Version 3 (modified by regis.lebrun@…, 12 years ago) (diff)



OpenTURNS is able to perform a complete probabilistic study:

  • The first step consists in quantifying uncertainty sources : OpenTURNS provides tools that can analyze data samples in order to chose the best uncertainty source modeling ;
  • The second step of a study allows to spread the uncertainty in a physical model ;
  • The third 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 0.9.1) for each step are listed below:

First step: Quantifying uncertainty sources

  • Empirical cumulative distribution function
  • Density by Kernel Smoothing (Gaussian Kernel)
  • Standard parametric models:
    • Normal
    • Gumbel
    • Logistic
    • Student
    • Exponential
    • Weibull
    • Gamma
    • Lognormal
    • Truncated Normal
    • Triangular distribution
    • Uniform
    • Beta
    • Geometric
    • Poisson
    • Multi-normal
  • Independent Copula
  • Normal 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

Second step: Uncertainty propagation

  • Min-Max Approach using Design of Experiments
  • 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 :
    • Cobyla
    • AbdoRackwitz
  • Calculation of Reliability index :
    • Hasofer reliability index
    • Generalized reliability index
    • Generalized Breitung reliability index
    • Generalized HohenBichler reliability index
    • Generalized Tvedt reliability index
  • Sphere sampling method
  • Design point validation : Strong Maximum Test
  • Estimating the probability of an event using Monte Carlo Sampling
  • Estimating the probability of an event using Importance Sampling
  • DEstimating the probability of an event using irectional Simulation
  • Estimating the probability of an event using Latin Hypercube Sampling
  • Estimating a quantile by Sampling / Wilk's Method
  • Response Surface by Taylor Extension
  • Polynomial response Surface
  • Response surface obtained by Least Square method

Third 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