ABOUT THE COURSE: The course introduces basic concepts of probability theory at the beginning, which is followed by the Level-2 reliability methods. The readers are then introduced to the intricacies of Monte-Carlo simulation and its advanced versions for variance reduction and subset simulation. The treatment of implicit limit states using RSM and recently developed SRSM techniques are explained separately with examples. With this knowledge of reliability analysis in hand, the course then aims to explain the applications of these methods for code calibrations and reliability analysis under multiple failure modes.INTENDED AUDIENCE: UG Final Year Students, PG Students, and Research Scholars.
Overview
Syllabus
Week 1: Theory of Probability-I: Probability Distributions (Discrete and Continuous), one-dimensional Random Variables (Discrete and Continuous) PDF & CDF.Week 2:Probability Theory-II: Functions of Random Variable, Algebra of Variance, Expectations, and moments.Week 3:Multi-dimensional Random Variables- Joint distributions, Conditional & Marginal PDF and PMF, Expectation Operator in Two dimensions, Covariance, and Correlation.Week 4:Reliability Levels: Level-2 Reliability Methods, Concept of Reliability Index, Cornell´s Reliability Index, Hasofer-Lind Reliability Index.Week 5:First Order Reliability Methods- Mean Value First Order Second Moment (MVFOSM) method, First Order Reliability Method (FORM), Rackwitz-Fiessler Algorithm.Week 6:Iso-probabilistic transformation of random variables: Morgenstern & NATAF Transformation, Rosenblatt Transformation: JPDF & JCDF. Application in FORM.Week 7:Introduction to Second Order Reliability Method (SORM): Breitung´s approximation, Tvedt´s Three Term approximation. Examples.Week 8:Simulation-Based Reliability Analysis- Monte-Carlo Simulation, Variance Reduction Technique, Importance Sampling method.Week 9:Metamodel-Based Reliability Analysis-I: Implicit Performance Function, Polynomial Response Surface Method (RSM).Week 10:Metamodel-Based Reliability Analysis-II: Moving Least Square Methods in metamodeling. Applications of MLS in surrogate modelling. Case Studies.Week 11:Code Calibration: Determination of partial safety factors, Optimal safety factors.Week 12:Case Studies: FEM Modelling for reliability analysis, Applications. Introduction to Stochastic FEM
Taught by
Prof. Arunasis Chakarborty
