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{"category":"course","subjects":["Risk Assessment and Management"],"number":"TC304-105","instructors":["Dr. Jie Zhang "]}
Probability Analysis in Civil Engineering
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Probability Analysis in Civil Engineering
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Module 1: Analytical models for modeling uncertainties
Chapter 1: Basics of probability theory
1.1 Set theory
1.2 Operating rules
1.3 Conditional probability
1.4 Total probability theorem
Chapter 1 Homework
Chapter 2: Random Variables (I)
2.1 Descriptors of discrete random variables
2.2 Descriptors of continuous random variables
2.3 Normal distribution
2.4 Lognormal distribution
2.5 Correlation coefficient
2.6Multivariate normal distribution
Chapter 2 Homework
Chapter 3: Random Variables (II)
3.1 Bernoulli sequence and return period
3.2 Determination of design value corresponding to a certain return period
3.3 Poisson process
Chapter 3 Homework
Module 2: Reliability methods
Chapter 4 Mean first order reliability method and pointe estimate method
4.1 Linear function of uncertain variables
4.2 Taylor series expansion
4.3 Point estimate method
Chapter 4 Homework
Chapter 5 Advanced First Order Reliability Method (AFORM)
5.1 Limitations of mean first order reliability method
5.2 Geometry interpretation of the reliability index
5.3 Solve reliability index in the u space
5.4 Solve reliability index in the n space
Chapter 5 Homework
Chapter 6 Response Surface Method
6.1 Regression analysis
6.2 Response surface method
6.3 Iterative RSM
Chapter 6 Homework
Chapter 7 Monte Carlo Simulation
7.1 Generating samples for random variables
7.2 Generating samples for random vectors
7.3 Integration with Monte Carlo simulation
7.4 Failure probability estimation
7.5 Importance sampling
Chapter 7 Homework
Module 3: Reliability-based design
Chapter 8 Load and Resistance Factor Design(I)
8.1 Uncertainty analysis of FOS
8.2 Reliability assessment of design FOS
8.3 Calibration of resistance factor
8.4 An application example
Chapter 8 Homework
Chapter 9 Load and Resistance Factor Design(II)
Load and Resistance Factor Design(II)
Chapter 9 Homework
Module 4: Bayesian methods for uncertainty reduction
Chapter 10 Concept of Bayesian Updating
10.1 Bayesian methods for discrete variables
10.2 Bayesian predictive probability
10.3 Bayesian methods for continuous variables
Chapter 10 Homework
Chapter 11 Methods for posterior inference(I)
11.1 Conjugate prior for a normal random variable
11.2 Conjugate prior for a multivariate normal vector
11.3 Example: design of pile foundations based on load test data
Chapter 11 Homework
Chapter 12 Methods for posterior inference(II)
12.1 Maximum posterior density method
12.2 System identification method for linear models
12.3 System identification method for nonlinear models
Chapter 12 Homework
