Handbook of probabilistic models PDF
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Handbook of Probabilistic Models Edited by Pijush Samui Department of Civil Engineering, NIT Patna, Bihar, India Dieu Tien Bui Department of Business and IT, School of Business University of South-Eastern Norway(USN), Telemark, Norway Subrata Chakraborty Department of Civil Engineering, Indian Institute of Engineering Science and Technology, Howrah, India Ravinesh C. Deo University of Southern Queensland Springfield, QLD, Australia Butterworth-HeinemannisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2020ElsevierInc.Allrightsreserved. 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LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-816514-0 ForinformationonallButterworth-Heinemannpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionEditor:MatthewDeans EditorialProjectManager:JoshuaMearns ProductionProjectManager:KameshRamajogi CoverDesigner:MilesHitchen TypesetbyTNQTechnologies Dedicated to my grandfather and grandmother Contributors Farid Wajdi Akashah, Centre for Building, Construction and Tropical Architecture (BuCTA), Faculty of Built Environment, University of Malaya, Kuala Lumpur, Malaysia HassanZ.AlGarni,DepartmentofElectricalandElectronicEngineeringTechnology, JubailIndustrialCollege,JubailIndustrialCity,SaudiArabia Mumtaz Ali, School of Agricultural Computational and Environmental Sciences, University of Southern Queensland, Springfield, QLD, Australia; Deakin-SWU Joint Research Centre on Big Data, School of Information Technology, Deakin University,Burwood,VIC,Australia ArmandoA.Apan,SchoolofCivilEngineeringandSurveying,UniversityofSouthern Queensland, Toowoomba,QLD, Australia AnjaliAwasthi,ConcordiaUniversity,CIISE,Montreal,QC,Canada Rahim Azadnia, Department of Agricultural Machinery Engineering, University of Tehran,Tehran,Iran Hamoon Azizsoltani, Department of Computer Science, North Carolina State Uni- versity,Raleigh,NC,UnitedStates MouradBelgasmia,DepartmentofCivilengineering,SetifUniversity,Setif,Algeria Omid Bozorg-Haddad, Department of Irrigation and Reclamation Engineering, Fac- ulty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources,UniversityofTehran,Tehran,Iran Tanmoy Chatterjee, College of Engineering, Swansea University, Bay Campus, Swansea, United Kingdom; Department of Civil Engineering, Indian Institute of TechnologyRoorkee,Roorkee,Uttarakhand, India Sourav Choudhary, Department of Civil Engineering, National Institute of Technol- ogyPatna,Patna,Bihar,India Rajib Chowdhury, Department of Civil Engineering, Indian Institute of Technology Roorkee,Roorkee,Uttarakhand, India Xuefeng Chu, Department of Civil and Environmental Engineering, North Dakota StateUniversity,Fargo,ND,UnitedStates KavinaS.Dayal,SchoolofAgriculturalComputationalandEnvironmentalSciences, UniversityofSouthernQueensland, Springfield,QLD,Australia Michael Delichatsios, Fire Safety Engineering Research and Technology Centre (FireSERT),UniversityofUlster,Newtownabbey,UnitedKingdom xix xx Contributors RavineshC.Deo,SchoolofAgriculturalComputationalandEnvironmentalSciences, UniversityofSouthernQueensland, Springfield,QLD,Australia S. Dey, Department of Mechanical Engineering, National Institute of Technology Silchar,Silchar,Assam,India NathanJ.Downs,SchoolofAgricultural,ComputationalandEnvironmentalSciences, UniversityofSouthernQueensland, Springfield,QLD,Australia Subhrajit Dutta, Assistant Professor, Department of Civil Engineering, National Institute of Technology Silchar, Silchar, Assam, India; National Institute of Tech- nologySilchar,Department ofCivilEngineering, Silchar,Assam,India AmirH.Gandomi,FacultyofEngineeringandInformationTechnology,Universityof TechnologySydney,Ultimo,NSW,Australia;SchoolofBusiness,StevensInstitute ofTechnology,Hoboken,NJ,UnitedStates J. Ramon Gaxiola-Camacho, Department of Civil Engineering, Autonomous Uni- versityofSinaloa,Culiacan, Sinaloa,Mexico Aboubaker Gherbi, Department of Civil engineering, Constantine University, Con- stantine,Algeria AchintyaHaldar,DepartmentofCivilandArchitecturalEngineeringandMechanics, UniversityofArizona,Tucson,AZ,UnitedStates Soheil Sadat Hosseini, Department of Electrical Engineering, Capitol Technology University, Laurel, MD, United States; Department of Electrical Engineering and ComputerScience,TheUniversityofToledo,Toledo,OH,UnitedStates PravinJagtap,DepartmentofCivilEngineering,IndianInstituteofTechnology(IIT) Delhi,NewDelhi,India Mohsin M. Jamali, College of Engineering, The University of Texas of the Permian Basin,Odessa,TX,UnitedStates Madan K. Jha, Agricultural and Food Engineering Department, Indian Institute of TechnologyKharagpur,Kharagpur,West Bengal,India ShahjahanKhan,SchoolofAgricultural,ComputationalandEnvironmentalSciences, Centre for Applied Climate Sciences, University of Southern Queensland, Too- woomba,QLD,Australia Anoop Kodakkal, Chair of Structural Analysis, Department of Civil, Geo and Envi- ronmentalEngineering,TechnischeUniversita¨tMu¨nchen(TUM),Munich,Germany R.R.Kumar,DepartmentofMechanicalEngineering,NationalInstituteofTechnology Silchar,Silchar,Assam,India Yuankai Li, University of Electronic Science and Technology of China, Chengdu, China Nehar Mandal, Department of Civil Engineering, National Institute of Technology Patna,Patna,Bihar,India Tek Maraseni, School of Agricultural, Computational and Environmental Sciences, UniversityofSouthernQueensland, Springfield,QLD,Australia Contributors xxi SamanMaroufpoor,Department ofIrrigationandReclamationEngineering,Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources, UniversityofTehran,Tehran,Iran Vasant Matsagar, Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi,NewDelhi,India Anke Meyer-Baese, Department of Scientific Computing, Florida State University, Tallahassee, FL,UnitedStates Behshad Mohebali, Department of Scientific Computing, Florida State University, Tallahassee, FL,UnitedStates Tanmoy Mukhopadhya, Department of Aerospace Engineering, Indian Institute of TechnologyKanpur,Kanpur,India Shahbaz Mushtaq, Centre for Applied Climate Sciences, University of Southern Queensland, Toowoomba,QLD, Australia S.Naskar,SchoolofEngineering,UniversityofAberdeen,Aberdeen,UnitedKingdom Thong Nguyen-Huy, School of Agricultural, Computational and Environmental Sci- ences, Centre for Applied Climate Sciences, University of Southern Queensland, Toowoomba,QLD,Australia WeiNing,SchoolofCivilEngineering, ChongqingUniversity,Chongqing,China Rachid Ouache, School of Engineering, Faculty of Applied Science, University of BritishColumbia,Okanagancampus,Kelowna,BC,Canada K.M.Pandey,DepartmentofMechanical Engineering,NationalInstituteofTechnol- ogySilchar,Silchar,Assam,India Thendiyath Roshni, Department of Civil Engineering, National Institute of Technol- ogyPatna,Patna,Bihar,India Zhang Runhong, School of Civil Engineering, Chongqing University, Chongqing, China Vikas KumarSharma, Institute of Infrastructute TechnologyResearch and Manage- ment(IITRAM),Department ofMathematics,Ahmedabad, Gujarat,India S. Sriramula, School of Engineering, University of Aberdeen, Aberdeen, United Kingdom Amirhessam Tahmassebi, Department of Scientific Computing, Florida State Uni- versity,Tallahassee, FL,UnitedStates Anthony Teck Chee Goh, School of Civil and Environmental Engineering, Nanyang TechnologicalUniversity,Singapore S. Mohsen Vazirizade, Department of Civil and Architectural Engineering and Mechanics, UniversityofArizona,Tucson,AZ,UnitedStates Francisco Javier Villegas-Mercado, Department of Civil and Architectural Engi- neering andMechanics,UniversityofArizona, Tucson,AZ,UnitedStates xxii Contributors Zhang Wengang, Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing, China; School of Civil Engi- neering, Chongqing University, Chongqing, China; National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas, Chongqing University,Chongqing,China LiYongqin,SchoolofCivilEngineering,ChongqingUniversity,Chongqing,China Jianping Zhang, Fire Safety Engineering Research and Technology Centre (Fire- SERT),UniversityofUlster,Newtownabbey,UnitedKingdom Chapter 1 Fundamentals of reliability analysis Achintya Haldar DepartmentofCivilandArchitecturalEngineeringandMechanics,UniversityofArizona,Tucson, AZ,UnitedStates 1. Introduction Thepresenceofuncertaintyineveryaspectofengineeringanalysisanddesign has been under consideration over a long period of time. In fact, a famous mathematician Pierre-Simon Laplace (1749e1827) wrote “. the principal means of ascertaining truth e induction, and analogy e are based on proba- bilities; so that the entire system of human knowledge is connected with the theory(of probability). ..It leavesno arbitrariness inthe choiceofopinions and sides to be taken; and by its use can always be determined the most advantageous choice. Thereby it supplements most happily the ignorance and weakness of the human mind.” (Laplace, 1951). Theaforementionedstatementsbyawell-knownscholarclearlyjustifythe need for this handbook. More recently, Freudenthal (1956), Ang and Tang (1975), Shinozuka (1983), and Haldar and Mahadevan (2000a) made similar comments justifying the needs for structural safety and reliability analyses. The related areas grew exponentially in the 1970s and 1980s. It appears that mostofthedesignguidelinesandcodeseitherhavebeenorareintheprocess of incorporating the risk-based design concept, at least in the US. This handbook is expected to be extremely valuable in moving in that direction. However, before moving forward, it is important to figure out what is the conceptofuncertainty,probability,reliability,stochasticity, etc.and howthey implicate the engineering analysis and design. Stochos is a Greek word for stochasticityoruncertainty.Ingeneral,mostobservablephenomenaofinterest to engineers produce multiple outcomes and cannot be predicted with certainty. Multiple outcomes may not have any pattern, and some outcomes may occur more frequently than others covering different regions of interest. Testing of identical specimens may not produce identical outcomes. The design wind velocity or rain fall at a site during the lifetime of a structure HandbookofProbabilisticModels.https://doi.org/10.1016/B978-0-12-816514-0.00001-1 Copyright©2020ElsevierInc.Allrightsreserved. 1 2 HandbookofProbabilisticModels cannotbepredictedwithcertainty.Wemayknowtheirupperandlowerlimits or bounds and the most likely value but not the design value for which a specific structure needs to be designed. This type of unpredictability is generallyrepresentedbyuncertaintyorrandomness.Complexityofaproblem may not have anything to dowith uncertainty. There is no doubt that landing onthemoonconsistsofnumerouscomplicatedandcomplexprocesses,butwe nevermissedthemoonwhenweattemptedtolandonit.Eventheoutcomeof a very simple task of tossing a coin cannot be predicted with certainty. Uncertainty is associated with most of the analysis and design of interest to engineers.Consideringtheunpredictabilityofmostofthedesignvariables,the basicchallengeistoassuresatisfactoryperformanceofengineeringsystemsin thepresenceofuncertainty.Thepresenceofuncertaintycannotbecompletely eliminated, but with reasonable efforts, its impact on the design can be appropriately managed. This observation clearly indicates that engineering systems cannot be designed “full-proof” or “risk-free.” There will always be some risk or probability of failure. For acceptable design, the amount of un- derlying risk needs to be minimized to an acceptable level or mitigated appropriately. Risk and reliability are complementary terms and need to be mathematically estimated using probability theory. Probability and statistics are not synonymous terms. Statistics is the mathematical quantification of uncertainty. Probability theory uses statistical information to estimate the likelihood of specific events. With this introduction, fundamentals of reliability analysis are briefly discussed in this introductory chapter. 2. Important steps in reliability evaluation Most engineering problems consist of multiple random variables (RVs). The first step is then the quantification of randomness in them, one variable at a time and jointly when possible. The uncertainty in an RV is generally described pictorially in terms of histogram and frequency diagrams or prob- ability density function (PDF) and analytically with the help of mean, vari- ance, standard deviation, coefficient of variation (COV), skewness, etc. They aresometimescollectivelydenotedasthestatisticsofanRV.FormultipleRVs, it is described as joint PDF, correlation coefficients, etc. Mean is the central tendency, variance and standard deviation indicate the dispersion from the mean, COV is the ratio of standard deviation and mean and represents the amount of uncertainty in a nondimensional way, and skewness represents thesymmetryinthedata,generallyexpressedintermsofskewnesscoefficient. For a known PDF, mean is the centroidal distance from the origin; it is also knownasthefirstmoment.VarianceisthemomentofinertiaofthePDFabout the mean; it is also known as the second moment. Skewness is the third moment of the PDF about the mean. For symmetric data, the skewness coefficient will be zero; more spread in the data above the mean will have positiveskewnesscoefficient,etc.Inthecontextofquantifyingrandomnessin
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