#Welded beam function

The welded beam function is defined as: $f(h,l,t) = \sqrt{\frac{a^2 + b^2 + abl}{\sqrt{0.25(l^2+(h+t)^2)}}}$ With: $a = \frac{6000}{\sqrt{2}hl}$ $b = \frac{6000(14 + 0.5l)*\sqrt{0.25(l^2+(h+t)^2)}}{2*[0.707hl(\frac{l^2}{12}+0.25*(h+t)^2)]}$

It has 3 dimension.

using Surrogates
using Plots
using LinearAlgebra
default()

Define the objective function:

function f(x)
h = x[1]
l = x[2]
t = x[3]
a = 6000/(sqrt(2)*h*l)
b = (6000*(14+0.5*l)*sqrt(0.25*(l^2+(h+t)^2)))/(2*(0.707*h*l*(l^2/12 + 0.25*(h+t)^2)))
return (sqrt(a^2+b^2 + l*a*b))/(sqrt(0.25*(l^2+(h+t)^2)))
end
f (generic function with 1 method)
n = 300
d = 3
lb = [0.125,5.0,5.0]
ub = [1.,10.,10.]
x = sample(n,lb,ub,SobolSample())
y = f.(x)
n_test = 1000
x_test = sample(n_test,lb,ub,GoldenSample());
y_true = f.(x_test);
1000-element Vector{Float64}:
6740.508578587182
1197.1253800426875
1915.2458846101658
1018.9473831316677
1454.0347358883528
953.2664882402732
1129.132275742336
4730.110633320883
997.0526115864634
3264.33995564987
⋮
3492.135795999712
2108.5771159104743
1245.5503962239757
791.9113295048217
2123.2975011112035
4137.832068034221
841.7984120749601
2645.0185659210442
766.4185051799487
my_rad = RadialBasis(x,y,lb,ub)
print("MSE Radial: $mse_rad") my_krig = Kriging(x,y,lb,ub) y_krig = my_krig.(x_test) mse_krig = norm(y_true - y_krig,2)/n_test print("MSE Kriging:$mse_krig")
print("MSE Lobachevsky: \$mse_rad")
MSE Radial: 16.649600969336714MSE Kriging: 13.119384472603581MSE Lobachevsky: 6.861386011105637