GAS-PATH DIAGNOSTICS AND PROGNOSTICS FOR AERO-ENGINES USING FUZZY LOGIC ...

274 Pages·2004·4.65 MB·English

CRANFIELD UNIVERSITY

LUCA MARINAI

GAS-PATH DIAGNOSTICS AND PROGNOSTICS
FOR AERO-ENGINES USING FUZZY LOGIC AND
TIME SERIES ANALYSIS

School of Engineering

PhD THESIS
CRANFIELD UNIVERSITY

SCHOOL OF ENGINEERING

PhD Thesis

July 2004

Luca Marinai

Gas-path Diagnostics and Prognostics for Aero-engines Using Fuzzy
Logic and Time Series Analysis

Supervisor: Professor Riti Singh

This thesis is submitted in partial fulfilment of the requirements for the degree of
Doctor of Philosophy

© Cranfield University 2004. All rights reserved. No part of this publication may
be reproduced without the written permission of the copyright holder
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ABSTRACT
Reducing the direct operating-costs is now crucial in order to ensure
competitive advantages for airlines and manufacturers, and so effective
advanced engine-condition monitoring methodologies are necessary. Hence
gas-path diagnostics and prognostics methods are reviewed and the
specifications for such effective tools deduced, together with their pertinent
future prospects.

First, the considerable value that a preliminary observability study adds to the
diagnostics process was recognised. A secure procedure has been devised: it
is capable of (i) the identification of the severity of correlations between any two
of the available measurements, as well as the correlations between any two of
the component changes, (ii) the identification of more complex correlations that
involve more than two changes in performance parameters, and (iii) the
quantification of the quality of the system observability through a pertinent
parameter. This enables comparisons among a significant number of
measurement set selections.
The core of the research is a novel gas-path diagnostics (GPD) method that
uses fuzzy logic in order to provide secure quantification of the gas-path
component faults. A fuzzy diagnostics system was set up for the Rolls-Royce
Trent 800 engine that relies on an extensive statement of fuzzy rules generated
using an engine model to achieve a quantitative solution through a non-linear
approach, which is competent to achieve (i) SFI (single fault isolation) in the
presence of noisy data, (ii) tuning over a known global deterioration level for all
the performance parameters (baseline) computed for the previous flight, (iii)
partial MFI (multiple fault isolation) with up to 2 degraded components (i.e. 4
performance parameters) considerably faulty at the same time, (iv) SFI while
isolating systematic errors in the measurements (biasses). A bias-tolerant
system was devised by means of the NOT logical operator and a new
formulation of the fuzzy rules that includes the location of the bias.
An innovative prognostics framework was devised, which uses ARIMA models
and regression models respectively for short and long term investigations, to
compute forecasts and the associated prediction intervals, which are aimed at
assisting the prognostics decision-making process. This is strictly related to the
diverse business intentions: in this study safety and economic related
applications are investigated. For example, the optimisation of the TBO (time
between overhauls) considering maintenance cost and additional fuel cost due
to the deterioration is studied and the potential cost savings for the operators
highlighted.

HMP 1.1 for performance analysis was developed: it is a health-monitoring and-
prognostics framework consisting of three modules that perform respectively
observability study, gas-path diagnostics and prognostics. The substantial
benefits that can be achieved with such a tool, relative to the enhanced
maintenance planning and improved mission scheduling, are discussed in the
thesis via applications to the Trent 800 engine.

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AKNOWLEDGEMENTS
I wish to express my gratitude and admiration to Professor Riti Singh, who firstly
gave me the opportunity to undertake this work, and then supported me through
the past three years providing me with his invaluable guidance, advice and all
the necessary means to achieve a successful outcome. He also encouraged
and enabled me to participate in a number of international conferences,
congresses and workshops which have been a fantastic experience.

Rolls Royce plc sponsored and supervised this research project within their
University Technology Centre (UTC) at Cranfield University. I would like to
thank Mr Phil Walsh, Mr Steve Brown, Mr John Martin and Dr Marco Zedda – of
the Performance Department of Rolls-Royce Civil Aerospace, Derby – as well
as Mr Barry Curnock, Mr Richard Dingley and Mr Paul Whatley – of the
Performance Department of Rolls-Royce Defence Aerospace, Bristol – for their
help, support and guidance during the development of the present work.

I am grateful to Professor Renzo Lazzeretti of the University of Pisa that
introduced me to Cranfield and guided me with his experience and wisdom.
Very special thanks also go to Professor Pericles Pilidis, Dr Ivan Li, Mr Richard
Hales and Miss Rachel Smith who gave me their support when I needed it, and
to all the rest of colleagues and friends of the UTC and of the Department of
Power, Propulsion and Aerospace Engineering. I wish to thank Professor
Douglas Probert, also editor of the Applied Energy Journal, for the valuable time
spent in helping to develop my technical writing skills and for his extensive
useful advice. Furthermore, I have been lucky while pursuing my doctorate in
that I have had the help of a number of MSc and Socrates students. So, thank
you very much to Amit, Giovanni, Jason, Priya, and Thierry.

Finally, I would like to take this opportunity to thank my parents and my sister
Luisa, for their extraordinary unconditional support and encouragement, all the
friends that made my stay at Cranfield enjoyable and memorable, and my
girlfriend Sandra that supported me through this experience.

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CONTENTS
Abstract..............................................................................................................3
Aknowledgements..............................................................................................4
Contents.............................................................................................................5
List of figures....................................................................................................10
List of tables.....................................................................................................14
Glossary of terms.............................................................................................16
Abbreviations....................................................................................................18
CHAPTER 1 - Intorduction: prospects for gas turbine health monitoring....21
1.1 Set the scene: novel opportunities in the gas turbine aftermarket.........21
1.1.1 Introduction.....................................................................................21
1.1.2 Market condition: need to reduce DOC..........................................22
1.1.2.1 Economic growth is the prime driver of demand......................23
1.1.3 Gas turbine industry’s point of view: the aftermarket......................25
1.1.3.1 Role of gas turbine aftermarket in the global civil air
transportation business.............................................................................25
1.1.3.2 Heightened competition and need for reducing DOC..............25
1.1.3.3 Opportunities in the aftermarket..............................................26
1.1.4 Strategic development: total care solutions....................................26
1.1.4.1 Airlines’ point of view...............................................................27
1.1.4.2 Engine manufacturers’ point of view........................................27
1.1.4.3 Competitive analysis: gas turbine manufacturers....................28
1.1.4.4 The answer and solution.........................................................28
1.1.5 Summary........................................................................................29
1.2 Engine-condition monitoring..................................................................30
1.2.1 Introduction.....................................................................................30
1.2.2 Maintenance methods....................................................................30
1.2.2.1 Run to failure...........................................................................30
1.2.2.2 Preventive maintenance..........................................................30
1.2.2.3 Condition-based maintenance.................................................31
1.2.3 Diagnostics and engine-health monitoring systems........................31
1.2.3.1 Concurrent techniques............................................................32
1.2.3.2 Benefits and concerns.............................................................32
1.2.4 Prognostics.....................................................................................33
1.2.5 Gas-path diagnostics and prognostics: an introduction..................33
1.2.6 Defence, marine and industrial applications...................................34
1.3 Research aim ........................................................................................36
1.3.1 Introduction.....................................................................................36
1.3.2 Research aim statement.................................................................36
1.3.3 Preliminary objectives of this research...........................................36
1.4 Subject matter covered: a guide to the thesis........................................37
CHAPTER 2 - Methodologies: state of the art............................................39
2.1 Problem definition: gas-path diagnostics and prognostics.....................39
2.1.1 Introduction.....................................................................................39
2.1.2 Gas turbine performance analysis: introduction .............................40
2.1.2.1 Performance modelling and analysis.......................................40
2.1.2.2 Complexity of the analysis problem.........................................41
2.1.2.3 Measurements uncertainty......................................................43
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2.1.3 Deterioration causes.......................................................................45
2.1.4 Evolution of the deterioration..........................................................47
2.1.5 Gradual and rapid deteriorations....................................................49
2.1.6 Summary: definition of the gas-path diagnostics and prognostics
problems.......................................................................................................51
2.2 Observability study: procedures ............................................................53
2.2.1 Introduction.....................................................................................53
2.2.2 Available sets of measurements.....................................................54
2.2.3 Test for correlation between measurements ..................................54
2.2.4 Test for correlation between performance parameter changes......55
2.2.5 Observability analysis.....................................................................57
2.2.6 Summary........................................................................................57
2.3 Gas-path diagnostics: a comparative review of procedures..................58
2.3.1 Introduction.....................................................................................58
2.3.2 Linear gas-path analysis with ICM inversion ..................................60
2.3.3 Non-linear gas-path analysis with ICM inversion............................61
2.3.4 Kalman filter based GPA: linear approach......................................62
2.3.5 Weighted least squares based GPA: linear approach....................65
2.3.6 Kalman filter based GPA: non-linear approach ..............................67
2.3.7 Non-linear GPD with genetic algorithms.........................................68
2.3.7.1 The objective function .............................................................69
2.3.7.2 A typical search-space............................................................70
2.3.7.3 Optimization technique: genetic algorithms.............................71
2.3.8 Artificial neural-network based GPD...............................................74
2.3.9 Bayesian belief networks based GPD............................................78
2.3.10 Expert systems...............................................................................80
2.3.11 Fuzzy-logic based GPD..................................................................80
2.3.12 Diagnosis with transient data..........................................................83
2.3.13 Summary and conclusions .............................................................84
2.4 Trending and prognostics......................................................................86
2.4.1 Introduction.....................................................................................86
2.4.2 Survey............................................................................................86
2.4.3 Prognostics strategies in engineering.............................................88
2.4.4 Summary and conclusions .............................................................89
2.5 Summary...............................................................................................90
CHAPTER 3 - Research objectives and strategy for the investigation........91
3.1 Introduction............................................................................................91
3.2 Gaps in contemporary methodologies: research objectives..................91
3.2.1 Contribution from current research.................................................93
3.2.2 Benefits from the current research.................................................95
3.3 Research strategy..................................................................................95
3.4 Summary and conclusions.....................................................................96
CHAPTER 4 - Gas-path diagnostics using Fuzzy Logic............................98
4.1 Introduction............................................................................................98
4.1.1 A guide through the chapter...........................................................98
4.2 Fuzzy logic systems...............................................................................99
4.2.1 Introduction.....................................................................................99
4.2.2 Fuzzy algebra: basic elements of a fuzzy system architecture.....100
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4.2.2.1 Fuzzy sets.............................................................................101
4.2.2.2 Logical operators...................................................................103
4.2.2.3 Fuzzy rules............................................................................104
4.2.3 Fuzzy inference systems..............................................................106
4.2.4 Fuzzy diagnostics system functionality via a graphical example..107
4.2.4.1 System set-up and fuzzy rules’ learning algorithm................108
4.2.4.2 Fuzzy inference.....................................................................113
4.2.4.3 Functionality considering the fuzzy inference diagram..........118
4.2.5 Algebraic form and conditional mean interpretation......................123
4.2.5.1 Fuzzy system as conditional mean........................................124
4.2.6 Comments on fuzzy rules for a diagnostics system......................128
4.2.6.1 Fuzzy systems and neural networks .....................................131
4.3 The Trent 800 engine and Instrumentation..........................................132
4.4 Observability study..............................................................................134
4.4.1 Introduction...................................................................................134
4.4.2 Exchange rate table and system matrix........................................135
4.4.3 Measurement correlations study...................................................136
4.4.4 Performance parameter correlations study...................................137
4.4.5 Current studies: enhanced observability study.............................139
4.4.5.1 A geometric interpretation.....................................................139
4.4.5.2 The mathematical formulation...............................................141
4.4.5.3 A possible application............................................................145
4.5 A fuzzy logic based diagnostics system for a three spool engine........147
4.5.1 Objectives and scope...................................................................147
4.5.2 The methodology and identification of the key parameters..........147
4.5.2.1 Fault levels combinations and if-then rules............................148
4.5.2.2 Input and output MFs ............................................................150
4.5.2.3 Fuzzy rules generation..........................................................152
4.5.2.4 Fuzzy inference: functional and system parameters.............153
4.5.3 Automated procedure...................................................................154
4.5.4 Sensitivity study: strategy.............................................................155
4.5.4.1 Reasons of the study and anticipation of the results.............155
4.5.4.2 Description of the case studies..............................................156
4.5.4.3 Three methods to estimate the system accuracy..................158
4.5.5 Sensitivity study: results...............................................................159
4.5.5.1 Choice of the functional parameters......................................159
4.5.5.2 Choice of the system parameters..........................................161
4.6 SFI accuracy and tuning......................................................................163
4.6.1 Approximation capability: accuracy..............................................163
4.6.1.1 Accuracy results: Method 2...................................................163
4.6.1.2 Accuracy results: Method 3...................................................164
4.6.1.3 Computational time required.................................................164
4.6.2 Diagnostics capability in the presence of sensor noise: accuracy 165
4.6.2.1 Remarks................................................................................169
4.6.3 Tuning capability to enhance the SFI role in GPD........................169
4.7 A fuzzy diagnostics system able of a partial MFI capability.................172
4.7.1 System Layout..............................................................................172
4.7.2 Partial MFI capability: results........................................................173
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4.7.2.1 Test cases.............................................................................173
4.7.2.2 Results: accuracy and computational time............................173
4.8 A bias-tolerant fuzzy diagnostics system.............................................175
4.8.1 The methodology: the use of the logical operator NOT to deal with
biasses .....................................................................................................175
4.8.1.1 The use of the NOT operator.................................................175
4.8.1.2 The use of the centre of maximum to devise a bias-tolerant
system and the role of the parameter A..................................................177
4.8.2 Results dealing with bias: case studies........................................179
4.8.2.1 System definition...................................................................179
4.8.2.2 Test cases.............................................................................179
4.8.2.3 Results: accuracy and computational time............................180
4.8.3 Remarks.......................................................................................181
4.9 Operating the diagnostics model through the GUI...............................182
4.10 Discussion and summary of the results...............................................183
4.10.1 Introduction...................................................................................183
4.10.2 Analysis of the results...................................................................183
4.11 Recommendations for future studies...................................................189
CHAPTER 5 - Gas-path prognostics using time-series analysis...............191
5.1 Introduction..........................................................................................191
5.1.1 A guide through the chapter.........................................................191
5.2 Prognostics and forecasting ................................................................192
5.2.1 Introduction...................................................................................193
5.2.2 Definition of the forecasting problem............................................195
5.2.3 Forecasting with time series analysis...........................................196
5.2.3.1 Quantitative forecasting methodologies: choice of the right
approach ..............................................................................................197
5.3 Short-term forecasting procedure: ARIMA...........................................199
5.3.1 Introduction...................................................................................199
5.3.2 ARIMA: theory..............................................................................200
5.3.2.1 Auto-regressive integrated moving average model...............201
5.3.2.2 Auto-correlation plot..............................................................202
5.3.2.3 Partial auto-correlation plot....................................................203
5.3.3 Estimating the parameters of an ARIMA model............................204
5.3.4 Diagnostic check..........................................................................204
5.3.5 Forecasting with ARIMA models...................................................205
5.3.5.1 Psi (Ψ) weights......................................................................205
5.3.5.2 Forecasting with the Ψ weights.............................................205
5.3.6 ARIMA model suitability................................................................206
5.3.7 Case study: TGT margin before returning to the maintenance facility
.....................................................................................................207
5.3.7.1 Performance rejections .........................................................208
5.3.7.2 Forecasting TGT changes.....................................................208
5.3.8 Case study: shaft speed in-flight data...........................................213
5.3.9 Summary......................................................................................215
5.4 Long-term forecasting procedure: regression......................................216
5.4.1 Introduction...................................................................................216
5.4.2 Deterioration modelling.................................................................216
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5.4.3 Smoothing pre-processor.............................................................219
5.4.3.1 Functionality of the smoothing pre-processor........................220
5.4.4 Trending algorithm........................................................................221
5.4.4.1 Linear model..........................................................................222
5.4.4.2 Non-linear models.................................................................223
5.4.4.3 Model selection.....................................................................225
5.4.5 Forecasts and prediction intervals................................................226
5.4.5.1 Prediction intervals: linear model...........................................227
5.4.5.2 Prediction intervals: non-linear models..................................228
5.4.6 Prediction procedure applications: functionality demonstration....230
5.4.6.1 Functionality of the prediction procedure...............................231
5.4.7 Case studies: maintenance versus operating costs......................235
5.4.7.1 Scenario 1: optimal TBO prognosis.......................................236
5.4.7.2 Scenario 2: optimal TTFO and TBO prognosis......................241
5.4.8 Summary......................................................................................243
5.5 Discussion and summary of the results...............................................244
5.5.1 Introduction...................................................................................244
5.5.2 Analysis of the results...................................................................244
5.6 Recommendations for future studies...................................................247
CHAPTER 6 - Conclusions & recommendations ......................................249
6.1 Introduction..........................................................................................249
6.2 New role for the gas turbine aftermarket..............................................250
6.3 Technical requirements drawn from the literature study......................250
6.4 Importance of the observability study..................................................251
6.5 Appropriateness of fuzzy-logic in gas-path diagnostics.......................252
6.6 Suitability of time-series analysis in gas-path prognostics...................254
6.7 Summary of contributions from this study............................................255
6.8 Summary of recommendations for future studies................................256
References.....................................................................................................257
Appendix A – The Trent 800...........................................................................264
Appendix B – Engine modelling......................................................................265
Appendix C – The software: Health Monitoring and Prognostics (HMP)........266

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LIST OF FIGURES
Figure 1: World GDP growth : deep recession and strong recovery (Airbus,
2002).........................................................................................................23
Figure 2: Air travel has grown more than six-fold during the past 30 years
(Boeing, 2003)...........................................................................................23
Figure 3: Growth in air travel is strongly correlated with the growth in GDP
(Airbus, 2002)............................................................................................24
Figure 4: Predicted air-world traffic growth (Airbus, 2002) ...............................24
Figure 5: Airline business breakdown (Singh, 2001)........................................25
Figure 6: Typical costs as fraction of a civil aircraft’s DOC (Rupp, 2002).........26
Figure 7: The market for power systems (Singh, 2001)....................................35
Figure 8: Typical gas turbine design procedure - Synthesis and Analysis
processes..................................................................................................40
Figure 9: Performance Analysis (Urban,1969).................................................41
Figure 10: The analysis process.......................................................................42
Figure 11: Calculation of measurement of deltas.............................................43
Figure 12: Measurement error..........................................................................43
Figure 13: Measurement Bias and Precision error...........................................44
Figure 14: Engine deterioration schematic (Wulf, 1980)...................................48
Figure 15: RB211 deterioration (Crosby, 1986)................................................48
Figure 16: Gradual vs. Rapid deterioration.......................................................50
Figure 17: Gas-Path Health Monitoring System...............................................51
Figure 18: Return on investment of an engine monitoring system....................53
Figure 19: System Matrix .................................................................................56
Figure 20: Simplified illustration of linear and non-linear GPA (Escher, 1995).61
Figure 21: Three types of estimation problems (estimation desired at time t)..62
Figure 22: Block diagram typically depicting system, measurement and
estimator...................................................................................................62
Figure 23: Non-Linear Engine Fault Diagnostic Model (Li, 2002).....................67
Figure 24: The diagnostics strategy (Zedda, 1999)..........................................69
Figure 25: A typical search-space (Zedda, 1999a)...........................................71
Figure 26: Single generation of GA reproduction cycle....................................72
Figure 27: A typical Multilayer Perceptron........................................................74
Figure 28: Modular ANN system for fault diagnostics (Zedda & Singh, 1998)..76
Figure 29: Structure of a PNN..........................................................................77
Figure 30: Auto Associative Network................................................................78
Figure 31: Typical BBN layout (Kadamb, 2003)...............................................79
Figure 32: Typical measurement deviation during transients...........................84
Figure 33: Hierarchy of prognostic approaches................................................88
Figure 34: Main window of HMP 1.1 for performance analysis, image courtesy
of Rolls-Royce...........................................................................................94
Figure 35: Fuzzy algebra and fuzzy logic inference.......................................101
Figure 36: Standard Set.................................................................................101
Figure 37: Diagram of a Standard Set............................................................101
Figure 38: Diagram of a Fuzzy Set.................................................................102
Figure 39: Diagram of two overlapping Fuzzy Sets........................................102
Figure 40 : standard logical operations ..........................................................103
Figure 41: Two-valued and multi-valued logic................................................104
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