Aslett L.J.M., Coolen F.P.A., De Bock J. (eds.) Uncertainty in Engineering: Introduction to Methods and Applications

Springer, 2021. —148 p.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.Preface
Introduction to Bayesian Statistical Inference
Introduction
Specification of the Prior
Conjugate Priors
Point Estimation
Credible Sets
Hypothesis Test
Model Selection
References
Sampling from Complex Probability Distributions: A Monte Carlo Primer for Engineers
Motivation
Generality of Expectations
Why Consider Monte Carlo?
Monte Carlo Estimators
Simple Monte Carlo Sampling Methods
Inverse Sampling
Rejection Sampling
Importance Sampling
Further Reading
References
Introduction to the Theory of Imprecise Probability
Introduction
Fundamental Concepts
Basic Concepts
Coherence
Previsions and Probabilities
Previsions as Prices for Gambles
Probabilities as Previsions of Indicator Gambles
Assessments of Lower Previsions
Working on Linear Spaces of Gambles
Sets of Probabilities
From Lower Previsions to Credal Sets
From Credal Sets to Lower Previsions
Basics of Conditioning
Remarks About Infinite Possibility Spaces
Conclusion
References
Imprecise Discrete-Time Markov Chains
Introduction
Precise Probability Models
Imprecise Probability Models
Discrete-Time Uncertain Processes
Imprecise Probability Trees
Imprecise Markov Chains
Examples
A Non-linear Perron–Frobenius Theorem, and Ergodicity
Conclusion
References
Statistics with Imprecise Probabilities—A Short Survey
Introduction
Some Elementary Background on Imprecise Probabilities
Types of Imprecision in Statistical Modelling
Statistical Modelling Under Model Imprecision
Probabilistic Assumptions on the Sampling Model Matter: Frequentist Statistics and Imprecise Probabilities
Model Imprecision and Generalized Bayesian Inference
Some Other Approaches
Statistical Modelling Under Data Imprecision
Concluding Remarks
References
Reliability
Introduction
System Reliability Methods
Fault Tree Analysis
Fault Tree Extensions: Common Cause Failures
Phased Mission Analysis
Basic Statistical Concepts and Methods for Reliability Data
Statistical Models for Reliability Data
Stochastic Processes in Reliability—Models and Inference
Simulation Methods for the Analysis of Complex Systems
Introduction
Reliability Modelling of Systems and Networks
Traditional Approaches
Interdependencies in Complex Systems
Load Flow Simulation
Simulation of Interdependent and Reconfigurable Systems
Maintenance Strategy Optimization
Case Study: Station Blackout Risk Assessment
Survival Signature Simulation
Systems with Imprecision
Case Study: Industrial Water Supply System
Final Remarks
References
Overview of Stochastic Model Updating in Aerospace Application Under Uncertainty Treatment
Introduction
Overview of the State of the Art: Deterministic or Stochastic?
Overall Technique Route of Stochastic Model Updating
Feature Extraction
Parameter Selection
Surrogate Modelling
Test Analysis Correlation: Uncertainty Quantification Metrics
Model Adjustment and Validation
Uncertainty Treatment in Parameter Calibration
The Bayesian Updating Framework
A Novel Uncertainty Quantification Metric
Example: The NASA UQ Challenge
Conclusions and Prospects
References
Aerospace Flight Modeling and Experimental Testing
Introduction
Aerospace Flights and Planetary Re-entry
Similitude Approach for Hypersonic Flows
Inviscid Hypersonics
Viscous Hypersonics
High-Temperature Hypersonics
Duplication of Dissociated Boundary Layer with Surface Reaction
Considering Flow Radiation
Ground Testing Strategy for High-Speed Re-entry
Conclusion
References