Uncertainty in Engineering: Introduction to Methods and Applications (SpringerBriefs in Statistics)

✍ Scribed by Louis J. M. Aslett (editor), Frank P. A. Coolen (editor), Jasper De Bock (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 148
• Category: Library

✦ Synopsis

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling.

Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.

✦ Table of Contents

Preface
Contents
1 Introduction to Bayesian Statistical Inference
1.1 Introduction
1.2 Specification of the Prior
1.2.1 Conjugate Priors
1.3 Point Estimation
1.4 Credible Sets
1.5 Hypothesis Test
1.5.1 Model Selection
References
2 Sampling from Complex Probability Distributions: A Monte Carlo Primer for Engineers
2.1 Motivation
2.1.1 Generality of Expectations
2.1.2 Why Consider Monte Carlo?
2.2 Monte Carlo Estimators
2.3 Simple Monte Carlo Sampling Methods
2.3.1 Inverse Sampling
2.3.2 Rejection Sampling
2.3.3 Importance Sampling
2.4 Further Reading
References
3 Introduction to the Theory of Imprecise Probability
3.1 Introduction
3.2 Fundamental Concepts
3.2.1 Basic Concepts
3.2.2 Coherence
3.3 Previsions and Probabilities
3.3.1 Previsions as Prices for Gambles
3.3.2 Probabilities as Previsions of Indicator Gambles
3.3.3 Assessments of Lower Previsions
3.3.4 Working on Linear Spaces of Gambles
3.4 Sets of Probabilities
3.4.1 From Lower Previsions to Credal Sets
3.4.2 From Credal Sets to Lower Previsions
3.5 Basics of Conditioning
3.6 Remarks About Infinite Possibility Spaces
3.7 Conclusion
References
4 Imprecise Discrete-Time Markov Chains
4.1 Introduction
4.2 Precise Probability Models
4.3 Imprecise Probability Models
4.4 Discrete-Time Uncertain Processes
4.5 Imprecise Probability Trees
4.6 Imprecise Markov Chains
4.7 Examples
4.8 A Non-linear Perron–Frobenius Theorem, and Ergodicity
4.9 Conclusion
References
5 Statistics with Imprecise Probabilities—A Short Survey
5.1 Introduction
5.2 Some Elementary Background on Imprecise Probabilities
5.3 Types of Imprecision in Statistical Modelling
5.4 Statistical Modelling Under Model Imprecision
5.4.1 Probabilistic Assumptions on the Sampling Model Matter: Frequentist Statistics and Imprecise Probabilities
5.4.2 Model Imprecision and Generalized Bayesian Inference
5.4.3 Some Other Approaches
5.5 Statistical Modelling Under Data Imprecision
5.6 Concluding Remarks
References
6 Reliability
6.1 Introduction
6.2 System Reliability Methods
6.2.1 Fault Tree Analysis
6.2.2 Fault Tree Extensions: Common Cause Failures
6.2.3 Phased Mission Analysis
6.3 Basic Statistical Concepts and Methods for Reliability Data
6.4 Statistical Models for Reliability Data
6.5 Stochastic Processes in Reliability—Models and Inference
7 Simulation Methods for the Analysis of Complex Systems
7.1 Introduction
7.2 Reliability Modelling of Systems and Networks
7.2.1 Traditional Approaches
7.2.2 Interdependencies in Complex Systems
7.3 Load Flow Simulation
7.3.1 Simulation of Interdependent and Reconfigurable Systems
7.3.2 Maintenance Strategy Optimization
7.3.3 Case Study: Station Blackout Risk Assessment
7.4 Survival Signature Simulation
7.4.1 Systems with Imprecision
7.4.2 Case Study: Industrial Water Supply System
7.5 Final Remarks
References
8 Overview of Stochastic Model Updating in Aerospace Application Under Uncertainty Treatment
8.1 Introduction
8.2 Overview of the State of the Art: Deterministic or Stochastic?
8.3 Overall Technique Route of Stochastic Model Updating
8.3.1 Feature Extraction
8.3.2 Parameter Selection
8.3.3 Surrogate Modelling
8.3.4 Test Analysis Correlation: Uncertainty Quantification Metrics
8.3.5 Model Adjustment and Validation
8.4 Uncertainty Treatment in Parameter Calibration
8.4.1 The Bayesian Updating Framework
8.4.2 A Novel Uncertainty Quantification Metric
8.5 Example: The NASA UQ Challenge
8.6 Conclusions and Prospects
References
9 Aerospace Flight Modeling and Experimental Testing
9.1 Introduction
9.2 Aerospace Flights and Planetary Re-entry
9.3 Similitude Approach for Hypersonic Flows
9.3.1 Inviscid Hypersonics
9.3.2 Viscous Hypersonics
9.3.3 High-Temperature Hypersonics
9.4 Duplication of Dissociated Boundary Layer with Surface Reaction
9.5 Considering Flow Radiation
9.6 Ground Testing Strategy for High-Speed Re-entry
9.7 Conclusion
References