The steel column problem is missing #82
Description
https://github.com/sofianehaddad/UQ_benchmark_models/blob/master/steel_column.py
https://www.sfu.ca/~ssurjano/steelcol.html
Description:
Dimensions: 9
The Steel Column function models the trade-off between cost and reliability for a steel column.
The cost for the steel column is: Cost = bt + 5h, where b is the mean flange breadth, t (mm) is the mean flange thickness (mm), and h is the mean profile height (mm). The column length L is 7500 mm. Eldred et al. (2008) use the values b = 300, d = 20 and h = 300.
| Fs ~ Lognormal(mean=400, standard deviation=35) | yield stress (MPa) |
|---|---|
| P1 ~ N(μ=500000, σ=50000) | dead weight load (N) |
| P2 ~ Gumbel(mean=600000, standard deviation=90000) | variable load (N) |
| P3 ~ Gumbel(mean=600000, standard deviation=90000) | variable load (N) |
| B ~ Lognormal(mean=b, standard deviation=3) | flange breadth (mm) |
| D ~ Lognormal(mean=t, standard deviation=2) | flange thickness (mm) |
| H ~ Lognormal(mean=h, standard deviation=5) | profile height (mm) |
| F0 ~ N(μ=30, σ=10) | initial deflection (mm) |
| E ~ Weibull(mean=210000, standard deviation=4200) | Young's modulus (MPa) |
var P := Pd + P1 + P2
var Eb = _pi^2 * E*B*D*H^2 / (2*L^2)
y := Fs - P*(1 / (2*B*D) + F0*Eb / (B*D*H*(Eb-P)) )