def gradfunc(x, f, g):
grad_obj = [0] * 2
grad_obj[:] = objGrad(x)
grad_con = np.zeros((2, 2))
try:
_, mpp_stress, _ = pma(
func=lambda u: fcn_g_stress(u, d=x, theta=theta),
gradFunc=lambda u: grad_g_stress(u, d=x, theta=theta),
u0=u0,
pf=pf_stress,
tfmJac=lambda u: dUdT(u, theta=theta),
That=That,
C=Con)
grad_con[0] = -sens_g_stress(U=mpp_stress, d=x, theta=theta)
_, mpp_disp, _ = pma(
func=lambda u: fcn_g_disp(u, d=x, theta=theta),
gradFunc=lambda u: grad_g_disp(u, d=x, theta=theta),
u0=u0,
pf=pf_disp,
tfmJac=lambda u: dUdT(u, theta=theta),
That=That,
C=Con)
grad_con[1] = -sens_g_disp(U=mpp_disp, d=x, theta=theta)
fail = 0
except ValueError:
fail = 1
return grad_obj, grad_con, fail
def objfunc(x):
# f = objective value
# g = [-gc_stress, -gc_disp]
f = obj(x)
g = [0] * 2
try:
gc_stress, _, _ = pma(
func=lambda u: fcn_g_stress(u, d=x, theta=theta),
gradFunc=lambda u: grad_g_stress(u, d=x, theta=theta),
u0=u0,
pf=pf_stress,
tfmJac=lambda u: dUdT(u, theta=theta),
That=That,
C=Con)
g[0] = -gc_stress
gc_disp, _, _ = pma(
func=lambda u: fcn_g_disp(u, d=x, theta=theta),
gradFunc=lambda u: grad_g_disp(u, d=x, theta=theta),
u0=u0,
pf=pf_disp,
tfmJac=lambda u: dUdT(u, theta=theta),
That=That,
C=Con)
g[1] = -gc_disp
fail = 0
except ValueError:
fail = 1
return f, g, fail
def run_FORM(d):
fcn = lambda u: fcn_g_stress(u, d=d) / scale
grd = lambda u: grad_g_stress(u, d=d) / scale
tfm = lambda u: dUdT(u)
u0 = np.ones(4) / np.sqrt(4)
g_cr, mpp, dgdU = pma(func=fcn,
gradFunc=grd,
u0=u0,
pf=0.1,
tfmJac=tfm,
That=np.diag([0.] * 4))
return g_cr, mpp
d0 = np.array([2.6999, 3.4098])
## Exact reliability analysis
pf_stress_ext = 1 - R_stress(d0)
print("pf_stress_ext = {}".format(pf_stress_ext))
## MCS
G_stress = fcn_g_stress(U, d=d0)
pf_stress_hat = np.mean(G_stress <= 0)
print("pf_stress_hat = {}".format(pf_stress_hat))
## PMA
tfm = lambda u: dUdT(u)
fcn_stress = lambda u: fcn_g_stress(u, d=d0) / 1e4
grd_stress = lambda u: grad_g_stress(u, d=d0) / 1e4
g_cr_stress, mpp_stress, dgdU_stress = pma(fcn_stress, grd_stress, u0,
pf_stress_ext, tfm, That)
print("g_stress = {0:5.4f}".format(g_cr_stress))
# print("mpp = {}".format(mpp))
# print("dgdU = {}".format(dgdU))
## Displacement
## --------------------------------------------------
d0 = np.array([2.448387, 3.888371])
## Analysis via Davies algorithm
pf_disp_ext = 1 - R_disp(d0)
print("pf_disp_ext = {}".format(pf_disp_ext))
## MCS
G_disp = fcn_g_disp(U, d=d0)
pf_disp_hat = np.mean(G_disp <= 0)