Overview

OpenTURNS is able to perform a complete probabilistic study:

  • The first step consists in identifying the numerical model through which one wants to propagate uncertainties, and to define the decision criteria
  • The second step consists in quantifying uncertainty sources : OpenTURNS provides tools that can analyze data samples in order to chose the best uncertainty source modeling ;
  • The third step of a study allows to propagate the uncertainty in the numerical model ;
  • The fourth step of a study gives the possibility to analyze the importance of each parameter (ranking uncertainty sources, sensitivity analysis).

All the OpenTURNS' features (of version 0.12.0) for each step are listed below:

First step: Quantifying uncertainty sources

  • Definition of the numerical model :
    • Link with external numerical simulation process (wrapper)
    • Analytical formulas
    • Python functions
    • Meta-model by Taylor Extension
    • Meta-model by Least Square method
  • Scalar failure criteria

Second step: Quantifying uncertainty sources

  • Empirical cumulative distribution function
  • Density by Kernel Smoothing (General Kernel Product)
  • Composed distribution (1D marginals and copula)
  • Composed copula (copulas linked by the Independent Copula)
  • Standard parametric models:
    • Normal
    • Gumbel
    • Logistic
    • Student
    • Exponential
    • Weibull
    • Gamma
    • Lognormal
    • Truncated Normal
    • Triangular distribution
    • Uniform
    • Beta
    • Geometric
    • Poisson
    • Multi-normal
    • Non-central Student
    • Epanechnikov
  • Independent Copula
  • Normal Copula
  • Clayton copula
  • Franck copula
  • Gumbel Copula
  • Using QQ-plot to compare two samples
  • Smirnov's test
  • Maximum Likehood Method
  • Graphical goodness-of-fit analysis
  • Chi-squared goodness-of-fit test
  • Kolmogorov Smirnov goodness-of-fit test
  • Cramer-Von Mises goodness-of-fit analysis
  • Anderson-Darling goodness-of-fit analysis
  • Bayesian Information Criterion
  • Pearson Correlation Coefficient
  • Pearson's correlation test
  • Spearman Correlation Coefficient
  • Spearman's correlation test
  • Chi-squared test for independence
  • Linear regression

Third step: Uncertainty propagation

  • Min-Max Approach using Design of Experiments
  • Deterministic Min-Max using TNC (Truncated Newton Constrained) algorithm
  • Quadratic Combination / Perturbation Method
  • Estimating the mean and variance using the MC Method
  • Iso-Probabilistic transformation preliminary to FORM-SORM methods
  • FORM
  • SORM
  • Optimization algorithms :
  • Calculation of Reliability index :
    • Hasofer reliability index
    • Generalized reliability index
    • Generalized Breitung reliability index
    • Generalized HohenBichler reliability index
    • Generalized Tvedt reliability index
  • Design point validation : Strong Maximum Test
  • Estimating the probability of an event :
    • Monte Carlo Sampling
    • Importance Sampling
    • Directional Simulation
    • Latin Hypercube Sampling
    • Controlled Importance Sampling in standard space
  • Estimating a quantile by Sampling / Wilk's Method

Fourth step: Ranking uncertainty sources / sensitivity analysis

  • Importance Factors derived from Quadratic Combination Method
  • Uncertainty ranking using Pearson's correlation
  • Uncertainty ranking using Spearman's correlation
  • Uncertainty ranking using Standard Regression Coefficients
  • Uncertainty ranking using Pearson's partial correlation coefficients
  • Uncertainty ranking using Partial Rank correlation coefficients
  • Importance Factors derived from FORM / SORM methods
  • Sensitivity Factors from FORM method