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damar-wicaksono / uqtestfuns

A Python3 library of test functions from the uncertainty quantification community with a common interface for validation and benchmarking purposes.
https://uqtestfuns.readthedocs.io/en/latest/
MIT License
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Implement the Convex Failure Domain reliability test function #269

Closed damar-wicaksono closed 1 year ago

damar-wicaksono commented 1 year ago

The two-dimensional test function is taken from [^1] and based on [^2]. The limit-state function reads:

$$ g(\boldsymbol{x}) = 0.1 (x_1 - x_2)^2 - \frac{(x_1 + x_2)}{\sqrt{2}} + 2.5, $$

where $X_1, X_2 \sim \mathcal{N}(0, 1)$.

[^1]: P. H. Waarts, Structural reliability using finite element analysis: an appraisal of DARS: directional adaptive response surface sampling. Delft: Delft University Press, 2000. [Online]. Available: https://repository.tudelft.nl/islandora/object/uuid%3A6e6d9a76-fd12-4220-9dc1-36515b3f638d

[^2]: A. Borri and E. Speranzini, “Structural reliability analysis using a standard deterministic finite element code,” Structural Safety, vol. 19, no. 4, pp. 361–382, Jan. 1997, doi: 10.1016/S0167-4730(97)00017-9.

damar-wicaksono commented 1 year ago

This issue has been resolved by PR #273.