This book shows in a comprehensive presentation how Bond Graph methodology can support model-based control, model-based fault diagnosis, fault accommodation, and failure prognosis by reviewing the state-of-the-art, presenting a hybrid integrated approach to Bond Graph model-based fault diagnosis and failure prognosis, and by providing a review of software that can be used for these tasks.
The structured text illustrates on numerous small examples how the computational structure superimposed on an acausal bond graph can be exploited to check for control properties such as structural observability and control lability, perform parameter estimation and fault detection and isolation, provide discrete values of an unknown degradation trend at sample points, and develop an inverse model for fault accommodation. The comprehensive presentation also covers failure prognosis based on continuous state estimation by means of filters or time series forecasting.
This book has been written for students specializing in the overlap of engineering and computer science as well as for researchers, and for engineers in industry working with modelling, simulation, control, fault diagnosis, and failure prognosis in various application fields and who might be interested to see how bond graph modelling can support their work.
- Presents a hybrid model-based, data-driven approach to failure prognosis
- Highlights synergies and relations between fault diagnosis and failure prognostic
- Discusses the importance of fault diagnosis and failure prognostic in various fields
Author(s): Wolfgang Borutzky
Publisher: Springer
Year: 2021
Language: English
Pages: 317
City: Cham
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
