Time Series Analysis Methods and Applications for Flight Data

244 Pages·2017·8.776 MB·English

by  Jianye Zhang, Peng Zhang (auth.)

Jianye Zhang · Peng Zhang
Time Series
Analysis
Methods and
Applications for
Flight Data
Time Series Analysis Methods and Applications
for Flight Data
Jianye Zhang Peng Zhang
(cid:129)
Time Series Analysis
Methods and Applications
for Flight Data
123
Jianye Zhang PengZhang
AirForce EngineeringUniversity AirForce EngineeringUniversity
Xi’an,Shaanxi Xi’an,Shaanxi
China China
ISBN978-3-662-53428-1 ISBN978-3-662-53430-4 (eBook)
DOI 10.1007/978-3-662-53430-4
TranslatedfromChinese
JointlypublishedwithNationalDefenseIndustryPress,Beijing,China
LibraryofCongressControlNumber:2016951706
©NationalDefenseIndustryPressandSpringer-VerlagBerlinHeidelberg2017
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Preface
Flight data automatically recorded and saved by FDRS in aircraft flight and
maintenance is a typical type of time series. The flight data of this type is a
recording of the operation states of the aircraft and its subsystems, as well as the
change trends of aircraft performance. More importantly, the accumulation of the
data along with time will produce massive data that can be used as a source of
authenticonboardevidenceofaircraftperformanceandcondition.Understandably,
itcanalsobeusedasapredicatorofoperationconditionofaircraftsystemsforthe
early warning of a possible malfunction. Therefore, effective use of the flight data,
anareathathasrecentlyattractedmuchresearcheffort,providesareliablebasisfor
on-conditionmaintenance,qualitycontrol,flightsafetyassessment,andairaccident
investigation as well.
While the development of science and technology benefits the world in the
information age, there is also an increasing conflict between data redundancy and
lack of knowledge. Information mining out of massive data on the one hand, and
transformation of the mined information into applicable knowledge on the other,
poses a challenge to the research and application offlight data. As a result of this,
researcheffortshavebeenmadetoanswertothechallenge,anddataminingisone
of them. As part of the effort to explore the theory and practice of data mining in
flightdataanalysis,andonthebasisoftheviewofflightdataastypicaltimeseries,
thepresentstudyprovidesadetailedandsystematicaccountoftheaimofflightdata
analysis,aswellasitsproceduresandimplementationtechnologies.Integratinginit
the latest development in control theory, test technology, and information pro-
cessing,thepresentstudyisalsoasummaryofthecontributionoftheresearchteam
to the study and application offlight data in the past 10 years.
The present volume is made up of six chapters. Chapter 1 is an introduction
of the research background, recalling and summarizing the basic notions, devel-
opments, and military application of the study offlight data. Chapter 2 deals with
flight data preprocessing, providing a theoretical basis, as well as a reliable data
source, for the discussion and practice of intelligent data mining in the following
chapters.Chapter3isanintroductionofARMAmodelfortimeseriesanalysis,and
its application and technological realization. In Chap. 4, methods of similarity
v
vi Preface
search of time series are proposed together with a theoretical account of the
methods. Chapter 5 focuses on elaborating flight-data-based second development
andadvancedapplicationforthepurposeofconditionmonitoring,failurediagnosis,
andtrendpredictionofaircraftanditssubsystemsbymeansofvariousdatamining
methods. Chapter 6 introduces system design and application of intelligent flight
data mining.
Many people have contributed to the completion of this book; among them are
Profs.LiXue-renandNiShi-hongfromAirForceEngineeringUniversity(AFEU),
and Prof. Pan Quan from Northwestern Polytechnical University (NWPU). We
gratefully acknowledge their help and guidance. It should also be acknowledged
that Liang Jian-hai, in his a postdoctoral research at NWPU, has contributed to
search and prediction algorithms. Our thanks also go to Song Ji-xue, Liu Bo-ning,
Wang Zhan-lei, postgraduates at AFEU, who have helped with the writing and
proofreading of some of the draft. Last but not least, we are grateful to all the
authors who have been consulted and quoted in the process of writing.
The authors hold themselves to be responsible for all the possible errors in the
volume, and welcome suggestions for its improvement.
ThebookhasbeenajointeffortofsixtranslatorswhoareallEnglishteachersat
AFEU. They are Zhao Donglin (Chap. 4), Wu Subin (Chap. 1 and 2), Zhang Jing
(Chap.5),WangNingwu(Chap.5),JiangFei(Chap.3),andJiangXuehong(Chap.6).
The completion of the English version is also a result of constant consultation and
discussion with the authors for appropriate comprehension and re-rendering of the
original text. The whole translation has been reviewed and revised by the authors,
ZhaoDonglinandWuSubin.
Xi’an, China Jianye Zhang
August, 2016 Peng Zhang
Contents
1 Introduction.... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Flight Data Recorder System .... .... .... .... .... ..... .... 1
1.1.1 Overview .... ..... .... .... .... .... .... ..... .... 1
1.1.2 Developments. ..... .... .... .... .... .... ..... .... 2
1.1.3 Military Applications .... .... .... .... .... ..... .... 10
1.2 Application Research for Flight Data.. .... .... .... ..... .... 11
1.2.1 Basic Concepts ..... .... .... .... .... .... ..... .... 11
1.2.2 Research Status..... .... .... .... .... .... ..... .... 12
1.3 Research Domain and Main Contents.. .... .... .... ..... .... 16
2 Preprocessing of Flight Data ... .... .... .... .... .... ..... .... 19
2.1 Support Degree-Based Amnesic Fusion Filtering Method
for Flight Data .. .... ..... .... .... .... .... .... ..... .... 19
2.1.1 Unified Error Model of Flight Data.. .... .... ..... .... 19
2.1.2 Support Degree-Based Amnesic Fusion Filtering
Algorithm .... ..... .... .... .... .... .... ..... .... 21
2.1.3 Application and Conclusion ... .... .... .... ..... .... 25
2.2 Missing Flight Data Filling Method Based on Comprehensive
Weighting Optimization .... .... .... .... .... .... ..... .... 30
2.2.1 Modified Neural Network Model Based on Mixed
Algorithm .... ..... .... .... .... .... .... ..... .... 30
2.2.2 Polynomial Fitting Model Based on Least Square
Method.. .... ..... .... .... .... .... .... ..... .... 31
2.2.3 Comprehensive Weighting Method to Fill the Missing
Values... .... ..... .... .... .... .... .... ..... .... 33
2.2.4 Simulated Analysis and Conclusion . .... .... ..... .... 34
vii
viii Contents
2.3 Flight Data Extension Method Based on Virtual Sensor
Technologies ... .... ..... .... .... .... .... .... ..... .... 35
2.3.1 Overview of Virtual Sensor Technologies. .... ..... .... 35
2.3.2 Virtual Flight Data Extension Based on Mathematical
Model... .... ..... .... .... .... .... .... ..... .... 36
2.3.3 Virtual Flight Data Extension Based on BP Network. .... 37
2.4 Self-expanding Genetic Algorithm for Feature Selection
in Monitoring Flight Data Capacity ... .... .... .... ..... .... 41
2.4.1 Feature Selection and Genetic Algorithm . .... ..... .... 42
2.4.2 Self-expanding Genetic Algorithm .. .... .... ..... .... 44
2.4.3 Case Verification and Assessment... .... .... ..... .... 47
2.5 Chaotic Property Analysis of Flight Data... .... .... ..... .... 49
2.5.1 Mathematical Description of Phase Space
Reconstruction of the Chaotic Series. .... .... ..... .... 50
2.5.2 Analysis and Verification of Chaotic Property . ..... .... 56
3 Typical Time Series Analysis of Flight Data
Based on ARMA Model .. ..... .... .... .... .... .... ..... .... 65
3.1 Theory of ARMA Model ... .... .... .... .... .... ..... .... 65
3.1.1 Mathematical Model. .... .... .... .... .... ..... .... 66
3.1.2 Modeling Process ... .... .... .... .... .... ..... .... 67
3.1.3 Estimation of Model Parameters.... .... .... ..... .... 70
3.1.4 Model Applicability Test.. .... .... .... .... ..... .... 73
3.1.5 Optimum Prediction . .... .... .... .... .... ..... .... 74
3.2 Trend of Parameter Monitoring Method Based on AR Model .... 75
3.2.1 Description for Steady State of Aircraft .. .... ..... .... 76
3.2.2 Extraction of Monitoring Parameters
Based on Rule Reasoning Machine.. .... .... ..... .... 76
3.2.3 Monitoring Method of Mean-Value and Range
Based on AR Model. .... .... .... .... .... ..... .... 80
3.2.4 Case Study and Effect Assessment .. .... .... ..... .... 81
4 Similarity Search for Flight Data.... .... .... .... .... ..... .... 87
4.1 The Method of Similarity Analysis of Time Series.... ..... .... 87
4.1.1 Overview .... ..... .... .... .... .... .... ..... .... 88
4.1.2 Time Series Dimension Reduction .. .... .... ..... .... 89
4.1.3 Similarity Measurement of Time Series .. .... ..... .... 100
4.2 Similarity Search Method in Time Series Based on Slope
Distance ... .... .... ..... .... .... .... .... .... ..... .... 109
4.2.1 Slope Set Representation of Time Series.. .... ..... .... 109
4.2.2 Slope Distance Measurement for Time Series.. ..... .... 110
4.2.3 Verification on Clustering of Flight Data
Based on Slope Distance.. .... .... .... .... ..... .... 111
Contents ix
4.3 Similarity Search Method in Time Series Based on Included
Angle Distance.. .... ..... .... .... .... .... .... ..... .... 114
4.3.1 Representation of Included Angle Set for Time Series .... 114
4.3.2 Included Angle Distance Measurement for Time Series ... 116
4.3.3 Verification on Clustering of Time Series
Based on Included Angle Distance.. .... .... ..... .... 118
4.4 Similarity Search Method in Time Series Based on Curvature
Distance ... .... .... ..... .... .... .... .... .... ..... .... 121
4.4.1 Data Preprocessing .. .... .... .... .... .... ..... .... 121
4.4.2 Representation of Curvature Set for Time Series..... .... 123
4.4.3 Curvature Distance Measurement for Time Series.... .... 125
4.4.4 Verification on Clustering of Flight Data
Based on Curvature.. .... .... .... .... .... ..... .... 127
4.5 Multivariable Flight Data Similarity Search Method Including
Changing Step to Set Data in Different Bins .... .... ..... .... 132
4.5.1 Piecewise Linear Representation for Time Series .... .... 132
4.5.2 Indexing Tag Based on Changing Step to Set Data
in Different Bins.... .... .... .... .... .... ..... .... 133
4.5.3 Similarity Search Method Including Changing Step
to Set Data in Different Bins... .... .... .... ..... .... 135
4.5.4 Verification on Clustering of Multivariable Flight Data
Based on Similarity Search Method Including
Changing Step to Set Data in Different Bins... ..... .... 136
4.6 Multivariable Flight Data Similarity Search Method
Based on QR decomposition of Correlation Coefficient Matrix ... 142
4.6.1 RepresentationofMatrixandPlotforMultivariableTime
Series ... .... ..... .... .... .... .... .... ..... .... 142
4.6.2 Correlative Representation of Matrix for Multivariable
Time Series... ..... .... .... .... .... .... ..... .... 143
4.6.3 QR Distance Measurement for Multivariable
Time Series... ..... .... .... .... .... .... ..... .... 144
4.6.4 Verification on Clustering of Multivariable Flight Data
Based on QR Distance ... .... .... .... .... ..... .... 147
5 Condition Monitoring and Trend Prediction
Based on Flight Data. .... ..... .... .... .... .... .... ..... .... 153
5.1 Clustering Methods Based on Flexible-Size Grid for Airplane
Equipment . .... .... ..... .... .... .... .... .... ..... .... 153
5.1.1 Clustering Methods of Multivariate Data . .... ..... .... 154
5.1.2 Clustering Method Based on Density Function. ..... .... 155
5.1.3 Shrinking Clustering Method Based on Flexible-Size
Grid .... .... ..... .... .... .... .... .... ..... .... 157
5.1.4 Monitoring Examples of Flight Equipment Status
Shrinking Clustering. .... .... .... .... .... ..... .... 165
x Contents
5.2 Mutability Fault Diagnosis Arithmetic
Based on Expert System.... .... .... .... .... .... ..... .... 170
5.2.1 Theory of Expert System . .... .... .... .... ..... .... 171
5.2.2 Main Functions of the Aircraft Fault Diagnosing Expert
System .. .... ..... .... .... .... .... .... ..... .... 175
5.2.3 Implementation and Evaluation. .... .... .... ..... .... 177
5.3 GradualFaultDiagnosisArithmeticBasedonDynamicPrinciple
Component Analysis.. ..... .... .... .... .... .... ..... .... 179
5.3.1 Overview of Principle Component Analysis ... ..... .... 179
5.3.2 Dynamic Principle Component Analysis Method .... .... 181
5.3.3 Fault Diagnosis Arithmetic Based on Dynamic Principle
Component Analysis. .... .... .... .... .... ..... .... 182
5.3.4 Simulation Evaluation of Fault Diagnosis. .... ..... .... 184
5.4 Engine Performance Parameter Prediction
Based on WLS-SVM . ..... .... .... .... .... .... ..... .... 187
5.4.1 Basic Theory of SVM.... .... .... .... .... ..... .... 187
5.4.2 The Weighted Least Square Support Vector Machine
Arithmetic (WLS-SVM) .. .... .... .... .... ..... .... 192
5.4.3 WLS-SVM Parametric Prediction Model . .... ..... .... 195
5.4.4 Application Example. .... .... .... .... .... ..... .... 198
5.5 Engine Performance Data Prediction on the Basis of Chaotic
Sequence .. .... .... ..... .... .... .... .... .... ..... .... 206
5.5.1 Chaos and Chaotic Sequence .. .... .... .... ..... .... 207
5.5.2 Prediction Model.... .... .... .... .... .... ..... .... 208
5.5.3 Application of the Model . .... .... .... .... ..... .... 209
6 Design and Implementation of Flight Data Mining System .... .... 215
6.1 Data Mining System.. ..... .... .... .... .... .... ..... .... 215
6.2 Flight Data Warehouse Modeling. .... .... .... .... ..... .... 217
6.2.1 The Special Characteristics of Flight Data .... ..... .... 217
6.2.2 Mining Goals of Flight Data... .... .... .... ..... .... 218
6.2.3 Flight Data Warehouse Modeling ... .... .... ..... .... 219
6.3 Design and Development of Prototype System... .... ..... .... 220
6.3.1 General Design..... .... .... .... .... .... ..... .... 220
6.3.2 Data Flow.... ..... .... .... .... .... .... ..... .... 222
6.3.3 Working Process.... .... .... .... .... .... ..... .... 222
6.3.4 Main Functions..... .... .... .... .... .... ..... .... 224
6.4 Summary .. .... .... ..... .... .... .... .... .... ..... .... 230
References.... .... .... .... ..... .... .... .... .... .... ..... .... 233