Examples Guide
OpenTURNS 1.7
Documentation built from package openturns-doc-16.03
2016/03/17 15:59:38

Contents

1 Example 1 : deviation of a cantilever beam

1.1 Presentation of the study case

1.2 Probabilistic modelisation

1.2.1 Marginal distributions

1.2.2 Dependence structure

1.3 Min/Max approach

1.3.1 Deterministic design of experiments

1.3.2 Random sampling

1.4 Central tendancy approach

1.4.1 Taylor variance decomposition

1.4.2 Random sampling

1.4.3 Kernel smoothing

1.5 Threshold exceedance approach

1.5.1 FORM

1.5.2 Monte Carlo simulation method

1.5.3 Directional Sampling method

1.5.4 Importance Sampling method

1.6 Response surface by polynomial chaos expansion

1.7 The Python script

1.8 Output of the Python script

1.9 Figures

1.10 Results comments

1.10.1 Min/Max approach

1.10.2 Central tendancy approach

1.10.3 Threshold exceedance approach

1.10.4 Response surface : Polynomial expansion chaos

2 Example 2: elastic truss structure

2.1 Problem statement

2.1.1 Physical model

2.1.2 Probabilistic model

2.2 Uncertainty and sensitivity analysis based on polynomial chaos expansions

2.2.1 Methodology to construct a sparse polynomial chaos approximation

2.2.1.1

2.2.1.2

2.2.1.3

2.2.2 Parametric study varying the degree of the metamodel

2.2.2.1

2.2.3 Second moments and sensitivity indices based on chaos coefficients

2.2.4 Distribution and higher-order moments analysis

2.3 Python scripts

2.3.1 Physical model – scriptExample_Truss_PhysicalModel.py

2.3.2 Probabilistic model – scriptExample_Truss_ProbaModel.py

2.3.3 Uncertainty analysis based on PC expansions – scriptExample_Truss_mainSparsePolyChaos.py