The two d.o.f. primary/secondary damped oscillator problem is missing

[mbaudin47]

This problem is presented in: "Analyse de sensibilité fiabiliste avec prise en compte d’incertitudes sur le modèle probabiliste", Vincent Chabridon. Thèse. 2018, pp.91-92.

A shorter presentation is given in:
"Benchmark reliability problems – A selected list." Jean-Marc Bourinet (2019). https://www.gdr-mascotnum.fr/media/ra_examples.pdf

[mbaudin47]

Below is a draft of implementation.

#
def oscillator(x):
	mp, ms, kp, ks, xip, xis, S0 = x
	omega_p = np.sqrt(kp/mp)
	omega_s = np.sqrt(ks/ms)
	gamma = ms/mp
	omega_a = 0.5*(omega_p+omega_s)
	xi_a = 0.5*(xip+xis)
	theta = 1./omega_a*(omega_p-omega_s)
	F = \
		3*ks*np.sqrt(np.pi*S0/(4.*xis*omega_s**3)*
		xi_a*xis/(xip*xis*(4.*xi_a**2+theta**2)+gamma*xi_a**2)*
		(xip*omega_p**3+xis*omega_s**3)*omega_p/(4.*xi_a*omega_a**4))
	return [F]
dim = 7
f = PythonFunction(dim, 1, oscillator)
mean_list = [1.5, 0.01, 1., 0.01, 0.05, 0.02, 100.]
cov_list = [0.1, 0.1, 0.2, 0.2, 0.4, 0.5, 0.1]
myCollection = DistributionCollection(dim)
for i, (mu, cov) in enumerate(zip(mean_list, cov_list)):
    myCollection[i] = LogNormal(mu, mu*cov, 0.0, LogNormal.MUSIGMA)
distribution = ComposedDistribution(myCollection)
rv = RandomVector(distribution)