*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)