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Table of Contents
Intro
Acknowledgements
Author biographies
Melanie Po-Leen Ooi
Arvind Rajan
Ye Chow Kuang
Serge Demidenko
Nomenclature
Outline placeholder
Greek symbols
Other symbols
Acronyms/abbreviations
Chapter 1 Introduction
References
Chapter 2 Uncertainty propagation
2.1 Averaging methods for estimating the measurand in nonlinear models
2.2 First-order linearisation and the normality assumption
2.3 The Monte Carlo method
2.4 The use of a mathematical representation of the probability density function
2.5 Uncertainty evaluation using moments
2.5.1 The normal distribution
2.5.2 The Cornish-Fisher expansion
2.5.3 The extended generalised lambda distribution
2.5.4 Tukey's gh distribution
2.5.5 The Pearson distribution
2.5.6 The Johnson distribution
2.5.7 The maximum entropy method
2.6 Summary
References
Chapter 3 Probabilistic design optimisation
3.1 Robust design optimisation
3.1.1 The univariate dimension reduction method
3.1.2 The performance moment integration method
3.2 Reliability-based design optimisation
3.2.1 Most probable point-based methods
3.2.2 The Monte Carlo method
3.2.3 Metamodels with direct sampling methods
3.2.4 Moment-based methods for RBDO
3.3 Reliability-based robust design optimisation
3.4 Summary
References
Chapter 4 Moment-based standard uncertainty in design optimisation
4.1 The derivation of the analytical moments of multivariate polynomials
4.1.1 The Mellin transform and the product of independent random variables
4.1.2 Applying the Mellin transform to analytical moments of multivariate polynomials
4.1.3 Moment calculation for positive-order variables, m∈Z+
4.1.4 Moment calculation for negative-order variables, m∉Z+
4.1.5 Extension to high-dimensional correlated variables.
4.2 A toolbox for moment-based standard uncertainty evaluation
4.3 Case studies for moment-based analytical standard uncertainty evaluation
4.3.1 Case study 1-monomial: magnetic force microscope
4.3.2 Case study 2-simple polynomial: microwave meter calibration
4.3.3 Case study 3-high-order Taylor series approximation: eddy current measurement
4.4 A general framework for analytical moment-based reliability and robustness analysis
4.5 Summary
References and further reading
Chapter 5 Moment-based expanded uncertainty evaluation in design optimization
5.1 The improved moment-constrained maximum entropy method
5.1.1 Setting the zero mean and unit variance
5.1.2 Finding integral limits
5.1.3 The modified Gram-Schmidt algorithm for polynomial orthogonalisation
5.2 Test distributions for benchmarking and performance analysis
5.2.1 Unimodal distributions
5.2.2 Multimodal distributions
5.2.3 A performance assessment framework that uses the benchmark test distributions
5.3 Reliability analysis of parametric distribution-fitting techniques: from unimodal to multimodal distributions
5.3.1 Unimodal distributions with four moments
5.3.2 Unimodal distributions with more than four moments
5.3.3 Multimodal distributions
5.3.4 Reliable regions for Tukey's gh method and the Cornish-Fisher technique
5.4 A toolbox for the MaxEnt algorithm
5.5 Summary
References
Chapter 6 Real-world design optimisation problems: applications and usefulness
6.1 The framework for probabilistic design optimisation
6.1.1 Local response surface modelling using multivariate polynomials
6.1.2 The selective sampling technique
6.2 Lithium-ion batteries: a reliability-based design optimisation framework
6.2.1 The finite element model of the lithium-ion battery.
6.2.2 Incorporating moment-based uncertainty evaluation
6.2.3 The resultant design
6.3 Vehicle design based on side-impact crashworthiness: the application of a reliability-based robust design optimisation problem
6.3.1 Problem formulation
6.3.2 Resultant design
6.4 Fuel cells: parameter optimisation for reliable and robust operation
6.4.1 Problem formulation
6.4.2 Sensitivity analysis
6.4.3 Determination of the optimal operating conditions for RBDO and RBRDO
6.5 Magnetic sensor module design
6.5.1 Problem formulation
6.5.2 The results of the PolyMoment-based RBDO method
6.6 A multistorey three-dimensional steel structure: reliability analysis and optimisation
6.6.1 Problem formulation
6.6.2 The resultant design and benchmarking
6.7 Summary
References
Chapter
Reference
Chapter
References.
Acknowledgements
Author biographies
Melanie Po-Leen Ooi
Arvind Rajan
Ye Chow Kuang
Serge Demidenko
Nomenclature
Outline placeholder
Greek symbols
Other symbols
Acronyms/abbreviations
Chapter 1 Introduction
References
Chapter 2 Uncertainty propagation
2.1 Averaging methods for estimating the measurand in nonlinear models
2.2 First-order linearisation and the normality assumption
2.3 The Monte Carlo method
2.4 The use of a mathematical representation of the probability density function
2.5 Uncertainty evaluation using moments
2.5.1 The normal distribution
2.5.2 The Cornish-Fisher expansion
2.5.3 The extended generalised lambda distribution
2.5.4 Tukey's gh distribution
2.5.5 The Pearson distribution
2.5.6 The Johnson distribution
2.5.7 The maximum entropy method
2.6 Summary
References
Chapter 3 Probabilistic design optimisation
3.1 Robust design optimisation
3.1.1 The univariate dimension reduction method
3.1.2 The performance moment integration method
3.2 Reliability-based design optimisation
3.2.1 Most probable point-based methods
3.2.2 The Monte Carlo method
3.2.3 Metamodels with direct sampling methods
3.2.4 Moment-based methods for RBDO
3.3 Reliability-based robust design optimisation
3.4 Summary
References
Chapter 4 Moment-based standard uncertainty in design optimisation
4.1 The derivation of the analytical moments of multivariate polynomials
4.1.1 The Mellin transform and the product of independent random variables
4.1.2 Applying the Mellin transform to analytical moments of multivariate polynomials
4.1.3 Moment calculation for positive-order variables, m∈Z+
4.1.4 Moment calculation for negative-order variables, m∉Z+
4.1.5 Extension to high-dimensional correlated variables.
4.2 A toolbox for moment-based standard uncertainty evaluation
4.3 Case studies for moment-based analytical standard uncertainty evaluation
4.3.1 Case study 1-monomial: magnetic force microscope
4.3.2 Case study 2-simple polynomial: microwave meter calibration
4.3.3 Case study 3-high-order Taylor series approximation: eddy current measurement
4.4 A general framework for analytical moment-based reliability and robustness analysis
4.5 Summary
References and further reading
Chapter 5 Moment-based expanded uncertainty evaluation in design optimization
5.1 The improved moment-constrained maximum entropy method
5.1.1 Setting the zero mean and unit variance
5.1.2 Finding integral limits
5.1.3 The modified Gram-Schmidt algorithm for polynomial orthogonalisation
5.2 Test distributions for benchmarking and performance analysis
5.2.1 Unimodal distributions
5.2.2 Multimodal distributions
5.2.3 A performance assessment framework that uses the benchmark test distributions
5.3 Reliability analysis of parametric distribution-fitting techniques: from unimodal to multimodal distributions
5.3.1 Unimodal distributions with four moments
5.3.2 Unimodal distributions with more than four moments
5.3.3 Multimodal distributions
5.3.4 Reliable regions for Tukey's gh method and the Cornish-Fisher technique
5.4 A toolbox for the MaxEnt algorithm
5.5 Summary
References
Chapter 6 Real-world design optimisation problems: applications and usefulness
6.1 The framework for probabilistic design optimisation
6.1.1 Local response surface modelling using multivariate polynomials
6.1.2 The selective sampling technique
6.2 Lithium-ion batteries: a reliability-based design optimisation framework
6.2.1 The finite element model of the lithium-ion battery.
6.2.2 Incorporating moment-based uncertainty evaluation
6.2.3 The resultant design
6.3 Vehicle design based on side-impact crashworthiness: the application of a reliability-based robust design optimisation problem
6.3.1 Problem formulation
6.3.2 Resultant design
6.4 Fuel cells: parameter optimisation for reliable and robust operation
6.4.1 Problem formulation
6.4.2 Sensitivity analysis
6.4.3 Determination of the optimal operating conditions for RBDO and RBRDO
6.5 Magnetic sensor module design
6.5.1 Problem formulation
6.5.2 The results of the PolyMoment-based RBDO method
6.6 A multistorey three-dimensional steel structure: reliability analysis and optimisation
6.6.1 Problem formulation
6.6.2 The resultant design and benchmarking
6.7 Summary
References
Chapter
Reference
Chapter
References.