105 6.2 Non-Bayesian vs. Bayesian 106 6.3 Performance Metrics and Bounds 107 6.3.1 Bias 107 6.3.2 Mean Square Error (MSE) 108 6.3.3 Performance Bounds 109 6.4 Statistics and Sufficient Statistics 110 6.5 MVU and BLU Estimators 111 6.6 BLUE for Linear Models 112 6.7 Example: BLUE of the Mean Value of Gaussian rvs 114 7 Parameter Estimation 117 7.1 Maximum Likelihood Estimation (MLE) 117 7.2 MLE for Gaussian Model 119 7.2.1 Additive Noise Model with 119 7.2.2 Additive Noise Model with 120 7.2.3 Additive Noise Model with Multiple Observations with Known 121 7.2.3.1 Linear Model 121 7.2.3.2 Model 122 7.2.3.3 Model 123 7.2.4 Model 123 7.2.5 Additive Noise Model with Multiple Observations with Unknown 124 7.3 Other Noise Models 125 7.4 MLE and Nuisance Parameters 126 7.5 MLE for Continuous-Time Signals 128 7.5.1 Example: Amplitude Estimation 129 7.5.2 MLE for Correlated Noise 130 7.6 MLE for Circular Complex Gaussian 131 7.7 Estimation in Phase/Frequency Modulations 131 7.7.1 MLE Phase Estimation 132 7.7.2 Phase Locked Loops 133 7.8 Least Square (LS) Estimation 135 7.8.1 Weighted LS with 136 7.8.2 LS Estimation and Linear Models 137 7.8.3 Under or Over-Parameterizing? 138 7.8.4 Constrained LS Estimation 139 7.9 Robust Estimation 140 8 Cramér–Rao Bound 143 8.1 Cramér–Rao Bound and Fisher Information Matrix 143 8.1.1 CRB for Scalar Problem (P=1) 143 8.1.2 CRB and Local Curvature of Log-Likelihood 144 8.1.3 CRB for Multiple Parameters (p 1) 144 8.2 Interpretation of CRB and Remarks 146 8.2.1 Variance of Each Parameter 146 8.2.2 Compactness of the Estimates 146 8.2.3 FIM for Known Parameters 147 8.2.4 Approximation of the Inverse of FIM 148 8.2.5 Estimation Decoupled From FIM 148 8.2.6 CRB and Nuisance Parameters 149 8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149 8.3 CRB and Variable Transformations 150 8.4 FIM for Gaussian Parametric Model 151 8.4.1 FIM for with 151 8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152 8.4.3 FIM for Circular Complex Model 152 Appendix A: Proof of CRB 154 Appendix B: FIM for Gaussian Model 156 Appendix C: Some Derivatives for MLE and CRB Computations 157 9 MLE and CRB for Some Selected Cases 159 9.1 Linear Regressions 159 9.2 Frequency Estimation 162 9.3 Estimation of Complex Sinusoid 164 9.3.1 Proper, Improper, and Non-Circular Signals 165 9.4 Time of Delay Estimation 166 9.5 Estimation of Max for Uniform pdf 170 9.6 Estimation of Occurrence Probability for Binary pdf 172 9.7 How to Optimize Histograms? 173 9.8 Logistic Regression 176 10 Numerical Analysis and Montecarlo Simulations 179 10.1 System Identification and Channel Estimation 181 10.1.1 Matlab Code and Results 184 10.2 Frequency Estimation 184 10.2.1 Variable (Coarse/Fine) Sampling 187 10.2.2 Local Parabolic Regression 189 10.2.3 Matlab Code and Results 190 10.3 Time of Delay Estimation 192 10.3.1 Granularity of Sampling in ToD Estimation 193 10.3.2 Matlab Code and Results 194 10.4 Doppler-Radar System by Frequency Estimation 196 10.4.1 EM Method 197 10.4.2 Matlab Code and Results 199 11 Bayesian Estimation 201 11.1 Additive Linear Model with Gaussian Noise 203 11.1.1 Gaussian A-priori: 204 11.1.2 Non-Gaussian A-Priori 206 11.1.3 Binary Signals: MMSE vs. MAP Estimators 207 11.1.4 Example: Impulse Noise Mitigation 210 11.2 Bayesian Estimation in Gaussian Settings 212 11.2.1 MMSE Estimator 213 11.2.2 MMSE Estimator for Linear Models 213 11.3 LMMSE Estimation and Orthogonality 215 11.4 Bayesian CRB 218 11.5 Mixing Bayesian and Non-Bayesian 220 11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220 11.5.2 Hybrid CRB 222 11.6 Expectation-Maximization (EM) 223 11.6.1 EM of the Sum of Signals in Gaussian Noise 224 11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227 11.6.3 Remarks 228 Appendix A: Gaussian Mixture pdf 229 12 Optimal Filtering 231 12.1 Wiener Filter 231 12.2 MMSE Deconvolution (or Equalization) 233 12.3 Linear Prediction 234 12.3.1 Yule–Walker Equations 235 12.4 LS Linear Prediction 237 12.5 Linear Prediction and AR Processes 239 12.6 Levinson Recursion and Lattice Predictors 241 13 Bayesian Tracking and Kalman Filter 245 13.1 Bayesian Tracking of State in Dynamic Systems 246 13.1.1 Evolution of the A-posteriori pdf 247 13.2 Kalman Filter (KF) 249 13.2.1 KF Equations 251 13.2.2 Remarks 253 13.3 Identification of Time-Varying Filters in Wireless Communication 255 13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257 13.5 Position Tracking by Multi-Lateration 258 13.5.1 Positioning and Noise 260 13.5.2 Example of Position Tracking 263 13.6 Non-Gaussian Pdf and Particle Filters264 14 Spectral Analysis 267 14.1 Periodogram 268 14.1.1 Bias of the Periodogram 268 14.1.2 Variance of the Periodogram 271 14.1.3 Filterbank Interpretation 273 14.1.4 Pdf of the Periodogram (White Gaussian Process) 274 14.1.5 Bias and Resolution 275 14.1.6 Variance Reduction and WOSA 278 14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280 14.2 Parametric Spectral Analysis 282 14.2.1 MLE and CRB 284 14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285 14.3 AR Spectral Analysis 286 14.3.1 MLE and CRB 286 14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289 14.3.3 Cramér–Rao Bound of Poles in AR Spectral Analysis 291 14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293 14.4 MA Spectral Analysis 296 14.5 ARMA Spectral Analysis 298 14.5.1 Cramér–Rao Bound for ARMA Spectral Analysis 300 Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302 Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303 Appendix C: Property of Monic Polynomial 306 Appendix D: Variance of Pole in AR(1) 307 15 Adaptive Filtering 309 15.1 Adaptive Interference Cancellation 311 15.2 Adaptive Equalization in Communication Systems 313 15.2.1 Wireless Communication Systems in Brief 313 15.2.2 Adaptive Equalization 315 15.3 Steepest Descent MSE Minimization 317 15.3.1 Convergence Analysis and Step-Size 318 15.3.2 An Intuitive View of Convergence Conditions 320 15.4 From Iterative to Adaptive Filters 323 15.5 LMS Algorithm and Stochastic Gradient 324 15.6 Convergence Analysis of LMS Algorithm 325 15.6.1 Convergence in the Mean 326 15.6.2 Convergence in the Mean Square 326 15.6.3 Excess MSE 329 15.7 Learning Curve of LMS 331 15.7.1 Optimization of the Step-Size 332 15.8 NLMS Updating and Non-Stationarity 333 15.9 Numerical Example: Adaptive Identification 334 15.10 RLS Algorithm 338 15.10.1 Convergence Analysis 339 15.10.2 Learning Curve of RLS 341 15.11 Exponentially-Weighted RLS 342 15.12 LMS vs. RLS 344 Appendix A: Convergence in Mean Square 344 16 Line Spectrum Analysis 347 16.1 Model Definition 349 16.1.1 Deterministic Signals 350 16.1.2 Random Signals 350 16.1.3 Properties of Structured Covariance 351 16.2 Maximum Likelihood and Cramér–Rao Bounds 352 16.2.1 Conditional ML 353 16.2.2 Cramér–Rao Bound for Conditional Model 354 16.2.3 Unconditional ML 356 16.2.4 Cramér–Rao Bound for Unconditional Model 356 16.2.5 Conditional vs. Unconditional Model & Bounds 357 16.3 High-Resolution Methods 357 16.3.1 Iterative Quadratic ML (IQML) 358 16.3.2 Prony Method 360 16.3.3 MUSIC 360 16.3.4 ESPRIT 363 16.3.5 Model Order 365 17 Equalization in Communication Engineering 367 17.1 Linear Equalization 369 17.1.1 Zero Forcing (ZF) Equalizer 370 17.1.2 Minimum Mean Square Error (MMSE) Equalizer 371 17.1.3 Finite-Length/Finite-Block Equalizer 371 17.2 Non-Linear Equalization 372 17.2.1 ZF-DFE 373 17.2.2 MMSE–DFE 374 17.2.3 Finite-Length MMSE–DFE 375 17.2.4 Asymptotic Performance for Infinite-Length Equalizers 376 17.3 MIMO Linear Equalization 377 17.3.1 ZF MIMO Equalization 377 17.3.2 MMSE MIMO Equalization 379 17.4 MIMO–DFE Equalization 379 17.4.1 Cholesky Factorization and Min/Max Phase Decomposition 379 17.4.2 MIMO–DFE 380 18 2D Signals and Physical Filters 383 18.1 2D Sinusoids 384 18.1.1 Moiré Pattern 386 18.2 2D Filtering 388 18.2.1 2D Random Fields 390 18.2.2 Wiener Filtering 391 18.2.3 Image Acquisition and Restoration 392 18.3 Diffusion Filtering 394 18.3.1 Evolution vs. Time: Fourier Method 394 18.3.2 Extrapolation of the Density 395 18.3.3 Effect of Phase-Shift 396 18.4 Laplace Equation and Exponential Filtering 398 18.5 Wavefield Propagation 400 18.5.1 Propagation/Backpropagation 400 18.5.2 Wavefield Extrapolation and Focusing 402 18.5.3 Exploding Reflector Model 402 18.5.4 Wavefield Extrapolation 404 18.5.5 Wavefield Focusing (or Migration) 406 Appendix A: Properties of 2D Signals 406 Appendix B: Properties of 2D Fourier Transform 410 Appendix C: Finite Difference Method for PDE-Diffusion 412 19 Array Processing 415 19.1 Narrowband Model 415 19.1.1 Multiple DoAs and Multiple Sources 419 19.1.2 Sensor Spacing Design 420 19.1.3 Spatial Resolution and Array Aperture 421 19.2 Beamforming and Signal Estimation 422 19.2.1 Conventional Beamforming 425 19.2.2 Capon Beamforming (MVDR) 426 19.2.3 Multiple-Constraint Beamforming 429 19.2.4 Max-SNR Beamforming 431 19.3 DoA Estimation 432 19.3.1 ML Estimation and CRB 433 19.3.2 Beamforming and Root-MVDR 434 20 Multichannel Time of Delay Estimation 435 20.1 Model Definition for ToD 440 20.2 High Resolution Method for ToD (L=1) 441 20.2.1 ToD in the Fourier Transformed Domain 441 20.2.2 CRB and Resolution 444 20.3 Difference of ToD (DToD) Estimation 445 20.3.1 Correlation Method for DToD 445 20.3.2 Generalized Correlation Method 448 20.4 Numerical Performance Analysis of DToD 452 20.5 Wavefront Estimation: Non-Parametric Method (L=1) 454 20.5.1 Wavefront Estimation in Remote Sensing and Geophysics 456 20.5.2 Narrowband Waveforms and 2D Phase Unwrapping 457 20.5.3 2D Phase Unwrapping in Regular Grid Spacing 458 20.6 Parametric ToD Estimation and Wideband Beamforming 460 20.6.1 Delay and Sum Beamforming 462 20.6.2 Wideband Beamforming After Fourier Transform 464 20.7 Appendix A: Properties of the Sample Correlations 465 20.8 Appendix B: How to Delay a Discrete-Time Signal? 466 20.9 Appendix C: Wavefront Estimation for 2D Arrays 467 21 Tomography 467 21.1 X-ray Tomography 471 21.1.1 Discrete Model 471 21.1.2 Maximum Likelihood 473 21.1.3 Emission Tomography 473 21.2 Algebraic Reconstruction Tomography (ART) 475 21.3 Reconstruction From Projections: Fourier Method 475 21.3.1 Backprojection Algorithm 476 21.3.2 How Many Projections to Use? 479 21.4 Traveltime Tomography 480 21.5 Internet (Network) Tomography 483 21.5.1 Latency Tomography 484 21.5.2 Packet-Loss Tomography 484 22 Cooperative Estimation 487 22.1 Consensus and Cooperation 490 22.1.1 Vox Populi: The Wisdom of Crowds 490 22.1.2 Cooperative Estimation as Simple Information Consensus 490 22.1.3 Weighted Cooperative Estimation ( ) 493 22.1.4 Distributed MLE ( ) 495 22.2 Distributed Estimation for Arbitrary Linear Models (p>1) 496 22.2.1 Centralized MLE 497 22.2.2 Distributed Weighted LS 498 22.2.3 Distributed MLE 500 22.2.4 Distributed Estimation for Under-Determined Systems 501 22.2.5 Stochastic Regressor Model 503 22.2.6 Cooperative Estimation in the Internet of Things (IoT) 503 22.2.7 Example: Iterative Distributed Estimation 505 22.3 Distributed Synchronization 506 22.3.1 Synchrony-States for Analog and Discrete-Time Clocks 507 22.3.2 Coupled Clocks 510 22.3.3 Internet Synchronization and the Network Time Protocol (NTP) 512 Appendix A: Basics of Undirected Graphs 515 23 Classification and Clustering 521 23.1 Historical Notes 522 23.2 Classification 523 23.2.1 Binary Detection Theory 523 23.2.2 Binary Classification of Gaussian Distributions 528 23.3 Classification of Signals in Additive Gaussian Noise 529 23.3.1 Detection of Known Signal 531 23.3.2 Classification of Multiple Signals 532 23.3.3 Generalized Likelihood Ratio Test (GLRT) 533 23.3.4 Detection of Random Signals 535 23.4 Bayesian Classification 536 23.4.1 To Classify or Not to Classify? 537 23.4.2 Bayes Risk 537 23.5 Pattern Recognition and Machine Learning 538 23.5.1 Linear Discriminant 539 23.5.2 Least Squares Classification 540 23.5.3 Support Vectors Principle 541 23.6 Clustering 543 23.6.1 K-Means Clustering 544 23.6.2 EM Clustering 545 References 549 Index 557

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Book SynopsisIntroduces basic concepts in probability and statistics to data science students, as well as engineers and scientists Aimed at undergraduate/graduate-level engineering and natural science students, this timely, fully updated edition of a popular book on statistics and probability shows how real-world problems can be solved using statistical concepts. It removes Excel exhibits and replaces them with R software throughout, and updates both MINITAB and JMP software instructions and content. A new chapter discussing data miningincluding big data, classification, machine learning, and visualizationis featured. Another new chapter covers cluster analysis methodologies in hierarchical, nonhierarchical, and model based clustering. The book also offers a chapter on Response Surfaces that previously appeared on the book's companion website. Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP, Second Edition is broken iTable of ContentsPreface xvii Acknowledgments xxi About The Companion Site xxiii 1 Introduction 1 1.1 Designed Experiment 2 1.1.1 Motivation for the Study 2 1.1.2 Investigation 3 1.1.3 Changing Criteria 3 1.1.4 A Summary of the Various Phases of the Investigation 5 1.2 A Survey 6 1.3 An Observational Study 6 1.4 A Set of Historical Data 7 1.5 A Brief Description of What is Covered in this Book 7 Part I Fundamentals of Probability and Statistics 2 Describing Data Graphically and Numerically 13 2.1 Getting Started with Statistics 14 2.1.1 What is Statistics? 14 2.1.2 Population and Sample in a Statistical Study 14 2.2 Classification of Various Types of Data 18 2.2.1 Nominal Data 18 2.2.2 Ordinal Data 19 2.2.3 Interval Data 19 2.2.4 Ratio Data 19 2.3 Frequency Distribution Tables for Qualitative and Quantitative Data 20 2.3.1 Qualitative Data 21 2.3.2 Quantitative Data 24 2.4 Graphical Description of Qualitative and Quantitative Data 30 2.4.1 Dot Plot 30 2.4.2 Pie Chart 31 2.4.3 Bar Chart 33 2.4.4 Histograms 37 2.4.5 Line Graph 44 2.4.6 Stem-and-Leaf Plot 45 2.5 Numerical Measures of Quantitative Data 50 2.5.1 Measures of Centrality 51 2.5.2 Measures of Dispersion 56 2.6 Numerical Measures of Grouped Data 67 2.6.1 Mean of a Grouped Data 67 2.6.2 Median of a Grouped Data 68 2.6.3 Mode of a Grouped Data 69 2.6.4 Variance of a Grouped Data 69 2.7 Measures of Relative Position 70 2.7.1 Percentiles 71 2.7.2 Quartiles 72 2.7.3 Interquartile Range (IQR) 72 2.7.4 Coefficient of Variation 73 2.8 Box-Whisker Plot 75 2.8.1 Construction of a Box Plot 75 2.8.2 How to Use the Box Plot 76 2.9 Measures of Association 80 2.10 Case Studies 84 2.10.1 About St. Luke’s Hospital 85 2.11 Using JMP 86 Review Practice Problems 87 3 Elements of Probability 97 3.1 Introduction 97 3.2 Random Experiments, Sample Spaces, and Events 98 3.2.1 Random Experiments and Sample Spaces 98 3.2.2 Events 99 3.3 Concepts of Probability 103 3.4 Techniques of Counting Sample Points 108 3.4.1 Tree Diagram 108 3.4.2 Permutations 110 3.4.3 Combinations 110 3.4.4 Arrangements of n Objects Involving Several Kinds of Objects 111 3.5 Conditional Probability 113 3.6 Bayes’s Theorem 116 3.7 Introducing Random Variables 120 Review Practice Problems 122 4 Discrete Random Variables and Some Important Discrete Probability Distributions 128 4.1 Graphical Descriptions of Discrete Distributions 129 4.2 Mean and Variance of a Discrete Random Variable 130 4.2.1 Expected Value of Discrete Random Variables and Their Functions 130 4.2.2 The Moment-Generating Function-Expected Value of a Special Function of X 133 4.3 The Discrete Uniform Distribution 136 4.4 The Hypergeometric Distribution 137 4.5 The Bernoulli Distribution 141 4.6 The Binomial Distribution 142 4.7 The Multinomial Distribution 146 4.8 The Poisson Distribution 147 4.8.1 Definition and Properties of the Poisson Distribution 147 4.8.2 Poisson Process 148 4.8.3 Poisson Distribution as a Limiting Form of the Binomial 148 4.9 The Negative Binomial Distribution 153 4.10 Some Derivations and Proofs (Optional) 156 4.11 A Case Study 156 4.12 Using JMP 157 Review Practice Problems 157 5 Continuous Random Variables and Some Important Continuous Probability Distributions 164 5.1 Continuous Random Variables 165 5.2 Mean and Variance of Continuous Random Variables 168 5.2.1 Expected Value of Continuous Random Variables and Their Functions 168 5.2.2 The Moment-Generating Function and Expected Value of a Special Function of X 171 5.3 Chebyshev’s Inequality 173 5.4 The Uniform Distribution 175 5.4.1 Definition and Properties 175 5.4.2 Mean and Standard Deviation of the Uniform Distribution 178 5.5 The Normal Distribution 180 5.5.1 Definition and Properties 180 5.5.2 The Standard Normal Distribution 182 5.5.3 The Moment-Generating Function of the Normal Distribution 187 5.6 Distribution of Linear Combination of Independent Normal Variables 189 5.7 Approximation of the Binomial and Poisson Distributions by the Normal Distribution 193 5.7.1 Approximation of the Binomial Distribution by the Normal Distribution 193 5.7.2 Approximation of the Poisson Distribution by the Normal Distribution 196 5.8 A Test of Normality 196 5.9 Probability Models Commonly used in Reliability Theory 201 5.9.1 The Lognormal Distribution 202 5.9.2 The Exponential Distribution 206 5.9.3 The Gamma Distribution 211 5.9.4 The Weibull Distribution 214 5.10 A Case Study 218 5.11 Using JMP 219 Review Practice Problems 220 6 Distribution of Functions Of Random Variables 228 6.1 Introduction 229 6.2 Distribution Functions of Two Random Variables 229 6.2.1 Case of Two Discrete Random Variables 229 6.2.2 Case of Two Continuous Random Variables 232 6.2.3 The Mean Value and Variance of Functions of Two Random Variables 233 6.2.4 Conditional Distributions 235 6.2.5 Correlation between Two Random Variables 238 6.2.6 Bivariate Normal Distribution 241 6.3 Extension to Several Random Variables 244 6.4 The Moment-Generating Function Revisited 245 Review Practice Problems 249 7 Sampling Distributions 253 7.1 Random Sampling 253 7.1.1 Random Sampling from an Infinite Population 254 7.1.2 Random Sampling from a Finite Population 256 7.2 The Sampling Distribution of the Sample Mean 258 7.2.1 Normal Sampled Population 258 7.2.2 Nonnormal Sampled Population 258 7.2.3 The Central Limit Theorem 259 7.3 Sampling from a Normal Population 264 7.3.1 The Chi-Square Distribution 264 7.3.2 The Student t-Distribution 271 7.3.3 Snedecor’s F-Distribution 276 7.4 Order Statistics 279 7.4.1 Distribution of the Largest Element in a Sample 280 7.4.2 Distribution of the Smallest Element in a Sample 281 7.4.3 Distribution of the Median of a Sample and of the kth Order Statistic 282 7.4.4 Other Uses of Order Statistics 284 7.5 Using JMP 286 Review Practice Problems 286 8 Estimation of Population Parameters 289 8.1 Introduction 290 8.2 Point Estimators for the Population Mean and Variance 290 8.2.1 Properties of Point Estimators 292 8.2.2 Methods of Finding Point Estimators 295 8.3 Interval Estimators for the Mean μ of a Normal Population 301 8.3.1 σ2 Known 301 8.3.2 σ2 Unknown 304 8.3.3 Sample Size is Large 306 8.4 Interval Estimators for The Difference of Means of Two Normal Populations 313 8.4.1 Variances are Known 313 8.4.2 Variances are Unknown 314 8.5 Interval Estimators for the Variance of a Normal Population 322 8.6 Interval Estimator for the Ratio of Variances of Two Normal Populations 327 8.7 Point and Interval Estimators for the Parameters of Binomial Populations 331 8.7.1 One Binomial Population 331 8.7.2 Two Binomial Populations 334 8.8 Determination of Sample Size 338 8.8.1 One Population Mean 339 8.8.2 Difference of Two Population Means 339 8.8.3 One Population Proportion 340 8.8.4 Difference of Two Population Proportions 341 8.9 Some Supplemental Information 343 8.10 A Case Study 343 8.11 Using JMP 343 Review Practice Problems 344 9 Hypothesis Testing 352 9.1 Introduction 353 9.2 Basic Concepts of Testing a Statistical Hypothesis 353 9.2.1 Hypothesis Formulation 353 9.2.2 Risk Assessment 355 9.3 Tests Concerning the Mean of a Normal Population Having Known Variance 358 9.3.1 Case of a One-Tail (Left-Sided) Test 358 9.3.2 Case of a One-Tail (Right-Sided) Test 362 9.3.3 Case of a Two-Tail Test 363 9.4 Tests Concerning the Mean of a Normal Population Having Unknown Variance 372 9.4.1 Case of a Left-Tail Test 372 9.4.2 Case of a Right-Tail Test 373 9.4.3 The Two-Tail Case 374 9.5 Large Sample Theory 378 9.6 Tests Concerning the Difference of Means of Two Populations Having Distributions with Known Variances 380 9.6.1 The Left-Tail Test 380 9.6.2 The Right-Tail Test 381 9.6.3 The Two-Tail Test 383 9.7 Tests Concerning the Difference of Means of Two Populations Having Normal Distributions with Unknown Variances 388 9.7.1 Two Population Variances are Equal 388 9.7.2 Two Population Variances are Unequal 392 9.7.3 The Paired t-Test 395 9.8 Testing Population Proportions 401 9.8.1 Test Concerning One Population Proportion 401 9.8.2 Test Concerning the Difference Between Two Population Proportions 405 9.9 Tests Concerning the Variance of a Normal Population 410 9.10 Tests Concerning the Ratio of Variances of Two Normal Populations 414 9.11 Testing of Statistical Hypotheses using Confidence Intervals 418 9.12 Sequential Tests of Hypotheses 422 9.12.1 A One-Tail Sequential Testing Procedure 422 9.12.2 A Two-Tail Sequential Testing Procedure 427 9.13 Case Studies 430 9.14 Using JMP 431 Review Practice Problems 431 Part II Statistics in Actions 10 Elements of Reliability Theory 445 10.1 The Reliability Function 446 10.1.1 The Hazard Rate Function 446 10.1.2 Employing the Hazard Function 455 10.2 Estimation: Exponential Distribution 457 10.3 Hypothesis Testing: Exponential Distribution 465 10.4 Estimation: Weibull Distribution 467 10.5 Case Studies 472 10.6 Using JMP 474 Review Practice Problems 474 11 On Data Mining 476 11.1 Introduction 476 11.2 What is Data Mining? 477 11.2.1 Big Data 477 11.3 Data Reduction 478 11.4 Data Visualization 481 11.5 Data Preparation 490 11.5.1 Missing Data 490 11.5.2 Outlier Detection and Remedial Measures 491 11.6 Classification 492 11.6.1 Evaluating a Classification Model 493 11.7 Decision Trees 499 11.7.1 Classification and Regression Trees (CART) 500 11.7.2 Further Reading 511 11.8 Case Studies 511 11.9 Using JMP 512 Review Practice Problems 512 12 Cluster Analysis 518 12.1 Introduction 518 12.2 Similarity Measures 519 12.2.1 Common Similarity Coefficients 524 12.3 Hierarchical Clustering Methods 525 12.3.1 Single Linkage 526 12.3.2 Complete Linkage 531 12.3.3 Average Linkage 534 12.3.4 Ward’s Hierarchical Clustering 536 12.4 Nonhierarchical Clustering Methods 538 12.4.1 K-Means Method 538 12.5 Density-Based Clustering 544 12.6 Model-Based Clustering 547 12.7 A Case Study 552 12.8 Using JMP 553 Review Practice Problems 553 13 Analysis of Categorical Data 558 13.1 Introduction 558 13.2 The Chi-Square Goodness-of-Fit Test 559 13.3 Contingency Tables 568 13.3.1 The 2 × 2 Case with Known Parameters 568 13.3.2 The 2 × 2 Case with Unknown Parameters 570 13.3.3 The r × s Contingency Table 572 13.4 Chi-Square Test for Homogeneity 577 13.5 Comments on the Distribution of the Lack-of-Fit Statistics 581 13.6 Case Studies 583 13.7 Using JMP 584 Review Practice Problems 585 14 Nonparametric Tests 591 14.1 Introduction 591 14.2 The Sign Test 592 14.2.1 One-Sample Test 592 14.2.2 The Wilcoxon Signed-Rank Test 595 14.2.3 Two-Sample Test 598 14.3 Mann–Whitney (Wilcoxon) W Test for Two Samples 604 14.4 Runs Test 608 14.4.1 Runs above and below the Median 608 14.4.2 The Wald–Wolfowitz Run Test 611 14.5 Spearman Rank Correlation 614 14.6 Using JMP 618 Review Practice Problems 618 15 Simple Linear Regression Analysis 622 15.1 Introduction 623 15.2 Fitting the Simple Linear Regression Model 624 15.2.1 Simple Linear Regression Model 624 15.2.2 Fitting a Straight Line by Least Squares 627 15.2.3 Sampling Distribution of the Estimators of Regression Coefficients 631 15.3 Unbiased Estimator of σ2 637 15.4 Further Inferences Concerning Regression Coefficients (β0, β1), E(Y ), and Y 639 15.4.1 Confidence Interval for β1 with Confidence Coefficient (1 − α) 639 15.4.2 Confidence Interval for β0 with Confidence Coefficient (1 − α) 640 15.4.3 Confidence Interval for E(Y |X) with Confidence Coefficient (1 − α) 642 15.4.4 Prediction Interval for a Future Observation Y with Confidence Coefficient (1 − α) 645 15.5 Tests of Hypotheses for β0 and β1 652 15.5.1 Test of Hypotheses for β1 652 15.5.2 Test of Hypotheses for β0 652 15.6 Analysis of Variance Approach to Simple Linear Regression Analysis 659 15.7 Residual Analysis 665 15.8 Transformations 674 15.9 Inference About ρ 681 15.10A Case Study 683 15.11 Using JMP 684 Review Practice Problems 684 16 Multiple Linear Regression Analysis 693 16.1 Introduction 694 16.2 Multiple Linear Regression Models 694 16.3 Estimation of Regression Coefficients 699 16.3.1 Estimation of Regression Coefficients Using Matrix Notation 701 16.3.2 Properties of the Least-Squares Estimators 703 16.3.3 The Analysis of Variance Table 704 16.3.4 More Inferences about Regression Coefficients 706 16.4 Multiple Linear Regression Model Using Quantitative and Qualitative Predictor Variables 714 16.4.1 Single Qualitative Variable with Two Categories 714 16.4.2 Single Qualitative Variable with Three or More Categories 716 16.5 Standardized Regression Coefficients 726 16.5.1 Multicollinearity 728 16.5.2 Consequences of Multicollinearity 729 16.6 Building Regression Type Prediction Models 730 16.6.1 First Variable to Enter into the Model 730 16.7 Residual Analysis and Certain Criteria for Model Selection 734 16.7.1 Residual Analysis 734 16.7.2 Certain Criteria for Model Selection 735 16.8 Logistic Regression 740 16.9 Case Studies 745 16.10 Using JMP 748 Review Practice Problems 748 17 Analysis of Variance 757 17.1 Introduction 758 17.2 The Design Models 758 17.2.1 Estimable Parameters 758 17.2.2 Estimable Functions 760 17.3 One-Way Experimental Layouts 761 17.3.1 The Model and Its Analysis 761 17.3.2 Confidence Intervals for Treatment Means 767 17.3.3 Multiple Comparisons 773 17.3.4 Determination of Sample Size 780 17.3.5 The Kruskal–Wallis Test for One-Way Layouts (Nonparametric Method) 781 17.4 Randomized Complete Block (RCB) Designs 785 17.4.1 The Friedman Fr-Test for Randomized Complete Block Design (Nonparametric Method) 792 17.4.2 Experiments with One Missing Observation in an RCB-Design Experiment 794 17.4.3 Experiments with Several Missing Observations in an RCB-Design Experiment 795 17.5 Two-Way Experimental Layouts 798 17.5.1 Two-Way Experimental Layouts with One Observation per Cell 800 17.5.2 Two-Way Experimental Layouts with r > 1 Observations per Cell 801 17.5.3 Blocking in Two-Way Experimental Layouts 810 17.5.4 Extending Two-Way Experimental Designs to n-Way Experimental Layouts 811 17.6 Latin Square Designs 813 17.7 Random-Effects and Mixed-Effects Models 820 17.7.1 Random-Effects Model 820 17.7.2 Mixed-Effects Model 822 17.7.3 Nested (Hierarchical) Designs 824 17.8 A Case Study 831 17.9 Using JMP 832 Review Practice Problems 832 18 The 2k Factorial Designs 847 18.1 Introduction 848 18.2 The Factorial Designs 848 18.3 The 2k Factorial Designs 850 18.4 Unreplicated 2k Factorial Designs 859 18.5 Blocking in the 2k Factorial Design 867 18.5.1 Confounding in the 2k Factorial Design 867 18.5.2 Yates’s Algorithm for the 2k Factorial Designs 875 18.6 The 2k Fractional Factorial Designs 877 18.6.1 One-half Replicate of a 2k Factorial Design 877 18.6.2 One-quarter Replicate of a 2k Factorial Design 882 18.7 Case Studies 887 18.8 Using JMP 889 Review Practice Problems 889 19 Response Surfaces 897 19.1 Introduction 897 19.1.1 Basic Concepts of Response Surface Methodology 898 19.2 First-Order Designs 903 19.3 Second-Order Designs 917 19.3.1 Central Composite Designs (CCDs) 918 19.3.2 Some Other First-Order and Second-Order Designs 928 19.4 Determination of Optimum or Near-Optimum Point 936 19.4.1 The Method of Steepest Ascent 937 19.4.2 Analysis of a Fitted Second-Order Response Surface 941 19.5 Anova Table for a Second-Order Model 946 19.6 Case Studies 948 19.7 Using JMP 950 Review Practice Problems 950 20 Statistical Quality Control—Phase I Control Charts 958 21 Statistical Quality Control—Phase II Control Charts 960 Appendices 961 Appendix A Statistical Tables 962 Appendix B Answers to Selected Problems 969 Appendix C Bibliography 992 Index 1003

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Book SynopsisThis book describes the basics and developments of the new XFEM approach to fracture analysis of structures and materials, providing state of the art techniques and algorithms for fracture analysis of structures.Table of ContentsPreface xiii Nomenclature xvii 1 Introduction 1 1.1 Composite Structures 1 1.2 Failures of Composites 2 1.2.1 Matrix Cracking 2 1.2.2 Delamination 2 1.2.3 Fibre/Matrix Debonding 2 1.2.4 Fibre Breakage 3 1.2.5 Macro Models of Cracking in Composites 3 1.3 Crack Analysis 3 1.3.1 Local and Non-Local Formulations 3 1.3.2 Theoretical Methods for Failure Analysis 5 1.4 Analytical Solutions for Composites 6 1.4.1 Continuum Models 6 1.4.2 Fracture Mechanics of Composites 6 1.5 Numerical Techniques 8 1.5.1 Boundary Element Method 8 1.5.2 Finite Element Method 8 1.5.3 Adaptive Finite/Discrete Element Method 10 1.5.4 Meshless Methods 10 1.5.5 Extended Finite Element Method 11 1.5.6 Extended Isogeometric Analysis 12 1.5.7 Multiscale Analysis 13 1.6 Scope of the Book 13 2 Fracture Mechanics, A Review 17 2.1 Introduction 17 2.2 Basics of Elasticity 20 2.2.1 Stress–Strain Relations 20 2.2.2 Airy Stress Function 22 2.2.3 Complex Stress Functions 22 2.3 Basics of LEFM 23 2.3.1 Fracture Mechanics 23 2.3.2 Infinite Tensile Plate with a Circular Hole 24 2.3.3 Infinite Tensile Plate with an Elliptical Hole 26 2.3.4 Westergaard Analysis of a Line Crack 28 2.3.5 Williams Solution of a Wedge Corner 29 2.4 Stress Intensity Factor, K 30 2.4.1 Definition of the Stress Intensity Factor 30 2.4.2 Examples of Stress Intensity Factors for LEFM 33 2.4.3 Griffith Energy Theories 35 2.4.4 Mixed Mode Crack Propagation 38 2.5 Classical Solution Procedures for K and G 41 2.5.1 Displacement Extrapolation/Correlation Method 41 2.5.2 Mode I Energy Release Rate 41 2.5.3 Mode I Stiffness Derivative/Virtual Crack Model 42 2.5.4 Two Virtual Crack Extensions for Mixed Mode Cases 42 2.5.5 Single Virtual Crack Extension Based on Displacement Decomposition 43 2.6 Quarter Point Singular Elements 44 2.7 J Integral 47 2.7.1 Generalization of J 48 2.7.2 Effect of Crack Surface Traction 48 2.7.3 Effect of Body Force 49 2.7.4 Equivalent Domain Integral (EDI) Method 49 2.7.5 Interaction Integral Method 49 2.8 Elastoplastic Fracture Mechanics (EPFM) 51 2.8.1 Plastic Zone 51 2.8.2 Crack-Tip Opening Displacements (CTOD) 53 2.8.3 J Integral for EPFM 55 3 Extended Finite Element Method 57 3.1 Introduction 57 3.2 Historic Development of XFEM 58 3.2.1 A Review of XFEM Development 58 3.2.2 A Review of XFEM Composite Analysis 62 3.3 Enriched Approximations 62 3.3.1 Partition of Unity 62 3.3.2 Intrinsic and Extrinsic Enrichments 63 3.3.3 Partition of Unity Finite Element Method 66 3.3.4 MLS Enrichment 66 3.3.5 Generalized Finite Element Method 67 3.3.6 Extended Finite Element Method 67 3.3.7 Generalized PU Enrichment 67 3.4 XFEM Formulation 67 3.4.1 Basic XFEM Approximation 68 3.4.2 Signed Distance Function 69 3.4.3 Modelling the Crack 70 3.4.4 Governing Equation 71 3.4.5 XFEM Discretization 72 3.4.6 Evaluation of Derivatives of Enrichment Functions 73 3.4.7 Selection of Nodes for Discontinuity Enrichment 75 3.4.8 Numerical Integration 77 3.5 XFEM Strong Discontinuity Enrichments 79 3.5.1 A Modified FE Shape Function 79 3.5.2 The Heaviside Function 81 3.5.3 The Sign Function 84 3.5.4 Strong Tangential Discontinuity 85 3.5.5 Crack Intersection 85 3.6 XFEM Weak Discontinuity Enrichments 86 3.7 XFEM Crack-Tip Enrichments 87 3.7.1 Isotropic Enrichment 87 3.7.2 Orthotropic Enrichment Functions 88 3.7.3 Bimaterial Enrichments 88 3.7.4 Orthotropic Bimaterial Enrichments 89 3.7.5 Dynamic Enrichment 89 3.7.6 Orthotropic Dynamic Enrichments for Moving Cracks 90 3.7.7 Bending Plates 91 3.7.8 Crack-Tip Enrichments in Shells 91 3.7.9 Electro-Mechanical Enrichment 92 3.7.10 Dislocation Enrichment 93 3.7.11 Hydraulic Fracture Enrichment 94 3.7.12 Plastic Enrichment 94 3.7.13 Viscoelastic Enrichment 95 3.7.14 Contact Corner Enrichment 96 3.7.15 Modification for Large Deformation Problems 97 3.7.16 Automatic Enrichment 99 3.8 Transition from Standard to Enriched Approximation 99 3.8.1 Linear Blending 100 3.8.2 Hierarchical Transition Domain 100 3.9 Tracking Moving Boundaries 103 3.9.1 Level Set Method 103 3.9.2 Alternative Methods 106 3.10 Numerical Simulations 107 3.10.1 A Central Crack in an Infinite Tensile Plate 107 3.10.2 An Edge Crack in a Finite Plate 109 3.10.3 Tensile Plate with a Central Inclined Crack 110 3.10.4 A Bending Plate in Fracture Mode III 111 3.10.5 Crack Propagation in a Shell 112 3.10.6 Shear Band Simulation 115 3.10.7 Fault Simulation 116 3.10.8 Sliding Contact Stress Singularity by PUFEM 119 3.10.9 Hydraulic Fracture 122 3.10.10 Dislocation Dynamics 126 4 Static Fracture Analysis of Composites 131 4.1 Introduction 131 4.2 Anisotropic Elasticity 134 4.2.1 Elasticity Solution 134 4.2.2 Anisotropic Stress Functions 136 4.3 Analytical Solutions for Near Crack Tip 137 4.3.1 The General Solution 137 4.3.2 Special Solutions for Different Types of Composites 140 4.4 Orthotropic Mixed Mode Fracture 142 4.4.1 Energy Release Rate for Anisotropic Materials 142 4.4.2 Anisotropic Singular Elements 142 4.4.3 SIF Calculation by Interaction Integral 143 4.4.4 Orthotropic Crack Propagation Criteria 147 4.5 Anisotropic XFEM 149 4.5.1 Governing Equation 149 4.5.2 XFEM Discretization 150 4.5.3 Orthotropic Enrichment Functions 151 4.6 Numerical Simulations 152 4.6.1 Plate with a Crack Parallel to the Material Axis of Orthotropy 152 4.6.2 Edge Crack with Several Orientations of the Axes of Orthotropy 155 4.6.3 Inclined Edge Notched Tensile Specimen 156 4.6.4 Central Slanted Crack 160 4.6.5 An Inclined Centre Crack in a Disk Subjected to Point Loads 164 4.6.6 Crack Propagation in an Orthotropic Beam 166 5 Dynamic Fracture Analysis of Composites 169 5.1 Introduction 169 5.1.1 Dynamic Fracture Mechanics 169 5.1.2 Dynamic Fracture Mechanics of Composites 170 5.1.3 Dynamic Fracture by XFEM 172 5.2 Analytical Solutions for Near Crack Tips in Dynamic States 173 5.2.1 Analytical Solution for a Propagating Crack in Isotropic Material 174 5.2.2 Asymptotic Solution for a Stationary Crack in Orthotropic Media 175 5.2.3 Analytical Solution for Near Crack Tip of a Propagating Crack in Orthotropic Material 176 5.3 Dynamic Stress Intensity Factors 178 5.3.1 Stationary and Moving Crack Dynamic Stress Intensity Factors 178 5.3.2 Dynamic Fracture Criteria 179 5.3.3 J Integral for Dynamic Problems 180 5.3.4 Domain Integral for Orthotropic Media 181 5.3.5 Interaction Integral 182 5.3.6 Crack-Axis Component of the Dynamic J Integral 183 5.3.7 Field Decomposition Technique 185 5.4 Dynamic XFEM 185 5.4.1 Dynamic Equations of Motion 185 5.4.2 XFEM Discretization 185 5.4.3 XFEM Enrichment Functions 187 5.4.4 Time Integration Schemes 191 5.5 Numerical Simulations 195 5.5.1 Plate with a Stationary Central Crack 195 5.5.2 Mode I Plate with an Edge Crack 196 5.5.3 Mixed Mode Edge Crack in Composite Plates 199 5.5.4 A Composite Plate with Double Edge Cracks under Impulsive Loading 210 5.5.5 Pre-Cracked Three Point Bending Beam under Impact Loading 213 5.5.6 Propagating Central Inclined Crack in a Circular Orthotropic Plate 217 6 Fracture Analysis of Functionally Graded Materials (FGMs) 225 6.1 Introduction 225 6.2 Analytical Solution for Near a Crack Tip 227 6.2.1 Average Material Properties 227 6.2.2 Mode I Near Tip Fields in FGM Composites 228 6.2.3 Stress and Displacement Field (Similar to Homogeneous Orthotropic Composites) 233 6.3 Stress Intensity Factor 235 6.3.1 J Integral 235 6.3.2 Interaction Integral 236 6.3.3 FGM Auxillary Fields 236 6.3.4 Isoparametric FGM 240 6.4 Crack Propagation in FGM Composites 240 6.5 Inhomogeneous XFEM 241 6.5.1 Governing Equation 241 6.5.2 XFEM Approximation 241 6.5.3 XFEM Discretization 243 6.6 Numerical Examples 244 6.6.1 Plate with a Centre Crack Parallel to the Material Gradient 244 6.6.2 Proportional FGM Plate with an Inclined Central Crack 247 6.6.3 Non-Proportional FGM Plate with a Fixed Inclined Central Crack 250 6.6.4 Rectangular Plate with an Inclined Crack (Non-Proportional Distribution) 251 6.6.5 Crack Propagation in a Four-Point FGM Beam 253 7 Delamination/Interlaminar Crack Analysis 261 7.1 Introduction 261 7.2 Fracture Mechanics for Bimaterial Interface Cracks 264 7.2.1 Isotropic Bimaterial Interfaces 265 7.2.2 Orthotropic Bimaterial Interface Cracks 266 7.2.3 Stress Contours for a Crack between Two Dissimilar Orthotropic Materials 270 7.3 Stress Intensity Factors for Interlaminar Cracks 271 7.4 Delamination Propagation 273 7.4.1 Fracture Energy-Based Criteria 273 7.4.2 Stress-Based Criteria 273 7.4.3 Contact-Based Criteria 274 7.5 Bimaterial XFEM 275 7.5.1 Governing Equation 275 7.5.2 XFEM Discretization 276 7.5.3 XFEM Enrichment Functions for Bimaterial Problems 278 7.5.4 Discretization and Integration 280 7.6 Numerical Examples 280 7.6.1 Central Crack in an Infinite Bimaterial Plate 280 7.6.2 Isotropic-Orthotropic Bimaterial Crack 289 7.6.3 Orthotropic Double Cantilever Beam 291 7.6.4 Concrete Beams Strengthened with Fully Bonded GFRP 294 7.6.5 FRP Reinforced Concrete Cantilever Beam Subjected to Edge Loadings 295 7.6.6 Delamination of Metallic I Beams Strengthened by FRP Strips 298 7.6.7 Variable Section Beam Reinforced by FRP 300 8 New Orthotropic Frontiers 303 8.1 Introduction 303 8.2 Orthotropic XIGA 303 8.2.1 NURBS Basis Function 304 8.2.2 Extended Isogeometric Analysis 305 8.2.3 XIGA Simulations 313 8.3 Orthotropic Dislocation Dynamics 321 8.3.1 Straight Dislocations in Anisotropic Materials 321 8.3.2 Edge Dislocations in Anisotropic Materials 322 8.3.3 Curve Dislocations in Anisotropic Materials 324 8.3.4 Anisotropic Dislocation XFEM 324 8.3.5 Plane Strain Anisotropic Solution 329 8.3.6 Individual Sliding Systems s1 and s2 in an Infinite Domain 330 8.3.7 Simultaneous Sliding Systems in an Infinite Domain 330 8.4 Other Anisotropic Applications 333 8.4.1 Biomechanics 333 8.4.2 Piezoelectric 335 References 339 Index 363

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Book SynopsisLikely to be the first textbook to be published on XFEM Concise, without completeness being compromised Emphasis on practical applications Comprehensive numerical examples in each chapter.Table of ContentsDedication. Preface . Nomenclature . Chapter 1 Introduction. 1.1 ANALYSIS OF STRUCTURES. 1.2 ANALYSIS OF DISCONTINUITIES. 1.3 FRACTURE MECHANICS. 1.4 CRACK MODELLING. 1.4.1 Local and non-local models. 1.4.2 Smeared crack model. 1.4.3 Discrete inter-element crack. 1.4.4 Discrete cracked element. 1.4.5 Singular elements. 1.4.6 Enriched elements. 1.5 ALTERNATIVE TECHNIQUES. 1.6 A REVIEW OF XFEM APPLICATIONS. 1.6.1 General aspects of XFEM. 1.6.2 Localisation and fracture. 1.6.3 Composites. 1.6.4 Contact. 1.6.5 Dynamics. 1.6.6 Large deformation/shells. 1.6.7 Multiscale. 1.6.8 Multiphase/solidification. 1.7 SCOPE OF THE BOOK. Chapter 2 Fracture Mechanics, a Review. 2.1 INTRODUCTION. 2.2 BASICS OF ELASTICITY. 2.2.1 Stress–strain relations. 2.2.2 Airy stress function. 2.2.3 Complex stress functions. 2.3 BASICS OF LEFM. 2.3.1 Fracture mechanics. 2.3.2 Circular hole. 2.3.3 Elliptical hole. 2.3.4 Westergaard analysis of a sharp crack. 2.4 STRESS INTENSITY FACTOR, K . 2.4.1 Definition of the stress intensity factor. 2.4.2 Examples of stress intensity factors for LEFM. 2.4.3 Griffith theories of strength and energy. 2.4.4 Brittle material. 2.4.5 Quasi-brittle material. 2.4.6 Crack stability. 2.4.7 Fixed grip versus fixed load. 2.4.8 Mixed mode crack propagation. 2.5 SOLUTION PROCEDURES FOR K AND G . 2.5.1 Displacement extrapolation/correlation method. 2.5.2 Mode I energy release rate. 2.5.3 Mode I stiffness derivative/virtual crack model. 2.5.4 Two virtual crack extensions for mixed mode cases. 2.5.5 Single virtual crack extension based on displacement decomposition. 2.5.6 Quarter point singular elements. 2.6 ELASTOPLASTIC FRACTURE MECHANICS (EPFM). 2.6.1 Plastic zone. 2.6.2 Crack tip opening displacements (CTOD). 2.6.3 J integral. 2.6.4 Plastic crack tip fields. 2.6.5 Generalisation of J . 2.7 NUMERICAL METHODS BASED ON THE J INTEGRAL. 2.7.1 Nodal solution. 2.7.2 General finite element solution. 2.7.3 Equivalent domain integral (EDI) method. 2.7.4 Interaction integral method. Chapter 3 Extended Finite Element Method for Isotropic Problems. 3.1 INTRODUCTION. 3.2 A REVIEW OF XFEM DEVELOPMENT. 3.3 BASICS OF FEM. 3.3.1 Isoparametric finite elements, a short review. 3.3.2 Finite element solutions for fracture mechanics. 3.4 PARTITION OF UNITY. 3.5 ENRICHMENT. 3.5.1 Intrinsic enrichment. 3.5.2 Extrinsic enrichment. 3.5.3 Partition of unity finite element method. 3.5.4 Generalised finite element method. 3.5.5 Extended finite element method. 3.5.6 Hp-clouds enrichment. 3.5.7 Generalisation of the PU enrichment. 3.5.8 Transition from standard to enriched approximation. 3.6 ISOTROPIC XFEM. 3.6.1 Basic XFEM approximation. 3.6.2 Signed distance function. 3.6.3 Modelling strong discontinuous fields. 3.6.4 Modelling weak discontinuous fields. 3.6.5 Plastic enrichment. 3.6.6 Selection of nodes for discontinuity enrichment. 3.6.7 Modelling the crack. 3.7 DISCRETIZATION AND INTEGRATION. 3.7.1 Governing equation. 3.7.2 XFEM discretization. 3.7.3 Element partitioning and numerical integration. 3.7.4 Crack intersection. 3.8 TRACKING MOVING BOUNDARIES. 3.8.1 Level set method. 3.8.2 Fast marching method. 3.8.3 Ordered upwind method. 3.9 NUMERICAL SIMULATIONS. 3.9.1 A tensile plate with a central crack. 3.9.2 Double edge cracks. 3.9.3 Double internal collinear cracks. 3.9.4 A central crack in an infinite plate. 3.9.5 An edge crack in a finite plate. Chapter 4 XFEM for Orthotropic Problems. 4.1 INTRODUCTION. 4.2 ANISOTROPIC ELASTICITY. 4.2.1 Elasticity solution. 4.2.2 Anisotropic stress functions. 4.2.3 Orthotropic mixed mode problems. 4.2.4 Energy release rate and stress intensity factor for anisotropic. materials. 4.2.5 Anisotropic singular elements. 4.3 ANALYTICAL SOLUTIONS FOR NEAR CRACK TIP. 4.3.1 Near crack tip displacement field (class I). 4.3.2 Near crack tip displacement field (class II). 4.3.3 Unified near crack tip displacement field (both classes). 4.4 ANISOTROPIC XFEM. 4.4.1 Governing equation. 4.4.2 XFEM discretization. 4.4.3 SIF calculations. 4.5 NUMERICAL SIMULATIONS. 4.5.1 Plate with a crack parallel to material axis of orthotropy. 4.5.2 Edge crack with several orientations of the axes of orthotropy. 4.5.3 Single edge notched tensile specimen with crack inclination. 4.5.4 Central slanted crack. 4.5.5 An inclined centre crack in a disk subjected to point loads. 4.5.6 A crack between orthotropic and isotropic materials subjected to. tensile tractions. Chapter 5 XFEM for Cohesive Cracks. 5.1 INTRODUCTION. 5.2 COHESIVE CRACKS. 5.2.1 Cohesive crack models. 5.2.2 Numerical models for cohesive cracks. 5.2.3 Crack propagation criteria. 5.2.4 Snap-back behaviour. 5.2.5 Griffith criterion for cohesive crack. 5.2.6 Cohesive crack model. 5.3 XFEM FOR COHESIVE CRACKS. 5.3.1 Enrichment functions. 5.3.2 Governing equations. 5.3.3 XFEM discretization. 5.4 NUMERICAL SIMULATIONS. 5.4.1 Mixed mode bending beam. 5.4.2 Four point bending beam. 5.4.3 Double cantilever beam. Chapter 6 New Frontiers. 6.1 INTRODUCTION. 6.2 INTERFACE CRACKS. 6.2.1 Elasticity solution for isotropic bimaterial interface. 6.2.2 Stability of interface cracks. 6.2.3 XFEM approximation for interface cracks. 6.3 CONTACT. 6.3.1 Numerical models for a contact problem. 6.3.2 XFEM modelling of a contact problem. 6.4 DYNAMIC FRACTURE. 6.4.1 Dynamic crack propagation by XFEM. 6.4.2 Dynamic LEFM. 6.4.3 Dynamic orthotropic LEFM. 6.4.4 Basic formulation of dynamic XFEM. 6.4.5 XFEM discretization. 6.4.6 Time integration. 6.4.7 Time finite element method. 6.4.8 Time extended finite element method. 6.5 MULTISCALE XFEM. 6.5.1 Basic formulation. 6.5.2 The zoom technique. 6.5.3 Homogenisation based techniques. 6.5.4 XFEM discretization. 6.6 MULTIPHASE XFEM. 6.6.1 Basic formulation. 6.6.2 XFEM approximation. 6.6.3 Two-phase fluid flow. 6.6.4 XFEM approximation. Chapter 7 XFEM Flow. 7.1 INTRODUCTION. 7.2 AVAILABLE OPEN-SOURCE XFEM. 7.3. FINITE ELEMENT ANALYSIS. 7.3.1 Defining the model. 7.3.2 Creating the finite element mesh. 7.3.3 Linear elastic analysis. 7.3.4 Large deformation. 7.3.5 Nonlinear (elastoplastic) analysis. 7.3.6 Material constitutive matrix. 7.4 XFEM. 7.4.1 Front tracking. 7.4.2 Enrichment detection. 7.4.3 Enrichment functions. 7.4.4 Ramp (transition) functions. 7.4.5 Evaluation of the B matrix. 7.5 NUMERICAL INTEGRATION. 7.5.1 Sub-quads. 7.5.2 Sub-triangles. 7.6 SOLVER. 7.6.1 XFEM degrees of freedom. 7.6.2 Time integration. 7.6.3 Simultaneous equations solver. 7.6.4 Crack length control. 7.7 POST-PROCESSING. 7.7.1 Stress intensity factor. 7.7.2 Crack growth. 7.7.3 Other applications. 7.8 CONFIGURATION UPDATE. References . Index

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Book SynopsisCivil and environmental engineers need an understanding of mathematical statistics and probability theory to deal with the variability that affects engineers' structures, soil pressures, river flows and the like. Students, too, need to get to grips with these rather difficult concepts. This book, written by engineers for engineers, tackles the subject in a clear, up-to-date manner using a process-orientated approach. It introduces the subjects of mathematical statistics and probability theory, and then addresses model estimation and testing, regression and multivariate methods, analysis of extreme events, simulation techniques, risk and reliability, and economic decision making. 325 examples and case studies from European and American practice are included and each chapter features realistic problems to be solved. For the second edition new sections have been added on Monte Carlo Markov chaiTable of ContentsPreface. Introduction. Preliminary data analysis. Basic probability concepts. Random variables and their properties. Probability distributions. Model estimation and testing. Methods of regression and multivariate analysis. Frequency analysis of extreme events. Simulation techniques for design. Risk and reliability analysis. Bayesian decision methods and parameter uncertainty. Appendixes Further mathematics Glossary of symbols Tables of selected distributions Brief answers to selected problems . Data lists. Index

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Book SynopsisThis is the first textbook to address quantified risk assessment (QRA) as specifically applied to offshore installations and operations. These minimalistic installations with no helideck and very limited safety systems will require a new approach to risk assessment and emergency planning, especially during manned periods involving W2W vessels.Trade Review“The book, which offers complete and up-to-date information about some environmental aspects and impacts, is useful for academics and students, as well as for professionals in the sector and regulatory authorities.” (Emilia Di Lorenzo, zbMATH 1427.91004, 2020)Table of ContentsPart III.- 14.Methodology for Quantified Risk Assessment.- 15.Analysis Techniques.- 16.Presentation of Risk Results from QRA Studies.- 17.Evaluation of Personnel Risk Levels.- 18.Environmental Risk Analysis.- 19.Approach to Risk Based Design.- 20.Risk based Emergency Response Planning.- Part IV.- 21.Use of Risk Analysis during the Operations Phase.- 22.Use of Risk Indicators for Major Hazard Risk.- 23.Barrier Management for Major Hazard Risk.- Appendix A.Overview of Software.- Appendix B.Overview of Fatalities in Norwegian Sector.- Appendix C.Network Resources.

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Book SynopsisOptimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques.In recent years the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications.Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications in a distinct part, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area, followed by chapters detailing applications to a wide range of real-world problems.The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand not only the importance of optimization methods to engineering but also the capabilities of current methods.

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Book SynopsisHighly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety.The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals—Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox—from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis—yet this understanding is the cornerstone of efficient algorithms.

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Book SynopsisThe Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers.Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

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Book SynopsisThis book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems.Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.

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Book SynopsisFit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems.Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond lecturing, assumes that the reader has taken a course on linear algebra, but reviews background as needed, and covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, a detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration, a discussion of the use of the SVD for assigning grades, and multigrid methods. This textbook is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It can be used in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory

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Book SynopsisCollecting a set of classical and emerging methods that otherwise would not be available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book is designed to bring together an eclectic group of researchers with a wide variety of applications and disciplines including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods. Inside, readers will find: Basic techniques of model-based image processing. A comprehensive treatment of Bayesian and regularized image reconstruction methods. An integrated treatment of advanced reconstruction techniques such as majorization, constrained optimization, ADMM, and Plug-and-Play methods for model integration. Foundations of Computational Imaging can be used in courses on Model-Based or Computational Imaging, Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. It is also for researchers or practitioners in medical imaging, scientific imaging, commercial imaging, or industrial imaging.

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Book SynopsisReduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications.This book will be of interest to researchers and graduate students in the field of reduced order modeling.

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Book SynopsisThe aim of this book is the study of signals and deterministic systems, linear, time-invariant, finite dimensions and causal. A set of useful tools is selected for the automatic and signal processing and methods of representation of dynamic linear systems are exposed, and analysis of their behavior. Finally we discuss the estimation, identification and synthesis of control laws for the purpose of stabilization and regulation.Table of ContentsPreface ix Chapter 1 Control, Servo-mechanisms and System Regulation 1 1.1. Introduction 1 1.1.1. Generalities and definitions 1 1.1.2. Control law synthesis 5 1.1.3. Comprehension and application exercises 7 1.2. Process control 11 1.2.1. Correction in the frequency domain 11 1.2.2. Phase advance controller and PD controller 12 1.2.3. Phase delay controller and integrator compensator 14 1.2.4. Proportional, integral and derivative (PID) control 17 1.3. Some application exercises 23 1.3.1. Identification of the transfer function and control 23 1.3.2. PI control 30 1.3.3. Phase advance control 33 1.4. Some application exercises 36 1.5. Application 1: stabilization of a rigid robot with pneumatic actuator 39 1.5.1. Conventional approach 41 1.6. Application 2: temperature control of an oven 51 1.6.1. Modeling and identification study 51 Chapter 2 System Process Control 55 2.1. Introduction 55 2.2. Modeling 55 2.2.1. Introduction 55 2.3. Governability, controllability and observability 56 2.3.1. Characteristic polynomial, minimal polynomial and Cayley–Hamilton theorem 56 2.3.2. Governability or controllability 56 2.3.3. Observability 63 2.3.4. Observer 68 2.3.5. Observer for state reconstruction 69 2.3.6. Minimal state–space representation 76 2.4. State feedback, control by poles placement and stability 79 2.4.1. State feedback control 79 2.4.2. Poles placement and stabilizability 80 2.4.3. Finite-time response for a discrete system, deadbeat response 83 2.4.4. Use of observers in control: separation principle 85 2.5. Linear quadratic (LQ) control 86 2.5.1. Linear quadratic regulator 89 2.6. Optimal control (LQ) 90 2.7. Comprehension and application exercises 94 Chapter 3 Actuators: Modeling and Analysis 117 3.1. Introduction: electric, hydraulic and pneumatic actuators 117 3.1.1. Representation methods for physical systems 118 3.1.2. Modeling of a few constituents of physical systems 120 3.2. Transmission chains, actuators and sensors 126 3.2.1. Electric actuators in robotics 126 3.2.2. Motor speed torque characteristic 131 3.2.3. Dynamic behavior or transient behavior 131 3.2.4. Electric systems motor load 134 3.3. Pneumatic actuators 137 3.3.1. Pneumatic system modeling 137 3.3.2. Frictions model 145 3.4. Hydraulic actuators 149 3.4.1. System description 149 3.4.2. Mechanical model 151 3.4.3. Hydraulic actuator model 152 3.5. Application exercises 155 Chapter 4 Digital Control and Polynomial Approach 161 4.1. Introduction to digital control 161 4.1.1. Digital controller synthesis by transposition 162 4.1.2. Euler’s transposition 164 4.1.3. Choice of the sampling period (Shannon’s theorem) 170 4.2. PID controller synthesis and its equivalent digital RST 171 4.2.1. Standard controllers 171 4.2.2. Study of digital PIDs 172 4.2.3. Digital RST controller synthesis 178 4.2.4. Choice of poles and zeros to compensate 179 4.2.5 Computation of polynomials R, S and T 180 4.2.6. Additional objectives for synthesis 181 4.3. Digital control by poles placement 182 4.3.1. Choice of the sampling period 183 4.4. Diophantine, Bézout, greatest common divisor, least common multiple and division 183 4.4.1. Polynomial arithmetic 183 4.4.2. Diophantine equation ax + by = c and Bachet–Bézout theorem 184 4.4.3. Bézout’s identity 185 4.4.4. Greatest common divisor 185 4.4.5. Least common multiple 185 4.5. A few comprehension and application exercises 186 Chapter 5 NAO Robot 193 5.1. Introduction 193 5.2. Home care project 194 5.2.1. Choregraphe software 194 5.2.2. Nao Matlab SDK research 199 5.2.3. Nao and home care 206 5.2.4. The actions to be made 207 5.3. Details of the various programs 208 5.3.1. Ask for news 208 5.3.2. CallFirefighters box 212 5.3.3. CallNeighbor box 213 5.3.4. CallFamily box 215 5.3.5. Collision detection 215 5.3.6. Special actions: waking-up 216 5.3.7. Morning hygiene 220 5.3.8. Gymnastics 221 5.3.9. Nurse call 225 5.3.10. Memory game 227 5.3.11. Drugs reminder 232 5.3.12. Reading 233 5.3.13. Listening to music 235 5.3.14. Multiplication game 239 5.3.15. Nao’s dance 243 5.3.16. Memory game 245 5.3.17. Detect person on the ground 247 5.3.18. At any time 251 5.4. Conclusion 253 5.4.1. Nao’s limitations and possible improvements 253 Chapter 6 Application Problems with Solutions 255 6.1. Exercise 6.1: car suspension 255 6.1.1. Modeling 256 6.1.2. Analysis 257 6.2. Exercise 6.2: electromechanical system 259 6.2.1. Modeling 260 6.2.2. Analysis 262 6.3. Exercises: identification and state–space representation 263 6.3.1. Exercise 6.3 263 6.3.2. Exercise 6.4 265 6.3.3. Exercise 6.5 268 6.3.4. Exercise 6.6 270 6.3.5. Exercise 6.7 276 6.4. Exercises: observation and control of nonlinear systems 278 6.4.1. Exercise 6.8 278 6.4.2. Exercise 6.9 280 6.4.3. Exercise 6.10 288 6.4.4. Exercise 6.11 291 6.4.5. Exercise 6.12 293 6.4.6. Exercise 6.13 296 6.4.7. Exercise 6.14 300 6.4.8. Exercise 6.15 300 Bibliography 307 Index 313

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Book SynopsisMost physical problems can be written in the form of mathematical equations (differential, integral, etc.). Mathematicians have always sought to find analytical solutions to the equations encountered in the different sciences of the engineer (mechanics, physics, biology, etc.). These equations are sometimes complicated and much effort is required to simplify them. In the middle of the 20th century, the arrival of the first computers gave birth to new methods of resolution that will be described by numerical methods. They allow solving numerically as precisely as possible the equations encountered (resulting from the modeling of course) and to approach the solution of the problems posed. The approximate solution is usually computed on a computer by means of a suitable algorithm. The objective of this book is to introduce and study the basic numerical methods and those advanced to be able to do scientific computation. The latter refers to the implementation of approaches adapted to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or engineering (structural mechanics, fluid mechanics, signal processing, etc.) .Table of ContentsPreface xi Part 1 Introduction 1 Chapter 1 Review of Linear Algebra 3 1.1. Vector spaces 3 1.1.1. General definitions 3 1.1.2. Free families, generating families and bases 4 1.2. Linear mappings 5 1.3. Matrices 7 1.3.1. Operations on matrices 7 1.3.2. Change-of-basis matrices 8 1.3.3. Matrix notations 9 1.4. Determinants 10 1.5. Scalar product 12 1.6. Vector norm 12 1.7. Matrix eigenvectors and eigenvalues 13 1.7.1. Definitions and properties 13 1.7.2. Matrix diagonalization 15 1.7.3. Triangularization of matrices 15 1.8 Using Matlab 16 Chapter 2 Numerical Precision 21 2.1. Introduction 21 2.2. Machine representations of numbers 22 2.3. Integers 23 2.3.1. External representation 23 2.3.2. Internal representation of positive integers 24 2.4. Real numbers 25 2.4.1. External representation 25 2.4.2. Internal encoding of real numbers 25 2.5. Representation errors 26 2.5.1. Properties of computer-based arithmetic 27 2.5.2. Operation of subtraction 28 2.5.3. Stability 29 2.6. Determining the best algorithm 29 2.7 Using Matlab 30 2.7.1. Definition of variables 30 2.7.2. Manipulating numbers 30 Part 2 Approximating Functions 35 Chapter 3 Polynomial Interpolation 37 3.1. Introduction 37 3.2. Interpolation problems 37 3.2.1. Linear interpolation 38 3.3. Polynomial interpolation techniques 38 3.4. Interpolation with the Lagrange basis 39 3.4.1. Polynomial interpolation error 43 3.4.2. Neville–Aitken method 46 3.5. Interpolation with the Newton basis 46 3.6. Interpolation using spline functions 48 3.6.1. Hermite interpolation 50 3.6.2. Spline interpolation error 55 3.7 Using Matlab 58 3.7.1. Operations on polynomials 58 3.7.2. Manipulating polynomials 59 3.7.3. Evaluation of polynomials 60 3.7.4. Linear and nonlinear interpolation 60 3.7.5. Lagrange function 63 3.7.6. Newton function 64 Chapter 4 Numerical Differentiation 67 4.1. First-order numerical derivatives and the truncation error 67 4.2. Higher-order numerical derivatives 70 4.3. Numerical derivatives and interpolation 71 4.4. Studying the differentiation error 73 4.5. Richardson extrapolation 77 4.6. Application to the heat equation 78 4.7 Using Matlab 81 Chapter 5 Numerical Integration 83 5.1. Introduction 83 5.2. Rectangle method 84 5.3. Trapezoidal rule 84 5.4. Simpson’s rule 87 5.5. Hermite’s rule 90 5.6. Newton–Côtes rules 91 5.7. Gauss–Legendre method 92 5.7.1. Problem statement 92 5.7.2. Legendre polynomials 94 5.7.3 Choosing the αi and xi (i = 0, . . . , n) 99 5.8 Using Matlab 100 5.8.1. Matlab functions for numerical integration 100 5.8.2. Trapezoidal rule 101 5.8.3. Simpson’s rule 103 Part 3 Solving Linear Systems 107 Chapter 6 Matrix Norm and Conditioning 109 6.1. Introduction 109 6.2. Matrix norm 109 6.3. Condition number of a matrix 113 6.3.1 Approximation of K(A) 116 6.4. Preconditioning 116 6.5 Using Matlab 117 6.5.1. Matrices and vectors 117 6.5.2. Condition number of a matrix 119 Chapter 7 Direct Methods 123 7.1. Introduction 123 7.2. Method of determinants or Cramer’s method 123 7.2.1. Matrix inversion by Cramer’s method 124 7.3. Systems with upper triangular matrices 124 7.4. Gaussian method 125 7.4.1. Solving multiple systems in parallel 129 7.5. Gauss–Jordan method 129 7.5.1. Underlying principle 129 7.5.2. Computing the inverse of a matrix with the Gauss–Jordan algorithm 131 7.6. LU decomposition 132 7.7. Thomas algorithm 133 7.8. Cholesky decomposition 134 7.9 Using Matlab 136 7.9.1. Matrix operations 136 7.9.2. Systems of linear equations 138 Chapter 8 Iterative Methods 147 8.1. Introduction 147 8.2. Classical iterative techniques 148 8.2.1. Jacobi method 149 8.2.2. Gauss–Seidel method 151 8.2.3. Relaxation method 152 8.2.4. Block forms of the Jacobi, Gauss–Seidel and relaxation methods 154 8.3. Convergence of iterative methods 155 8.4. Conjugate gradient method 157 8.5 Using Matlab 159 8.5.1. Jacobi method 159 8.5.2. Relaxation method 160 Chapter 9 Numerical Methods for Computing Eigenvalues and Eigenvectors 163 9.1. Introduction 163 9.2. Computing det (A − λI) directly 164 9.3. Krylov methods 166 9.4. LeVerrier method 167 9.5. Jacobi method 168 9.6. Power iteration method 171 9.6.1. Deflation algorithm 172 9.7. Inverse power method 173 9.8. Givens–Householder method 174 9.8.1. Givens algorithm 175 9.9 Using Matlab 176 9.9.1. Application to a buckling beam 177 Chapter 10 Least-squares Approximation 185 10.1. Introduction 185 10.2. Analytic formulation 185 10.3. Algebraic formulation 191 10.3.1. Standard results on orthogonality 191 10.3.2. Least-squares problem 191 10.3.3. Solving by orthogonalization 192 10.4. Numerically solving linear equations by QR factorization 193 10.4.1. Householder transformations 193 10.4.2. QR factorization 193 10.4.3. Application to the least-squares problem 193 10.5. Applications 194 10.5.1. Curve fitting 194 10.5.2. Approximations of derivatives 195 10.6 Using Matlab 195 Part 4 Appendices 199 Appendix 1 Introduction to Matlab 201 Appendix 2 Introduction to Optimization 209 Bibliography 215 Index 217

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Book SynopsisThe purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or of engineering (mechanics of structures, mechanics of fluids, treatment signal, etc.). Each chapter of this book recalls the essence of the different methods resolution and presents several applications in the field of engineering as well as programs developed under Matlab software.Table of ContentsPreface ix Part 1. Solving Equations 1 Chapter 1. Solving Nonlinear Equations 3 1.1 Introduction 3 1.2 Separating the roots 3 1.3 Approximating a separated root 4 1.3.1 Bisection method (or dichotomy method) 4 1.3.2 Fixed-point method 6 1.3.3 First convergence criterion 7 1.3.4 Iterative stopping criteria.8 1.3.5 Second convergence criterion (local criterion) 9 1.3.6 Newton’s method (or the method of tangents) 10 1.3.7 Secant method 12 1.3.8 Regula falsi method (or false position method) 17 1.4 Order of an iterative process.19 1.5 Using Matlab 19 1.5.1 Finding the roots of polynomials 19 1.5.2 Bisection method 21 1.5.3 Newton’s method 22 Chapter 2. Numerically Solving Differential Equations 25 2.1 Introduction 25 2.2 Cauchy problem and discretization 27 2.3 Euler’s method 30 2.3.1 Interpretation 30 2.3.2 Convergence 30 2.4 One-step Runge–Kutta method 31 2.4.1 Second-order Runge–Kutta method 32 2.4.2 Fourth-order Runge–Kutta method 33 2.5 Multi-step Adams methods 36 2.5.1 Open Adams methods 36 2.5.2 Closed Adams formulas 39 2.6 Predictor–Corrector method.41 2.7 Using Matlab 43 Part 2. Solving PDEs 47 Chapter 3. Finite Difference Methods 49 3.1 Introduction 49 3.2 Presentation of the finite difference method 51 3.2.1 Convergence, consistency and stability 53 3.2.2 Courant–Friedrichs–Lewy condition 56 3.2.3 Von Neumann stability analysis 57 3.3 Hyperbolic equations 58 3.3.1 Key results 59 3.3.2 Numerical schemes for solving the transport equation 63 3.3.3 Wave equation 66 3.3.4 Burgers equation 68 3.4 Elliptic equations 72 3.4.1 Poisson equation 72 3.5 Parabolic equations 74 3.5.1 Heat equation 74 3.6 Using Matlab 76 Chapter 4. Finite Element Method 83 4.1 Introduction 83 4.2 One-dimensional finite element methods 83 4.3 Two-dimensional finite element methods 88 4.4 General procedure of the method 93 4.5 Finite element method for computing elastic structures 93 4.5.1 Linear elasticity 93 4.5.2 Variational formulation of the linear elasticity problem 97 4.5.3 Planar linear elasticity problems 99 4.5.4 Applying the finite element method to planar problems 101 4.5.5 Axisymmetric problems.105 4.5.6 Three-dimensional problems 107 4.6 Using Matlab 107 4.6.1 Solving Poisson’s equation 108 4.6.2 Solving the heat equation.111 4.6.3 Computing structures 112 Chapter 5. Finite Volume Methods 117 5.1 Introduction 117 5.2 Finite volume method (FVM) 118 5.2.1 Conservation properties of the method 118 5.2.2 The stages of the method.119 5.2.3 Convergence 120 5.2.4 Consistency 120 5.2.5 Stability 120 5.3 Advection schemes 121 5.3.1 Two-dimensional FVM. 126 5.3.2 Convection-diffusion equation 129 5.3.3 Central differencing scheme 131 5.3.4 Upwind (decentered) scheme 133 5.3.5 Hybrid scheme 136 5.3.6 Power-law scheme 136 5.3.7 QUICK scheme 137 5.3.8 Higher-order schemes 139 5.3.9 Unsteady one-dimensional convection-diffusion Equation 140 5.3.10 Explicit scheme 142 5.3.11 Crank–Nicolson scheme.142 5.3.12 Implicit scheme 143 5.4 Using Matlab 144 Chapter 6. Meshless Methods. 147 6.1 Introduction 147 6.2 Limitations of the FEM and motivation of meshless methods 148 6.3 Examples of meshless methods148 6.3.1 Advantages of meshless methods 149 6.3.2 Disadvantages of meshless methods150 6.3.3 Comparison of the finite element method and meshless methods 151 6.4 Basis of meshless methods 151 6.4.1 Approximations 151 6.4.2 Kernel (weight) functions.152 6.4.3 Completeness 152 6.4.4 Partition of unity 152 6.5 Meshless method (EFG) 153 6.5.1 Theory 153 6.5.2 Moving Least-Squares Approximation 153 6.6 Application of the meshless method to elasticity 163 6.6.1 Formulation of static linear elasticity 163 6.6.2 Imposing essential boundary conditions 165 6.7 Numerical examples 170 6.7.1 Fixed-free beam 170 6.7.2 Compressed block 171 6.8 Using Matlab 173 Part 3. Appendices 179 Appendix 1181 Appendix 2189 Bibliography 195 Index 199

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Book SynopsisElectromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing. In this book, the Method of Moments (MoM) is applied to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Since the problem is considered to be 2D, the integral equations (IEs) are scalar and only the TE (transverse electric) and TM (transverse magnetic) polarizations are addressed (no cross-polarizations occur). In Chapter 1, the MoM is applied to convert the IEs into a linear system, while Chapter 2 compares the MoM with the exact solution of the field scattered by a cylinder in free space, and with the Physical Optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM, of the coherent and incoherent intensities scattered by a random rough surface and an object below a random rough surface. The final chapter presents the same results as in Chapter 3, but for an object above a random rough surface. In these last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks. Contents 1. Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces. 2. Validation of the Method of Moments for a Single Scatterer. 3. Scattering from Two Illuminated Scatterers. 4. Scattering from Two Scatterers Where Only One is Illuminated. Appendix. Matlab Codes. About the Authors Christophe Bourlier works at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) as well as being a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conference papers. Nicolas Pinel is currently working as a Research Engineer at the IETR laboratory at Polytech Nantes and is about to join Alyotech Technologies in Rennes, France. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers. Gildas Kubické is in charge of the “Expertise in electroMagnetism and Computation” (EMC) laboratory at the DGA (Direction Générale de l’Armement), French Ministry of Defense, where he works in the field of radar signatures and electromagnetic stealth. His research interests include electromagnetic scattering and radar cross-section modeling.Table of ContentsPREFACE ix INTRODUCTION xi CHAPTER 1. INTEGRAL EQUATIONS FOR A SINGLE SCATTERER: METHOD OF MOMENTS AND ROUGH SURFACES 1 1.1. Introduction 1 1.2. Integral equations 2 1.3. Method of moments with point-matching method 12 1.4. Application to a surface 14 1.5. Forward–Backward (FB) method 19 1.6. Random rough surface generation 21 CHAPTER 2. VALIDATION OF THE METHOD OF MOMENTS FOR A SINGLE SCATTERER 31 2.1. Introduction 31 2.2. Solutions of a scattering problem 31 2.3. Comparison with the exact solution of a circular cylinder in free space 34 2.4. PO approximation 55 2.5. FB method 69 2.6. Conclusion 71 CHAPTER 3. SCATTERING FROM TWO ILLUMINATED SCATTERERS 73 3.1. Introduction 73 3.2. Integral equations and method of moments 75 3.3. Efficient inversion of the impedance matrix: E-PILE method for two scatterers 86 3.4. E-PILE method combined with PO and FB 94 3.5. Conclusion 107 CHAPTER 4. SCATTERING FROM TWO SCATTERERS WHERE ONLY ONE IS ILLUMINATED 109 4.1. Introduction 109 4.2. Integral equations and method of moments 110 4.3. Efficient inversion of the impedance matrix: PILE method 122 4.4. PILE method combined with FB or PO 128 4.5. Conclusion 138 APPENDIX MATLAB CODES 139 BIBLIOGRAPHY 141 INDEX 147

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Book SynopsisAdvanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.Table of ContentsForeword ix Introduction xi Chapter 1. A First Encounter with Graphs 1 1.1. A few definitions 1 1.1.1. Directed graphs 1 1.1.2. Unoriented graphs 9 1.2. Paths and connected components 14 1.2.1. Connected components 16 1.2.2. Stronger notions of connectivity 18 1.3. Eulerian graphs 23 1.4. Defining Hamiltonian graphs 25 1.5. Distance and shortest path 27 1.6. A few applications 30 1.7. Comments 35 1.8. Exercises 37 Chapter 2. A Glimpse at Complexity Theory 43 2.1. Some complexity classes 43 2.2. Polynomial reductions 46 2.3. More hard problems in graph theory 49 Chapter 3. Hamiltonian Graphs 53 3.1. A necessary condition 53 3.2. A theorem of Dirac 55 3.3. A theorem of Ore and the closure of a graph 56 3.4. Chvátal’s condition on degrees 59 3.5. Partition of Kn into Hamiltonian circuits 62 3.6. De Bruijn graphs and magic tricks 65 3.7. Exercises 68 Chapter 4. Topological Sort and Graph Traversals 69 4.1. Trees 69 4.2. Acyclic graphs 79 4.3. Exercises 82 Chapter 5. Building New Graphs from Old Ones 85 5.1. Some natural transformations 85 5.2. Products 90 5.3. Quotients 92 5.4. Counting spanning trees 93 5.5. Unraveling 94 5.6. Exercises 96 Chapter 6. Planar Graphs 99 6.1. Formal definitions 99 6.2. Euler’s formula 104 6.3. Steinitz’ theorem 109 6.4. About the four-color theorem 113 6.5. The five-color theorem 115 6.6. From Kuratowski’s theorem to minors 120 6.7. Exercises 123 Chapter 7. Colorings 127 7.1. Homomorphisms of graphs 127 7.2. A digression: isomorphisms and labeled vertices 131 7.3. Link with colorings 134 7.4. Chromatic number and chromatic polynomial 136 7.5. Ramsey numbers 140 7.6. Exercises 147 Chapter 8. Algebraic Graph Theory 151 8.1. Prerequisites 151 8.2. Adjacency matrix 154 8.3. Playing with linear recurrences 160 8.4. Interpretation of the coefficients 168 8.5. A theorem of Hoffman 169 8.6. Counting directed spanning trees 172 8.7. Comments 177 8.8. Exercises 178 Chapter 9. Perron–Frobenius Theory 183 9.1. Primitive graphs and Perron’s theorem 183 9.2. Irreducible graphs 188 9.3. Applications 190 9.4. Asymptotic properties 195 9.4.1. Canonical form 196 9.4.2. Graphs with primitive components 197 9.4.3. Structure of connected graphs 206 9.4.4. Period and the Perron–Frobenius theorem 214 9.4.5. Concluding examples 218 9.5. The case of polynomial growth 224 9.6. Exercises 231 Chapter 10. Google’s Page Rank 233 10.1. Defining the Google matrix 238 10.2. Harvesting the primitivity of the Google matrix 241 10.3. Computation 246 10.4. Probabilistic interpretation 246 10.5. Dependence on the parameter α 247 10.6. Comments 248 Bibliography 249 Index 263

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Book SynopsisThis book gives new insight on plate models in the linear elasticity framework tacking into account heterogeneities and thickness effects. It is targeted to graduate students how want to discover plate models but deals also with latest developments on higher order models. Plates models are both an ancient matter and a still active field of research. First attempts date back to the beginning of the 19th century with Sophie Germain. Very efficient models have been suggested for homogeneous and isotropic plates by Love (1888) for thin plates and Reissner (1945) for thick plates. However, the extension of such models to more general situations --such as laminated plates with highly anisotropic layers-- and periodic plates --such as honeycomb sandwich panels-- raised a number of difficulties. An extremely wide literature is accessible on these questions, from very simplistic approaches, which are very limited, to extremely elaborated mathematical theories, which might refrain the beginner. Starting from continuum mechanics concepts, this book introduces plate models of progressive complexity and tackles rigorously the influence of the thickness of the plate and of the heterogeneity. It provides also latest research results. The major part of the book deals with a new theory which is the extension to general situations of the well established Reissner-Mindlin theory. These results are completely new and give a new insight to some aspects of plate theories which were controversial till recently.Table of ContentsIntroduction xi Chapter 1. Linear Elasticity 1 1.1. Notations 1 1.2. Stress 3 1.3. Linearized strains 6 1.4. Small perturbations 8 1.5. Linear elasticity 8 1.6. Boundary value problem in linear elasticity 10 1.7. Variational formulations. 11 1.7.1. Compatible strains and stresses 11 1.7.2. Principle of minimum of potential energy 13 1.7.3. Principle of minimum of complementary energy 14 1.7.4. Two-energy principle 15 1.8. Anisotropy 15 1.8.1. Voigt notations 15 1.8.2. Material symmetries 17 1.8.3. Orthotropy 20 1.8.4. Transverse isotropy 22 1.8.5. Isotropy 23 Part 1. Thin Laminated Plates 27 Chapter 2. A Static Approach for Deriving the Kirchhoff–Love Model for Thin Homogeneous Plates 29 2.1. The 3D problem 29 2.2. Thin plate subjected to in-plane loading 32 2.2.1. The plane-stress 2D elasticity problem 33 2.2.2. Application of the two-energy principle 34 2.2.3. In-plane surfacic forces on ∂Ω ± 336 2.2.4. Dirichlet conditions on the lateral boundary of the plate 38 2.3. Thin plate subjected to out-of-plane loading 40 2.3.1. The Kirchhoff–Love plate model 41 2.3.2. Application of the two-energy principle 47 Chapter 3. The Kirchhoff–Love Model for Thin Laminated Plates 53 3.1. The 3D problem 53 3.2. Deriving the Kirchhoff–Love plate model 55 3.2.1. The generalized plate stresses 55 3.2.2. Static variational formulation of the Kirchhoff–Love plate model 56 3.2.3. Direct formulation of the Kirchhoff–Love plate model 58 3.3. Application of the two-energy principle 59 Part 2. Thick Laminated Plates 65 Chapter 4. Thick Homogeneous Plate Subjected to Out-of-Plane Loading 67 4.1. The 3D problem 67 4.2. The Reissner–Mindlin plate model. 69 4.2.1. The 3D stress distribution in the Kirchhoff–Love plate model 69 4.2.2. Formulation of the Reissner–Mindlin plate model 71 4.2.3. Characterization of the Reissner–Mindlin stress solution 72 4.2.4. The Reissner–Mindlin kinematics 73 4.2.5. Derivation of the direct formulation of the Reissner–Mindlin plate model 74 4.2.6. The relations between generalized plate displacements and 3D displacements 76 Chapter 5. Thick Symmetric Laminated Plate Subjected to Out-of-Plane Loading 81 5.1. Notations 81 5.2. The 3D problem 82 5.3. The generalized Reissner plate model 85 5.3.1. The 3D stress distribution in the Kirchhoff–Love plate model 85 5.3.2. Formulation of the generalized Reissner plate model 90 5.3.3. The subspaces of generalized stresses 91 5.3.4. The generalized Reissner equilibrium equations 95 5.3.5. Characterization of the generalized Reissner stress solution 97 5.3.6. The generalized Reissner kinematics 98 5.3.7. Derivation of the direct formulation of the generalized Reissner plate model 100 5.3.8. The relationships between generalized plate displacements and 3D displacements 102 5.4. Derivation of the Bending-Gradient plate model 106 5.5. The case of isotropic homogeneous plates 109 5.6. Bending-Gradient or Reissner–Mindlin plate model? 111 5.6.1. When does the Bending-Gradient model degenerate into the Reissner–Mindlin’s model? 112 5.6.2. The shear compliance projection of the Bending-Gradient model onto the Reissner–Mindlin model 113 5.6.3. The shear stiffness projection of the Bending-Gradient model onto the Reissner–Mindlin model 115 5.6.4. The cylindrical bending projection of the Bending-Gradient model onto the Reissner–Mindlin model 116 Chapter 6. The Bending-Gradient Theory 117 6.1. The 3D problem 117 6.2. The Bending-Gradient problem 119 6.2.1. Generalized stresses 119 6.2.2. Equilibrium equations 121 6.2.3. Generalized displacements 122 6.2.4. Constitutive equations 122 6.2.5. Summary of the Bending-Gradient plate model 123 6.2.6. Field localization 123 6.3. Variational formulations 125 6.3.1. Minimum of the potential energy 126 6.3.2. Minimum of the complementary energy 127 6.4. Boundary conditions 128 6.4.1. Free boundary condition 129 6.4.2. Simple support boundary condition 130 6.4.3. Clamped boundary condition 131 6.5. Voigt notations 131 6.5.1. In-plane variables and constitutive equations 131 6.5.2. Generalized shear variables and constitutive equations 132 6.5.3. Field localization 135 6.6. Symmetries 136 6.6.1. Transformation formulas 136 6.6.2. Orthotropy 139 6.6.3. π/2 invariance 140 6.6.4. Square symmetry 140 6.6.5. Isotropy 140 6.6.6. The remarkable case of functionally graded materials 142 Chapter 7. Application to Laminates 145 7.1. Laminated plate configuration 145 7.2. Localization fields 146 7.2.1. In-plane stress unit distributions (bending stress) 147 7.2.2. Transverse shear unit distributions (generalized shear stress) 148 7.3. Distance between the Reissner–Mindlin and the Bending-Gradient model 149 7.4. Cylindrical bending 150 7.4.1. Closed-form solution for the Bending-Gradient model 152 7.4.2. Comparison of field distributions 155 7.4.3. Empirical error estimates and convergence rate 160 7.4.4. Influence of the bending direction 161 7.5. Conclusion 163 Part 3 Periodic Plates 167 Chapter 8. Thin Periodic Plates 169 8.1. The 3D problem 169 8.2. The homogenized plate problem 173 8.3. Determination of the homogenized plate elastic stiffness tensors 174 8.4. A first justification: the asymptotic effective elastic properties of periodic plates 181 8.5. Effect of symmetries 184 8.5.1. Symmetric periodic plate 185 8.5.2. Material symmetry of the homogenized plate 186 8.5.3. Important special cases 187 8.5.4. Rectangular parallelepipedic unit cell 189 8.6. Second justification: the asymptotic expansion method 194 Chapter 9. Thick Periodic Plates 205 9.1. The 3D problem 206 9.2. The asymptotic solution 208 9.3. The Bending-Gradient homogenization scheme 209 9.3.1. Motivation and descrition of the approach 210 9.3.2. Introduction of corrective terms to the asymptotic solution 210 9.3.3. Identification of the localization tensors 212 9.3.4. Identification of the Bending-Gradient compliance tensor 214 Chapter 10. Application to Cellular Sandwich Panels 219 10.1. Introduction 219 10.2. Questions raised by sandwich panel shear force stiffness 220 10.2.1. The case of homogeneous cores 221 10.2.2. The case of cellular cores 223 10.3. The membrane and bending behavior of sandwich panels 225 10.3.1. The case of homogeneous cores 225 10.3.2. The case of cellular cores 226 10.4. The transverse shear behavior of sandwich panels 229 10.4.1. The case of homogeneous cores 229 10.4.2. A direct homogenization scheme for cellular sandwich panel shear force stiffness 230 10.4.3. Discussion 232 10.5. Application to a sandwich panel including Miura-ori 235 10.5.1. Folded cores 236 10.5.2. Description of the sandwich panel including the folded core 237 10.5.3. Symmetries of Miura-ori 238 10.5.4. Implementation 239 10.5.5. Results 241 10.5.6. Discussion on shear force stiffness 250 10.5.7. Consequence of skins distortion 255 10.6. Conclusion 257 Chapter 11. Application to Space Frames 259 11.1. Introduction 259 11.2. Homogenization of a periodic space frame as a thick plate 261 11.2.1. Homogenization scheme 261 11.3. Homogenization of a square lattice as a Bending-Gradient plate 268 11.3.1. The unit-cell 268 11.3.2. Kirchhoff–Love auxiliary problem 269 11.3.3. Bending-Gradient and Reissner–Mindlin auxiliary problems 270 11.3.4. Difference between Reissner–Mindlin and Bending-Gradient constitutive equation 273 11.4. Cylindrical bending of a square beam lattice 274 11.4.1. Lattice at 0° 274 11.4.2. Lattice at 45° 276 11.5. Discussion 282 11.6. Conclusion 283 Bibliography 285 Index 293

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Book SynopsisThis book presents real-world examples of formal techniques in an industrial context. It covers formal methods such as SCADE and/or the B Method, in various fields such as railways, aeronautics, and the automotive industry. The purpose of this book is to present a summary of experience on the use of “formal methods” (based on formal techniques such as proof, abstract interpretation and model-checking) in industrial examples of complex systems, based on the experience of people currently involved in the creation and assessment of safety critical system software. The involvement of people from within the industry allows the authors to avoid the usual confidentiality problems which can arise and thus enables them to supply new useful information (photos, architecture plans, real examples, etc.).Table of Contents1. Presentation of the B Method, Jean-Louis Boulanger. 2. Atelier B, Thierry Lecomte. 3. B Tools, Jean-Louis Boulanger. 4. The B Method at Siemens, Daniel Dolle. 5. Industrial Applications for Modeling with the B Method, Thierry Lecomte. 6. Formalization of Digital Circuits Using the B Method, Jean-Louis Boulanger. 7. Pragmatic Use of B: The Power of Formal Methods without the Bulk, Christophe Metayer, François Bustany, Mathieu Clabaut. 8. BRILLANT/BCaml—AFreeTools Platform for the B Method, Samuel Colin, Dorian Petit. 9. Translating B and Event-B Machines to Java and JML, Néstor Catano, Víctor Rivera, Camilo Rueday and Tim Wahlsz. 10. Event B, Dominique Méry, Neeraj Kumar Singh. 11. B-RAIL: UML to B Transformation in Modeling a Level Crossing, Jean-Louis Boulanger. 12. Feasibility of the Use of Formal Methods for Manufacturing Systems, Pascal Lamy, Philippe Charpentier, Jean-François Petinand Dominique Evrot. 13. B Extended to Floating-Point Numbers: Is It Sufficient for Proving Avionics Software?, Jean-Louis Dufour. 14. From Animation to Data Validation: The ProB Constraint Solver 10 Years On, Michael Leuschel, Jens Bendisposto,Ivo Dobrikov, Sebastian Krings, Daniel Plagge. 15. Unified Train Driving Policy, Alexei Iliasov,Ilya Lopatkin, Alexander Romanovsky.

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Book SynopsisThis volume contains contributions from speakers at the 4th International Symposium on Finite Volumes for Complex Applications, held in Marrakech, Morocco, in July 2005. The subject of these papers ranges from theoretical and numerical results to physical applications. Topics covered include: Theoretical and numerical results • theoretical foundation • convergence • new finite volume schemes • adaptivity • higher order discretization and parallelization Physical applications • multiphase flow and flows through porous media • turbulent flows • shallow water problems • stiff source terms • cryogenic applications • medical and biological applications • image processing Papers on Industrial codes, as well as interdisciplinary approaches are also included in these proceedings.Table of ContentsTheoretical and numerical results; theoretical foundation; convergence; new finite volume schemes; adaptivity; higher order discretization and parallelization; Physical applications; multiphase flow and flows through porous media; turbulent flows; shallow water problems; stiff source terms; cryogenic applications; medical and biological applications; image processing; Papers on Industrial codes, as well as interdisciplinary approaches are also included in these proceedings.

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Book SynopsisThis book provides the tools for analyzing data in Python: different types of filters are introduced and explained, such as FIR-, IIR- and morphological filters, as well as their application to one- and two-dimensional data. The required mathematics are kept to a minimum, and numerous examples and working Python programs are included for a quick start. The goal of the book is to enable also novice users to choose appropriate methods and to complete real-world tasks such as differentiation, integration, and smoothing of time series, or simple edge detection in images. An introductory section provides help and tips for getting Python installed and configured on your computer. More advanced chapters provide a practical introduction to the Fourier transform and its applications such as sound processing, as well as to the solution of equations of motion with the Laplace transform. A brief excursion into machine learning shows the powerful tools that are available with Python. This book also provides tips for an efficient programming work flow: from the use of a debugger for finding mistakes, code-versioning with git to avoid the loss of working programs, to the construction of graphical user interfaces (GUIs) for the visualization of data. Working, well-documented Python solutions are included for all exercises, and IPython/Jupyter notebooks provide additional help to get people started and outlooks for the interested reader.Table of ContentsIntroduction.- Python.- Data Input.- Data Display.- Data Filtering.- Event- and Feature-Finding.- Statistics.- Parameter Fitting.- Spectral Signal Analysis.- Solving Equations of Motion.- Machine Learning.- Useful Programming Tools.

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Book SynopsisThe book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.Table of ContentsM. Herty et al., Reconstruction of traffic speed distributions from kinetic models with uncertainties.- M. Herty et al., From kinetic to macroscopic models and back.- R. Ramadan et al., Structural Properties of the Stability of Jamitons.- C. Balzotti and E. Iacomini, Stop-and-go waves: A Microscopic and a Macroscopic Description.- F. A. Chiarello, An overview of non-local traffic flow models.

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Book SynopsisThis textbook introduces the concepts and tools that biomedical and chemical engineering students need to know in order to translate engineering problems into a numerical representation using scientific fundamentals. Modeling concepts focus on problems that are directly related to biomedical and chemical engineering. A variety of computational tools are presented, including MATLAB, Excel, Mathcad, and COMSOL, and a brief introduction to each tool is accompanied by multiple computer lab experiences. The numerical methods covered are basic linear algebra and basic statistics, and traditional methods like Newton’s method, Euler Integration, and trapezoidal integration. The book presents the reader with numerous examples and worked problems, and practice problems are included at the end of each chapter.Table of ContentsList of Examples.- List of Definitions.- Foreword.- Modern Engineering.- Mathematical Fundamentals .- Engineering Modeling.- Computational Problem Solving.- Introduction to MATLAB.- Linear Algebra.- Solving Problems Numerically.- Spreadsheets.- Basic Statistics and Probability.- Linearity.- Forces.- Classes of Numerical Problems.- Introduction to COMSOL.- Tips on Presenting Your Work.- Technical Writing Suggestions.- Lecture Notes.

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Book SynopsisThis book lists current and potential biomedical uses of computational intelligence methods. These methods are used in diagnostics and treatment of such diseases as cancer, cardiac diseases, pneumonia, stroke, and COVID-19. Many biomedical problems are difficult; so, often, the current methods are not sufficient, new methods need to be developed. To confidently apply the new methods to critical life-and-death medical situations, it is important to first test these methods on less critical applications. The book describes several such promising new methods that have been tested on problems from agriculture, computer networks, economics and business, pavement engineering, politics, quantum computing, robotics, etc. This book helps practitioners and researchers to learn more about computational intelligence methods and their biomedical applications—and to further develop this important research direction.Table of ContentsPart I: Biomedical Applications of Computational Intelligence Techniques.- Bilattice CADIAG-II: Theory and Experimental Results.- A Combination Model of Robust Principal Component Analysis and Multiple Kernel Learning for Cancer Patient Stratification.- Attention U-Net with Active Contour based Hybrid Loss for Brain Tumor Segmentation.- Refining Skip Connections by Fusing Multi-scaled Context in Neural Network for Cardiac MR Image Segmentation.- End-to-end Hand Rehabilitation System with Single-shot Gesture Classification for Stroke Patients.- Feature Selection based on Shapley Additive Explanations on Metagenomic Data for Colorectal Cancer Diagnosis.- Clinical Decision Support Systems for Pneumonia Diagnosis using Gradient-weighted Class Activation Mapping and Convolutional Neural Networks.- Improving 3D Hand Pose Estimation with Synthetic RGB Image Enhancement using RetinexNet and Dehazing.- Imbalance in Learning Chest X-ray Images for COVID-19 Detection.- Deep Learning based COVID-19 Diagnosis by Joint Classification and Segmentation.- Part II: General Computational Intelligence Techniques and Their Applications.- Why It Is Sufficient to Have Real-Valued Amplitudes in Quantum Computing.

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Book SynopsisThis book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.Table of ContentsOn the diffusion with decaying time dependent diffusivity: Formulations and approximate solutions pertinent to diffusion in concretes.- Laminar convection of power-law fluids in differentially heated closed region: CFD analysis.- Mathematical perspective of Hodgkin-Huxley model and bifurcation analysis.

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Book SynopsisThis volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems.The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.Table of ContentsNonlinear modelling and control of self-balancing human transporter (Makkar).- Nonlinear tourist flows in Barcelona (Trullols).- Convergence of dual infinity series (Klimenda).- Full spectrum analysis for studying the backward whirl in accelerated rotor systems (Alshudeifat).- Switched Reluctance Motor dynamic eccentricity modelling (Lorencki).- Harmonic transfer path analysis of a wine refrigerator (Hörtnagel).- Risk related prediction for recurrent stroke and post-stroke epilepsy using Fractional Fourier Transform analysis of EEG signals (Dulf).- Chaos, bifurcations and strange attractors in environmental radioactivity dynamics of some geosystems (Ternovsky).- Dynamics of chains as a tool to study thermomechanical properties of proteins (Weber).- Evaluation of the crane’s actuators strength based on the results obtained from dynamics model (Urbaś).- Nonlinear dynamics of atomic and molecular systems in an electromagnetic field: Deterministic chaos and strange attractors (Glushkov).- Deterministic chaos, bifurcations and strange attractors in nonlinear dynamics of relativistic backward-wave tube (Ternovsky).- Detection of chaotic behavior of the dynamical system using methods of deformable active contours (Ruchkin).- Dynamics of sensing element of micro- and nanoelectromechanical sensors as anisotropic size-dependent plate (Barulina).- Dynamic analysis and damage of composite layered plates reinforced by unidirectional fibers subjected low velocity impact (Soukup).- Identification of nonlinear joint interface parameters using instantaneous power flow balance approach (Rajan).- Numerical procedure for sensitivity analysis of hybrid systems (Pytlak).- Asymptotic stability of fractional variable order discrete-time equations with terms of convolution operators (Mozyrska).- Dynamics of circular plates under selected heat loadings (Doneva).- A Rulkov neuronal model with Caputo fractional variable-order differences of convolution type (Mozyrska).- Electrostatically actuated initially curved micro beams: analytical and finite element modelling (Mozhgova).- Numerical and analytical investigation of chatter suppression by parametric excitation (Dohnal).- Nonlinear study of a pneumatic artificial muscle (PAM) under superharmonic resonance condition using method of multiple scales (Kalita).- Two-mode long-wave low-frequency approximations for anti-plane shear deformation of a high-contrast asymmetric laminate (Kaplunov).- A study on the coefficient of restitution effect on single-sided vibro-impact nonlinear energy sink (Saeed).

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Book SynopsisThis book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments. The majority of the papers presented in this book is authored by the participants in The Joint Meeting 6th International Conference on Dynamics, Games, and Science – DGSVI – JOLATE and in the 21st ICABR Conference. The scientific scope of the conferences is focused on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology, and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of the conference is to bring together some of the world experts in mathematics, economics, and other applied sciences that reinforce ongoing projects and establish future works and collaborations.Table of ContentsA. Afsar, F. Martins, Bruno M. P. M. Oliveira, and A. A. Pinto, Immune response model fitting to CD4+ T cell data in lymphocytic choriomeningitis virus LCMV infection.- U. Agyüz, V. Purutçuoglu, E. Purutçuoglu and Y. Ürün, Construction of a New Model to Investigate Breast Cancer Data.- I. Baltas, M. Szczepanski, L. Dopierala, K. Kolodziejczyk, G.-W. Weber and A. N. Yannacopoulos, Optimal Pension Fund Management Under Risk and Uncertainty: The Case Study of Poland.- M. Bujidos-Casado, J. Navío-Marco and B. Rodrigo-Moya, Collaborative Innovation of Spanish SMEs in the European context: A compared study.- G. G. de Castro, A. O. Lopes and G. Mantovani, Haar systems, KMS states on von Neumann algebras and C*-algebras on dynamically defined groupoids and Noncommutative Integration.- C. Çıtak, T. Aksu, Ö. Harputlu and Gerhard-Wilhelm Weber, Mixed Compression Air-Intake Design for High-Speed Transportation.- D. Czerkawski, J. Małecka, G. Wilhelm Weber and B. Kjamili, Social Entrepreneurship Business Models for Handicapped People - Polish & Turkish case study of sharing public goods by doing business.- H. H. Ferreira, A. O. Lopes and E. R. Oliveira, An iterative process for approximating subactions.- A. D. Garcia and M. A. Szybisz, "Beat the gun": The phenomenon of liquidity.- E. Gómez-Escalonilla and Laura Parte, Board Knowledge and Bank Risk-Taking. An International Analysis.- F. Jiménez-Delgado, M. Dolores Reina-Paz, Israel J ThuissardVasallo and David Sanz-Rosa, The shopping experience in virtual sales: A study of the influence of website atmosphere on purchase intention.- Kyung B. Kim and José M. Labeaga, European Mobile Phone Industry: Demand Estimation Using Discrete Random Coefficients Models.- A. O. Lopes and M. Sebastiani, On Bertelson-Gromov Dynamical Morse Entropy, Rogério Martins, Synchronisation of weakly coupled oscillators.- Z. Kamisli Ozturk, Y. Cetin, Y. Isik and Z. I. Erzurum Cicek, Demand Forecasting with Clustering and Artificial Neural Networks Methods: an Application for Stock Keeping Units.- O. Palanci, S.Z. Alparslan Gok and Gerhard-Wilhelm Weber, On the Grey Obligation Rules.- Juan Diego Paredes-Gázquez, Eva Pardo and José Miguel Rodríguez-Fernández, Robustness checks in composite indicators: A responsible approach.- Elena V. Ravve, Zeev Volkovich, Gerhard-Wilhelm Weber, A Logic-Based Approach to Incremental Reasoning on Multi-Agent Systems.

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Book SynopsisThis book comprises high-quality refereed research papers presented at the Fourth International Conference on Computer Science, Engineering and Education Applications (ICCSEEA2021), held in Kyiv, Ukraine, on January 23–24, 2021, organized jointly by the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, National Aviation University, and the International Research Association of Modern Education and Computer Science. The topics discussed in the book include state-of-the-art papers in computer science, artificial intelligence, engineering techniques, genetic coding systems, deep learning with its medical applications, and knowledge representation with its applications in education. It is an excellent source of references for researchers, graduate students, engineers, management practitioners, and undergraduate students interested in computer science and their applications in engineering and education.Table of ContentsAutomatic Beam Aiming of the Laser Optical Reference System at the Center of Reflector to Improve the Accuracy and Reliability of Dynamic Positioning.- Decision Support System in Sprinkler Irrigation based on a Fractional Moisture Transport Model.- Automated Pipeline for Training Dataset Creation from Unlabeled Audios for Automatic Speech Recognition.- Estimation of Hurst index and Traffic Simulation.- Diagnosis of Rail Circuits by means of Fiber-optic Cable.- Complex Model for Personal Data Management of Online Project Users.- Nonparametric Change Point Detection Algorithms in the Monitoring Data.

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Book SynopsisThis book offers an overview of current and recent methods for the analysis of the nonstationary processes, focusing on cyclostationary systems that are ubiquitous in various application fields. Based on the 13th Workshop on Nonstationary Systems and Their Applications, held on February 3-5, 2020, in Grodek nad Dunajcem, Poland, the book merges theoretical contributions describing new statistical and intelligent methods for analyzing nonstationary processes, and applied works showing how the proposed methods can be implemented in practice and do perform in real-world case studies. A significant part of the book is dedicated to nonstationary systems applications, with a special emphasis on those in condition monitoring. Table of Contents.-

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Book SynopsisThis text provides a complete and thorough derivation of the mathematical theory of shell structures. Many books on shells only give the key equations or snippets of theory, skipping all of the mathematical steps required to solve for the key equations. This is understandable, because of the mathematical complexity of shell structures. Thus, the reader must just accept the design equations blindly, without achieving a complete understanding of shell theory. This book, therefore, fills this gap by providing a complete picture of shell theory. Class tested over three university post-graduate courses and one public course on shell structures, the book is mathematically intensive, but it written in an accessible style ideal for students of engineering mechanics in civil and mechanical engineers concentrations, as well as practicing structural engineers looking for a reference on shells.Table of Contents Chapter 1 Introduction Chapter 2 Construction Materials and Stress Flow 2.1 Introduction 2.2 The basic characteristics of stresses and strains 2.3 Economy of stresses 2.4 The flawed nature of construction materials 2.5 The flow of stress in flat and curved walls 2.6 The flow of stress around openings 2.7 Exercises Chapter 3 Cylindrical Shells 3.1 Introduction 3.2 The membrane theory of cylindrical shells 3.3 Displacement theory for membrane stresses 3.4 Boundary effects 3.5 Displacement theory for the boundary effects 3.6 Compatibility equations 3.7 Steps in solving for the deformations and stresses in the shell 3.8 Worked example 3.9 Exercises Chapter 4 Circular Domes 4.1 Introduction 4.2 The membrane theory of the circular dome 4.3 Displacement theory 4.4 Boundary effects 4.5 Displacement theory of the boundary effects 4.6 Compatibility equations 4.7 Steps in solving the deformations and stresses in the shell 4.8 Worked example 4.9 Exercises Chapter 5 Derivatives of Dome Theory: The Conoidal, Elliptical, Conical and Hyperbolic shells 5.1 Introduction 5.2 Conical shells 5.3 Elliptical dome 5.4 Conoidal dome 5.5 Hyperbolic shell 5.6 Example solutions and a comparison of the circular, concoidal, elliptical and conical domes 5.7 Exercises Chapter 6 The Circular Barrel Vault 6.1 Introduction 6.2 Membrane theory of the barrel vault 6.3 Deformation theory 6.4 Shallow shell theory to solve for the boundary effects 6.5 Edge beams 6.6 Steps in solving the deformations and stresses in the shell 6.7 Worked examples 6.8 Exercises Chapter 7 Catenary Arches and Domes 7.1 Introduction 7.2 The catenary arch 7.3 The funicular arch 7.4 Membrane theory of catenary domes 7.5 Worked examples 7.6 Exercises Appendix A and B

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Book SynopsisThis book offers a unique compendium of the authors´ own research on the use of theoretical stability analysis, showing how to take advantage of local stability design and ultimate boundedness for practical robot control. It addresses researchers and postgraduate students dealing with control theory, particularly with nonlinear systems. Thanks to the numerous worked examples, it could also be used as a textbook in postgraduate courses.Trade Review“The book is stimulating and addressed to a large spectrum of specialists (mechanical, electrical, control engineers and applied mathematicians working in rational mechanics, differential equations and control theory). It can be approached successfully by graduates and post-graduates of the aforementioned fields.” (Vladimir Răsvan, zbMATH 1489.93001, 2022)Table of ContentsA General Overview of Robot Manipulators.- Position, Orientation and Velocity of Rigid Robot Manipulators.- Dynamics of Rigid Robot Manipulators.- Mathematical Background.- Common Control Approaches for Robot Manipulators.

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Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.

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Book SynopsisThis book introduces Mechanistic Data Science (MDS) as a structured methodology for combining data science tools with mathematical scientific principles (i.e., “mechanistic” principles) to solve intractable problems. Traditional data science methodologies require copious quantities of data to show a reliable pattern, but the amount of required data can be greatly reduced by considering the mathematical science principles. MDS is presented here in six easy-to-follow modules: 1) Multimodal data generation and collection, 2) extraction of mechanistic features, 3) knowledge-driven dimension reduction, 4) reduced order surrogate models, 5) deep learning for regression and classification, and 6) system and design. These data science and mechanistic analysis steps are presented in an intuitive manner that emphasizes practical concepts for solving engineering problems as well as real-life problems. This book is written in a spectral style and is ideal as an entry level textbook for engineering and data science undergraduate and graduate students, practicing scientists and engineers, as well as STEM (Science, Technology, Engineering, Mathematics) high school students and teachers.Table of Contents1-Introduction to Mechanistic Data Science 2-Multimodal Data Generation and Collection 3-Optimization and Regression 4-Extraction of Mechanistic Features 5-Knowledge-Driven Dimension Reduction and Reduced Order Surrogate Models 6-Deep Learning for Regression and Classification 7-System and Design

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Book SynopsisThis book contains works on mathematical and simulation modeling of processes in various domains: ecology and geographic information systems, IT, industry, and project management. The development of complex multicomponent systems requires an increase in accuracy, efficiency, and adequacy while reducing the cost of their creation. The studies presented in the book are useful to specialists who involved in the development of real events models-analog, management and decision-making models, production models, and software products. Scientists can get acquainted with the latest research in various decisions proposed by leading scholars and identify promising directions for solving complex scientific and practical problems. The chapters of this book contain the contributions presented on the 16th International Scientific-practical Conference, MODS, June 28–July 01, 2021, Chernihiv, Ukraine.Table of ContentsMathematical Modeling of Information System Designing Master Plan of the Building Territory Based on OLAP Technology.- Models and information technologies of coverage of the territory by sensors with energy consumption optimization.- Transport of Reactive Tracer in Compacting Multi-fraction Bottom Sediments.- Pillars for establishing a durable and future-proof IT architecture maturing along with the NSC: Approaches from Continuous Integration to Service Mesh.- Optimal Control of Buried Point Sources in a Two-Dimensional Richards-Klute Equation.

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Book SynopsisThis book presents a comprehensive reference source for dynamic and innovative research in the field of cyber security, focusing on nature-inspired research and applications. The authors present the design and development of future-ready cyber security measures, providing a critical and descriptive examination of all facets of cyber security with a special focus on recent technologies and applications. The book showcases the advanced defensive cyber security mechanism that is a requirement in the industry and highlights measures that provide efficient and fast solutions. The authors explore the potential of AI-based and nature-inspired based computing compatibilities in establishing an adaptive defense mechanism system. The book focuses on current research while highlighting the empirical results along with theoretical concepts to provide a reference for students, researchers, scholars, professionals, and practitioners in the field of cyber security and analytics. This book features contributions from leading scholars from all over the world.Table of Contents1) Nature-inspired Cyber Security and Resilience: An Overview2) Detection of Reconnaissance Attacks on IoT Devices Using Deep Neural Networks3) Particle Swarm Optimization driven DSE based Low Cost Hardware Security for Securing DSP IP Cores4) Malicious Activity Detection in IoT Networks: A Nature-Inspired Approach5) Nature-inspired malware & anomaly detection in android-based systems6) A Review of Artificial Intelligence and Machine Learning Methods for Cybersecurity Applications7) A Nature Inspired DNA Encoding Technique for Quantum Session Key Exchange Protocol8) Novel Hybridized Crow Optimization for Secure Data Transmission in Cyber Networks9) Malware attacks: Dimensions, Impact, and Defenses

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Book SynopsisThis book contains the papers presented at the XXX International Congress INGEGRAF, “Digital Engineering, its application in Research, Development and Innovation”, held on 24–25 June 2021 in Valencia, Spain.The book reports on cutting-edge topics in product design and manufacturing, such as industrial methods for integrated product and process design; innovative design; and computer-aided design. Further topics covered include virtual simulation and reverse engineering; additive manufacturing; product manufacturing; engineering methods in medicine and education; representation techniques; and nautical, engineering and construction, aeronautics and aerospace design and modeling. The book has six sections, reflecting the focus and primary themes of the conference. The contributions presented here will not only provide researchers, engineers, and experts in a range of industrial engineering subfields with extensive information to support their daily work; but also they are intended to stimulate new research directions, advanced applications of the methods discussed, and future interdisciplinary collaborations.Table of ContentsPrefaceOrganization Committee, Scientific Committee Part 1 - Engineering and Construction - New Methodologies BIM Part 2 - Teaching - Learning in Graphic Engineering Part 3 - Product Design & Development Part 4 - Manufacturing and Industrial Process Design Part 5 - Graphical Bioengineering Part 6 - Innovation in Design

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Book SynopsisThe developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.Table of Contents1 Carolyn Woeber, Advances in H-P Mesh Adaptation for Finite Element Methods.- 2 Chiara Nardoni, Remeshing techniques in shape and topology optimization.- 3 Dimitrios Papadimitrakis, Building direction fields on the medial object to generate 3D domain decompositions for hexahedral meshing.- 4 Franck Ledoux, Interecode hexahedral meshing from Eulerian to Lagrangian simulations.- 5 Jean-Francois Remacle, A robust approach for mesh generation of surfaces with irregular/singular parametrizations.6 Jens Lang, Sample Adaptive Multilevel Stochastic Collocation Schemes in Uncertainty Quantification of Gas Transport in Networks.- 7 Jessica Zhang, Hexahedral dominant mesh generation and spline modeling for isogeometric analysis.- 8 Juan José Ródenas, Mesh adaptivity in the framework of the Cartesian grid finite element method, cgFEM.- 9 Mario Ricchiuto, h- and r-adaptation on simplicial meshes: implementation and applications.- 10 Onkar Sahni, Geometry and Adaptive Mesh Update Procedures for Ballistics Simulations.- 11 Per-Olof Persson, HOIST: High-Order Implicit Shock Tracking using an optimization-based discontinuous Galerkin method.- 12 Rainald Lohner, Breakthrough ‘workarounds’ in unstructured mesh generation.- 13 Simone Appella, An adaptive moving mesh method with conservative interpolation based on local projection.- 14 Suzanne Shontz, Global optimization strategies for automated edge grid generation.

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Book SynopsisThis book commemorates Eric Goles’s achievements in science and engineering. Eric Goles is one of the world leaders in the field of automata and complexity. His groundbreaking discoveries are in the theory and analysis of complex systems, particularly in the field of discrete systems dynamics such as neural networks, automata networks, majority networks, bootstrap percolation models, cellular automata, computational complexity theory, discrete mathematics, and theoretical computer science. Topics include cellular automata, complex networks, models of computation, expansive systems, sandpile automata, Penrose tilings, Boolean automata, models of infection, Fibonacci trees, dominos, reversible automata, and fungal automata. The chapters are authored by world leaders in computer science, physics, mathematics, and engineering. The book will be a pleasure to explore for readers from all walks of life, from undergraduate students to university professors, from mathematicians, computer scientists, and engineers to chemists and biologists.Table of ContentsAbout Eric Goles.- Seven things I know about them.- Distortion in automorphisms of expansive systems.- Periods in the Q2R, X2R and Kawasaki-Q2R cellular automata.

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Book SynopsisThis book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.

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Book SynopsisThis book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.

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Book SynopsisThis book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science.“Mathematicians have never been comfortable handling infinities… But an entirely new type of mathematics looks set to by-pass the problem… Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem… ”MIT Technology Review“These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing.“I am sure that the new approach … will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science.“Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing.“The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort.” P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft ComputingTrade Review“This book could have deep impact upon not only local, global, multi-objective optimization and machine learning, but also possibly on applied mathematics more broadly and numerical computation. People interested in new ideas for computer science and its foundations and possibly even the philosophy of mathematics will find this volume interesting, as would those working in theoretical or applied optimization.” (Jonathan Gillard, Optimization Letters, Vol. 17 (2), 2023)Table of ContentsA New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals.- Nonlinear Optimization: A Brief Overview.- The role of grossone in Nonlinear Programming and Exact Penalty Methods.

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Book SynopsisThis open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain.Trade Review“The book represents an excellent introduction and hands-on guide to this important and exciting field, for applied mathematicians and image processing practitioners … . It is, perhaps, most beneficial, to electrical and computer science majors who wish to rapidly immerse themselves in the field, in a manner that is mathematically correct and sound, yet also practical.” (Emil Saucan, zbMATH 1501.92001, 2023)Table of ContentsIntroduction.- Working with magnetic resonance images of the brain.- From T1 images to numerical simulation.- Introducing heterogeneities.- Introducing directionality with diffusion tensors.- Simulating anisotropic diffusion in heterogeneous brain regions.- Concluding remarks and outlook.- References.- Index.

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Book SynopsisThis book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.Trade Review“The book is a very interesting contribution to the recent developments in fractional calculus, which is widely studied due to its numerous applications in many scientific fields.” (Carlo Bardaro, Mathematical Reviews, September, 2023)Table of ContentsBasic abstract fractional monotone approximation.- Abstract bivariate left fractional monotone constrained approximation by pseudo-polynomials.- Conclusion.

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Book SynopsisThis book is based on the best papers accepted for presentation during the International Conference on Mathematics and its Applications in New Computer Systems (MANCS-2021), Russia.The book includes research materials on modern mathematical problems, solutions in the field of cryptography, data analysis and modular computing, as well as scientific computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in mathematical solutions to cryptography issues are devoted to secret sharing schemes, public key systems, private key systems, n-degree comparisons, modular arithmetic of simple, addition of points of an elliptic curve, Hasse theorem, homomorphic encryption and learning with error, and modifications of the RSA system. Furthermore, issues in data analysis and modular computing include contributions in the field of mathematical statistics, machine learning methods, deep learning, and neural networks. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of cryptography, information security, parallel computing, computer technology, and mathematical education.

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Book SynopsisThe textbook covers the most popular transforms used in electrical engineering along with the mathematical foundations of the transforms, uniquely bringing together the two in a single text. Geared towards an upper-undergraduate or graduate-level class, the book covers the most-used transforms including Fourier, Laplace, Discrete Fourier, z-, short-time Fourier, and discrete cosine transforms. The book includes the complex numbers, complex functions, and complex integration that are fundamental to understand the transforms. The author strives to make the study of the subject approachable by appealing to the use of popular software like LabVIEW virtual instruments, Matlab m-files, and C programming resources. Computer projects at the end of chapters further enhance the learning process. The book is based on the author’s years of teachıng Engineering Mathematics and Signal courses and can be used in both electrical engineering and mathematics curriculum. Presents both electrical engineering transforms and their mathematical foundations in an understandable, pedagogical, and applicable approach; Covers the most common transforms for electronics and communications engineers including Laplace transform, the Fourier transform, STFT, the z-transform; Features LabVIEW virtual instrument (vi) files, LTSpice simulation files, MATLAB m files, and computer projects in the chapter problems. Table of ContentsIntroduction.- I BACKGROUND.- Complex Numbers.- Functions of a Complex Variable.- Complex Integration.- II TRANSFORMS.- The Laplace Transform.- The Fourier Series.- The Fourier Transform.- Short-Time-Fourier Transform.- Fast Fourier Transform.- z Transform.- Discrete Cosine Transform.- Conclusion.

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