Bond Graph Modelling for Control, Fault Diagnosis and Failure Prognosis

Preface
Contents
Abbreviations
1 Introduction
	1.1 Motivation
	1.2 Organisation of the Book
	References
2 Structural Properties of Bond Graphs for Model-Based Control
	2.1 Structural Observability and Structural Controllability
		2.1.1 Bond Graph-Based Analysis of Structural State Observability
		2.1.2 Bond Graph-Based Analysis of Structural State Controllability
			Example: Masses-Spring Oscillator
			Check for Structural Controllability on a Bond Graph
			Check for Structural Observability on a Bond Graph
			Example: RC Network
	2.2 Transfer Functions
		Example: LC Network
		2.2.1 Mason's Loop Rule
		2.2.2 Application of Mason's Loop Rule Directly on a Causal Bond Graph
		Example: DC Motor Drive
	2.3 Bond Graphs and Block Diagrams
	2.4 Bicausal Bond Graphs
	2.5 Parameter Estimation Based on Bicausal Bond Graphs
		Example 1: Parameter Estimation Applied to a Two-Tank System
		Controllability and Observability
		Estimating the Resistance of Valve 1
		Example 2: Two-Tank System with Two Pressure Sensors
	2.6 Inverse System Models
	2.7 System Inversion Based on Bicausal Bond Graphs
		Example: Bicausal Bond Graph-Based System Inversion Applied to a RLC Circuit
	2.8 Bond Graph-Based Stability Analysis
		Illustrative Example 1
		Illustrative Example 2
	2.9 Summary
	References
3 Fault Diagnosis
	3.1 Types of Faults
	3.2 Signal Preprocessing
		3.2.1 Savitzky–Golay Filter
		3.2.2 State Variable Filters
	3.3 Data-Driven Methods
	3.4 Filters for Estimating the State of Health of a System
		3.4.1 Discrete-Time Linear Kalman Filter
		3.4.2 Particle Filters
	3.5 Bond Graph Model-Based Fault Detection and Isolation
		3.5.1 Observer-Based Fault Detection
		3.5.2 Fault Detection and Isolation Based on Analytical Redundancy Relations Derived from a Bond Graph
		3.5.3 Avoiding Differentiation of Measurements
		3.5.4 Parametric Fault Isolation and Fault Estimation
	3.6 Robustness with Regard to Parameter Uncertainties
		3.6.1 Uncertain BGs
		3.6.2 BGs in Linear Fractional Transformation Form
		3.6.3 Incremental BGs and Adaptive Fault Thresholds
	3.7 Measurement Uncertainties, Sensor Faults, and Actuator Faults
		3.7.1 Accounting for Measurement Uncertainties and Sensor Faults in a BG
		3.7.2 Representing Actuator Faults in a BG
	3.8 Sensor Placement on Diagnostic Bond Graphs and Fault Isolation
		3.8.1 Graphical Approach to Sensor Placement and Fault Isolation
		3.8.2 Faulty Sensors
		3.8.3 Hybrid Models
	3.9 Summary
	References
4 Failure Prognostic
	4.1 Introduction
	4.2 Data-Driven Failure Prognostic
		4.2.1 Stochastic Data-Driven Methods
			Bayesian Networks
		4.2.2 Statistical Data-Driven Methods
			Linear Regression
			Recursive Least Square Method
			Forgetting Factor Recursive Least Square Method
			Sliding Window Recursive Least Squares ARMA Parameter Estimation
			Combining Identification of a System with Deteriorating Behaviour and Failure Prognostic Based on Kalman Filtering
		4.2.3 Neural Networks
	4.3 Model-Based Failure Prognostic
		Physics-Based Failure Prognostic
		Hybrid Failure Prognostic
	4.4 Determination of a Degradation Model from ARRs
	4.5 A Hybrid Bond Graph Model-Based Data-Driven Approach
		4.5.1 Bicausal Bond Graph-Based Online Estimation of Unknown Degradation Data
			Example: Boost Converter
			Fault Detection and Isolation
			Estimating the Unknown Degradation of the Load Resistance
			Estimating the Unknown Parameter Degradation of a Storage Element
		4.5.2 ARR-Based Estimation of Degradation Dataon Two DBGs
			Example: Boost Converter
			Derivation of ARRs from the First Stage DBG
			Determination of Degradation Functions from ARRs of the Second Stage DBG
		4.5.3 Learning a Mathematical Degradation Model
		4.5.4 Projection and RUL Estimation
			Accuracy of Regression and Prediction
			Failure Prognostic for Hybrid Systems
	4.6 Uncertainties in Hybrid Failure Prognostic
		Modelling Uncertainties
		Measurement Uncertainties
		Statistical and Environment Uncertainties
		Degradation Model Uncertainties
		Prediction Uncertainties
		Prognostic Metrics
		Risk Assessment
		Failure Threshold
		Onset of the Degradation and Start of the Prediction
		Some Advantages of the Presented Hybrid Method
	4.7 Summary
	References
5 Fault Tolerant Control
	5.1 Introduction
		Bond Graph Modelling and FTC
	5.2 Fault Accommodation Using an Inverse Faulty System Model
	5.3 Implicit System Inversion
	5.4 Input Reconstruction from a Bicausal Bond Graph of the Inverse Faulty System
		Example: Input Reconstruction on the Bicausal BG of a DC Motor Drive
	5.5 Passive Fault Tolerant Control by Means of an Overwhelming Controller
	5.6 Summary
	References
6 Software Support
	6.1 Model Development and Simulation of the Dynamic System Behaviour
	6.2 Model-Based Control
		6.2.1 Observability and Controllability
		6.2.2 Design of a Luenberger Observer in Octave
		6.2.3 Parameter Estimation and System Inversion on a Bicausal Bond Graph
	6.3 Fault Diagnosis
		6.3.1 Signal Preprocessing
		6.3.2 State Estimation and Observer-Based Fault Detection
		6.3.3 FDI Based on ARRs Derived from a DBG
		6.3.4 Combined Bond Graph Model-Based Data-Driven Failure Prognosis
			Bond Graph Model-Based Generation of Discrete Degradation Data
	6.4 Summary
	References
7 Applications
	7.1 Introduction
	7.2 Half-Wave Voltage Doubler
		7.2.1 Modelling and Analysis of the Voltage Doubler
			A Switched LTI Model
			Implementation of the LTI System
			Simulation Results
		7.2.2 Fault Diagnosis on the Voltage Doubler
			Fault Scenario 1: Exponential Decline of the Output Capacitance C̃2(t) as of a Time Instant t1
			Fault Scenario 2: Open Circuit of Diode D1
	7.3 Reconstruction of the Capacitance of a Leaking Electrolytic Capacitor
		7.3.1 Estimation of the Decaying Capacitance Based on a Bicausal BG
		7.3.2 ARR-Based Estimation of the Capacitance Degradation Values
		7.3.3 RUL Prediction
	7.4 External Leakage from a Closed Loop Three Tanks System
		7.4.1 Modelling and Analysis of the System
			Open Loop System
			Closed Loop System
			Fault Scenario: Hole of Increasing Size in the Bottom of Tank 3
		7.4.2 RUL Estimation
	7.5 Fault Signature Matrix of a Hydraulic Actuator with Leakage
	7.6 Internal Friction in a Permanent Magnet DC Motor
		7.6.1 Modelling of the DC Motor Drive
		7.6.2 Fault Detection
		7.6.3 Fault Scenario: Friction in the DC Motor Increases Linearly as of a Time Instant
		7.6.4 RUL Estimation
	7.7 Fault Accommodation in an Open Loop DC Motor Drive
		7.7.1 Fault Scenario 1: Increase in the Motor Armature Resistance
			Analytical Determination of Steady State Values
			Simulation of the Recovery from the Fault
		7.7.2 Fault Scenario 2: Leakage in the Buck Converter Capacitor
			Determination of a New System Input
			Analytical Determination of Steady State Values
			Simulation of the Recovery from the Fault
	7.8 Robust Overwhelming Control of a Mechanical Oscillator
		Simulation of the Closed Loop Oscillator
	7.9 Summary
	References
8 Conclusions
	Model-Based Control
	Fault Detection and Isolation
	Failure Prognosis
	Fault Tolerant Control
	Some Subjects of Further Work
	References
A Some Definitions
	A.1 Fault Diagnosis
	A.2 Failure Prognostic
	References
B Short Introduction into Bond Graph Modelling
	B.1 Basic Concepts
		B.1.1 Power Variables and Energy Variables
		B.1.2 Analogies
		B.1.3 Hierarchical Bond Graph Models
	B.2 Bond Graph Elements
		B.2.1 Supply and Absorption of Energy
		B.2.2 Energy Storage
		B.2.3 Irreversible Transformation of Energy into Heat
		B.2.4 Reversible Transformation of Energy
		B.2.5 Power Conservative Distribution of Energy
	B.3 Systematic Construction of Acausal Bond Graphs
		B.3.1 Mechanical Subsystems (Translation and Fixed-Axis Rotation)
		B.3.2 Non-mechanical Subsystems
		B.3.3 Assignment of Power Reference Directions
	B.4 The Concept of Computational Causality at Power Ports
		B.4.1 Rules for Computational Causalities at Power Ports
		B.4.2 Sequential Assignment of Computational Causalities
		Sequential Causality Assignment Procedure (SCAP)
	B.5 Derivation of Equations from Causal Bond Graphs
		B.5.1 Procedure for Manually Deducing Equations from a Causal Bond Graph
		B.5.2 A Circuit with an Operational Amplifier
		B.5.3 A Switched Circuit
	B.6 Characteristic Bond Graph Features in a Nutshell
	B.7 Bond Graphs: A Core Model Representation
	B.8 Summary
	References
C Some Mathematical Background
	C.1 A Lyapunov Function
	C.2 LaSalle's Invariance Principle
	C.3 Implicit Function Theorem
	C.4 Inverse Model of Non-reduced Order
	References
Glossary
	References
Index