Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering PDF
Preview Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering
Interdisciplinary Applied Mathematics 47 Christian Soize Uncertainty Quantifi cation An Accelerated Course with Advanced Applications in Computational Engineering Uncertainty Quantification Interdisciplinary Applied Mathematics Volume 47 Editors S.S.Antman,UniversityofMaryland,CollegePark,MD,USA [email protected] L.Greengard,NewYorkUniversity,NewYork,NY,USA [email protected] P.J.Holmes,PrincetonUniversity,Princeton,NJ,USA [email protected] Advisors L.Glass,McGillUniversity,Montreal,QB,Canada A.Goriely,UniversityofOxford,Oxford,UK R.Kohn,NewYorkUniversity,NewYork,USA P.S.Krishnaprasad,UniversityofMaryland,CollegePark,MD,USA J.D.Murray,UniversityofOxford,Oxford,UK C.Peskin,NewYorkUniversity,NewYork,USA S.S.Sastry,UniversityofCalifornia,Berkeley,CA,USA J.Sneyd,UniversityofAuckland,Auckland,NewZealand Moreinformationaboutthisseriesathttp://www.springer.com/series/1390 Christian Soize Uncertainty Quantification An Accelerated Course with Advanced Applications in Computational Engineering 123 ChristianSoize LaboratoireMode´lisationetSimulation Multi-Echelle(MSME) Universite´Paris-EstMarne-la-Valle´e (UPEM) Marne-la-Valle´e,France ISSN0939-6047 ISSN2196-9973 (electronic) InterdisciplinaryAppliedMathematics ISBN978-3-319-54338-3 ISBN978-3-319-54339-0 (eBook) DOI10.1007/978-3-319-54339-0 LibraryofCongressControlNumber:2017937717 Mathematics Subject Classification (2010): 15B52, 35Q62, 35Q74, 35R30, 35R60, 37N15, 47H40, 60G60,60H25,60J22,62B10,62C10,62F15 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Foreword Innumerical modeling and simulation,some degree of uncertainty isinevitable in the ability of the model to truly describe the physics of interest and/or in the data this model uses to assist in describing these physics. For this reason, and because numericalpredictionsareoftenthebasisofengineeringdecisions,uncertaintyquan- tification has been a subject of concern for many years. With the advent of multi- scaleandmultiphysicsmodeling,findingpracticalandyetrigorouswaystointerpret uncertaintyandcharacterizeitsimpactontheassessmentofprobableoutcomeshas becomeevermorechallenging.Thisbookcontributestopavingthewayformeeting thisobjectiveoneday. Thebookfocusesprimarilyonfundamentalnotionsinthestochasticmodelingof uncertaintiesandtheirquantificationincomputationalmodels.Mechanicalsystems are the privileged applications because of the additional expertise of the author in thisfield.Allofaleatory,epistemic,parametric,andnonparametricuncertaintiesare addressed. The book begins with a description of those fundamental mathematical tools ofprobabilityandstatisticsthataredirectlyusefulforuncertaintyquantification.It proceedswithawell-carriedoutdescriptionofsomebasicandafewmoreadvanced methodsforconstructingstochasticmodelsofuncertainties.Itpaysparticularatten- tiontotheproblemofcalibratingandidentifyingastochasticmodelofuncertainties when experimental data is available. For completeness, italsooverviews the main approachesthathavebeendevelopedforanalyzingthepropagationofuncertainties incomputationalmodels.Coveringallofthesetopicsinlessthan330pages,mak- ingtheminterestingtofaculty,students,researchers,andpractitioners,isadaunting challenge.Theauthorhasovercomethisdifficultybyskillfullyorganizingthecon- tentofthisbookandreferringtomathematicalproofsratherthanderivingthemin themiddleofhigh-leveldescriptions. I have been privileged to read and study the lecture notes on which this book is based. I have found them to be among the mostuseful ones for my understand- ing of the topic. Consequently, I invited the author to deliver in February 2015 at StanfordUniversityanacceleratedcourseonUncertaintyQuantificationinCompu- tational Mechanics based on these lecture notes. Given the success of this course, v vi Foreword I invited the author again in June 2016 to give a shorter version at the Aberdeen ProvingGroundsiteoftheArmyResearchLaboratory(ARL).Thecoursewaswell attendedbyscientistsandengineersfromARLrepresentingfivedifferentlaboratory divisionsandseveralgraduatestudents.Forallthesereasons,Iexpectthisbookto beausefulreferenceandasourceofinspiration. StanfordUniversity CharbelFarhat Stanford,CA,USA November23,2016 Preface Thisbookresultsfromacoursedevelopedbytheauthorandreflectsbothhisown andcollaborativeresearchregardingthedevelopmentandimplementationofuncer- taintyquantification(UQ)techniquesforlarge-scaleapplicationsoverthelasttwo decades. Theobjectivesofthisbookaretopresentfundamentalnotionsforthestochastic modelingofuncertaintiesandtheirquantificationincomputationalmodelsencoun- tered in computational sciences and engineering. The text covers basic methods andnoveladvancedtechniquestoquantifyuncertaintiesinlarge-scaleengineering and science models. It focuses on aleatory and epistemic uncertainties, parametric uncertainties (associated with the parameters of computational models), and non- parametric uncertainties (induced by modeling errors). The text covers mainly the basic methods and novel advanced methodologies for constructing the stochastic modeling of uncertainties. To this effect, it presents only the fundamental math- ematical tools of probability and statistics that are directly useful for uncertainty quantification and overviews the main approaches for studying the propagation of uncertainties in computational models. Important methods are also presented for performing robust analysis of computational models with respect to uncertainties, robustupdatingofsuchcomputationalmodels,robustoptimization,anddesignun- deruncertainties.Italsocarriesoutthecalibrationandidentificationofthestochas- tic model of uncertainties when experimental data is available. The methods are illustratedonadvancedapplicationsincomputationalengineering,suchasincom- putational structural dynamics and vibroacoustics of complex mechanical systems andinmicromechanicsandmultiscalemechanicsofheterogeneousmaterials. This book is intended to be a graduate-type textbook for graduate students, en- gineers, doctoral students, postdocs, researchers, assistant professors, professors, etc. For learning a difficult interdisciplinary domain, such as the UQ domain, the fundamentaldifficultyisnottheaccesstotheknowledgebutisrelatedtotheunder- standingoftheknowledgeorganization,tothelevelofexpertisethatisrequiredfor solving a complex problem, and to the use of methods that are scientifically vali- dated.Suchanexpertiseisobtainedbythinkingandnotbycarryingoutexercises. vii viii Preface Theaimoftheauthoristoproposeagraduate-typetextbookthatleadsthereaderto thinkandnottotrainhim/herwithexercises. Thewritingstylehasdeliberatelybeenchosenasshortanddirect,avoidingun- necessary mathematical details that may prevent access to a quick understanding of the concepts, ideas, and methods. Nevertheless, all the mathematics tools that arepresentedareabsolutelycorrectandscientificallyrigorous.Alltherequiredhy- potheses for using them are given and explained. Any approximation that is intro- duced is commented and the limitations are specified. The useful references are givenforareaderwhoisinterestedinfindingthemathematicaldetailsforproving some mathematical results. A short paragraph is written at the beginning of each chapter,summarizingtheobjectivesofthechapterandexplainingtheinterconnec- tionsbetweenthechapters.Thechaptershavealargenumberofsubsectionswhich will allow readers to clearly find and learn about specific topics that are useful to fulfillthebroaderchapterobjectives. Anobjectiveofthisbookistopresentconstructivemethodsforsolvingadvanced applications and not to re-explain in detail the classical statistical tools, which are alreadydevelopedinexcellenttextbooksinwhichthereareacademicexamplesthat allowfortrainingtheundergraduatestudents. Themainobjectiveiseffectivelytonotrecopyonemoretimetheclassicalstatis- ticalmethodsforsolvingacademicproblemsinsmalldimensionwithaverysmall numberofscalarrandomvariables.Thebookpresentsclassicalandadvancedmath- ematical tools from the probability theory and novel methodologies in computa- tional statistics that are necessary for solving the large-scale computational mod- els with uncertainty quantification in high dimension. The book presents a set of mathematical tools,their organization, and theirinterconnections, which allow for constructingefficientmethodologiesthatarerequiredforsolvingchallenginglarge- scale problems that are encountered in computational engineering. The book pro- posestothereadersaclearandidentifiedstrategyforsolvingcomplexproblems. The book includes several topics that are not covered in published research monographs or texts on UQ. This includes random matrix theory for uncertainty quantification,asignificantpartofthetheoryonstochasticdifferentialequations,the useofmaximumentropyandpolynomialchaostechniquestoconstructpriorproba- bilitydistributions,theidentificationofnon-Gaussiantensor-valuedrandomfieldsin highstochasticdimensionbysolvingstatisticalinverseproblemrelatedtostochastic boundaryvalueproblem,andtherobustanalysisfordesignandoptimization.Many of these topics appear in research papers, but this is the first time that all of these topicsarepresentedinaunifiedmanner.Anothernovelaspectofthisbookisthefact thatitaddressesuncertaintyquantificationforlarge-scaleengineeringapplications, which differentiates the methods proposed in this book from classical approaches. Thetheory,themethodologies,theirimplementation,andtheirexperimentalvalida- tions are illustrated by large-scale applications, including computational structural dynamicsandvibroacousticsandsolidmechanicsofcontinuummedia. Universite´ Paris-EstMarne-la-Valle´e ChristianSoize Marne-la-Valle´e,France November24,2016 Acknowledgments I thank Professor Charbel Farhat from Stanford University for inviting me to give thisacceleratedcoursethatIhaveespeciallywrittenforthisoccasionandgivingme theopportunitytowritesuchanacceleratedcourseonthebasisofresearchyearsthat Ihavecarriedoutintheareaofuncertaintyquantification.Thankstohisinvitation, IspentaveryexcitingperiodforteachingandresearchatStanfordUniversity. Ithankallthecolleagues,researchers,doctoralstudents,andpostdocswhohave workedwithmesinceyear2000onimportantsubjectsrelatedtouncertaintyquan- tificationandwhoaremycoauthorsinthepapersreferencedinthisbook: AllainJM,ArnouxA,ArnstM,AvalosJ,BatouA,Capiez-LernoutE,CapillonR, CataldoE,ChebliH,ChenC,Cle´mentA,ClouteauD,CottereauR,DesceliersC, Duchereau J, Duhamel D, Durand JF, Ezvan O, Farhat C, Fernandez C, Funfschilling C, Gagliardini L, Ghanem R, Gharbi H, Grimal Q, Guilleminot J, Heck JV, Kassem M, Le TT, Leissing T, Lestoille N, Macocco K, Mbaye L, Mignolet MP, Naili S, Nguyen MT, Nouy A, Ohayon R, Pellissetti M, Perrin G, Poloskov IE, Pradlwarter H, Rochinha FA, Ritto TG, Sakji S, Sampaio R, SchuellerGI,andTalmantM. IwouldliketoparticularlythankProfessorRogerGhanemfromtheUniversity ofSouthernCaliforniaandProfessorMarcMignoletfromArizonaStateUniversity, withwhichwehavealwayscarriedoutexcitingscientificcollaborations. Ithankmygreatfriend,ProfessorRogerOhayon,fromCNAMinFrancewho,in additionofourfructuousandintensivescientificcollaborations,hascarefullyreread themanuscriptofthisbook. ix
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