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

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 = [1.0, 10.0, 10.0]
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}:
  771.0823205963742
 1772.0181002240734
 1894.2311631006585
 2432.4828193756566
 3600.698808592067
 1357.8910082598372
  692.2721564421482
 1514.5691059655971
 1728.9867561309597
 2424.2244222060053
    ⋮
 1188.882636805807
 1320.960470719742
 3656.0830399874962
 2798.505549546646
  895.313208180534
 2238.202723259607
 1074.691329648047
 2714.186286418774
 3513.30129940843

my_rad = RadialBasis(x, y, lb, ub)
y_rad = my_rad.(x_test)
mse_rad = norm(y_true - y_rad, 2) / n_test
println("MSE Radial: $mse_rad")

my_loba = LobachevskySurrogate(x, y, lb, ub)
y_loba = my_loba.(x_test)
mse_rad = norm(y_true - y_loba, 2) / n_test
println("MSE Lobachevsky: $mse_rad")

MSE Radial: 18.18856498302441
MSE Lobachevsky: 7.914342983463342