Prognostics and Health Management

List of Figures xi Series Editor's Foreword xxi Preface xxiii Acknowledgments xxvii 1 Introduction to Prognostics 1 1.1 What Is Prognostics? 1 1.1.1 Chapter Objectives 1 1.1.2 Chapter Organization 3 1.2 Foundation of Reliability Theory 3 1.2.1 Time-to-Failure Distributions 4 1.2.2 Probability and Reliability 6 1.2.3 Probability Density Function 7 1.2.4 Relationships of Distributions 10 1.2.5 Failure Rate 10 1.2.6 Expected Value and Variance 16 1.3 Failure Distributions Under Extreme Stress Levels 18 1.3.1 Basic Models 18 1.3.2 Cumulative Damage Models 21 1.3.3 General Exponential Models 21 1.4 Uncertainty Measures in Parameter Estimation 23 1.5 Expected Number of Failures 26 1.5.1 Minimal Repair 26 1.5.2 Failure Replacement 28 1.5.3 Decreased Number of Failures Due to Partial Repairs 30 1.5.4 Decreased Age Due to Partial Repairs 30 1.6 System Reliability and Prognosis and Health Management 31 1.6.1 General Framework for a CBM-Based PHM System 32 1.6.2 Relationship of PHM to System Reliability 34 1.6.3 Degradation Progression Signature (DPS) and Prognostics 35 1.6.4 Ideal Functional Failure Signature (FFS) and Prognostics 37 1.6.5 Non-ideal FFS and Prognostics 41 1.7 Prognostic Information 41 1.7.1 Non-ideality: Initial-Estimate Error and Remaining Useful Life (RUL) 42 1.7.2 Convergence of RUL Estimates Given an Initial Estimate Error 44 1.7.3 Prognostic Distance (PD) and Convergence 45 1.7.4 Convergence: Figure of Merit (Chi alpha) 45 1.7.5 Other Sources of Non-ideality in FFS Data 46 1.8 Decisions on Cost and Benefits 47 1.8.1 Product Selection 47 1.8.2 Optimal Maintenance Scheduling 49 1.8.3 Condition-Based Maintenance or Replacement 54 1.8.4 Preventive Replacement Scheduling 55 1.8.5 Model Variants and Extensions 58 1.9 Introduction to PHM: Summary 60 References 60 Further Reading 62 2 Approaches for Prognosis and Health Management/Monitoring (PHM) 63 2.1 Introduction to Approaches for Prognosis and Health Management/Monitoring (PHM) 63 2.1.1 Model-Based Prognostic Approaches 63 2.1.2 Data-Driven Prognostic Approaches 63 2.1.3 Hybrid Prognostic Approaches 64 2.1.4 Chapter Objectives 64 2.1.5 Chapter Organization 64 2.2 Model-Based Prognostics 65 2.2.1 Analytical Modeling 66 2.2.2 Distribution Modeling 71 2.2.3 Physics of Failure (PoF) and Reliability Modeling 72 2.2.4 Acceleration Factor (AF) 74 2.2.5 Complexity Related to Reliability Modeling 76 2.2.6 Failure Distribution 78 2.2.7 Multiple Modes of Failure: Failure Rate and FIT 79 2.2.8 Advantages and Disadvantages of Model-Based Prognostics 79 2.3 Data-Driven Prognostics 80 2.3.1 Statistical Methods 80 2.3.2 Machine Learning (ML): Classification and Clustering 85 2.4 Hybrid-Driven Prognostics 90 2.5 An Approach to Condition-Based Maintenance (CBM) 92 2.5.1 Modeling of Condition-Based Data (CBD) Signatures 92 2.5.2 Comparison of Methodologies: Life Consumption and CBD Signature 92 2.5.3 CBD-Signature Modeling: An Illustration 93 2.6 Approaches to PHM: Summary 103 References 103 Further Reading 106 3 Failure Progression Signatures 107 3.1 Introduction to Failure Signatures 107 3.1.1 Chapter Objectives 107 3.1.2 Chapter Organization 108 3.2 Basic Types of Signatures 108 3.2.1 CBD Signature 109 3.2.2 FFP Signature 114 3.2.3 Transforming FFP into FFS 118 3.2.4 Transforming FFP into a Degradation Progression Signature (DPS) 120 3.2.5 Transforming DPS into DPS-Based FFS 122 3.3 Model Verification 124 3.3.1 Signature Classification 124 3.3.2 Verifying CBD Modeling 125 3.3.3 Verifying FFP Modeling 127 3.3.4 Verifying DPS Modeling 128 3.3.5 Verifying DPS-Based FFS Modeling 129 3.4 Evaluation of FFS Curves: Nonlinearity 130 3.4.1 Sensing System 132 3.4.2 FFS Nonlinearity 132 3.5 Summary of Data Transforms 134 3.6 Degradation Rate 140 3.6.1 Constant Degradation Rate: Linear DPS-Based FFS 140 3.6.2 Nonlinear Degradation Rate 141 3.7 Failure Progression Signatures and System Nodes 142 3.8 Failure Progression Signatures: Summary 144 References 145 Further Reading 146 4 Heuristic-Based Approach to Modeling CBD Signatures 147 4.1 Introduction to Heuristic-Based Modeling of Signatures 147 4.1.1 Review of Chapter 3 147 4.1.2 Theory: Heuristic Modeling of CBD Signatures 149 4.1.3 Chapter Objectives 150 4.1.4 Chapter Organization 151 4.2 General Modeling Considerations: CBD Signatures 151 4.2.1 Noise Margin 152 4.2.2 Definition of a Degradation-Signature Model 152 4.2.3 Feature Data: Nominal Value 152 4.2.4 Feature Data, Fault-to-Failure Progression Signature, and Degradation-Signature Model 153 4.2.5 Approach to Transforming CBD Signatures into FFS Data 153 4.3 CBD Modeling: Degradation-Signature Models 154 4.3.1 Representative Examples: Degradation-Signature Models 155 4.3.2 Example Plots of Representative FFP Degradation Signatures 167 4.3.3 Converting Decreasing Signatures to Increasing Signatures 167 4.4 DPS Modeling: FFP to DPS Transform Models 168 4.4.1 Developing Transform Models: FFP to DPS 168 4.4.2 Example Plots of FFP Signatures and DPS Signatures 177 4.5 FFS Modeling: Failure Level and Signature Modeling 177 4.5.1 Developing DPS-Based Failure Level (FL) Models Using FFP Defined Failure Levels 177 4.5.2 Modeling Results for Failure Levels: FFP-Based and DPS-Based 182 4.5.3 Transforming DPS Data into FFS Data 183 4.6 Heuristic-Based Approach to Modeling of Signatures: Summary 183 References 186 Further Reading 187 5 Non-Ideal Data: Effects and Conditioning 189 5.1 Introduction to Non-Ideal Data: Effects and Conditioning 189 5.1.1 Review of Chapter 4 189 5.1.2 Data Acquisition, Manipulation, and Transformation 189 5.1.3 Chapter Objectives 191 5.1.4 Chapter Organization 194 5.2 Heuristic-Based Approach Applied to Non-Ideal CBD Signatures 194 5.2.1 Summary of a Heuristic-Based Approach Applied to Non-Ideal CBD Signatures 195 5.2.2 Example Target for Prognostic Enabling 196 5.2.3 Noise is an Issue in Achieving High Accuracy in Prognostic Information 200 5.3 Errors and Non-Ideality in FFS Data 202 5.3.1 Noise Margin and Offset Errors 202 5.3.2 Measurement Error, Uncertainty, and Sampling 203 5.3.3 Other Sources of Noise 214 5.3.4 Data Smoothing and Non-Ideality in FFS Data 218 5.4 Heuristic Method for Adjusting FFS Data 223 5.4.1 Description of a Method for Adjusting FFS Data 223 5.4.2 Adjusted FFS Data 224 5.4.3 Data Conditioning: Another Example Data Set 225 5.5 Summary: Non-Ideal Data, Effects, and Conditioning 227 References 229 Further Reading 230 6 Design: Robust Prototype of an Exemplary PHM System 233 6.1 PHM System: Review 233 6.1.1 Chapter 1: Introduction to Prognostics 233 6.1.2 Chapter 2: Prognostic Approaches for Prognosis and Health Management 234 6.1.3 Chapter 3: Failure Progression Signatures 237 6.1.4 Chapter 4: Heuristic-Based Approach to Modeling CBD Signatures 239 6.1.5 Chapter 5: Non-Ideal Data: Effects and Conditioning 239 6.1.6 Chapter Objectives 243 6.1.7 Chapter Organization 245 6.2 Design Approaches for a PHM System 246 6.2.1 Selecting and Evaluating Targets and Their Failure Modes 247 6.2.2 Offline Prognostic Approaches: Selecting Results 248 6.2.3 Selecting a Base Architecture for the Online Phase 248 6.3 Sampling and Polling 249 6.3.1 Continual - Periodic Sampling 249 6.3.2 Periodic-Burst Sampling 250 6.3.3 Polling 252 6.4 Initial Design Specifications 253 6.4.1 Operation: Test/Demonstration vs. Real 253 6.4.2 Test Bed 255 6.4.3 Test Bed: Results 260 6.5 Special RMS Method for AC Phase Currents 261 6.5.1 Peak-RMS Method 263 6.5.2 Special Peak-RMS Method: Base Computational Routine 263 6.5.3 Special Peak-RMS Method: FFP Computational Routine 264 6.5.4 Peak-RMS Method: EMA 265 6.6 Diagnostic and Prognostic Procedure 274 6.6.1 SMPS Power Supply 274 6.6.2 EMA 275 6.7 Specifications: Robustness and Capability 275 6.7.1 Node-Based Architecture 276 6.7.2 Example Design 277 6.8 Node Specifications 279 6.8.1 System Node Definition 279 6.8.2 Node Definition 279 6.8.3 Other Node Definitions for the Prototype PHM System 287 6.9 System Verification and Performance Metrics 288 6.9.1 Offset Types of Errors 288 6.9.2 Uncertainty in Determining Prognostic Distance 292 6.9.3 Estimating Convergence to Within PHalpha 296 6.9.4 Performance Metrics 297 6.9.5 Prognostic Information: RUL, SoH, PH, and Degradation 299 6.10 System Verification: Advanced Prognostics 300 6.10.1 SMPS: FFP Signature Directly to FFS 300 6.10.2 SMPS: FFP Signature to DPS to FFS 301 6.11 PHM System Verification: EMA Faults 303 6.11.1 EMA: Load (Friction) Type of Fault 304 6.11.2 EMA: Winding Type of Fault 307 6.11.3 EMA: Power-Switching Transistor Type of Fault 307 6.12 PHM System Verification: Functional Integration 307 6.12.1 Functional Integration: Control and Data Flow 307 6.12.2 System Performance Metrics: Summary 309 6.12.3 PHM System: Plans 311 6.13 Summary: A Robust Prototype PHM System 315 References 316 Further Reading 317 7 Prognostic Enabling: Selection, Evaluation, and Other Considerations 319 7.1 Introduction to Prognostic Enabling 319 7.1.1 Review of Chapter 6 319 7.1.2 Electronic Health Solutions 320 7.1.3 Critical Systems and Advance Warning 322 7.1.4 Reduction in Maintenance 322 7.1.5 Health Management, Maintenance, and Logistics 323 7.1.6 Chapter Objectives 325 7.1.7 Chapter Organization 325 7.2 Prognostic Targets: Evaluation, Selection, and Specifications 325 7.2.1 Criteria for Evaluation, Selection, and Winnowing 326 7.2.2 Meaning of MTBF and MTTF 326 7.2.3 MTTF and MTBF Uncertainty 328 7.2.4 TTF and PITTFF 329 7.3 Example: Cost-Benefit of Prognostic Approaches 332 7.3.1 Cost-Benefit Situations 333 7.3.2 Cost Analyses 336 7.4 Reliability: Bathtub Curve 342 7.4.1 Bathtub Curve: MTBF and MTTF 343 7.4.2 Trigger Point and Prognostic Distance 343 7.5 Chapter Summary and Book Conclusion 344 References 345 Further Reading 346 Index 347