Stochastic Structural Optimization presents a comprehensive picture of robust design optimization of structures, focused on nonparametric stochastic-based methodologies. Good practical structural design accounts for uncertainty, for which reliability-based design offers a standard approach, usually incorporating assumptions on probability functions which are often unknown. By comparison, a worst-case approach with bounded support used as a robust design offers simplicity and a lower level of sensitivity. Linking structural optimization with these two approaches by a unified framework of non-parametric stochastic methodologies provides a rigorous theoretical background and high level of practicality. This text shows how to use this theoretical framework in civil and mechanical engineering practice to design a safe structure which accounts for uncertainty.
Connects theory with practice in the robust design optimization of structures
Advanced enough to support sound practical designs
This book provides comprehensive coverage for engineers and graduate students in civil and mechanical engineering.
Makoto Yamakawa is a Professor at Tokyo University of Science, and a member of the Advisory Board of the 2020 Asian Congress of Structural and Multidisciplinary Optimization.
Makoto Ohsaki is a Professor at Kyoto University, Japan, treasurer of the International Association for Shell & Spatial Structures and former President of the Asian Society for Structural and Multidisciplinary Optimization.
Author(s): Makoto Yamakawa, Makoto Ohsaki
Publisher: CRC Press
Year: 2023
Language: English
Pages: 266
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Chapter 1: Basic Concepts and Examples
1.1. Overview of stochastic structural optimization
1.2. Structural optimization
1.2.1. Basics of Structural Optimization
1.2.2. Structural Compliance Optimization
1.2.3. Illustrative Example: Compliance Minimization of a Two-bar Structure
1.3. Stochasticity and robustness
1.3.1. Categories of Uncertainty
1.3.2. Deterministic Measures: Worst-case Approach
1.3.3. Expectancy Measures
1.3.4. Probabilistic Threshold Measures
1.3.5. Illustrative Example: Worst-case Approach
1.4. Probability-based structural optimization
1.4.1. Central Moments
1.4.2. Order Statistics and Tolerance Intervals
1.4.3. Illustrative Example: Probabilistic Worst-case Approach
1.4.4. L-moments
1.4.5. Maximum Entropy Principle
1.4.6. Illustrative Example: L-moments and Maximum Entropy Method
1.5. Summary
Chapter 2: Stochastic Optimization
2.1. Introduction
2.2. Basic theory of stochasticity and randomness
2.2.1. Concepts of Random Variable
2.2.2. Concepts of Random Process
2.3. Stochastic methods
2.3.1. Random Search Methods
2.3.2. Convergence of PRS
2.3.3. Curse of Dimensionality
2.3.4. Population-based Search Methods
2.4. Stopping rules for stochastic optimization
2.5. Summary
Chapter 3: Random Search-based Optimization
3.1. Introduction
3.2. Random search for worst-case design
3.2.1. Two-level Optimization Problem
3.2.2. Optimization Methods
3.2.3. Mathematical Example
3.2.4. Worst-case Design of Building Frame
3.3. Stopping rule of random multi-start local search
3.3.1. Local Search
3.3.2. Stopping Rule Using Attractors
3.3.3. Numerical Examples
3.4. Summary
Chapter 4: Order Statistics-based Robust Design Optimization
4.1. Introduction
4.2. Order statistics-based robustness evaluation
4.2.1. Two-level Optimization Problem
4.2.2. Random Sampling and Probabilistic Constraints Utilizing Order Statistics
4.2.3. Stopping Rules of Order Statistics-based Random Search
4.2.4. Simple Mathematical Example
4.2.5. Robust Design Optimization of Building Frame
4.3. Order statistics-based robust design optimization
4.3.1. Formulation of a Simplified Problem
4.3.2. Seismic Motion Considering Uncertain Properties of Surface Ground
4.4. Sampling method with linear constraints
4.4.1. Formulation of a Robust Design Problem with Polytope
4.4.2. Barrier Monte Carlo method
4.4.3. Application to Seismic Design Problem
4.5. Summary
Chapter 5: Robust Geometry and Topology Optimization
5.1. Introduction
5.2. Order statistics-based robust topology optimization for plane frames
5.2.1. Robust Geometry and Topology Optimization Problem
5.2.2. Penalization of Stress and Geometrical Stiffness
5.2.3. Numerical Example
5.3. Quantile-based robust frame topology optimization
5.3.1. Quantile-based SORA and Estimation of Quantile
5.3.2. Shape and Topology Optimization of Plane Frames Under Uncertainty
5.4. Stochastic fail-safe topology optimization
5.4.1. Fail-safe Topology Optimization
5.4.2. Stochastic Gradient Descent
5.4.3. Numerical Example
5.5. Summary
Chapter 6: Multi-objective Robust Optimization Approach
6.1. Introduction
6.2. Robustness level using order statistics
6.3. Formulation of multi-objective optimization problem
6.4. Application to engineering problems
6.4.1. Plane Truss Subjected to Static Load
6.4.2. Shear Frame Subjected to Seismic Excitation
6.5. Shape and topology optimization of plane frame
6.5.1. Multi-objective Optimization Problem
6.5.2. Robust Shape and Topology Optimization of Plane Frame
6.5.3. Numerical Example
6.6. Summary
Chapter 7: Surrogate-assisted and Reliability-based Optimization
7.1. Introduction
7.2. Gaussian process model and expected improvement
7.2.1. Gaussian Process Model
7.2.2. Expected Improvement for the Worst Response Function
7.2.3. Direct Search Method Enhanced by EGO
7.2.4. Numerical Example
7.3. Sequential mixture of Gaussian process models
7.3.1. Formulation of Design Problems
7.3.2. Mixture of Gaussian Processes
7.3.3. A Sequential Deterministic Optimization for RBDO
7.3.4. Example: Ten-bar Truss
7.4. Reliability-based multi-objective Bayesian optimization
7.4.1. Formulation of Design Problems
7.4.2. Bayesian Optimization
7.4.3. Solution Procedure Using Bayesian Optimization
7.4.4. Example: Two-bar Truss
7.5. Summary
Appendix
A.1. Test functions
A.2. Distribution of content ratio
A.3. Tabu search
A.4. Force density method
A.5. Clustering dataset using Gaussian mixture model
A.6. Saddlepoint approximation
A.7. Multi-objective optimization problem
Bibliography
Index
