CE 410/510 PROBABILITY IN CIVIL ENGINEERING
Instructor: Achintya Haldar
Office: 220E, CE Bldg.
Phone: 621-2142
Email:
OBJECTIVE OF THE COURSE
Outlines the extent of uncertainties under which civil engineering designs and decisions are made. Theory and application. Advanced topics in risk-based engineering design. System reliability concepts. Statistical decision theory and its application in civil engineering. Identifying and modeling non-deterministic problems in engineering in understanding many recently issued engineering codes.
TEXT (Preferred)
1. Haldar, A., and Mahadevan, S., Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, New York, 2000.
(Reference Book)
2. Haldar, A., and Mahadevan, S., Reliability Assessment Using Stochastic Finite Element Analysis, John Wiley & Sons, New York, 2000.
"... The principal means for ascertaining truth - induction and analogy - are based on probabilities; so that the entire system of human knowledge is connected with the theory (of probability) "
“It is seen in this essay that the theory of probabilities is at bottom only common sense reduced to calculus; it makes us appreciate with exactitude that which exact minds feel by a sort of instinct without being able ofttimes to give reason for it. It leaves no arbitrariness in the choice of opinions 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.”
Pierre Simon de Laplace
A Philosophical Essay on Probability, 1816
MEETING TIME: 12:30 - 1:45, TTH
MEETING PLACE: ECE 102
GRADING SYSTEMS
Homework 15%
2- One Hour Exams 45%
1- Final Exam 40%
_______
100%
FINAL EXAM: December 16, 2010 (Thursday), 11 to 1 p.m.
Office Hours: Open office hours
COURSE OUTLINE
1. Role of Probability in Engineering
2. Basic Probability Concepts - A Review
2.1 Events and Probability
2.2 Elements of set Theory
2.3 Mathematics of Probability
2.4 Useful Probability Distribution
2.5 Applications to Civil Engineering Problems
3. Analytical Models of Load and Resistance Parameters
3.1 Probability Distribution of Load and Resistance Parameters
3.2 Estimation of Parameters Considering Inherent Variability and Estimation Error
4. Randomness in Response Variables
4.1 Known Functional Relationship
4.2 Exact Solution
4.3 Partial and Approximate Solution
4.4 Multiple Random Variables with Unknown Relationships
5. Design Formats
5.1 Formats for Reliability-Based Design
5.2 Safety-Index Formats
6. Estimation of Risk of an Element
6.1 One Parameter Each in Load and Resistance Models
6.2 Multiple Parameters in Load and Resistance Models
6.3 Close form Solution
6.4 Approximate First-Order Second Moment Reliability Approach
6.5 Advanced Second-Moment Method
6.6 Applications in Civil Engineering Problems
7. Risk Evaluation
7.1 For a Component
7.2 For a System
8. Simulation Techniques
8.1 Monte Carlo Simulation Technique
8.2 Variance Reduction Techniques
8.3 Simulations for Correlated Random Variables
9. Special Topics
9.1 Stochastic Finite Element Method
9.2 Stochastic Optimization