Digital Twin: A Dynamic System and Computing Perspective

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Authors' Biographies
Chapter 1: Introduction and Background
	1.1. Introduction
	1.2. Modeling and Simulation
	1.3. Sensors and Actuators
	1.4. Signal Processing
	1.5. Estimation Algorithms
	1.6. Industry 4.0
	1.7. Applications
		1.7.1. Maintenance
		1.7.2. Manufacturing
		1.7.3. Smart Cities
Chapter 2: Computing and Digital Twin
	2.1. Digital Twin Use Cases and the Internet of Things (IoT)
	2.2. Edge Computing
	2.3. Telecom and 5G
	2.4. Cloud
		2.4.1. Microsoft Azure
		2.4.2. Amazon AWS
	2.5. Big Data
		2.5.1. Analytics with Big Data
	2.6. Google Tensorflow
	2.7. Blockchain and Digital Twin
Chapter 3: Dynamic Systems
	3.1. Single-Degree-of-Freedom Undamped Systems
		3.1.1. Natural Frequency
		3.1.2. Dynamic Response
			3.1.2.1. Impulse Response Function
	3.2. Single-Degree-of-Freedom Viscously Damped Systems
		3.2.1. Natural Frequency
		3.2.2. Dynamic Response
			3.2.2.1. Impulse Response and Frequency Response Function
	3.3. Multiple-Degree-of-Freedom Undamped Systems
		3.3.1. Modal Analysis
		3.3.2. Dynamic Response
			3.3.2.1. Frequency-Domain Analysis
			3.3.2.2. Time-Domain Analysis
	3.4. Proportionally Damped Systems
		3.4.1. Condition for Proportional Damping
		3.4.2. Generalized Proportional Damping
		3.4.3. Dynamic Response
			3.4.3.1. Frequency-Domain Analysis
			3.4.3.2. Time-Domain Analysis
	3.5. Nonproportionally Damped Systems
		3.5.1. Free Vibration and Complex Modes
			3.5.1.1. The State-Space Method
			3.5.1.2. Approximate Methods in the Configuration Space
		3.5.2. Dynamic Response
			3.5.2.1. Frequency-Domain Analysis
			3.5.2.2. Time-Domain Analysis
	3.6. Summary
Chapter 4: Stochastic Analysis
	4.1. Probability Theory
		4.1.1. Probability Space
		4.1.2. Random Variable
		4.1.3. Hilbert Space
	4.2. Reliability
		4.2.1. Sources of Uncertainties
		4.2.2. Random Variables and Limit State Function
		4.2.3. Earlier Methods
	4.3. Simulation Methods in UQ and Reliability
		4.3.1. Direct Monte Carlo Simulation
		4.3.2. Importance Sampling
		4.3.3. Stratified Sampling
		4.3.4. Directional Sampling
		4.3.5. Subset Simulation
	4.4. Robustness
Chapter 5: Digital Twin of Dynamic Systems
	5.1. Dynamic Model of the Digital Twin
		5.1.1. Single-Degree-of-Freedom System: The Nominal Model
		5.1.2. The Digital Twin Model
	5.2. Digital Twin via Stiffness Evolution
		5.2.1. Exact Natural Frequency Data Is Available
		5.2.2. Natural Frequency Data Is Available with Errors
		5.2.3. Natural Frequency Data Is Available with Error Estimates
		5.2.4. Numerical Illustrations
	5.3. Digital Twin via Mass Evolution
		5.3.1. Exact Natural Frequency Data Is Available
		5.3.2. Natural Frequency Data Is Available with Errors
		5.3.3. Natural Frequency Data Is Available with Error Estimates
		5.3.4. Numerical Illustrations
	5.4. Digital Twin via Mass and Stiffness Evolution
		5.4.1. Exact Natural Frequency Data Is Available
		5.4.2. Exact Natural Frequency Data Is Available with Errors
		5.4.3. Exact Natural Frequency Data Is Available with Error Estimates
		5.4.4. Numerical Illustrations
	5.5. Discussions
	5.6. Summary
Chapter 6: Machine Learning and Surrogate Models
	6.1. Analysis of Variance Decomposition
		6.1.1. Proposed G-ANOVA
			6.1.1.1. Statistical Moments
	6.2. Polynomial Chaos Expansion
	6.3. Support Vector Machines
	6.4. Neural Networks
	6.5. Gaussian Process
	6.6. Hybrid Polynomial Correlated Function Expansion
Chapter 7: Surrogate-Based Digital Twin of Dynamic System
	7.1. The Dynamic Model of the Digital Twin
	7.2. Overview of Gaussian Process Emulators
	7.3. Gaussian Process-Based Digital Twin
		7.3.1. Digital Twin via Stiffness Evolution
			7.3.1.1. Formulation
			7.3.1.2. Numerical Illustration
		7.3.2. Digital Twin via Mass Evolution
			7.3.2.1. Formulation
			7.3.2.2. Numerical Illustration
		7.3.3. Digital Twin via Mass and Stiffness Evolution
			7.3.3.1. Formulation
			7.3.3.2. Numerical Illustration
	7.4. Discussion
	7.5. Summary
Chapter 8: Digital Twin at Multiple Time Scales
	8.1. The Problem Statement
	8.2. Digital Twin for Multi-Timescale Dynamical Systems
		8.2.1. Data Collection and Processing
			8.2.1.1. Stiffness Degradation
			8.2.1.2. Mass Evolution
			8.2.1.3. Mass and Stiffness Evolution
		8.2.2. Mixture of Experts with Gaussian Process
		8.2.3. Algorithm
	8.3. Illustration of the Proposed Framework
		8.3.1. Digital Twin via Stiffness Evolution
		8.3.2. Digital Twin via Mass Evolution
		8.3.3. Digital Twin via Mass and Stiffness Evolution
	8.4. Summary
Chapter 9: Digital Twin of Nonlinear MDOF Systems
	9.1. Physics-Based Nominal Model
		9.1.1. Stochastic Nonlinear MDOF System: the Nominal Model
		9.1.2. The Digital Twin
		9.1.3. Problem Statement
	9.2. Bayesian Filtering Algorithm
		9.2.1. Unscented Kalman Filter
			9.2.1.1. Algorithm
	9.3. Supervised Machine Learning Algorithm
	9.4. High Fidelity Predictive Model
	9.5. Examples
		9.5.1. 2-DOF System with Duffing Oscillator
		9.5.2. 7-DOF System with Duffing van der Pol Oscillator
Bibliography
Index