Tutorial 1 – Reliability analysis
In this tutorial we use Fesslix for reliability analysis.
As reliability method we employ Subset Simulation [1].
1 Primary Reliability Tutorials
The following limit-state function is analyzed:
where 
denotes the number of random variables in the problem (
in this example)
and 
denotes the 
th random variable.
Each 
is an exponential random variable with parameter 
.
This example problem is also discussed in [2] in combination with Subset Simulation.
The problem is solved using different variants to formulate the limit-state function:
denotes the number of random variables in the problem ( in this example)
and denotes the th random variable.
Each is an exponential random variable with parameter .
This example problem is also discussed in [2] in combination with Subset Simulation.
The problem is solved using different variants to formulate the limit-state function:
Overview
- Tutorial 1a: Analytical solution
- Tutorial 1b: Limit-state function formulated directly in Fesslix
- Tutorial 1c: Matlab/Octave limit-state function
- Tutorial 1d: Python limit-state function
- Tutorial 1e: C++ limit-state function
- Tutorial 1f: Fortran limit-state function
- Tutorial 1g: Limit-state function evaluated with external application
2 Secondary Reliability Tutorials
A reliability analyisis employing Subset Simulation is also performed in Tutorial 5c
(2D FE-plate with spatially uncertain Young's modulus).
3 References
- [1] Au, S. K., & Beck, J. L. (2001). Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics, 16(4), 263-277. doi:10.1016/S0266-8920(01)00019-4
- [2] Papaioannou I., Betz W., Zwirglmaier K., Straub D. (2015): MCMC Algorithms for Subset Simulation. Probabilistic Engineering Mechanics, 41, 89-103. doi:10.1016/j.probengmech.2015.06.006