Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach

217 Pages·2015·5.56 MB·English

by  Jerome Morio

Estimation of Rare Event Probabilities
in Complex Aerospace and Other Systems
A Practical Approach
Relatedtitle
RareEventSimulationUsingMonteCarloMethods
(ISBN978-0-47077-269-0)
Woodhead Publishing in Mechanical
Engineering: Number 720
Estimation of Rare Event
Probabilities in Complex
Aerospace and Other
Systems
A Practical Approach
Jérôme Morio and Mathieu Balesdent
AMSTERDAM(cid:129)BOSTON(cid:129)CAMBRIDGE (cid:129)HEIDELBERG
LONDON (cid:129)NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO
SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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To mywifeAnne,J.M.
To myfather,M.B.
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Contents
Preface xi
Foreword xiii
Biographyoftheexternalcontributorstothisbook xv
Abbreviations xvii
1 Introductiontorareeventprobabilityestimation 1
J.Morio,M.Balesdent
1.1 Thebookpurposes 1
1.2 Whataretheeventsofinterestconsideredinthisbook? 1
1.3 Thebookorganization 2
Reference 2
Part One Essentialbackground inmathematicsand system
analysis 3
2 Basicsofprobabilityandstatistics 5
J.Morio,M.Balesdent
2.1 Probabilitytheoryoperators 5
2.2 Modelingandsamplegenerationofrandomvariablepdfs 15
2.3 Convergencetheoremsandgeneralstatisticalmethods 24
References 31
3 Theformalismofrareeventprobabilityestimation
incomplexsystems 33
J.Morio,M.Balesdent
3.1 Input–outputsystem 33
3.2 Time-variantsystem 34
3.3 Characterizationofaprobabilityestimation 36
References 37
Part Two Practicaloverviewofthe mainrareevent
estimationtechniques 39
4 Introduction 41
M.Balesdent,J.Morio
4.1 Categoriesofestimationmethods 41
viii Contents
4.2 Generalnotations 41
4.3 Descriptionofthetoycases 42
References 44
5 Simulationtechniques 45
M.Balesdent,J.Morio,C.Vergé,R.Pastel
5.1 CrudeMonteCarlo 45
5.2 Simplevariancereductiontechniques 48
5.3 Importancesampling 53
5.4 Adaptivesplittingtechnique 68
References 73
6 Statisticaltechniques 77
J.Morio,D.Jacquemart,M.Balesdent
6.1 Extremevaluetheory 77
6.2 Largedeviationtheory 82
References 84
7 Reliabilitybasedapproaches 87
J.Morio,M.Balesdent
7.1 First-orderandsecond-orderreliabilitymethods 87
7.2 Linesampling 91
7.3 Directionalsampling 94
7.4 Stratifiedsampling 98
7.5 Geometricalmethods 106
References 106
8 Methodsforhigh-dimensionalandcomputationallyintensivemodels 109
M.Balesdent,L.Brevault,S.Lacaze,S.Missoum,J.Morio
8.1 Sensitivityanalysis 109
8.2 Surrogatemodelsforrareeventestimation 117
References 132
9 Specialdevelopmentsfortime-variantsystems 137
D.Jacquemart,J.Morio,F.LeGland,M.Balesdent
9.1 Generalnotations 137
9.2 Toycase 137
9.3 CrudeMonteCarlo 138
9.4 Importancesampling 140
9.5 Importancesplitting 143
9.6 Weightedimportanceresampling 147
9.7 Extremevaluetheory 150
References 152
Contents ix
Part Three Benchmark ofthemethodstoaerospace
problems 155
10 Estimationoflaunchvehiclestagefalloutzone 157
L.Brevault,M.Balesdent,J.Morio
10.1 Principle 157
10.2 Simulationdescription 157
10.3 Analysisoftheinputspace 159
10.4 Estimationresults 159
10.5 Conclusion 167
11 Estimationofcollisionprobabilitybetweenspacedebrisandsatellites 169
J.Morio,J.C.DoladoPérez,C.Vergé,R.Pastel,M.Balesdent
11.1 Principle 169
11.2 Simulationdescription 169
11.3 Analysisoftheinputspace 171
11.4 Estimationresults 171
11.5 Conclusion 175
References 175
12 Analysisofextremeaircraftwakevortexcirculations 177
J.Morio,I.DeVisscher,M.Duponcheel,G.Winckelmans,D.Jacquemart,
M.Balesdent
12.1 Principle 177
12.2 Simulationdescription 177
12.3 Estimationresults 179
12.4 Conclusion 180
References 181
13 Estimationofconflictprobabilitybetweenaircraft 183
J.Morio,D.Jacquemart,M.Balesdent
13.1 Principle 183
13.2 Simulationdescription 185
13.3 Estimationresults 185
13.4 Conclusion 187
References 188
Part Four Practicalguidelinesofrareeventprobability
estimation 189
14 Synthesisofrareeventprobabilityestimationmethodsfor
input–outputsystems 191
J.Morio,M.Balesdent
14.1 Synthesis 191
14.2 Someremarksforasuccessfulpracticalrareeventprobability
estimation 192