Reliability

In earlier times the suitability of a structural design was assessed by judgment, experiments, and simple analysis. In the twentieth century the concept of stress became dominant as a failure criterion, with “allowable stress” as the primary design paradigm. That approach was extended to “limit-state design” in the 1980s supported by the reliability methods described on this page. Optimization algorithms are included here because they appear in reliability analysis, and because they support reliability-based design optimization. Almost all the notes on this page are relevant when I teach CIVL 518. 


INTRODUCTION
Notes
Uncertainty
Set Theory
Probability Theory
Examples
Chevalier de Meres First Problem
Chevalier de Meres Second Problem
Probability of Cancelled Meeting
Probability of Wood Defect
Bayesian Concrete Testing
PROBABILISTIC MODELS
Notes
Random Variables
Linear Regression Models
Hazard Curves and Fragility Functions
Damage Accumulation Models
Size Effect Models
Bayesian Network Models
Bayesian Hierarchical Models
Bernoulli Sequences
Poisson Processes
Continuous Stochastic Processes
Examples
Crack Detection
Fragility Functions and Hazard Curves
Python
Plot Distributions (Screenshot)
Variable Inference (Screenshot)
Model Inference (Screenshot)
PROBABILISTIC METHODS
Notes
Functions and Transformations
MVFOSM, FORM, SORM
Sampling
System Reliability
Load Combination
Code Calibration
Stochastic Dynamics
Fatigue
Examples
Basic Limit-state Function
Quadratic Limit-state Function
CalREL Limit-state Function
Poisson Occurrences
Annual Reliability Index
Random Vibrations with Gaussian Process
Python
modifyCorrelationMatrix()
transform_y_to_x()
dg()
Cholesky’s Algorithm
FORM Analysis (Screenshot)
Sampling Analysis (Screenshot)
OPTIMAL DECISIONS
Notes
Decision Criteria
1D Optimization Algorithms
Multivariate Optimization Algorithms
Discounting
Examples
The St Petersburg Paradox
Python
f() and h()
nablaF()
goldenSectionLineSearch()
newtonLineSearch()
bisectionLineSearch()
secantLineSearch()
armijoLineSearch()
steepestDescentSearchDirection()
conjugateGradientSearchDirection()
quasiNewtonSearchDirection()
Downhill Simplex Optimization Analysis (Screenshot)
Directional Line Search Optimization Analysis
1D Optimization Analysis (Screenshot)