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I want to thank my partner Brian Gordon and son Floris Swanepoel who walked the journey of a doctoral study with me for a second time. Without your love, support and encouragement it would not have been possible.

I also dedicate this thesis to my beloved Rottweiler, Ethan, who so diligently and many times till very late at night, lay at my feet in my study as I worked on my research. You were the best research assistant anyone could wish for! I just wish you could have finished the 2nd PhD journey with me. I miss you so much, at least Baxi took over the late night shifts from you as first research support assistant – he has not failed you.

I further dedicate the thesis in loving memory to my parents Koos van Straten (1935–2009) and Hannetjie van Straten (1937–2010) who always believed in me and empowered me to be the best person and engineer I can possibly be. They taught me that impossible is not a fact, but merely a dare to achieve excellence, and that we all have the power to positively change the world with our own unique contribution.

This work is for all the condition monitoring specialists with whom I have had the privilege to collaborate in the quest for optimal plant asset monitoring and asset management. Their belief in the power of condition monitoring and pushing of the conventional technology boundaries strengthened my belief that analytics capability will mature to the point where we can truly unleash plant condition monitoring as a next level enabler for improved asset management.

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TABL

ABSTR OPSOM ACKNO Abbrevi Definitio Energy CHAPT 1.1  1.2  1.3  1.3.1  1.3.2  1.3.3  1.3.4  1.4  1.5  1.6  1.7  1.8  1.9  CHAPT 2.1  2.1.1  2.1.2  2.1.3 

Tabl

LE OF CO

RACT ... MMING ... OWLEDGEM ations ... ons ... Terms ... TER 1 – IN Intro Bac Res Ineff Proc Adva Prob Rati Hyp Res Res Exc Kno TER 2 – LI The ISO Relia Adve

le of Co

ONTENTS

... ... MENTS ... ... ... ... NTRODUCT oduction ... ckground ... search Prob ficient Cond cess Plant C anced Anal blem to be r ionale and pothesis/Th search Aim search Sco lusions/De owledge Ga TERATURE Drive for I 55001 and ability Base ent of the S

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... ... ... ... ... ... TION ... ... ... blems to be dition Monito Control and lytics Applic researched Justificati heories ... s and Obje pe ... elimitations ap to be clo E REVIEW mproved A other Asse e Optimisati Smart Utility ... ... ... ... ... ... ... ... ... e investiga oring Progr d Design Ba cation and M ... on ... ... ectives ... ... s ... osed ... ... Asset Mana et Managem on (RBO) In y ... ... ... ... ... ... ... ... ... ... ated ... rams ... ase Complex Maturity in P ... ... ... ... ... ... ... ... agement ... ment Initiativ nitiatives ... ... ... ... ... ... ... ... ... ... ... ... ... xities ... Power Utiliti ... ... ... ... ... ... ... ... ... ves ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ies ... ... ... ... ... ... ... ... ... ... ... ... ... ... XV ... XVI ... XVII ... xviii ... xxii ... xxxv ... 1 ... 1 ... 2 ... 3 ... 3 ... 4 ... 5 ... 6 ... 8 ... 11 ... 12 ... 14 ... 16 ... 17 ... 20 ... 20 ... 20 ... 21 ... 23

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2.2  Condition Monitoring in Industry ... 24 

2.2.1  Condition Monitoring Pervasiveness ... 24 

2.2.2  The Aim of Condition Monitoring ... 26 

2.2.3  The use of Remote Monitoring Diagnostic Centres (RMDC’s) ... 27 

2.3  Condition Monitoring Trends ... 28 

2.3.1  Condition Monitoring Strategic Trends ... 28 

2.3.2  Condition Monitoring Technology Trends ... 29 

2.3.3  Condition Monitoring Focus in the SA Power Utility ... 31 

2.3.4  Challenges with CM ISO Standards ... 33 

2.3.5  Typical Factors impacting CM data analytics ... 34 

2.3.6  Successes of good CM Programs ... 35 

2.3.7  Typical CM Program Challenges ... 37 

2.4  Influence of Design Base on Plant Performance and Health Assessments ... 38 

2.5  Influence of Operating Design Base Management on Performance ... 40 

2.6  Influence of Maintenance Base Management on Plant Performance and Reliability ... 41 

2.7  Advanced Analytics ... 42 

2.7.1  Challenges with Plant Data as building blocks for Plant Asset analytics ... 44 

2.7.2  Dealing with the complexities of “Big Data” ... 47 

2.7.3  The IT–OT Technology challenges ... 49 

2.7.4  Typical Applications for Advanced Analytics and Simulation Capability ... 50 

2.7.5  The Benefits of Simulators and Plant Simulation Technology ... 52 

2.7.6  The Value of 3D Visualisation and improved Information Delivery Strategies .... 52 

2.7.7  Artificial Intelligence as an Advanced Analytics Option ... 53 

2.7.8  Vibration Monitoring Frameworks – New Approaches ... 56 

2.7.9  Current Condition Monitoring Frameworks in the Advanced Analytics Landscape ... 57 

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2.7.11  Asset Management and Manufacturing Frameworks – New Approaches ... 62 

2.8  Conclusion ... 63 

CHAPTER 3 – RESEARCH METHODOLOGY ... 65 

3.1  Research Methods ... 65 

3.1.1  Method to establish the Advanced Analytics Fault Model Framework ... 65 

3.1.2  The CBRS Advanced Analytics Simulator Framework in OSA–EAITM context ... 70 

3.1.3  V&V of the proposed Advanced Analytics Simulator Framework ... 74 

3.1.4  Auto–Regression Moving Average Analytical Method (Advanced CM Analytics) ... 76 

3.1.5  P2P Analytical Methodology as a V&V Method ... 78 

3.2  Research Methodology Justification ... 80 

3.3  Research Population ... 81 

3.4  Research Sampling, Data Collection Techniques & Methods ... 82 

3.4.1  Data Collection and Research Sample Set ... 82 

3.4.2  Data Collection and Conversion Requirements ... 83 

3.4.3  Conventional CM Data Analytics Methods ... 86 

3.4.4  Introducing Advanced Data Analytics Methods ... 89 

3.4.5  Ensemble Learning to enhance CM Data Analytics ... 90 

3.4.6  Data Analytics for Severity Indication – (Amplitude as Severity Indicator) ... 91 

3.4.6.1  Feature Extraction to Identify SFFoI’s ... 91 

3.4.6.2  Fault Threshold Model Concept ... 92 

3.4.6.3  Importance of Correct Failure Thresholds: The Water Ejector Case Study ... 96 

3.4.6.4  Importance of Correct Failure Thresholds: Main Turbine AC Drive Lube Oil Pump ... 101 

3.4.7  Data Analytics Method for Failure Progression (Fault Progression Timeline) ... 104 

3.4.8  Data Analytics Categories Applicable to the Research Study ... 106 

3.4.9  Data Diagnostic methods relevant to the Research Study ... 107 

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3.5.1  Framework Construct Verification and Validation Strategy ... 108 

3.5.2  Analytical Framework Fault Model Internal Validation Strategy ... 109 

3.5.3  Analytical Framework Fault Models External Validation ... 110 

3.5.4  Data Reliability ... 110 

3.5.5  Analytical Framework and Fault Model Reliability ... 112 

3.6  Conclusion ... 113 

CHAPTER 4 – CURRENT CONDITION MONITORING PROGRAM ... 114 

4.1  Introduction ... 114 

4.2  Evaluation of current status ... 114 

4.2.1  Extent of Current Program ... 114 

4.2.2  The RMDC Facility in the Power Utility ... 115 

4.2.3  Successes of current CM Program ... 115 

4.2.4  Challenges with current CM Program ... 116 

4.2.5  Use of Advanced Analytics in current CM Program ... 117 

4.3  Evaluation of problem plant areas ... 118 

4.3.1  Impact of Balance of Plant equipment and systems on Power Utility EAF ... 118 

4.4  Aspects influencing the current CM Program Value Proposition ... 122 

4.4.1  Heuristic Knowledge ... 122 

4.4.2  Fault and Failure Statistics ... 123 

4.4.3  Design Base Information Availability & Change Management ... 123 

4.4.4  Availability of Detailed Plant Process Models ... 124 

4.4.5  Quality of Maintenance and Operating History Data Capturing ... 125 

4.4.6  Quality of Condition Monitoring data ... 125 

4.4.7  Interpretation of Condition Monitoring data ... 127 

4.5  Recommendations and Remedial Actions ... 134 

4.5.1  Heuristic Knowledge ... 134 

4.5.2  Fault and Failure Statistics ... 134 

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4.5.5  Quality of Maintenance and Operating History Data Capturing ... 138 

4.5.6  Quality of Condition Monitoring data ... 138 

4.5.6.1  Data Capturing ... 138 

4.5.6.2  Analytics Software Configuration ... 140 

4.5.6.3  Analytical Rule Set Application ... 140 

4.5.6.4  Analytical Capabilities & Consistency in Evaluation ... 141 

4.6  Conclusion ... 141 

CHAPTER 5 – THE CBRS FRAMEWORK ELEMENTS AND V&V APPROACH ... 141 

5.1  Introduction ... 141 

5.2  The Research Advanced Analytics Framework ... 141 

5.3  Heuristic Model Knowledge Base ... 142 

5.3.1  Analytical Knowledge ... 142 

5.3.2  Heuristic Knowledge ... 142 

5.4  Inference Analytical Engine ... 143 

5.4.1  Analytical Problem Solution ... 143 

5.4.2  Heuristic Problem Solution ... 144 

5.5  Fault Behaviour Explanation ... 145 

5.6  Complex Fault Response ... 145 

5.7  CBRS Advanced Analytics Framework Validation Methodology ... 148 

5.7.1  Phase 1: Knowledge Base Inference Analytical Engine Development ... 148 

5.7.2  Phase 2: Advanced Data Analytics Software Platform Enablement ... 149 

5.7.3  Phase 3: Fault Trigger Automation and Self–Learning/Optimisation ... 150 

5.8  Construct Verification of the Proposed CBRS Advanced Analytics Framework ... 150 

5.9  Validation of the Proposed CBRS Analytical Framework ... 151 

5.10  Conclusion ... 152 

CHAPTER 6 – MILLING PLANT KNOWLEDGE BASE ... 154 

6.1  Introduction ... 154 

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6.2.1  Milling Plant Process Design and Philosophy ... 154 

6.2.2  Plant System Design Basis ... 157 

6.2.2.1  Overall System Design and Operating Principles ... 157 

6.2.2.2  Mill Drive Motor ... 161 

6.2.2.3  Mill Drive Single Reduction Gearbox ... 165 

6.2.2.4  Mill Drive Couplings ... 168 

6.2.2.5  Mill Pinion & Girth Gear ... 171 

6.2.3  Plant Maintenance Baseline ... 172 

6.2.3.1  High Voltage Motor ... 172 

6.2.3.2  Flexible Coupling ... 172 

6.2.3.3  Single Reduction Gearbox ... 173 

6.2.3.4  Mill with Pinion/Girthgear Drive ... 173 

6.2.4  Milling Plant Operating Baseline ... 174 

6.2.4.1  Mill Control Design Philosophy Considerations ... 174 

6.2.4.2  Case Study: Design Base Operating and Control Philosophy not considered ... 177 

6.2.4.3  Boiler Master Control ... 181 

6.2.4.4  Auto/Manual Station for Total Fuel ... 183 

6.2.4.5  Calorific Value (C.V.) Correction ... 183 

6.2.4.6  Primary Air Flow Control ... 184 

6.2.4.7  Secondary Air Pressure Control ... 187 

6.2.4.8  Primary Air Fan Control ... 188 

6.2.4.9  Mill Feeder Control ... 189 

6.2.4.10  Mill Temperature control ... 190 

6.2.4.11  Mill Bypass Air Control ... 192 

6.2.4.12  Control System Details ... 193 

6.2.4.13  The Unit Coordinator (Used together with the “Capability Computer”) ... 195 

6.2.4.14  Mill Secondary Air Flow Control ... 198 

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6.3.1  Equipment/Component Fault Tree Analysis (FTA) ... 199 

6.3.1.1  Mill Drive High Voltage Motor ... 200 

6.3.1.2  Mill Drive Flexible Couplings ... 201 

6.3.1.3  Mill Drive Single Reduction Gearbox ... 202 

6.3.1.4  Mill Pinion/Girthgear Drive ... 203 

6.3.2  Fault and Failure Statistics Evaluation ... 204 

6.3.3  EPRI Database Comparison (Failure Mode External Validation) ... 205 

6.3.3.1  High Voltage Motor Failure Mode Comparison ... 205 

6.3.3.2  Elastomeric Coupling (“Bibby) Failure Mode Comparison ... 206 

6.3.3.3  Reduction Gearbox Failure Mode Comparison ... 207 

6.3.3.4  Pinion–Girthgear Drive Failure Mode Comparison ... 207 

6.3.3.5  Mill Barring Gear Drive Failure Mode Comparison ... 208 

6.3.3.6  Mill Process Fault and Failure Mode Comparison ... 209 

6.4  Reliability Baseline Configuration ... 209 

6.4.1  Vibration and Condition Monitoring Data Acquisition Configuration ... 209 

6.4.2  Vibration Data Acquisition – Measurement Point Configuration ... 210 

6.4.3  Vibration Data Analysis Considerations ... 213 

6.4.3.1  Motor ... 213 

6.4.3.2  Coupling considerations ... 214 

6.4.3.3  Reduction Gearbox considerations ... 215 

6.4.3.4  Pinion/Girthgear considerations ... 215 

6.4.4  Plant Process Control Data ... 216 

6.4.5  Process Control and Environmental Impacts ... 216 

6.5  Conclusion ... 217 

CHAPTER 7 – MILLING PLANT INFERENCE ANALYTICAL ENGINE ... 218 

7.1  Introduction ... 218 

7.2  Approach in documenting the Inference Analytical Framework ... 218 

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7.3.2  Failure Degradation Timeline – Inference Logical Model ... 220 

7.3.3  Performance Degradation – Inference Logical Model ... 222 

7.4  Heuristic Inference Specifics ... 225 

7.4.1  Application of Comparative Peer–to–Peer (P2P) Analytics ... 225 

7.4.2  Fault Response Considerations ... 225 

7.4.3  Complex Fault Response Considerations ... 226 

7.4.4  Severity Classification Considerations ... 226 

7.4.5  Performance Degradation Considerations ... 227 

7.4.6  Dealing with False–Positives and False–Negatives ... 227 

7.5  Fault Model Use Case Details – HV Motor ... 227 

7.5.1  Ideal/Optimal Vibration Behaviour Patterns ... 227 

7.5.2  Fault Frequencies of Interest – HV Motor ... 229 

7.5.3  Fault Condition Use Case 1: Motor Rotor Bar Defects ... 233 

7.5.4  Fault Condition Use Case 2: Motor Electrical Supply Phase Imbalance ... 250 

7.5.5  Fault Condition Use Case 3: Complex Fault – Coupling Defect ... 261 

7.6  CBRS Framework Self-Learning Aspects ... 277 

7.6.1  Early CBRS Fault Model Framework Self-Learning Successes ... 277 

7.6.2  Visualization of Fault Condition Behaviour Patterns ... 279 

7.7  CBRS Framework Continuous Improvement ... 281 

7.7.1  Considering Operational Experiences ... 281 

7.7.2  Asset Optimisation Initiatives ... 282 

7.7.3  Improved Plant Monitoring and Integration with Control System Data ... 282 

7.8  Conclusions ... 283 

CHAPTER 8 – MILLING PLANT ADVANCED ANALYTICS OUTCOME EVALUATION AND EXERNAL VALIDATION ... 284 

8.1  Introduction ... 284 

8.2  CBRS Anomaly Qualification Elements Evaluation ... 285 

8.2.1  Analytical Plant Process Model ... 285 

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8.2.3  Fault and Failure Statistical Matching ... 286 

8.2.3.1  Interpretation of ARMA Outcomes ... 286 

8.2.3.2  Importance of ARMA Outcome ... 288 

8.2.3.3  Using ARMA to identify SFFoI’s for the Use Case Fault Conditions ... 289 

8.2.3.4  Rotor Bar Defect ARMA Analysis and Discussion ... 290 

8.2.3.5  Electrical Phase Imbalance ARMA Analysis and Discussion ... 293 

8.2.3.6  Coupling Defect (Complex Fault) ARMA Analysis and Discussion ... 297 

8.2.4  Design Base Deviation Confirmation ... 300 

8.2.5  Operating and Maintenance Base Trigger Matching ... 308 

8.2.6  Process Control Historical Matching ... 308 

8.3  CBRS Failure Model Evaluation and Fault Hypothesis Confirmation Elements Evaluation ... 309 

8.3.1  Fault Hypothesis Testing ... 309 

8.3.2  Hypothesis Model Test ... 312 

8.3.3  Fault Recognition ... 312 

8.3.4  Fault Reduction and Re-ordering ... 313 

8.3.5  Threshold Logic Testing ... 314 

8.3.6  Fault Hypothesis Test ... 314 

8.3.6.1  Motor Use Case 1 Results Discussion and Interpretation ... 314 

8.3.6.2  Motor Use Case 2 Results Discussion and Interpretation ... 314 

8.3.6.3  Motor Use Case 3 Results Discussion and Interpretation ... 315 

8.3.6.4  Combined Fault Condition Results Discussion and Interpretation ... 315 

8.3.7  Residual Generation ... 319 

8.3.8  Symptom Evaluation and Confirmation ... 321 

8.3.9  Diagnosis Justification ... 321 

8.3.10  Peer-to-Peer (P2P) Comparison ... 321 

8.3.11  Re-enforcement Symptom Evaluation and Confirmation ... 321 

8.3.12  Fault Behaviour Characteristic Comparison ... 322 

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8.3.14  Performance Degradation Index Matching ... 323 

8.4  CBRS Remedial Action Elements Evaluation ... 323 

8.4.1  Recommended Action(s) Effectiveness ... 323 

8.4.2  Remedial Action Justification ... 323 

8.4.3  Complex Fault Response ... 324 

8.5  CBRS Fault Analytics Classification Elements Evaluation ... 324 

8.5.1  Fault Confirmation ... 324 

8.5.2  FMEA and Fault Cause(s) Pattern Confirmation ... 324 

8.5.3  Fault Type, Severity Class & Remedial Action Confirmation ... 324 

8.6  CBRS Self-Learning Elements Evaluation ... 325 

8.6.1  Self-Learning ... 325 

8.6.2  Fault Model Optimisation ... 327 

8.7  CBRS Integration with Plant Control and Data Historians ... 327 

8.7.1  Integration Considerations ... 327 

8.7.2  Data Format Considerations ... 328 

8.7.3  External Validation System (PRISM™) ... 328 

8.8  Overall Failure Fault Model Evaluation ... 329 

8.8.1  Overall Fault Hypothesis Model Success Rate ... 329 

8.8.2  Fault Model Verification ... 330 

8.8.3  Fault Model Internal Validation ... 330 

8.8.4  Fault Model External Validation ... 330 

8.9  CBRS Analytical Framework - Overall Results Interpretation ... 331 

8.9.1  CBRS Analytical Framework ... 331 

8.9.2  CBRS Fault Model Development and Implementation Methodology ... 333 

8.9.3  Generic Nature of CBRS Framework and Analytical Fault Models ... 334 

8.9.4  Design Base Adjustments Required for Analytical Model ... 334 

8.10  Conclusion ... 335 

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9.1.1  The CBRS Analytical Framework – Conceptual Platform ... 336 

9.2  The IPI-BIM Framework ... 337 

9.3  Integrating the CBRS Analytical Framework into the IPI-BIM System Landscape ... 338 

9.4  CBRS Analytical Platform Elements ... 339 

9.4.1  Information Delivery ... 339 

9.4.2  Design Basis Parameters ... 340 

9.4.3  Fault Tree and Failure Analytics ... 340 

9.4.4  Failure Pattern Recognition and Models ... 341 

9.4.5  On-line Status Trending and Visualisation ... 341 

9.4.6  Controllable Parameter Trending ... 342 

9.4.7  Flownex™ Process Simulation Model ... 343 

9.4.8  PRISM™™ Simulation Models ... 344 

9.5  Capability to deliver on the elements of the CBRS Analytical Platform .... 345 

9.5.1  3D Model ... 345 

9.5.2  Design Basis Information ... 346 

9.5.3  Flownex™ Plant Process Simulation Information ... 346 

9.5.4  Plant Control Data Information ... 346 

9.5.5  Plant Status and Controllable Parameter Trend Information ... 347 

9.5.6  The Knowledge Base Inference Analytical Engine ... 347 

9.5.7  Potential Secondary Elements of the CBRS Platform ... 348 

9.6  Control System and Plant Data Historian Integration Considerations ... 348 

9.7  Condition Monitoring and Diagnostic Software Integration Considerations ... 349 

9.8  Information Integration Considerations ... 349 

9.8.1  Success in Integrating Proposed CBRS Elements ... 350 

9.8.2  Predictive Capability Evaluation ... 350 

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CHAPTER 10 – RESEARCH STUDY HYPOTHESIS CONFIRMATION AND INTERPRETATION ... 352  10.1  Introduction ... 352  10.2  Hypothesis 1 ... 352  10.2.1  Hypothesis 1 Confirmation ... 352  10.2.2  Hypothesis 1 Interpretation ... 353  10.3  Hypothesis 2 ... 354  10.3.1  Hypothesis 2 Confirmation ... 354  10.3.2  Hypothesis 2 Interpretation ... 355  10.4  Hypothesis 3 ... 357  10.4.1  Hypothesis 3 Confirmation ... 357  10.4.2  Hypothesis 3 Interpretation ... 357  10.5  Hypothesis 4 ... 358  10.5.1  Hypothesis 4 Confirmation ... 358  10.5.2  Hypothesis 4 Interpretation ... 358  10.6  Hypothesis 5 ... 359  10.6.1  Hypothesis 5 Confirmation ... 359  10.6.2  Hypothesis 5 Interpretation ... 360  10.7  Conclusion ... 361 

CHAPTER 11 – RESEARCH STUDY CONCLUSION ... 362 

11.1  The CBRS Analytical Framework Delivered ... 362 

11.2  The End State Vision ... 363 

11.3  Further Research Areas ... 364 

11.3.1  CBRS Framework ... 365 

11.3.2  Equipment Fault Models ... 365 

11.3.3  Advanced Analytics Methodology ... 369 

11.3.4  Reliability Simulator Enhancements ... 369 

11.3.5  Cost Saving/Cost Avoidance Reporting ... 370 

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11.4.1  Level of Generic Use–ability of Horizontal Tube Mill Fault Model ... 370 

11.4.2  Use of Raw Time Waveform Overall Value Data ... 370 

11.4.3  Gearbox Historical Data Value for Fault Model Use ... 371 

11.5  Contribution of this Research Study ... 372 

11.6  Final Thoughts on using Advanced Analytics for Plant Asset Management ... 373 

BIBLIOGRAPHY ... 375 

ANNEXURES ... 388 

Annexure A – Additional Technical Data ... 388 

A–1: Rolling Element Bearing Calculation Formulae ... 388 

Annexure B – EPRI Plant Maintenance Template Inventory ... 389 

Annexure C – EPRI FMEA Data for Milling Plant Components ... 396 

C–1: High Voltage Electrical Motor (PMT 2035) ... 396 

C–2: Elastomeric Couplings (PMT 1036) ... 403 

C–3: Tube Mill – Main Reduction Gearbox (PMT 1153) ... 404 

C–4: Tube Mill – Girth and Pinion Gear Drive (PMT 1152) ... 406 

C–5: Tube Mill – Trunnion Bearing Lubrication System (PMT 1162) ... 408 

C–6: Tube Mill – Mill Drum (PMT 1157) ... 410 

Annexure D – Ideal/Optimal Equipment Vibration Behaviour ... 411 

D–1: High Voltage Electrical Motor – Ideal Conditions ... 411 

D–2: Electrical Motor – Example of Completed Fault Model Template ... 423 

D–3: Single Reduction Gearbox Heuristic Knowledge Model ... 427 

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ABBREVIATION MEANING

EPRI Electric Power Research Institute

ERP Enterprise Resource Planning

EXCO Executive Committee

FAT Factory Acceptance Testing

FFoI Fault Frequency of Interest

FFT Fast Fourier Transform

FMA Failure Mode Analysis

Fmax Maximum Oscillation Frequency

FMEA/FMECA Failure Mode Effect Analysis/Failure Mode Effect Criticality Analysis

FRF Frequency Response Function

FTA Fault Tree Analysis

FTF Fundamental Train Frequency

GCMS Generic Component Maintenance Strategy

GGGS Girth Gear Grease System

GT Group Technology Division

GTCHR Gross Turbine Cycle Heat Rate

HAZOP Hazardous Operation Analysis

HP High Pressure

Hpv Horizontal, PeakVue Reading

HV High Voltage

IAE Inference Analytical Engine

IAEA International Atomic Energy Agency

IEEE Institute of Electrical and Electronics Engineers

IGCC Integrated Generation Control Centre

IoT Internet of Things

IRM Integrated risk management

IM Information Management

ISO International Standards Organisation

IT Information Technology

IT–OT Information Technology – Operations Technology

KPI Key Performance Indicators

LF Line Frequency

LH Left Hand

LL Lower Limit

LLF Log Likelihood Function (Statistical method)

LP Low Pressure

LTIR Lost–time incidence rate

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ABBREVIATION MEANING

MCR Maximum Continuous Rating

MTBF Mean Time Between Failures

MTTR Mean Time To Repair

mS milli–Second

mV milliVolt

MW Megawatt

NDE Non–Drive End

NERSA National Energy Regulator of South Africa

NP Number of Poles

O&M Operate and Maintain

OEM Original Equipment Manufacturer

OHS Occupational Health and Safety

OOTB Out of the Box

P&ID Piping and Instrumentation Diagram

P2P Peer to Peer

PACF Partial Auto-Correlation Function

PBS Plant Breakdown Structure

PCLF Planned Capability Loss Factor

PdM Predictive Maintenance

PDS Plant Data Store (also known as Plant Data Historian System)

PEIC Production Engineering Integration – Coal

PESTEL Political, Economic, Social, Technological, Environmental and Legal

(Sphere)

PF Pulverised Fuel

PFMA Public Finance Management Act

PLC Programmable Logic Controller

PM Preventive Maintenance Tasks

PoC Proof of Concept

QC/QA Quality Control/Quality Assurance

RAM Reliability, Availability, Maintainability

RBO Reliability Basis Optimisation

RBP Rotor Bar Pass

RCM Reliability Centred Maintenance

RH Right Hand

RMDC Remote Monitoring and Diagnostics Centre

RMS Root–mean–square

ROA Return–on–Asset

ROI Return–On–Investment

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ABBREVIATION MEANING

RTF Run to Failure

RUL Remaining Useful Life

SCADA System Control and Data Acquisition (Plant control system technology)

SCM Supply Chain Management

SCOT Study Committee of Technology

SFFoI Specific Fault Frequency of Interest

SHEQ Safety, Health, Environment and Quality

SLA Service Level Agreements

SLD Single Line Diagram

SOC State-owned company

SOP Standard Operational Procedure

SoW Scope of Work

SSP Stator Slot Pass

STDEV Standard Deviation

t.b.d. to be determined

UAT User Acceptance Testing

UCF Unit Capability Factor

UCLF Unplanned Capability Loss Factor

UL Upper Limit

URS User Requirement Specification

V&V Validation and Verification

VAT Value-added tax (RSA)

WAN Wide Area Network

WEC World Energy Council

WG Work Group (In the SCOT context)

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T Adaptiv Advanc Akaike-Criterion Aliasing ARCH E

Defi

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initions

s Boostin each misclas models Adaptiv problem distribu concen way th the fol majorit all case cs The us monito advanc conditio Advan future approa are unl n The A quality models each o selectio In sou (alias) sampli For sou In sign causes anothe results the orig A tim autoco conditio the squ shown ng is a met new mod ssified. The s, is used fo ve Boosting ms. As an ution D that ntrate on dif at that the lowing sam ty voting. T es have equ se of plant i oring and ced/comple on and mak nced Analyt outcomes. aches to bu likely to disc kaike Inform of statistica s for the da of the othe on. nd and im frequency ng. For ima und, it prod nal process s different s er) when sa from a sig ginal contin me serie orrelation in onal hetero uared value to be signif EXPLA

hod that inc el with d en the ense or prediction g (AdaBoos example, fo t is update fficult cases earlier, mis mple. The c he distribut ual probabi information control. x data an ke decisions tics is a gro Advanced usiness inte cover mation Crit al models f ata, AIC est er models. age genera along wit ages, this p uces a buzz sing and re signals to b ampled. It a nal reconst uous signa es exhibi n the squar oscedasticity es of time se ficant, it usu NATORY C crementally data that emble, whic n. st) is an ext or AdaBoos d in such a s. This is a sclassified classifiers a tion begins lity to be dra and data b Apply nalysis and s based on ouping of an d Analytics lligence (BI terion (AIC for a given imates the Thus, AIC ation, alias h the corr roduces a j z. elated disci become ind also refers tructed from l. ting con red series— y (ARCH) e eries are au ually create COMMENTS y creates an the previo ch is a com tension of b st.M1, samp a way that chieved by cases are re then com as a unifo awn into the beyond the ying analy d processi these analy nalytic tech produce in I) –such as ) is an est set of data quality of e C provides ing is the rect one w jagged edg plines, alia distinguisha to the dist m samples ditional —is said to effects. A s uto-correlat s a questio S n ensemble ously train mbination of boosting to ples are dra successive adjusting D likely to be mbined wit rm distribut e first data s convention ytical mo ng to ana ytical outco niques use nsights that s query and timator of t . Given a c each model a means generation when doing e, or stair– sing is an ble (or alia tortion or a that are dif heterosced o have auto statistical e ted, and if th nable data-by training ned model f all trained multi-class awn from a e classifiers D in such a e present in h weighted tion so that subset S1. nal realm of odels and alyse plant mes. d to predict t traditional d reporting– the relative collection of , relative to for model of a false frequency –step effect. effect that ases of one artefact that fferent from asticity—or oregressive ffect where his effect is -set. g l d s a s a n d t f d t t l – e f o l e y . t e t m r e e s

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TERM EXPLANATORY COMMENTS

ARCH models are commonly employed in modelling financial time series that exhibit time-varying volatility clustering, i.e. periods of swings interspersed with periods of relative calm. In this research, this model will have relevance for fault conditions where fault conditions are suddenly triggered following long periods of low-level vibration (and virtually no indication of the fault condition).

ARMA Prediction

In the statistical analysis of time series, autoregressive–moving–

average (ARMA) models provide a parsimonious description of a

(weakly) stationary stochastic process in terms of two polynomials, one for the autoregression and the second for the moving average. The general ARMA model was described in the 1951 thesis of Peter Whittle, “Hypothesis testing in time series analysis”.

Given a time series of data X, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The AR part involves regressing the variable on its own lagged (i.e., past) values. The MA part involves modelling the error term as a linear combination of error terms occurring contemporaneously and at various times in the past.

Artificial Intelligence (A.I.)

1. A branch of computer science dealing with the simulation of intelligent behaviour in computers

2. The capability of a machine to imitate intelligent human behaviour.

Auto–Regression The autoregressive model specifies that the output variable depends

linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation.

Bagging Bagging is a technique which is based on the combination of models

fitted to randomly selected samples of a training data set to decrease the variance of the prediction model. The technique was developed by Efron in his research [Efron, 1979].

Ball Pass Frequency Inner (BPFI)

Ball pass frequency of the outer race that is the frequency created when all the rolling elements roll across a defect in the inner race of a rolling element bearing.

Ball Pass Frequency Outer (BPFO)

Ball pass frequency of the outer race that is the frequency created when all the rolling elements roll across a defect in the outer race of a rolling element bearing.

Ball Spin Frequency (BSF)

The circular frequency of each rolling element as it spins when the bearing is rotating.

Brownfields

An existing onshore or offshore facility, e.g. ‘brownfield modification’ is an upgrade to an existing facility.

Brownfield land (Civil Engineering) means places where new buildings may need to be designed and erected considering the other structures and services already in place.

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TERM EXPLANATORY COMMENTS

Causality The statistical term (also called “Causation”) indicates that one event is

the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect.

In the context of the research, part of the ARMA analysis involved an evaluation of there is causality between FFoI’s identified as indicators of fault conditions.

Complex Number A complex number is a quantity of the form v + iw, where v and w are

real numbers; and I represent the unit imaginary numbers equal to the positive square root of –1. The set of complex numbers is two– dimensional, and a coordinate plane is required to illustrate them graphically.

This is in contrast to the real numbers, which are one–dimensional, and can be illustrated by a simple number line. The rectangular complex number plane is constructed by arranging the real numbers along the horizontal axis, and the imaginary numbers along the vertical axis.

Confidence Measurement

A technique is used to estimate the confidence of the algorithm about its own decision. A majority of hypotheses agreeing on given instances can be interpreted as an indication of confidence in the decision proposed. Cycles per milli–

Second

A period of 1 Millisecond is equal to 1 000 Hertz frequency. Period is the inverse of frequency: 1 Hz = 1 / 0.001 cpmS.

Demodulation Demodulation uses a user-specified band–pass or high–pass filter to

remove all low–frequency components in the vibration signal. The signal is amplified and amplitude demodulated, which creates a low–frequency signal consisting of the envelope of the original signal. The amplitude of the original signal is not maintained when demodulation is used.

This technique is used with low-speed equipment that has rolling element bearings – in this case, demodulation uses a series of signal processing methods on a raw acceleration signal to extract the defect over–roll signals from the background vibration.

It is largely independent of accelerometer model and resonant response and thus a preferred method over Sensor Resonance to amplify bearing fault frequencies in the acceleration data “noise floor” generated at low speeds.

Design Basis (Base) Set of conditions, needs, and requirements taken into account in designing a facility or product.

Discrete Fourier Transform (DFT)

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally–spaced samples of a function into a same–length sequence of equally–spaced samples of the discrete–time Fourier transform (DTFT), which is a complex–valued function of frequency. Doornik Chi-Square

Test

A multivariate normality test to test for skewness. The Doornik-Hansen chi-square (χ2) test is used in statistics for checking bivariate normality of the response.

Energy Availability Factor (EAF)

The “availability factor” of a power plant is the amount of time that it is able to produce electricity over a certain period, divided by the amount of the time in the period. Occasions, where only partial capacity is available, may or may not be deducted.

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T Ensemb Eskom Sustain Perform (ESPI) False N False P Fast Fo Transfo Fmax Forced Fourier Fundam Frequen Greenfie TERM ble Learning ability mance Index Negative Positive ourier orm outage Analysis mental Train ncy (FTF) elds Where The av The ca availab utilizati g Ensem classifi problem perform x The in measu A false indicate A false “false a does n The F transfo Discret Fourier space) Ft is t frequen The sh for em unavai In mat functio trigono series a funct of heat A fast transfo a signa in the f n The fu a rollin A new offshor they are, vailability fa apacity facto bility factor ion of the po mble learnin

ers, are int m. Ense mance of an ndex cover res to score e negative es that a co e positive e alarm”, is a ot. Fast Fourie orms. A fa te Fourier t r analysis c ) to a repres the unity c ncy, also so hutdown of ergency rea lable for loa thematics, ns may be ometric func and is nam tion as a su t transfer. Fourier tra orm (DFT) o al from its o frequency d ndamental g element b w field dev re. EXPLA the metric actor should or for a pe for the sam ower plant. ng is a te tentionally c mble learn n algorithmi ring techni e sustainab error, or in ondition doe error, or in a result that er Transfo ast Fourier transform ( converts a s sentation in current gain ometimes ca a generati asons or a ad due to un Fourier an e represen ctions. Four med after Jo um of trigono nsform (FF of a sequen original dom domain and Train Frequ bearing con velopment r NATORY C is titled eq d not be co

riod will alw me period. chnique w created and ning is us c computat cal, econo ble performa short a fal es not hold, short a fa t indicates rm is a r transform DFT) of a signal from the frequen n frequency alled max o ng unit, tra condition i nanticipated nalysis is nted or app rier analysis seph Fourie ometric fun FT) algorithm nce; or its in main (often t vice versa. uency, i.e. nfiguration. requiring n COMMENTS quivalent av onfused wit ways be les The differe here multip d combined sually appl tional mode omic, envir ance. lse negative while in fac alse positive a given co common a (FFT) alg sequence, its original ncy domain y. Fmax is oscillation fr ansmission n which ge d breakdow the study proximated s grew from er, who sho

ctions grea m compute nverse. Fou ime or spac frequency o new facilitie S vailability fa th the capa ss than the ence depen ple models d to solve a ied to inc l. ronmental e, is a test ct, it does. e, common ndition exis algorithm f gorithm com or its inve domain (of and vice v the unity p requency. line or ano enerating eq wn. of the wa by sums m the study owed that re atly simplifie es the discr urier analys ce) to a rep of the beari es, either o ctor (EAF). acity factor. equivalent nds on the s, such as a particular crease the and social t result that nly called a sts, when it for Fourier mputes the erse (IFFT). ften time or ersa. power gain other facility quipment is ay general of simpler y of Fourier epresenting es the study rete Fourier sis converts resentation ing cage of onshore or . t e s r e l t a t r e r n y s l r r g y r s n f r

(27)

TERM EXPLANATORY COMMENTS

A greenfield project is one that lacks constraints imposed by prior work. The analogy is to that of construction on greenfield land where there is no need to work within the constraints of existing buildings or infrastructure

Goodness-of-Fit checks

Statistical analysis that is done to examines the values of an ARMA model’s parameters for stability, specifically considering aspects like stationarity, invertibility, and causality.

Histogram A histogram is an accurate representation of the distribution of numerical

data. It is an estimate of the probability distribution of a continuous variable (quantitative variable) and was first introduced by Karl Pearson. It is many times displayed as a bar graph plot.

To construct a histogram, the first step is to "bin" the range of values— that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent and are often (but are not required to be) of equal size.

If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency — the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies. It then shows the proportion of cases that fall into each of several categories, with the sum of the heights equalling 1.

A Plot generated to evaluate the distribution of data to determine data distribution values. Data is sorted into bins/containers and are evaluated inters of lower and upper limits. Based on the averaging the intent is to demonstrate that sufficient data is available that is considered acceptable and statistically “normal” for the expected and predicted distribution.

Independent Identically

Distributed Random Variables (iid’s)

In probability theory and statistics, a sequence or other collection of random variables are independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent

Independent Power Producer (IPP)

Any entity, other than Eskom, that owns or operates, in whole or in part, one or more independent power production facilities.

Invertibility A statistical term used in ARMA modelling. It that refers to the fact that

the moving average (MA) models (models in which the dependent variable could be written as a weighted average of current and past innovations, which are uncorrelated mean zero random noises) can be written as an autoregressive (AR) model (models in which the dependent variable could be written as a weighted averages of past observations of the dependent variable).

If ARMA models (models in which contain both autoregressive components and moving average components) can be written as AR models, we say that the time series model is invertible.

The essential concept is whether the innovations/noises can be inverted into a representation of past observations.

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TERM EXPLANATORY COMMENTS

This notion is very much important if one wants to forecast the future values of the dependent variable, a very relevant issue for future prediction of the failure condition.

The forecasting task (prediction) will be impossible when the innovations are not invertible (i.e., the innovations in the past cannot be estimated, as it is cannot be observed). If the model is not invertible, even though the innovations can still be represented by observations of the future, this will not be helpful at all for forecasting purposes.

ISO 55001 Following the use of PAS 55 that was increasingly recognised as a

generically applicable definition of good practices in the optimized management of physical assets, it was transformed to become an international standard, which is available in three parts:

 ISO 55000 provides an overview of the subject of asset management and the standard terms and definitions.

 ISO 55001 is the requirements specification for an integrated, effective management system for asset management.

 IS0 55002 provides guidance for the implementation of such a system.

IT–OT While there is no industry–standard definitions of IT and OT in the

electric power industry, it is possible to delineate the two:

 OT is typically associated with field-based devices connected to the distribution system, and the infrastructure for monitoring and controlling those devices. This includes control centre based systems such as Supervisory Control and Data Acquisition (SCADA) and Distribution Management Systems (DMS). Most communications are performed device–to–device, or device–to– computer, with relatively little human interaction.

 IT is traditionally associated with back-office information systems used for conducting business-type transactions, such as cost and tax accounting, billing and revenue collection, asset tracking and depreciation, human resource records and timekeeping, and customer records. Manual data entry is often involved, and the computing resources have tended to be centred in offices, server rooms, and corporate data centres. 

Jarque-Bera Test The Jarque–Bera test is a goodness-of-fit test of whether sample data

have the “skew–ness” and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. It is a type of Lagrange multiplier test, which is a test for normality.

Kilowatt-hour (kWh) The basic unit of electric energy equal to one kilowatt of power supplied

to or taken from an electric circuit steadily for one hour; one kilowatt-hour equals 1,000 watt-hours.

Kurtosis In probability theory and statistics, Kurtosis (“curved, arching”) is a

measure of the “tailed–ness” of the probability distribution of a real-valued random variable.

Kurtosis is a descriptor of the shape of a probability distribution and there are different ways of quantifying it for a theoretical distribution and

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TERM EXPLANATORY COMMENTS

The standard measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population.

This number is related to the tails of the distribution, not its peak. For the purpose of this research study, this standard measure is applicable. The kurtosis of any univariate normal distribution is 3. It is common to compare the kurtosis of a distribution to this value. Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is “flat-topped” as sometimes reported. Rather, it means the distribution produces fewer and less extreme outliers than does the normal distribution. An example of a platykurtic distribution is the uniform distribution, which does not produce outliers.

Distributions with kurtosis greater than 3 are said to be leptokurtic. An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution. It is also common practice to use an adjusted version of Pearson’s kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the normal distribution.

Some authors use “kurtosis” by itself to refer to the excess kurtosis but this create issues in cases where excess kurtosis is explicitly meant. Excess Kurtosis is evaluated during statistical residual analysis to determine whether there are indications of questionable data that result in severe outliers (aka “fat-tails” that are shown at the end of a chart when data is graphed) and whether the data population has a propensity for producing such outliers.

Leakage Effect Also called “DFT Leakage Effect”. The term ‘leakage’ usually refers to

the effect of windowing, which is the product of s (t) with a different kind of function, the window function. Window functions happen to have a finite duration, but that is not necessary to create leakage. Multiplication by a time–variant function is sufficient.

Leakage caused by a window function is most easily characterized by its effect on a sinusoidal s(t) function, whose un–windowed Fourier transform is zero for all but one frequency.

The Fourier transform of a function of time, s (t), is a complex–valued function of frequency, S(f), often referred to as a frequency spectrum. Any linear time-invariant operation on s (t) produces a new spectrum of the form H(f)•S(f), which changes the relative magnitudes and/or angles (phase) of the non–zero values of S(f).

Any other type of operation creates new frequency components that may be referred to as spectral leakage in the broadest sense. Sampling, for instance, produces leakage, which we call aliases of the original spectral component. For Fourier transform purposes, sampling is modelled as a product between s (t) and a Dirac comb function.

The spectrum of a product is the convolution between S(f) and another function, which inevitably creates the new frequency components.

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TERM EXPLANATORY COMMENTS

Learn++ Learn++ is an incremental learning algorithm that was introduced by

Polikar and co-workers in their research. It is based on adaptive boost techniques (AdaBoost) and applies multiple classifiers to enable the computational AI system to learn incrementally.

The algorithm operates on the concept of using many classifiers that are weak learners to give a good overall classification. The weak learners are trained on a separate subset of the training data and then the classifiers are combined using a weighted majority vote.

The weights for the weighted majority vote are chosen using the performance of the classifiers on the entire training dataset. Each classifier is trained using a training subset that is drawn according to a specified distribution. The classifiers are trained using a weak learn algorithm (“WeakLearn”). The requirement for the WeakLearn algorithm is that it must give a classification rate of less than 50% initially.

Lines of Resolution

The frequency resolution is defined as the baseband frequency span divided by the number of lines selected for the analysis of the input signal to display the spectrum in the frequency range selected. If a spectrum is collected with a Fmax of 1,600 Hz with 800 lines of resolution, the resolution on the plot will be 1,600 / 800 or 2 Hz.

This means that if there is a vibration signal at 100 Hz and another at 101 Hz, it will not be able to see both of them because the maximum resolution is not small enough to resolve them. The two will appear as one peak. In converting a time–based dataset (analogue signal) into a frequency–based dataset (digital signal), the digital conversion process must follow the Nyquist Theorem, which dictates that the sample rate for a particular process must exceed twice the maximum frequency of the spectrum. This is necessary to prevent aliasing – a situation in which unwanted frequency components appear in a signal that was not present originally.

The typical number of lines of frequency resolution in modern digital signal processes is selectable and is normally 400, 800, 1,600, 3,200, 6,400, 12,800 lines. The greater the number of lines of resolution the narrower the effective bandwidth of each spectral line, but the longer the analysis time (t = 1/(Hz/line)).

The correct use of lines of resolution becomes critical when sideband analysis is performed as it can differentiate at a sufficient level to pinpoint the fault conditions better e.g. difference between a 1 x running speed sideband compared to a 2 x Line Frequency sideband around a fundamental fault frequency).[Thomson, WT, 2017]

Lost–time incident rate

A proportional representation of the occurrence of lost–time injuries over 12 months.

Maintenance Base A formal process of defining the maintenance tasks, frequencies and

scope of work required to maintain a plant according to the prescribed Design Basis. A standardised methodology, rule–set, and definitions would be used to build the maintenance basis.

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TERM EXPLANATORY COMMENTS

Megawatt One million watts

Megawatt-hour One thousand kilowatt-hours or one million watt–hours.

MIMOSA MIMOSA is a non–profit trade association, which develops and

encourages adoption of open information standards for operations and maintenance. MIMOSA is composed of industrial asset management system providers and industrial asset system end–users that develop open information integration specifications for managing physical assets.

Modulus In mathematics, the absolute value or modulus |x| of a real number x is

the non–negative value of x without regard to its sign. Namely, |x| = x for a positive x, |x| = −x for a negative x (in which case –x is positive), and |0| = 0.

For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.

Mothballed Plant (i.e. power stations) placed in long-term storage.

Moving Average In statistics, a moving average (rolling average or running average) is a

calculation to analyse data points by creating series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include simple, and cumulative, or weighted forms.

Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initially fixed subset of the number series. Then the subset is modified by “shifting forward”; that is, excluding the first number of the series and including the next value in the subset.

A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles.

Nyquist Theorem The Nyquist Theorem, also known as the sampling theorem, is a

principle that engineers follow in the digitization of analogue signals. For analogue–to–digital conversion (ADC) to result in a faithful reproduction of the signal, slices, called samples, of the analogue waveform must be taken frequently. The number of samples per second is called the sampling rate or sampling frequency.

According to the Nyquist Theorem, the sampling rate must be at least 2xfmax, or twice the highest analogue frequency component. The sampling in an analogue–to–digital converter is actuated by a pulse generator (clock).

If the sampling rate is less than 2xFmax, some of the highest frequency components in the analogue input signal will not be correctly represented in the digitized output.

When such a digital signal is converted back to analogue form by a digital–to–analogue converter, false frequency components appear that were not in the original analogue signal. This undesirable condition is a form of distortion called aliasing.

Operating Base The operating envelope as defined by the Plant Design Base indicating

safe operating values, operating criteria and requirements to be met in order to ensure operations within the design life and parameter limits.

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TERM EXPLANATORY COMMENTS

Outage The period in which a generating unit, transmission line, or other facility

is out of service.

P2P (Peer–to–Peer) It is a specific form of relational dynamic, is based on the assumed

equipotency of its participants, organized through the free cooperation of equals in view of the performance of a common task, for the creation of a common good, with forms of decision–making and autonomy that are widely distributed throughout the network.

P2P Copula

(Probability Theory) Analytics

In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform.

Copulas are used to describe the dependence between random variables. Recently, copula functions have been successfully applied to the database formulation for the reliability analysis of highway bridges, and to various multivariate simulationstudies in civil, mechanical and offshore engineering.

P-Value The probability under the null hypothesis that test statistics (the ARMA

score) are at least as extreme as observed.

Parameter A parameter generally is any characteristic that can help in defining or

classifying a particular system (meaning an event, project, object, situation, etc.).

That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

PAS–55 PAS 55 is the British Standards Institution’s (BSI) Publicly Available

Specification for the optimized management of physical assets – it provides clear definitions and a 28–point requirements specification for establishing and verifying a joined–up, optimized and whole–life management system for all types of physical assets.

PeakVue® The analyser can use PeakVue® technology or demodulation when

collecting data. PeakVue® technology samples data faster than demodulation to detect high–frequency stress waves. PeakVue data is trend–able, but demodulation is not.

PeakVue® technology lets you find bearing or gear defects earlier than other measurements. PeakVue® technology removes normal vibration signals and captures the actual amplitude of high–frequency impacts from bearing or gear defects. Bearing defect frequencies appear in the PeakVue® spectrum at their fundamental frequencies and harmonics. The peaks are non–synchronous. Gear defects appear as peaks at the gear’s shaft turning speed frequency and harmonics. The amplitudes in PeakVue® data may be very low.

PeakVue® technology passes the input signal through a band–pass or high–pass filter and samples with the peak detector. PeakVue technology allows numerous predefined maximum frequency values. PeakVue® waveform data is corrected so that all peaks in the data display on the positive side of the waveform.

Trending of the G’s Peak to Peak waveform value is the most important parameter to trend on a PeakVue measurement to determine fault severity.

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