Add the Two-Dimensional Reliability Test Function Example 1 from Grandhi and Wang (1999) #342
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The first reliabity test function from Grandhi and Wang (1999)1 is defined as follows:
where$\boldsymbol{x} = \{ x_1, x_2 \}$ is the vector of input variables modeled as two independent standard normal random variables.$a$ and $b$ . In the original paper $a$ is fixed to $2.0$ while different $b$ values were considered ($\pm 0.5$ , $\pm 2$ , $\pm 4$ ).
The function is parametrized by the parameters
Footnotes
R. V. Grandhi and L. Wang, “Higher-order failure probability calculation using nonlinear approximations,” Computer Methods in Applied Mechanics and Engineering, vol. 168, no. 1–4, pp. 185–206, Jan. 1999, doi: 10.1016/S0045-7825(98)00140-6. ↩
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