CHAPTER 1: Introduction to Prognostics 1.1 What is Prognostics? 1 1.1.1 Objectives for this Chapter 3 1.1.2 Chapter Organization 3 1.2 Foundation of Reliability Theory 4 1.2.

1 Time-to-Failure Distributions 4 1.2.2 Probability and Reliability 7 1.2.3 Probability Density Function 8 1.2.4 Relationships of Distributions 12 1.2.

5 Failure Rate 13 1.2.6 Expected Value and Variance 21 1.3 Failure Distributions under Extreme Stress Levels 23 1.3.1 Basic Models 23 1.3.2 Cumulative Damage Models 26 1.

3.3 General Exponential Models 28 1.4 Uncertainty Measures in Parameter Estimation 30 1.5 Expected Number of Failures 34 1.5.1 Minimal Repair 35 1.5.2 Failure Replacement 37 1.

5.3 Decreased Number of Failures Due to Partial Repairs 39 1.5.4 Decreased Age Due to Partial Repairs 40 1.6 System Reliability & Prognosis and Health Management 41 1.6.1 General Framework for a CBM-based PHM System 42 1.6.

2 Relationship of PHM to System Reliability 44 1.6.3 Degradation Progression Signature (DPS) and Prognostics 45 1.6.4 Ideal Functional Failure Signature (FFS) and Prognostics 48 1.6.5 Non-ideal FFS and Prognostics 51 1.7 Prognostic Information 52 1.

7.1 Non-ideality: Initial-Estimate Error and Remaining Useful Life (RUL) 52 1.7.2 Convergence of RUL Estimates Given an Initial Estimate Error 54 1.7.3 Prognostic Distance (PD) and Convergence 56 1.7.4 Convergence: Figure of Merit (xα) 56 1.

7.5 Other Sources of Non-ideality in FFS Data 57 1.8 Decisions on Cost and Benefits 57 1.8.1 Product Selection 58 1.8.2 Optimal Maintenance Scheduling 61 1.8.

3 Condition-based Maintenance or Replacement 65 1.8.4 Preventive Replacement Scheduling 67 1.8.5 Model Variants and Extensions 70 1.9 Introduction to PHM: Summary 72 CHAPTER 2: APPROACHES FOR PROGNOSIS AND HEALTH MANAGEMENT (PHM) 1 2.1 Approaches for Prognosis and Health Management (PHM) 1 2.1.

1 Model-based Prognostic Approaches 1 2.1.2 Data-driven Prognostic Approaches 2 2.1.3 Hybrid Prognostic Approaches 2 2.1.4 Objectives for this Chapter 3 2.1.

5 Chapter Organization 3 2.2 Model-based Prognostics 2.2.1 Analytical Modeling 5 2.2.2 Distribution Modeling 10 2.2.3 Physics of Failure (PoF) and Reliability Modeling 12 2.

2.4 Acceleration Factor (AF) 14 2.2.5 Complexity Related to Reliability Modeling 16 2.2.6 Failure Distribution 18 2.2.7 Multiple Modes of Failure: Failure Rate and FIT 19 2.

2.8 Advantages and Disadvantages of Model-based Prognostics 19 2.3 Data-driven Prognostics 20 2.3.1 Statistical Methods 20 2.3.2 Machine Learning (ML): Classification and Clustering 26 2.4 Hybrid-driven Prognostics 31 2.

5 An Approach to Condition-based Maintenance (CBM) 33 2.5.1 Modeling of Condition-based Data (CBD) Signatures 33 2.5.2 Comparison of Methodologies: Life Consumption and CBD Signature 34 2.5.3 CBD-signature Modeling: An Illustration . 35 2.

6 Approaches to PHM: Summary 43 CHAPTER 3 FAILURE PROGRESSION SIGNATURES 1 3.1 Introduction to Failure Signatures 1 3.2 Basic Types of Signatures 3 3.2.1 CBD Signature 3 3.2.2 FFP Signature 9 3.2.

3 Transform FFP into FFS 12 3.2.4 Transform FFP into Degradation Progression Signature (DPS) 13 3.2.5 Transform DPS into DPS-based FFS 16 3.3 Model Verification 17 3.3.1 Signature Classification 17 3.

3.2 Verify CBD Modeling 18 3.3.3 Verify FFP Modeling 20 3.3.4 Verify DPS Modeling 20 3.3.5 Verify DPS-based FFS Modeling 21 3.

4 Evaluation of FFS Curves: Nonlinearity 22 3.4.1 Sensing System 22 3.4.2 FFS Nonlinearity 23 3.5 Summary of Data Transforms 25 3.6 Degradation Rate 29 3.6.

1 Constant Degradation Rate: Linear DPS-based FFS 29 3.6.2 Non-linear Degradation Rate 30 3.7 Failure Progression Signatures and System Nodes 32 3.8 Failure Progression Signatures: Summary 33 CHAPTER 4: HEURISTIC-BASED APPROACH TO MODELING CBD SIGNATURES 1 4.1 Introduction to Heuristic-based Approach to Modeling CBD Signatures 1 4.1.1 Review of Chapter 3 3 4.

1.2 Theory: Heuristic Modeling of CBD Signatures 3 4.1.3 Objectives for this Chapter 4 4.1.4 Chapter Organization 5 4.2 General Modeling Considerations: CBD Signatures 4.2.

1 Noise Margin 6 4.2.2 Definition of a Degradation-Signature Model 6 4.2.3 Feature Data: Nominal Value 7 4.2.4 Feature Data, Fault-to-failure Progression Signature, and Degradation-signature Model 7 4.2.

5 Approach to Transforming CBD Signatures into FFS Data 8 4.3 CBD Modeling: Degradation-Signature Models 9 4.3.1 Representative Examples: Degradation-Signature Models 9 4.3.2 Example Plots of Representative FFP Degradation Signatures 13 4.3.3 Convert Decreasing Signatures to Increasing Signatures 17 4.

4 DPS Modeling: FFP to DPS Transform Models 18 4.4.1 Develop Transform Models: FFP to DPS 18 4.4.2 Example Plots of FFP Signatures and DPS Signatures 21 4.5 FFS Modeling: Failure Level and Signature Modeling 24 4.5.1 Develop DPS-based FL Models using FFP Defined Failure Levels 24 4.

5.2 Modeling Results for Failure Levels: FFP-based and DSP-based 27 4.5.3 Transforming DPS Data into FFS Data 31 4.6 Heuristic-based Approach to Modeling of Signatures: Summary 32 CHAPTER 5: NON-IDEAL DATA: EFFECTS AND CONDITIONING 1 5.1 Introduction to Non-ideal Data: Effects and Conditioning 1 5.1.1 Review of Chapter 4 2 5.

1.2 Data Acquisition, Manipulation, and Transforming 3 5.1.3 Objectives for this Chapter 3 5.1.4 Chapter Organization 4 5.2 Heuristic-based Approach Applied to Non-ideal CBD Signatures 6 5.2.

1 Summary of a Heuristic-based Approach Applied to Non-ideal CBD Signatures 6 5.2.2 Example Target for Prognostic Enabling 7 5.2.3 Noise is an Issue in Achieving High Accuracy in Prognostic Information 11 5.3 Errors and Non-ideality in FFS Data 12 5.3.1 Noise Margin and Offset Errors 12 5.

3.2 Measurement Error, Uncertainty, and Sampling 14 5.3.3 Other Sources of Noise 22 5.3.4 Data Smoothing and Non-Ideality in FFS Data 26 5.4 Heuristic Method for Adjusting FFS Data 30 5.4.

1 Description of a Method for Adjusting FFS Data 31 5.4.2 Adjusted FFS Data 31 5.4.3 Data Conditioning: Another Example Data Set 32 5.5 Summary: Non-ideal Data, Effects and Conditioning 34 CHAPTER 6: DESIGN: ROBUST PROTOTYPE OF AN EXEMPLARY PHM SYSTEM 1 6.1 PHM System: Review 1 6.1.

1 Chapter 1: Introduction to Prognostics 1 6.1.2 Chapter 2: Prognostic Approaches for Prognosis and Health Management 4 6.1.3 Chapter 3: Failure Progression Signatures 7 6.1.4 Chapter 4: Heuristic-based Approach to Modeling CBD Signatures 10 6.1.

5 Chapter 5: Non-ideal Data: Effects and Conditioning 10 6.1.6 Objectives for this Chapter 12 6.1.7 Chapter Organization 13 6.2 Design Approaches for a PHM System 15 6.2.1 Select and Evaluate Targets and Their Failure Modes 15 6.

2.2 Offline Prognostic Approaches: Selection of Results 16 6.2.3 Select a Base Architecture for the Online Phase 17 6.3 Sampling and Polling 17 6.3.1 Continual - Periodic Sampling 18 6.3.

2 Periodic-burst Sampling 18 6.3.3 Polling 21 6.4 Initial Design Specifications 21 6.4.1 Operation: Test/Demonstration versus Real 22 6.4.2 Test Bed 24 6.

4.3 Test Bed: Results 27 6.5 Special RMS Method for AC Phase Currents 29 6.5.1 Peak-RMS Method 29 6.5.2 Special Peak RMS: Base Computational Routine 30 6.5.

3 Special Peak RMS: FFP Computational Routine 31 6.5.4 Peak RMS: EMA 31 6.6 Diagnostic and Prognostic Procedure 38 6.6.1 SMPS Power Supply 38 6.6.2 EMA 39 6.

7 Specifications: Robustness and Capability 39 6.7.1 Node-based Architecture 39 6.7.2 Example Design 41 6.8 Node Specifications 42 6.8.1 System Node Definition 42 6.

8.2 Node Definition 44 6.8.3 Other Node Definitions for the Prototype PHM System 50 6.9 System Verification and Performance Metrics 51 6.9.1 Offset Types of Errors 53 6.9.

2 Uncertainty in Determining Prognostic Distance 55 6.9.3 Estimating Convergence to Within P 6.9.4 Performance Metrics 59 6.9.5 Prognostic Information: RUL, SoH, PH, and Degradation 61 6.10 System Verification: Advanced Prognostics 61 6.

10.1 SMPS: FFP Signature Directly to FFS 62 6.10.2 SMPS: FFP Signature to DPS to FFS 62 6.11 PHM System Verification: EMA Faults 65 6.11.1 EMA: Load (Friction) Type of Fault 65 Chapter 7 PROGNOSTIC ENABLING: SELECTION, EVALUATION, AND OTHER CONSIDERATIONS 1 7.1 Introduction to Prognostic Enabling 1 7.

1.1 Review of Chapter 61 7.1.2 Electronic Health Solutions 2 7.1.3 Critical Systems and Advance Warning 4 7.1.4 Reduction in Maintenance 4 7.

1.5 Health Management, Maintenance, and Logistics 5 7.1.6 Objectives for this Chapter 7 7.1.7 Chapter Organization 7 7.2 Prognostic Targets: Evaluation, Selection, and Specifications 8 7.2.

1 Criteria for Evaluation, Selection, and Winnowing 8 7.2.2 Meaning of MTBF and MTTF 8 7.2.3 MTTF and MTBF Uncertainty 1.