ASRAnetStructural Reliability & Risk Assessment4-8 July 2016Wuhan, ChinaLecture 17: Monte Carlo SimulationProfessor Purnendu K. DasB.E., M.E., PhD, CEng, CMarEng, FRINA, FIStructE, FIMarEST
Structural Reliability & Risk Assessment 4 – 8 July 2016 Wuhan, China Lecture 17: Monte Carlo Simulation Professor Purnendu K. Das B.E., M.E., PhD, CEng, CMarEng, FRINA, FIStructE, FIMarEST 1
CONTENTSMONTECARLOSIMULATION- GenerationofRandomNumbers-Generationofrandomnumberswithagiventypeofdistribution-Generationofrandomnumberswithastandardnormaldistribution-Generationofrandomnumberswithlog-normaldistribution-ErrorEstimationofMonteCarloSimulationOTHERSIMULATIONBASEDMETHODS-ImportanceSampling Method-SelectionofImportanceSamplingFunctionEXAMPLESCLOSINGREMARKS
CONTENTS • MONTE CARLO SIMULATION – Generation of Random Numbers – Generation of random numbers with a given type of distribution – Generation of random numbers with a standard normal distribution – Generation of random numbers with log-normal distribution – Error Estimation of Monte Carlo Simulation • OTHER SIMULATION BASED METHODS – Importance Sampling Method – Selection of Importance Sampling Function • EXAMPLES • CLOSING REMARKS 2
CONTENTSMONTECARLOSIMULATION-GenerationofRandomNumbers-Generationofrandomnumberswithagiventypeofdistribution- Generationofrandomnumberswithastandardnormal distribution-Generationofrandomnumberswithlog-normaldistributionErrorEstimationofMonteCarloSimulationOTHERSIMULATIONBASEDMETHODSImportanceSamplingMethod-Selectionof ImportanceSamplingFunctionEXAMPLESCLOSINGREMARKS3
CONTENTS • MONTE CARLO SIMULATION – Generation of Random Numbers – Generation of random numbers with a given type of distribution – Generation of random numbers with a standard normal distribution – Generation of random numbers with log-normal distribution – Error Estimation of Monte Carlo Simulation • OTHER SIMULATION BASED METHODS – Importance Sampling Method – Selection of Importance Sampling Function • EXAMPLES • CLOSING REMARKS 3
P = P(g(X)≤ 0)=J... fx(X)dXg(x)<0Where X = (X1,., Xi..., Xn) are random variablesInMonteCarlosimulationPf = P(g(X)≤0) ~ rN
g 0 Pf P g 0 . f x ( ) d X X X X Where X = (X1,., Xi., Xn) are random variables t f f N n P P g X 0 In Monte Carlo simulation 4
g(X)= R - LForexample, ifWerandomlygeneratenumbersforRandL,LetussaythenumbergeneratedareasfollowsRLg(X)2019>020.518.5>019.819.3>019.419.5<019.719.6>05
For example, if gX R L We randomly generate numbers for R and L, Let us say the number generated are as follows: R L g(X) 20 19 >0 20.5 18.5 >0 19.8 19.3 >0 19.4 19.5 <0 19.7 19.6 >0 5