Design Optimization Under Uncertainty

✍ Scribed by Weifei Hu

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 282
• Category: Library

✦ Synopsis

This book introduces the fundamentals of probability, statistical, and reliability concepts, the classical methods of uncertainty quantification and analytical reliability analysis, and the state-of-the-art approaches of design optimization under uncertainty (e.g., reliability-based design optimization and robust design optimization). The topics include basic concepts of probability and distributions, uncertainty quantification using probabilistic methods, classical reliability analysis methods, time-variant reliability analysis methods, fundamentals of deterministic design optimization, reliability-based design optimization, robust design optimization, other methods of design optimization under uncertainty, and engineering applications of design optimization under uncertainty.

✦ Table of Contents

Preface
Contents
About the Author
Chapter 1: Basic Concepts of Probability and Reliability
1.1 Probability Theory
1.1.1 Definition of Probability
1.1.2 Basic Probability Theorem
1.1.3 Conditional Probability
1.1.4 Independence
1.2 Random Variable
1.2.1 Discrete Random Variable
1.2.2 Continuous Random Variable
1.2.3 Transformation of Random Variables
1.2.4 Expectation
1.2.5 Variance
1.2.6 Covariance
1.3 Probability Distribution
1.3.1 Typical Distributions of Discrete Random Variables
1.3.2 Typical Distributions of Continuous Random Variables
1.4 Reliability
1.4.1 Basic Concepts of Reliability
1.4.2 Importance of Reliability Assessment
References
Chapter 2: Uncertainty Modeling
2.1 Introduction
2.2 Uncertainty Quantification
2.2.1 Probabilistic Methods
2.2.1.1 Maximum Entropy Distribution
2.2.1.2 Method of Moments
2.2.1.3 Maximum Likelihood Estimation
2.2.2 Non-probabilistic Methods
2.2.2.1 Probability Box
2.2.2.2 Interval Analysis
2.3 Uncertainty Propagation
2.3.1 Distribution Function Transformation Method
2.3.2 Monte Carlo Simulation Method
2.3.3 Evidence Theory
References
Chapter 3: Surrogate Modeling
3.1 Introduction
3.2 Surrogate Modeling Methods
3.2.1 Response Surface Method
3.2.2 Radial Basis Function
3.2.3 Support Vector Regression
3.2.4 Kriging
3.2.5 Performance Evaluation of Surrogate Models
3.3 Adaptive Sampling Methods
3.3.1 Steps of Adaptive Sampling Methods
3.3.2 General Features of Adaptive Sampling Schemes
3.3.3 Techniques for Exploitation and Exploration
3.4 An Effective Strategy for Adaptive Sampling
3.4.1 Voronoi Tessellation
3.4.2 Metrics for Evaluating the Existing Samples
3.4.3 Identification of Sensitive Voronoi Cell
3.4.4 Determination of the Location of New Sample Point
References
Chapter 4: Model Verification & Validation
4.1 Introduction
4.2 Model Verification
4.2.1 Code Verification
4.2.2 Calculation Verification
4.3 Model Validation
4.3.1 Area Metric
4.3.2 Evaluating at Multiple Validation Sites
4.3.3 Validating with Multiple Correlated Outputs
4.3.4 Interval Metric
4.3.5 Model Validation with Limited Data
References
Chapter 5: Time-Independent Reliability Analysis
5.1 Basic Concept of Reliability
5.1.1 Introduction
5.1.2 Concept of Reliability
5.2 MPP-Based Methods for Reliability Analysis
5.2.1 First-Order Reliability Method
5.2.2 Second-Order Reliability Method
5.3 Sampling Methods for Reliability Analysis
5.3.1 Monte Carlo Simulation
5.3.2 Importance Sampling
5.3.3 Other Methods
References
Chapter 6: Time-Dependent Reliability Analysis
6.1 Basic Concept of Time-Dependent Reliability Analysis
6.1.1 Introduction
6.1.2 Mathematical Expression of Time-Dependent Reliability Analysis Problem
6.2 Expansion of the Stochastic Process
6.3 Outcrossing Rate Methods
6.4 Extreme Value Methods
6.4.1 Nested Extreme Response Surface Approach
6.4.2 Other Methods
6.5 Response Surrogate-Based Methods
6.5.1 Confidence-Based Adaptive Extreme Response Surface Method
6.5.2 Equivalent Stochastic Process Transformation Method
6.5.3 Instantaneous Response Surface Method
6.5.4 Real-Time Estimation Error-Guided Active Learning Kriging Method
6.5.5 Surrogate-Based Time-Dependent Reliability Analysis Method
References
Chapter 7: Reliability-Based Design Optimization
7.1 Basic Concept
7.2 Problem Statement and Formulation
7.3 Most Probable Point-Based RBDO
7.3.1 Reliability Index Approach and Performance Measure Approach
7.3.2 Numerical Reliability Analysis Method Based on RIA
7.3.3 Numerical Reliability Analysis Method Based on PMA
7.3.4 Full Loop of MPP-Based RBDO
7.4 Sampling-Based RBDO
7.4.1 Monte Carlo Simulation
7.4.2 Surrogate Model
7.4.3 Stochastic Sensitivity Analysis Based on Surrogate Model
7.5 Double-Loop, Single-Loop, and Decoupled RBDO
7.5.1 Double-Loop RBDO
7.5.2 Single-Loop RBDO
7.5.3 Decoupled RBDO
References
Chapter 8: Robust Design Optimization
8.1 Introduction
8.2 Problem Statement and Formulation
8.3 Main Procedure of RDO
8.4 RDO Methods
8.4.1 Weighted Sum Method
8.4.2 Compromise Programming Method
8.4.3 Physical Programming Method
8.4.4 Normal Boundary Intersection Method
8.4.5 Evolutionary Multi-objective Optimization Method
8.5 Reliability-Based Robust Design Optimization
References
Chapter 9: Physics-Informed Neural Networks for Design Optimization Under Uncertainty
9.1 Introduction
9.2 Basis of Physics-Informed Neural Network
9.2.1 Basic Structure of Multi-layer Perceptron
9.2.2 Loss Construction Based on Priori Knowledge
9.2.3 A Basic Example of PINN
9.3 Reliability Analysis Based on Physics-Informed Neutral Network
9.4 PINN-Based Design Optimization Under Uncertainty
References
Chapter 10: Engineering Applications of Design Optimization Under Uncertainty
10.1 RBDO Engineering Applications
10.1.1 Aeronautical Engineering
10.1.1.1 VS Composites Plate
10.1.1.2 Compressor Disc
10.1.1.3 Aircraft Tail Fuselage
10.1.1.4 Real-World Engineering Application
10.1.2 Ocean Engineering
10.1.2.1 Autonomous Underwater Vehicle´s Head Pressure Shell
10.1.2.2 Wellhead Platform
10.1.2.3 Offshore Wind Turbine Blades
10.1.2.4 Real-World Engineering Application
10.1.3 Bridge Engineering
10.1.3.1 Bridge Corrosion
10.1.3.2 Bridge Traffic Load
10.1.3.3 Bridge Flutter
10.1.3.4 Real-World Engineering Application
10.1.4 Vehicle Engineering
10.1.4.1 Variable Blank Variable Section Shape Front Longitudinal Beam
10.1.4.2 Carbon Fiber Reinforced Polymer Composites
10.1.4.3 Reducer Housing
10.1.4.4 Real-World Engineering Application
10.1.5 Summary
10.2 RDO Engineering Applications
10.2.1 Energy Management
10.2.1.1 Wind Energy
10.2.1.2 Solar Energy
10.2.1.3 Power System
10.2.1.4 Real-World Engineering Application
10.2.2 Logistics Scheduling
10.2.2.1 Home Health Care Routing and Scheduling Problem
10.2.2.2 Emergency Logistics Planning and Scheduling
10.2.2.3 Electric Vehicle Logistics and Distribution Dispatch
10.2.2.4 Real-World Engineering Application
10.2.3 Closed-Loop Supply Chain
10.2.3.1 Closed-Loop Supply Chain Network for Perishable Goods
10.2.3.2 Closed-Loop Supply Chain Network for Disposable Home Appliances
10.2.3.3 A Closed-Loop Supply Chain Network for Durable Goods
10.2.3.4 Real-World Engineering Application
10.2.4 Summary
10.3 Research Outlook of Design Optimal Under Uncertainty
10.3.1 Challenges and Prospects of RBDO
10.3.2 Challenges and Prospects of RDO
References
Index