Masters Courses (University of
Tokyo)
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8. |
PROBABILISTIC
METHODS IN CIVIL ENGINEERING |
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by
Fumio YAMAZAKI & Masato ABE |
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1. Introduction |
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2.
Fundamentals of Probability Theory
2.1 Events and Probability
2.2 Axioms and Theorems of
Probability Theory
2.3 Conditional Probability 2.4 Bayse' Theorem |
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3.
Random Variables and Probability Distributions
3.1 Random Variables
3.2 Normal Distribution
3.3 Logarithmic Normal Distribution
3.4 Multiple Random Variables 3.5 Functions of Random Variables |
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4.
Probabilistic Models and Observed Data
4.1 Point Estimation of Parameters
4.2 Interval Estimation of the Mean
4.3 Interval Estimation of the
Variance
4.4 Probability Paper 4.5 Hypothesis Testing Goodness-of-fit Tests |
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5.
Monte Carlo Simulation
5.1 Simulation and Monte Carlo
Methods
5.2 Generation of Random Numbers
5.3 Simulation of Random Vectors
5.4 Monte Carlo Simulation for
Structural Engineering Problems 5.5 Other Statistical Approaches |
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6.
Stochastic Fields and Stochastic Finite Element Analysis
6.1 Stochastic Processes and
Stochastic Fields
6.2 Simulation of 1D-1V Stationary
Stochastic Processes
6.3 Simulation of General
Stochastic Fields
6.4 AR/MA/ARMA Models
6.5Introduction
to Perturbation Method 6.6 Perturbation Formulation for Stochastic FEM |
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-- by Dr. M. ABE -- (tentative) |
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7. Reliability Analysis |
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8. Reliability-based Structural Design and Design Code |
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9. Behavior of Linear Systems Subject to Stochastic Input |
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