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Uncertainty Quantification and Stochastic Modeling with Matlab.
Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London : Kidlington, Oxford :
ISTE Press Ltd ; Elsevier Ltd.,
2015.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover ; Uncertainty Quantification and Stochastic Modeling with Matlab� ; Copyright ; Contents ; Introduction ; Chapter 1: Elements of Probability Theory and Stochastic Processes ; 1.1. Notation ; 1.2. Numerical Characteristics of Finite Populations ; 1.3. Matlab Implementation; 1.4. Couples of Numerical Characteristics ; 1.5. Matlab Implementation ; 1.6. Hilbertian Properties of the Numerical Characteristics ; 1.7. Measure and Probability ; 1.8. Construction of Measures ; 1.9. Measures, Probability and Integrals in Infinite Dimensional Spaces ; 1.10. Random Variables.
- 1.11. Hilbertian Properties of Random Variables 1.12. Sequences of Random Variables ; 1.13. Some Usual Distributions ; 1.14. Samples of Random Variables ; 1.15. Gaussian Samples ; 1.16. Stochastic Processes ; 1.17. Hilbertian Structure ; 1.18. Wiener Process ; 1.19. Ito Integrals ; 1.20. Ito Calculus ; Chapter 2: Maximum Entropy and Information ; 2.1. Construction of a Stochastic Model ; 2.2. The Principle of Maximum Entropy ; 2.3. Generating Samples of Random Variables, Random Vectors and Stochastic Processes.
- 2.4. Karhunen-Lo�eve Expansions and Numerical Generation of Variates from Stochastic Processes Chapter 3: Representation of Random Variables ; 3.1. Approximations Based on Hilbertian Properties ; 3.2. Approximations Based on Statistical Properties (Moment Matching Method); 3.3. Interpolation-Based Approximations (Collocation); Chapter 4: Linear Algebraic Equations Under Uncertainty ; 4.1. Representation of the Solution of Uncertain Linear Systems ; 4.2. Representation of Eigenvalues and Eigenvectors of Uncertain Matrices ; 4.3. Stochastic Methods for Deterministic Linear Systems.
- Chapter 5: Nonlinear Algebraic Equations Involving Random Parameters 5.1. Nonlinear Systems of Algebraic Equations ; 5.2. Numerical Solution of Noisy Deterministic Systems of Nonlinear Equations ; Chapter 6: Differential Equations Under Uncertainty ; 6.1. The Case of Linear Differential Equations ; 6.2. The Case of Nonlinear Differential Equations ; 6.3. The Case of Partial Differential Equations ; 6.4. Reduction of Hamiltonian Systems ; 6.5. Local Solution of Deterministic Differential Equations by Stochastic Simulation ; 6.6. Statistics of Dynamical Systems.
- Chapter 7: Optimization Under Uncertainty 7.1. Representation of the Solutions in Unconstrained Optimization ; 7.2. Stochastic Methods in Deterministic Continuous Optimization ; 7.3. Population-Based Methods; 7.4. Determination of Starting Points ; Chapter 8: Reliability-Based Optimization ; 8.1. The Model Situation ; 8.2. Reliability Index ; 8.3. FORM; 8.4. The Bi-Level or Double-Loop Method; 8.5. One-Level or Single-Loop Approach ; 8.6. Safety Factors ; Bibliography ; Index.