Reliability & Sensitivity¶
Central dispersion¶
Evaluate the mean of a random vector by simulations
Analyse the central tendency of a cantilever beam
Estimate moments from Taylor expansions
Reliability¶
Estimate a probability with Monte Carlo
Use a randomized QMC algorithm
Use the Adaptive Directional Stratification Algorithm
Use the post-analytical importance sampling algorithm
Use the Directional Sampling Algorithm
Specify a simulation algorithm
Estimate a flooding probability
Use the Importance Sampling algorithm
Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability
Estimate a buckling probability
Exploitation of simulation algorithm results
Use the FORM algorithm in case of several design points
Use the FORM - SORM algorithms
Non parametric Adaptive Importance Sampling (NAIS)
Test the design point with the Strong Maximum Test
Time variant system reliability problem
Create unions or intersections of events
Axial stressed beam : comparing different methods to estimate a probability
An illustrated example of a FORM probability estimate
Cross Entropy Importance Sampling
Using the FORM - SORM algorithms on a nonlinear function
Reliability processes¶
Create an event based on a process
Estimate a process-based event probability
Estimate Sobol indices on a field to point function
Sensitivity analysis¶
Sobol’ sensitivity indices using rank-based algorithm
Parallel coordinates graph as sensitivity tool
Estimate Sobol’ indices for a function with multivariate output
Sobol’ sensitivity indices from chaos
The HSIC sensitivity indices: the Ishigami model
Example of sensitivity analyses on the wing weight model
Design of experiments¶
Create a composite design of experiments
Create a Monte Carlo design of experiments
Probabilistic design of experiments
Compute the L2 error between two functions
Create a random design of experiments
Create mixed deterministic and probabilistic designs of experiments
Create a design of experiments with discrete and continuous variables
Deterministic design of experiments
Create a deterministic design of experiments
Generate low discrepancy sequences
Optimize an LHS design of experiments
Merge nodes in Smolyak quadrature