def profiles():
reinf = ContinuousFibers(r=0.0035,
tau=RV('uniform', loc=1., scale=3.0),
V_f=0.1,
E_f=200e3,
xi=RV('weibull_min', loc=0., shape=1000., scale=.01),
label='carbon',
n_int=30)
ccb = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf],
Ll=1.,
Lr=1.,
w=.0056)
# ccb = CompositeCrackBridge(E_m=25e13,
# reinforcement_lst=[reinf],
# Ll=2.,
# Lr=2.,
# w=.0088)
ccb.damage
for i, depsf in enumerate(ccb.sorted_depsf):
epsf_x = np.maximum(ccb._epsf0_arr[i] - depsf * np.abs(ccb._x_arr), ccb._epsm_arr)
if i == 0:
plt.plot(ccb._x_arr, epsf_x, color='black', label='fibers')
else:
plt.plot(ccb._x_arr, epsf_x, color='black')
plt.plot(ccb._x_arr, ccb._epsm_arr, lw=2, color='blue', label='matrix')
plt.legend(loc='best')
plt.ylabel('matrix and fiber strain [-]')
plt.ylabel('long. position [mm]')
plt.show()
def fcn2min(params, x, data):
shape = params['shape'].value
scale = params['scale'].value
loc = params['loc'].value
# m = params['f_shape'].value
# sV0 = params['f_scale'].value
sV0 = 0.0076
m = 6.7
tau = RV('gamma', shape=shape, scale=scale, loc=loc)
n_int = 500
p_arr = np.linspace(0.5 / n_int, 1 - 0.5 / n_int, n_int)
tau_arr = tau.ppf(p_arr) + 1e-10
r = 3.5e-3
E_f = 182e3
T = 2. * tau_arr / r
# scale parameter with respect to a reference volume
s = ((T * (m + 1.) * sV0 ** m) /
(2. * E_f * pi * r ** 2)) ** (1. / (m + 1.))
ef0 = np.sqrt(x[:, np.newaxis] * T[np.newaxis, :] / E_f)
Gxi = 1 - np.exp(-(ef0 / s) ** (m + 1.))
mu_int = ef0 * (1 - Gxi)
sigma = mu_int * E_f
return np.sum(sigma, axis=1) / n_int * (11. * 0.445) / 1000 - data
def T_effect():
strength_CB = []
strength_MC = []
m_arr = np.linspace(.5, 5., 30)
for m in m_arr:
# strengths.append(sigmac_max(l)[0])
# print 'strentgth = ', strengths[-1]
w_CB = np.linspace(0.0, .5, 100)
w_MC = np.linspace(0.0, .03, 100)
sigma_c_CB = -sigmac(
w_CB, 1000., RV('weibull_min', shape=m, scale=0.1, loc=0.0),
5.0)
sigma_c_MC = -sigmac(
w_MC, 1.0, RV('weibull_min', shape=m, scale=0.1, loc=0.0), 5.0)
strength_CB.append(np.max(sigma_c_CB))
strength_MC.append(np.max(sigma_c_MC))
# plt.plot(w_CB, sigma_c_CB, label='CB')
# plt.plot(w_CB, sigma_c_MC, label='MC')
# plt.show()
COV = [
np.sqrt(weibull_min(m, scale=0.1).var()) /
weibull_min(m, scale=0.1).mean() for m in m_arr
]
CB_arr = np.ones_like(np.array([strength_CB]))
MC_arr = np.array([strength_MC]) / np.array([strength_CB])
plt.plot(COV, CB_arr.flatten())
plt.plot(COV, MC_arr.flatten())
plt.ylim(0)
plt.show()
def mean_CB():
w_arr = np.linspace(0., .5, 200)
micro = GFRCMicro(FilamentCB=CBShortFiber)
meso = GFRCMeso(micro_model=micro, N_fil=100)
macro = GFRCMacro(meso_model=meso,
W=40.,
H=40.,
L=200.,
Lf=18.,
Vf=.001)
theta_dict = dict(tau=RV('uniform', loc=0.001, scale=0.4),
r=3.5e-3,
E_f=70e3,
le=9.0,
phi=0.0,
snub=0.5,
xi=RV('weibull_min', shape=5., scale=0.025),
spall=0.5)
mean_r, var_r = macro.mean_response(w_arr, theta_dict)
plt.plot(w_arr,
mean_r,
lw=2,
label='tau $\sim$ $\mathcal{U}(0.1,0.8)$')
plt.plot(w_arr, mean_r + np.sqrt(var_r), lw=2)
plt.plot(w_arr, mean_r - np.sqrt(var_r), lw=2)
plt.xlabel('crack opening w [mm]')
plt.ylabel('force [N]')
plt.legend(loc='best')
plt.show()
def k_COV_plots(k_arr, COV_arr):
sig_max_arr = np.zeros((len(k_arr), len(COV_arr)))
wmax_arr = np.zeros((len(k_arr), len(COV_arr)))
mu_r, mu_tau = 0.01, 0.1
for i, k in enumerate(k_arr):
for j, cov in enumerate(COV_arr):
Vf = Vf_k(k)
loc_r = mu_r * (1 - cov * np.sqrt(3.0))
scale_r = cov * 2 * np.sqrt(3.0) * mu_r
loc_tau = mu_tau * (1 - cov * np.sqrt(3.0))
scale_tau = cov * 2 * np.sqrt(3.0) * mu_tau
reinf = ContinuousFibers(r=RV('uniform', loc=loc_r, scale=scale_r),
tau=RV('uniform',
loc=loc_tau,
scale=scale_tau),
xi=WeibullFibers(shape=7.0, sV0=0.003),
V_f=Vf,
E_f=200e3,
n_int=100)
ccb_view.model.reinforcement_lst = [reinf]
sig_max, wmax = ccb_view.sigma_c_max
sig_max_arr[i, j] = sig_max / Vf
wmax_arr[i, j] = wmax
ctrl_vars = orthogonalize([np.arange(len(k_arr)), np.arange(len(COV_arr))])
print sig_max_arr
print wmax_arr
mlab.surf(ctrl_vars[0], ctrl_vars[1], sig_max_arr / np.max(sig_max_arr))
mlab.surf(ctrl_vars[0], ctrl_vars[1], wmax_arr / np.max(wmax_arr))
mlab.show()
def mean_bundle():
w_arr = np.linspace(0., .5, 150)
micro = GFRCMicro(FilamentCB=CBShortFiber)
meso = GFRCMeso(micro_model=micro, N_fil=100)
theta_dict = dict(tau=RV('uniform', loc=0.01, scale=0.4),
r=3.5e-3,
E_f=70e3,
le=RV('uniform', loc=0.0, scale=9.0),
phi=RV('sin2x', scale=1.0),
snub=0.5,
xi=RV('weibull_min', shape=5., scale=0.025),
spall=0.5)
# mean_resp = meso.mean_response(w_arr, theta_dict)
# plt.plot(w_arr, mean_resp, lw=2, color='black')
for j in range(3):
print j
mean_resp = 0.0
for i in range(100):
phic_i = sin2x(scale=1).rvs(1)
le_i = uniform(loc=0.0, scale=9.).rvs(1)
theta_dict['phi'] = float(phic_i)
theta_dict['le'] = float(le_i)
mean_resp_i = meso.mean_response(w_arr, theta_dict)
mean_resp += mean_resp_i / 100.
plt.plot(w_arr, mean_resp, lw=1)
plt.show()
def k_influence_rand(k_arr):
fig = plt.figure()
ax1 = fig.add_subplot(111)
fig2 = plt.figure()
ax2 = fig2.add_subplot(111)
for i, m in enumerate([4., 8., 30.]):
sig_max_lst = []
wmax_lst = []
for ki in k_arr:
Vf = Vf_k(ki)
reinf = ContinuousFibers(r=RV('uniform', loc=.005, scale=.01),
tau=RV('uniform', loc=.05, scale=.1),
xi=WeibullFibers(shape=m, sV0=0.003),
V_f=Vf,
E_f=200e3,
n_int=100)
mur = reinf.r._distr.mean
mutau = reinf.tau._distr.mean
muxi = reinf.xi.mean(2 * mutau / mur / reinf.E_f, mur)
g = gamma(1. + 1. / (1 + m))
sV0 = ((muxi / g)**(m + 1) * (pi * mur**3 * reinf.E_f) /
(mutau * (m + 1)))**(1. / m)
reinf.xi.sV0 = sV0
ccb_view.model.reinforcement_lst = [reinf]
sig_max, wmax = ccb_view.sigma_c_max
sig_max_lst.append(sig_max / Vf)
wmax_lst.append(wmax)
ax1.plot(k_arr, np.array(sig_max_lst) / sig_max_lst[0])
ax2.plot(k_arr, np.array(wmax_lst) / wmax_lst[0], label=str(m))
ax1.set_ylim(0)
ax2.set_ylim(0)
def fcn2min(shape, scale, loc, x):
# shape = params['shape'].value
# scale = params['scale'].value
# loc = params['loc'].value
# m = params['f_shape'].value
# sV0 = params['f_scale'].value
sV0 = 0.0069
m = 7.1
tau = RV('gamma', shape=shape, scale=scale, loc=loc)
n_int = 500
p_arr = np.linspace(0.5 / n_int, 1 - 0.5 / n_int, n_int)
tau_arr = tau.ppf(p_arr) + 1e-10
r = 3.5e-3
E_f = 180e3
# lm = 1000
#
# def cdf(e, depsf, r, lm, m, sV0):
# '''weibull_fibers_cdf_mc'''
# s = ((depsf * (m + 1.) * sV0 ** m) /
# (2. * pi * r ** 2.)) ** (1. / (m + 1.))
# a0 = (e + 1e-15) / depsf
# expfree = (e / s) ** (m + 1.)
# expfixed = a0 / \
# (lm / 2.0) * (e / s) ** (m + 1) * \
# (1. - (1. - lm / 2.0 / a0) ** (m + 1.))
# print expfree
# print expfixed
# mask = a0 < lm / 2.0
# exp = expfree * mask + \
# np.nan_to_num(expfixed * (mask == False))
# return 1. - np.exp(- exp)
#
# T = 2. * tau_arr / r + 1e-10
# ef0cb = np.sqrt(x[:, np.newaxis] * T[np.newaxis, :] / E_f)
# ef0lin = x[:, np.newaxis] / lm + \
# T[np.newaxis, :] * lm / 4. / E_f
# depsf = T / E_f
# a0 = ef0cb / depsf
# mask = a0 < lm / 2.0
# e = ef0cb * mask + ef0lin * (mask == False)
# Gxi = cdf(e, depsf, r, lm, m, sV0)
# mu_int = e * (1. - Gxi)
# sigma = mu_int * E_f
T = 2. * tau_arr / r
# scale parameter with respect to a reference volume
s = ((T * (m + 1.) * sV0 ** m) /
(2. * E_f * pi * r ** 2)) ** (1. / (m + 1.))
ef0 = np.sqrt(x[:, np.newaxis] * T[np.newaxis, :] / E_f)
Gxi = 1 - np.exp(-(ef0 / s) ** (m + 1.))
mu_int = ef0 * (1 - Gxi)
sigma = mu_int * E_f
return np.sum(sigma, axis=1) / n_int * (11. * 0.445) / 1000
def fcn2min(params, x, data):
""" model decaying sine wave, subtract data"""
shape = params['shape'].value
scale = params['scale'].value
m = params['f_shape'].value
sV0 = params['f_scale'].value
# m = 8.806672387136711
# sV0 = 0.013415768576509945
# sV0 = 3243. / \
# (182e3 * (pi * 3.5e-3 ** 2 * 50.) ** (-1. / m) * gamma(1 + 1. / m))
# shape = 0.0505
# scale = 2.276
# CS = 12.
# mu_tau = 1.3 * 3.5e-3 * 3.6 * (1. - 0.01) / (2. * 0.01 * CS)
# scale = mu_tau / shape
tau = RV('gamma', shape=shape, scale=scale, loc=0.)
n_int = 500
p_arr = np.linspace(0.5 / n_int, 1 - 0.5 / n_int, n_int)
tau_arr = tau.ppf(p_arr) + 1e-10
r = 3.5e-3
E_f = 180e3
lm = 1000.
def cdf(e, depsf, r, lm, m, sV0):
'''weibull_fibers_cdf_mc'''
s = ((depsf * (m + 1.) * sV0 ** m) /
(2. * pi * r ** 2.)) ** (1. / (m + 1.))
a0 = (e + 1e-15) / depsf
expfree = (e / s) ** (m + 1)
expfixed = a0 / \
(lm / 2.0) * (e / s) ** (m + 1) * \
(1. - (1. - lm / 2.0 / a0) ** (m + 1.))
mask = a0 < lm / 2.0
exp = expfree * mask + \
np.nan_to_num(expfixed * (mask == False))
return 1. - np.exp(- exp)
T = 2. * tau_arr / r + 1e-10
ef0cb = np.sqrt(x[:, np.newaxis] * T[np.newaxis, :] / E_f)
ef0lin = x[:, np.newaxis] / lm + \
T[np.newaxis, :] * lm / 4. / E_f
depsf = T / E_f
a0 = ef0cb / depsf
mask = a0 < lm / 2.0
e = ef0cb * mask + ef0lin * (mask == False)
Gxi = cdf(e, depsf, r, lm, m, sV0)
mu_int = e * (1. - Gxi)
sigma = mu_int * E_f
return np.sum(sigma, axis=1) / n_int * (11. * 0.445) / 1000 - data
def m_effect():
m_xi_arr = np.linspace(1., 20., 15)
m_tau_arr = np.linspace(0.3, 5.0, 10)
try:
res_file = open('res_m.pkl', 'rb')
res_arr = pickle.load(res_file)
res_file.close()
# for res_part in res_arr:
# plt.plot(m_xi_arr, res_part)
# plt.show()
eps_vars = orthogonalize([np.arange(15), np.arange(10)])
resCB = np.ones_like(res_arr)
resMC = res_arr
mlab.surf(eps_vars[0], eps_vars[1], resCB * 10)
mlab.surf(eps_vars[0], eps_vars[1], resMC * 10)
mlab.show()
except:
res_arr = []
for m_tau in m_tau_arr:
strength_CB = []
strength_MC = []
for m_xi in m_xi_arr:
wmCB, smCB = maxsigma(
1000.,
RV('weibull_min', shape=m_tau, scale=0.1, loc=0.0),
m_xi)
wmMC, smMC = maxsigma(
1., RV('weibull_min', shape=m_tau, scale=0.1, loc=0.0),
m_xi)
# w_CB = np.linspace(0.0,100./m**2,200)
# w_MC = np.linspace(0.0,1.5/m**2,200)
# plt.plot(wmCB, smCB, 'ro')
# plt.plot(wmMC, smMC, 'bo')
# sigma_c_CB = sigmac(w_CB, 1000., RV('weibull_min', shape=3.0, scale=0.1, loc=0.0), m)
# sigma_c_MC = sigmac(w_MC, 1.0, RV('weibull_min', shape=3.0, scale=0.1, loc=0.0), m)
# plt.plot(w_CB, sigma_c_CB, label='CB')
# plt.plot(w_MC, sigma_c_MC, label='MC')
# plt.show()
strength_CB.append(smCB)
strength_MC.append(smMC)
CB_arr = np.ones_like(np.array([strength_CB]))
MC_arr = np.array([strength_MC]) / np.array([strength_CB])
res_arr.append(MC_arr.flatten())
plt.plot(m_xi_arr, CB_arr.flatten(), lw=2., color='black')
plt.plot(m_xi_arr, MC_arr.flatten(), label=str(m_tau) + ' MC')
res_arr = np.array(res_arr)
file_res = open('res_m.pkl', 'wb')
pickle.dump(res_arr, file_res, -1)
file_res.close()
plt.legend(loc='best')
plt.ylim(0)
plt.show()
def short_fibers_lf():
w = np.linspace(0.0, 0.02, 200)
Ef = sf_spirrid.theta_vars['E_f']
Vf = 0.01
sf_spirrid.eps_vars['w'] = w
sf_spirrid.theta_vars['le'] = RV('uniform', scale=5.0, loc=0.0)
plt.plot(w, sf_spirrid.mu_q_arr * Ef * Vf / 2., label='10.0')
sf_spirrid.theta_vars['le'] = RV('uniform', scale=7.0, loc=0.0)
plt.plot(w, sf_spirrid.mu_q_arr * Ef * Vf / 2., label='14.0')
sf_spirrid.theta_vars['le'] = RV('uniform', scale=9.0, loc=0.0)
plt.plot(w, sf_spirrid.mu_q_arr * Ef * Vf / 2., label='18.0')
plt.legend(loc='best')
plt.show()
def model_free(self, tau_loc, tau_shape, tau_scale):
xi_shape = 6.7
#xi_scale = 3243. / (182e3 * (pi * 3.5e-3 **2 * 50.)**(-1./xi_shape)*gamma(1+1./xi_shape))
xi_scale = 7.6e-3
#CS=8.
#mu_tau = 1.3 * self.r * 3.6 * (1.-0.01) / (2. * 0.01 * CS)
#tau_scale = (mu_tau - tau_loc)/tau_shape
#xi_scale = 0.0077
#xi_shape = 6.7
#tau_scale = (mu_tau - tau_loc)/tau_shape
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
tau = RV('gamma', shape=tau_shape, scale=tau_scale, loc=tau_loc)
w = self.w
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau,
E_f=self.Ef,
V_f=self.V_f,
r=self.r,
m=xi_shape,
sV0=xi_scale)
spirrid.n_int = 5000
sigma_c = spirrid.mu_q_arr / self.r**2
plt.plot(w, sigma_c)
return sigma_c
def strength():
length = 2000.
nx = 2000
cracks = []
strengths = []
maxsigma = [12., 15., 20., 22., 24.]
Vfs = [0.05, 0.01, 0.013, 0.017, 0.02]
for i, Vf in enumerate(Vfs):
random_field = RandomField(
seed=False,
lacor=5.0,
length=length,
nx=800,
nsim=1,
loc=.0,
shape=8.,
scale=3.2,
)
reinf1 = ContinuousFibers(r=0.0035,
tau=RV('weibull_min',
loc=0.0,
shape=1.,
scale=0.03),
V_f=Vf,
E_f=180e3,
xi=fibers_MC(m=5.0, sV0=0.003),
label='carbon',
n_int=500)
CB_model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf1],
)
scm = SCM(
length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, maxsigma[i], 100),
)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, lw=1, label=str(Vf))
strengths.append(np.max(sigma))
cracks.append(len(scm_view.model.cracks_list[-1]))
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.figure()
plt.plot(Vfs, strengths, label='strengths')
plt.figure()
plt.plot(Vfs, cracks, label='cracks')
print strengths
print cracks
def _get_model_extrapolate(self):
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
sV0 = self.sV0
V_f = 1.0
r = 3.5e-3
m = self.m
tau = RV('gamma',
shape=self.tau_shape,
scale=self.tau_scale,
loc=self.tau_loc)
n_int = self.n_int
w = self.w2
lm = self.lm
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau,
E_f=self.Ef,
V_f=V_f,
r=r,
m=m,
sV0=sV0,
lm=lm)
spirrid.n_int = n_int
sigma_c = spirrid.mu_q_arr / self.r**2
return sigma_c
def model_rand(params, *args):
w = args[0]
sV0, tau_scale = params
E_f = 180e3
V_f = 1.0
r = 3.45e-3
m = 4.
tau = RV('weibull_min', shape=.4, scale=tau_scale, loc=0.009)
# a_lower = 0.0
# tau = RV('piecewise_uniform', shape=0.0, scale=1.0)
# tau._distr.distr_type.distribution.a_lower = a_lower
# tau._distr.distr_type.distribution.a_upper = a_upper
# tau._distr.distr_type.distribution.b_lower = a_upper
# tau._distr.distr_type.distribution.b_upper = b_upper
# tau._distr.distr_type.distribution.ratio = ratio
n_int = 100
spirrid.eps_vars=dict(w=w)
spirrid.theta_vars=dict(tau=tau, E_f=E_f, V_f=V_f, r=r, m=m, sV0=sV0)
spirrid.n_int=n_int
if isinstance(r, RV):
r_arr = np.linspace(r.ppf(0.001), r.ppf(0.999), 300)
Er = np.trapz(r_arr ** 2 * r.pdf(r_arr), r_arr)
else:
Er = r ** 2
sigma_c = spirrid.mu_q_arr / Er
return sigma_c
def analytical_comparison():
'''for the case when tau is deterministic,
there is an analytical solution.
The differences are caused by the additional matrix
stiffness due to broken fibers, which are in the CB model
added to matrix stiffness. As the matrix E grows and the V_f
decreases, the solutions tend to get closer'''
tau, E_f, E_m, V_f = 0.1, 72e3, 25e3, 0.2
r, shape, scale = 0.001, 5., 0.02
# analytical solution for damage controlled test
ctrl_damage = np.linspace(0.0, .99, 100)
def crackbridge(w, tau, E_f, E_m, V_f, r, omega):
Kf = E_f * V_f * (1 - omega)
Km = E_m * (1 - V_f) + E_f * V_f * omega
Kc = Kf + Km
T = 2. * tau * V_f * (1. - omega) / r
c = np.sqrt(Kc * T / Km / Kf)
return c * np.sqrt(w) * (1 - omega)
def w_omega(tau, E_f, E_m, V_f, r, omega, shape, scale):
Kf = E_f * V_f * (1 - omega)
Km = E_m * (1 - V_f) + E_f * V_f * omega
Kc = Kf + Km
T = 2. * tau * V_f * (1. - omega) / r
return (-np.log(1. - omega)) ** (2. / shape) \
* scale ** 2 * Km * Kf / Kc / T
w_lst = [
w_omega(tau, E_f, E_m, V_f, r, omega, shape, scale)
for omega in ctrl_damage
]
epsf = crackbridge(np.array(w_lst), tau, E_f, E_m, V_f, r, ctrl_damage)
plt.plot(np.array(w_lst),
epsf * E_f * V_f,
color='red',
lw=4,
ls='dashed',
label='analytical')
reinf = Reinforcement(r=r,
tau=tau,
V_f=V_f,
E_f=E_f,
xi=RV('weibull_min', shape=shape, scale=scale),
n_int=20)
ccb = CompositeCrackBridge(E_m=E_m,
reinforcement_lst=[reinf],
Ll=1000.,
Lr=1000.)
stress = []
w_arr = np.linspace(0.0, np.max(w_lst), 100)
for w in w_arr:
ccb_view.model.w = w
stress.append(ccb_view.sigma_c)
plt.plot(w_arr, stress, color='blue', lw=2, label='CB model')
plt.legend(loc='best')
def mean_filament():
w_arr = np.linspace(0., .5, 200)
micro = GFRCMicro(FilamentCB=CBShortFiber)
theta_dict = dict(tau=RV('uniform', loc=0.01, scale=0.4),
r=3.5e-3,
E_f=70e3,
le=9.0,
phi=1.0,
snub=0.5,
xi=RV('weibull_min', shape=5., scale=0.025),
spall=0.5)
mean_resp = micro.mean_response(w_arr, theta_dict)
var_resp = micro.var_response(w_arr, theta_dict)
plt.plot(w_arr, mean_resp, lw=2)
plt.plot(w_arr, mean_resp + np.sqrt(var_resp), lw=2, ls='dashed')
plt.plot(w_arr, mean_resp - np.sqrt(var_resp), lw=2, ls='dashed')
plt.show()
def short_fibers_CHOB():
cb = CBShortFiber()
Ef = 200e3
Vf = 0.015
r = 0.088
Lc = 400.
Ac = 1600.
lf = 14.
spirrid = SPIRRID(q=cb,
sampling_type='PGrid',
eps_vars=dict(w=np.array([100.0])),
theta_vars=dict(tau=1.8,
E_f=Ef,
r=r,
le=RV('uniform', scale=lf / 2., loc=0.0),
phi=RV('sin2x', scale=1.0),
snub=.87,
xi=20e10),
n_int=100)
spirrid.codegen.implicit_var_eval = True
var_e = spirrid.var_q_arr
mu_e = spirrid.mu_q_arr
Af = pi * r**2
p = lf / 2. / Lc
n = Ac * Lc * Vf / Af / lf
mu_strength = Ef * Vf / 2. * mu_e
var_strength = (Ef * Vf / 2.)**2 / n / p * (var_e + (1. - p) * mu_e**2)
n = np.arange(10)
distr = norm(loc=mu_strength, scale=var_strength**(0.5))
sig_arr = np.linspace(mu_strength / 2., mu_strength * 1.5, 1000)
CDF1 = distr.cdf(sig_arr)
CDF2 = 1 - (1 - CDF1)**2
CDF10 = 1 - (1 - CDF1)**10
plt.figure()
plt.plot(sig_arr, CDF1, label='strength distr 1')
plt.plot(sig_arr, CDF2, label='strength distr 2')
plt.plot(sig_arr, CDF10, label='strength distr 10')
plt.figure()
cracks = np.linspace(1, 100, 500)
plt.plot(cracks, distr.ppf(1. - 0.5**(1. / cracks)), label='0.5')
plt.plot(cracks, distr.ppf(1. - 0.99999**(1. / cracks)), label='0.000001')
plt.ylim(1.0, 3.0)
plt.legend()
plt.show()
def func1(w_arr, k):
tau = RV('gamma', shape=k, scale=scale, loc=0.)
n_int = 500
p_arr = np.linspace(0.5 / n_int, 1 - 0.5 / n_int, n_int)
tau_arr = tau.ppf(p_arr) + 1e-10
# sV0 = sV0
# m = m
r = 3.5e-3
E_f = 180e3
lm = 1000.
def cdf(e, depsf, r, lm, m, sV0):
'''weibull_fibers_cdf_mc'''
s = ((depsf * (m + 1.) * sV0 ** m) /
(2. * pi * r ** 2.)) ** (1. / (m + 1.))
a0 = (e + 1e-15) / depsf
expfree = (e / s) ** (m + 1.)
expfixed = a0 / \
(lm / 2.0) * (e / s) ** (m + 1.) * \
(1. - (1. - lm / 2.0 / a0) ** (m + 1.))
mask = a0 < lm / 2.0
exp = expfree * mask + \
np.nan_to_num(expfixed * (mask == False))
return 1. - np.exp(- exp)
T = 2. * tau_arr / r + 1e-10
ef0cb = np.sqrt(w_arr[:, np.newaxis] * T[np.newaxis, :] / E_f)
ef0lin = w_arr[:, np.newaxis] / lm + \
T[np.newaxis, :] * lm / 4. / E_f
depsf = T / E_f
a0 = ef0cb / depsf
mask = a0 < lm / 2.0
e = ef0cb * mask + ef0lin * (mask == False)
Gxi = cdf(e, depsf, r, lm, m, sV0)
# plt.plot(w_arr, np.average(Gxi, axis=1), label='s='+str(s)+'m='+str(m))
mu_int = e * (1. - Gxi)
sigma = mu_int * E_f
return np.sum(sigma, axis=1) / n_int * (11. * 0.445) / 1000
def lackoffit(m, sV0, shape, scale, x, data):
""" model decaying sine wave, subtract data"""
tau = RV('gamma', shape=shape, scale=scale, loc=0.)
n_int = 500
p_arr = np.linspace(0.5 / n_int, 1 - 0.5 / n_int, n_int)
tau_arr = tau.ppf(p_arr) + 1e-10
r = 3.5e-3
E_f = 180e3
lm = 1000.
def cdf(e, depsf, r, lm, m, sV0):
'''weibull_fibers_cdf_mc'''
s = ((depsf * (m + 1.) * sV0 ** m) /
(2. * pi * r ** 2.)) ** (1. / (m + 1.))
a0 = (e + 1e-15) / depsf
expfree = (e / s) ** (m + 1.)
expfixed = a0 / \
(lm / 2.0) * (e / s) ** (m + 1.) * \
(1. - (1. - lm / 2.0 / a0) ** (m + 1.))
mask = a0 < lm / 2.0
exp = expfree * mask + \
np.nan_to_num(expfixed * (mask == False))
return 1. - np.exp(- exp)
T = 2. * tau_arr / r + 1e-10
ef0cb = np.sqrt(x[:, np.newaxis] * T[np.newaxis, :] / E_f)
ef0lin = x[:, np.newaxis] / lm + \
T[np.newaxis, :] * lm / 4. / E_f
depsf = T / E_f
a0 = ef0cb / depsf
mask = a0 < lm / 2.0
e = ef0cb * mask + ef0lin * (mask == False)
Gxi = cdf(e, depsf, r, lm, m, sV0)
mu_int = e * (1. - Gxi)
sigma = mu_int * E_f
residual = np.sum(sigma, axis=1) / n_int * (11. * 0.445) / 1000 - data
return np.sum(residual ** 2)
def simplified():
cb = CBClampedRandXi()
spirrid = SPIRRID(q=cb,
sampling_type='PGrid',
theta_vars=dict(tau=RV('gamma',
loc=0.0055,
scale=0.7,
shape=0.2),
E_f=200e3,
V_f=0.01,
r=0.00345,
m=7.0,
sV0=0.0042,
lm=1000.),
n_int=200)
def sigmac(w, lm):
spirrid.eps_vars['w'] = np.array([w])
spirrid.theta_vars['lm'] = lm
sigma_c = spirrid.mu_q_arr / spirrid.theta_vars['r']**2
return sigma_c
def maxsigma(lm):
def minfunc(w):
res = sigmac(w, lm)
return -res * (w < 200.) + 1e-5 * w**2
w_max = minimize_scalar(minfunc, bracket=(0.0001, 0.0002))
return w_max.x, sigmac(w_max.x, lm) / spirrid.theta_vars['V_f']
sigmaf = []
w_lst = []
lcs = 1. / np.linspace(8.4, 300.0, 20)
for lcsi in lcs:
print lcsi
wi, sigi = maxsigma(1. / lcsi)
sigmaf.append(sigi)
w_lst.append(wi)
plt.plot(lcs, sigmaf)
plt.plot(1. / 13.7, 1201, 'ro')
plt.plot(1. / 9.7, 1373, 'bo')
plt.errorbar(1. / 13.7, 1201, 104.4)
plt.errorbar(1. / 9.7, 1373, 36.4)
plt.ylim(0)
plt.figure()
plt.plot(lcs, w_lst)
plt.plot(1. / 13.7, 0.088, 'ro')
plt.plot(1. / 9.7, 0.05, 'bo')
plt.errorbar(1. / 13.7, 0.088, 0.003)
plt.errorbar(1. / 9.7, 0.05, 0.005)
plt.ylim(0)
plt.show()
def sigma_c_arr(k_lst, mu_r, mu_tau, COV_r_lst, COV_tau_lst):
w_arr = np.linspace(0.0, 1.0, 200)
for ki in k_lst:
Vf = Vf_k(ki)
for i, cov_r in enumerate(COV_r_lst):
loc_r = mu_r * (1 - cov_r * np.sqrt(3.0))
scale_r = cov_r * 2 * np.sqrt(3.0) * mu_r
loc_tau = mu_tau * (1 - COV_tau_lst[i] * np.sqrt(3.0))
scale_tau = COV_tau_lst[i] * 2 * np.sqrt(3.0) * mu_tau
reinf = ContinuousFibers(r=RV('uniform', loc=loc_r, scale=scale_r),
tau=RV('uniform',
loc=loc_tau,
scale=scale_tau),
V_f=Vf,
E_f=200e3,
xi=WeibullFibers(shape=7., sV0=0.003),
n_int=50)
ccb_view.model.reinforcement_lst = [reinf]
#sig_max, wmax = ccb_view.sigma_c_max
#ccb_view.model.w = wmax
sigma = ccb_view.sigma_c_arr(w_arr)
plt.plot(w_arr, sigma / Vf, lw=2, label=str(ki))
def k_influence(k_lst, mu_r, mu_tau, COV_r_lst, COV_tau_lst):
k_arr = np.linspace(0.001, 0.8, 50)
for i, cov_r in enumerate(COV_r_lst):
epsf_max_lst = []
loc_r = mu_r * (1 - cov_r * np.sqrt(3.0))
scale_r = cov_r * 2 * np.sqrt(3.0) * mu_r
loc_tau = mu_tau * (1 - COV_tau_lst[i] * np.sqrt(3.0))
scale_tau = COV_tau_lst[i] * 2 * np.sqrt(3.0) * mu_tau
for ki in k_arr:
Vf = Vf_k(ki)
ccb_view.model.w = 0.5
reinf = ContinuousFibers(
r=RV('uniform', loc=loc_r, scale=scale_r),
tau=RV('uniform', loc=loc_tau, scale=scale_tau),
V_f=Vf,
E_f=200e3,
xi=100., #WeibullFibers(shape=5., sV0=0.003),
n_int=200)
ccb_view.model.reinforcement_lst = [reinf]
epsf_max_lst.append(np.max(ccb_view.mu_epsf_arr))
plt.plot(k_arr, np.array(epsf_max_lst) * reinf.E_f)
plt.ylim(0, 3000)
plt.xlim(0, 0.8)
def short_fibers_strength_var():
sf_spirrid.codegen.implicit_var_eval = True
sf_spirrid.eps_vars['w'] = np.array([1000.])
var = sf_spirrid.var_q_arr
mu = sf_spirrid.mu_q_arr
cov_e = np.sqrt(var) / mu
Vf = 0.01
r = sf_spirrid.theta_vars['r']
Af = pi * r**2
Lc = 100.
Ac = 1600.
lf = 14.0
Ac_arr = np.linspace(1600.0, 6400., 200)
COV_Ac = np.sqrt(2. * Af / Vf / Ac_arr) * np.sqrt(cov_e**2 +
(1. - lf / 2. / Lc))
#plt.plot(Ac_arr, COV_Ac, label='COV')
Vf_arr = np.linspace(0.01, 0.04, 200)
COV_Vf = np.sqrt(2. * Af / Vf_arr / Ac) * np.sqrt(cov_e**2 +
(1. - lf / 2. / Lc))
#plt.plot(Vf_arr, COV_Vf, label='COVVf',ls='dashed',lw=3)
COV_lf = []
lf_arr = np.linspace(1., 30., 100)
for lfi in lf_arr:
sf_spirrid.theta_vars['le'] = RV('uniform', scale=lf / 2., loc=0.0)
var = sf_spirrid.var_q_arr
mu = sf_spirrid.mu_q_arr
cov_e = np.sqrt(var) / mu
COV = np.sqrt(2. * Af / Vf / Ac) * np.sqrt(cov_e**2 +
(1. - lfi / 2. / Lc))
COV_lf.append(COV)
# plt.plot(lf_arr, COV_lf, label='COV_lf')
COV_Lc = []
Lc_arr = np.linspace(50., 1000., 100)
for Lci in Lc_arr:
var = sf_spirrid.var_q_arr
mu = sf_spirrid.mu_q_arr
cov_e = np.sqrt(var) / mu
COV = np.sqrt(2. * Af / Vf / Ac) * np.sqrt(cov_e**2 +
(1. - lf / 2. / Lci))
COV_Lc.append(COV)
#plt.plot(Lc_arr, COV_Lc, label='COV_Lc')
plt.ylim(0, 0.08)
plt.legend()
plt.show()
def profiles(k_lst, mu_r, mu_tau, COV_r_lst, COV_tau_lst):
for ki in k_lst:
Vf = Vf_k(ki)
ccb_view.model.w = 0.5
for i, cov_r in enumerate(COV_r_lst):
loc_r = mu_r * (1 - cov_r * np.sqrt(3.0))
scale_r = cov_r * 2 * np.sqrt(3.0) * mu_r
loc_tau = mu_tau * (1 - COV_tau_lst[i] * np.sqrt(3.0))
scale_tau = COV_tau_lst[i] * 2 * np.sqrt(3.0) * mu_tau
reinf = ContinuousFibers(
r=RV('uniform', loc=loc_r, scale=scale_r),
tau=RV('uniform', loc=loc_tau, scale=scale_tau),
V_f=Vf,
E_f=200e3,
xi=100., #WeibullFibers(shape=5., sV0=0.003),
n_int=50)
ccb_view.model.reinforcement_lst = [reinf]
#sig_max, wmax = ccb_view.sigma_c_max
#ccb_view.model.w = wmax
x = ccb_view.x_arr[1:-1]
epsm = ccb_view.epsm_arr[1:-1]
plt.plot(x, epsm, lw=2)
plt.xlim(0, 300)
def fcn2min(x):
""" model decaying sine wave, subtract data"""
shape = 0.0539
scale = 1.44
loc = 0.00126
m = 6.7
sV0 = 0.0076
tau = RV('gamma', shape=shape, scale=scale, loc=loc)
n_int = 500
p_arr = np.linspace(0.5 / n_int, 1 - 0.5 / n_int, n_int)
tau_arr = tau.ppf(p_arr) + 1e-10
r = 3.5e-3
E_f = 180e3
T = 2. * tau_arr / r
# scale parameter with respect to a reference volume
s = ((T * (m + 1.) * sV0 ** m) /
(2. * E_f * pi * r ** 2)) ** (1. / (m + 1.))
ef0 = np.sqrt(x[:, np.newaxis] * T[np.newaxis, :] / E_f)
Gxi = 1 - np.exp(-(ef0 / s) ** (m + 1.))
mu_int = ef0 * (1 - Gxi)
sigma = mu_int * E_f
return np.sum(sigma, axis=1) / n_int * (11. * 0.445) / 1000
def sigmamu_shape_study():
length = 2000.
nx = 3000
lacor = 1.0
sigmamumin = 3.0
reinf = ContinuousFibers(r=0.0035,
tau=RV('gamma', shape=0.2, scale=0.5),
V_f=0.01,
E_f=180e3,
xi=1000.,
label='carbon',
n_int=500)
ccb = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf],
)
#for mm in [5., 10., 15., 20., 25., 30., 35.]:
for mm in [5., 10., 15., 20., 30.]:
fLc = (lacor/(lacor+length))**(1./mm)
sm = sigmamumin / (fLc * gamma(1. + 1 / mm))
random_field = RandomField(seed=True,
lacor=1.,
length=length,
nx=500,
nsim=1,
loc=.0,
shape=mm,
scale=sm,
distr_type='Weibull')
scm = SCM(length=length,
nx=nx,
random_field=random_field,
CB_model=ccb,
load_sigma_c_arr=np.linspace(0.01, 20., 200),
n_BC_CB=15)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, label='mm = ' + str(mm) + ' sm = ' + str(sm))
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.legend(loc='best')
plt.xlim(0)
plt.ylim(0)
plt.show()
def p_tau():
length = 5000.
nx = 5000
for tau_shape in [1.0, 2.0, 1000.]:
random_field = RandomField(seed=False,
lacor=5.0,
length=length,
nx=1000,
nsim=1,
loc=.0,
shape=8.,
scale=3.2,
distribution='Weibull')
reinf1 = ContinuousFibers(r=0.0035,
tau=RV('weibull_min',
loc=0.0,
shape=tau_shape,
scale=0.03),
V_f=0.01,
E_f=180e3,
xi=fibers_MC(m=5.0, sV0=10.003),
label='carbon',
n_int=500)
CB_model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf1],
)
scm = SCM(
length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 8., 100),
)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, lw=1, label=str(tau_shape))
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
def random_tau():
w_arr = np.linspace(0., .3, 200)
micro = GFRCMicro(resp_func=CBShortFiber)
meso = GFRCMeso(micro_model=micro)
macro = GFRCMacro(meso_model=meso,
W=40.,
H=40.,
L=200.,
Lf=18.,
r=8e-3,
Vf=.00020,
N_fil=100,
Ef=70e3,
snub=0.5,
xi=1e15,
tau=RV('uniform', loc=0.1, scale=0.7),
spall=0.5,
w_arr=w_arr,
phi=0.0)
mean_resp, var_resp = macro.CB_response_asymptotic
mean_N_fib = macro.N_fib_bridging.mean()
plt.plot(w_arr,
mean_resp * macro.N_fil * pi * (macro.r)**2 / macro.Vf /
mean_N_fib,
lw=2,
label='tau $\sim$ $\mathcal{U}(0.1,0.8)$')
for t in np.linspace(0.1, 0.8, 8):
macro.tau = t
mean_resp, var_resp = macro.CB_response_asymptotic
mean_N_fib = macro.N_fib_bridging.mean()
plt.plot(w_arr,
mean_resp * macro.N_fil * pi * (macro.r)**2 / macro.Vf /
mean_N_fib,
lw=1,
color='black',
label='tau = ' + str(t))
#plt.plot(w_arr, mean_r + np.sqrt(var_r), lw=2)
#plt.plot(w_arr, mean_r - np.sqrt(var_r), lw=2)
plt.xlabel('crack opening w [mm]')
plt.ylabel('force [N]')
#plt.legend(loc='best')
plt.show()
def variancePb():
points = 0.0
for i in range(100):
le = uniform(0.0, 9.0).rvs(1)
w_arr = np.array([0.1])
micro = GFRCMicro(resp_func=CBShortFiber)
meso = GFRCMeso(micro_model=micro)
theta_dict = dict(tau=RV('uniform', loc=0.1, scale=0.7),
r=8e-3,
E_f=70e3,
le=le,
phi=0.0,
snub=0.5,
xi=1e15,
spall=0.5)
points += meso.get_MC_response(
w_arr, theta_dict, N_fil=20)**2 - meso.get_asymptotic_response(
w_arr, theta_dict)[0]**2
print var
def ld():
length = 1000.
nx = 3000
random_field = RandomField(seed=True,
lacor=1.,
length=length,
nx=1000,
nsim=1,
loc=.0,
shape=45.,
scale=3.360,
distr_type='Weibull')
reinf_cont = ContinuousFibers(r=3.5e-3,
tau=RV('gamma', loc=0.0, scale=1.534, shape=.0615),
V_f=0.01,
E_f=181e3,
xi=fibers_MC(m=8.6, sV0=11.4e-3),
label='carbon',
n_int=100)
CB_model = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf_cont],
)
scm = SCM(length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 30., 200),
n_BC_CB = 12)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, color='black', lw=2, label='continuous fibers')
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.show()
def mechanisms():
m = 5.15004407
sV0 = 0.00915595
r = 3.5e-3
Ef = 181e3
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb,
sampling_type='LHS',
theta_vars=dict(E_f=Ef,
sV0=sV0,
V_f=1.0,
r=r,
m=m,
tau=RV('gamma', shape=0.03684979, scale=3.75278102, loc=0.0),
lm=1000.),
n_int=100,
)
lm_arr = np.linspace(1000., 3., 20)
sigma_u_hommech = []
for lm_i in lm_arr:
spirrid.theta_vars['lm'] = lm_i
max_w = min(30., lm_i * 0.07)
w_arr = np.linspace(0.0, max_w, 200)
spirrid.eps_vars = dict(w=w_arr)
sig_w = spirrid.mu_q_arr / r ** 2
plt.plot(w_arr, sig_w)
plt.show()
sigma_u_hommech.append(np.max(sig_w))
sigma_u_hommech = np.array(sigma_u_hommech)
plt.plot(lm_arr, sigma_u_hommech)#/np.min(sigma_u_hommech))
plt.xlabel('crack spacing')
plt.ylabel('normalized strength')
plt.show()
def multiple_phi():
w_arr = np.linspace(0., .3, 200)
micro = GFRCMicro(resp_func=CBShortFiber)
meso = GFRCMeso(micro_model=micro)
macro = GFRCMacro(meso_model=meso,
phi=0.0,
W=40.,
H=40.,
L=200.,
Lf=18.,
r=8e-3,
Vf=.00020,
N_fil=100,
Ef=70e3,
snub=0.5,
xi=1e15,
tau=RV('uniform', loc=0.1, scale=0.7),
w_arr=w_arr,
spall=0.5)
for i, p in enumerate(np.linspace(15.0, 75.0, 5)):
macro.phi = p / 180. * pi
mean_resp, var_resp = macro.CB_response_asymptotic
mean_N_fib = macro.N_fib_bridging.mean()
plt.plot(w_arr,
mean_resp * macro.N_fil * pi * (macro.r)**2 / macro.Vf /
mean_N_fib,
lw=1 + (i / 2),
label='phi = ' + str(p))
#plt.plot(w_arr, mean_r + np.sqrt(var_r), lw=2)
#plt.plot(w_arr, mean_r - np.sqrt(var_r), lw=2)
plt.xlabel('crack opening w [mm]')
plt.ylabel('force [N]')
plt.legend(loc='best')
plt.show()
from depend_CB_model import CompositeCrackBridge
from depend_CB_postprocessor import CompositeCrackBridgeView
from reinforcement import Reinforcement, WeibullFibers
from spirrid.rv import RV
from matplotlib import pyplot as plt
import numpy as np
if __name__ == '__main__':
# AR-glass
reinf1 = Reinforcement(
r=0.001, #RV('uniform', loc=0.012, scale=0.002),
tau=0.1, #RV('uniform', loc=.3, scale=.1),
V_f=0.2,
E_f=72e3,
xi=RV('weibull_min', shape=5., scale=.02),
n_int=50)
# carbon
reinf2 = Reinforcement(r=RV('uniform', loc=0.002, scale=0.002),
tau=RV('uniform', loc=.6, scale=.1),
V_f=0.05,
E_f=200e3,
xi=RV('weibull_min', shape=10., scale=.015),
n_int=15)
# instance of CompCrackBridge with matrix E and BC
model = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf1],
Ll=10.,
Lr=20.)
if __name__ == '__main__':
from etsproxy.mayavi import mlab
from stats.spirrid import make_ogrid as orthogonalize
from matplotlib import pyplot as plt
from quaducom.micro.resp_func.cb_emtrx_clamped_fiber_stress import \
CBEMClampedFiberStressSP
from quaducom.micro.resp_func.cb_emtrx_clamped_fiber_stress_residual \
import CBEMClampedFiberStressResidualSP
# filaments
r = 0.00345
V_f = 0.0103
tau = 0.1 # RV('uniform', loc=0.02, scale=.2)
E_f = 200e3
E_m = 25e3
l = RV('uniform', scale=20., loc=2.)
theta = 0.0
xi = RV('weibull_min', scale=0.01, shape=5)
phi = 1.
Ll = 40.
Lr = 20.
s0 = 0.01
m = 5.0
Pf = RV('uniform', loc=0., scale=1.0)
rf = CBEMClampedFiberStressSP()
ra = RangeAdaption(
load_sigma_c_max=22.0,
load_n_sigma_c=30,
n_w=100,
n_x=101,
'''
Created on Jun 21, 2018
@author: liyin
'''
import matplotlib.pyplot as plt
from spirrid.rv import RV
import numpy as np
tau=RV('gamma', loc=0.001260, scale=1.440, shape=0.0539)
tau_1=RV('beta', loc=0.001260, scale=1.440, shape=0.0539)
x = np.linspace(0, 10, 1000)
y = tau_1.pdf(x)
plt.plot(x,y)
plt.show()
'''
Created on 15.10.2015
@author: Yingxiong
'''
from spirrid.rv import RV
import numpy as np
import matplotlib.pyplot as plt
tau = RV('gamma', shape=0.539, scale=1.44, loc=0.00126)
x = np.linspace(0, 1, 1000)
y = tau.pdf(x)
plt.plot(x, y)
plt.xlabel('bond strength [Mpa]')
plt.title('probability distribution function')
plt.show()
#-------------------------------------------------------------------------------
#
# Copyright (c) 2012
# IMB, RWTH Aachen University,
# ISM, Brno University of Technology
# All rights reserved.
#
# This software is provided without warranty under the terms of the BSD
# license included in the Spirrid top directory "licence.txt" and may be
# redistributed only under the conditions described in the aforementioned
# license.
#
# Thanks for using Simvisage open source!
#
#-------------------------------------------------------------------------------
if __name__ == '__main__':
from spirrid.rv import RV
from etsproxy.traits.ui.api import View, Item
v = View(Item('type', label = 'Distribution type'),
Item('loc', label = 'Location'),
Item('scale', label = 'Scale'),
Item('shape', label = 'Shape'),
title = 'Random variable',
buttons = ['OK', 'Cancel'])
rv = RV(type = 'norm', scale = 10, shape = 1)
rv.configure_traits(view = v)
sampling = Property(depends_on = 'sampling')
@cached_property
def _get_sampling(self):
return self.sampling_type_(randomization = self)
codegen_type = Trait('numpy',
{'numpy' : CodeGenNumpyFactory(),
'weave' : CodeGenCFactory(),
'cython' : CodeGenCythonFactory()},
codegen = True)
codegen = Property(depends_on = 'sampling, codegen')
@cached_property
def _get_codegen(self):
return self.codegen_type_(spirrid = self)
mu_q_arr = Property(depends_on = 'sampling, codegen')
@cached_property
def _get_mu_q_arr(self):
'''getter for mean value array property .
'''
e_orth = make_ogrid(self.evar_lst)
mu_q_method = self.codegen.get_code()
mu_q_arr, var_q_arr = mu_q_method(*e_orth)
return mu_q_arr
if __name__ == '__main__':
s = SPIRRID(q = lambda eps, theta: theta * eps,
eps_vars = {'eps' : [0.1, 0.2, 0.3] },
theta_vars = {'theta' : RV('norm', 1.0, 1.0)})
print 'mean values', s.mu_q_arr
import numpy as np
from spirrid.rv import RV
from stats.pdistrib.weibull_fibers_composite_distr import \
WeibullFibers, fibers_MC
tau_shape = [0.079392235619918011, 0.070557619484416842, 0.063299300020833421, 0.057273453501868139, 0.052218314012133477, 0.04793148098051675]
tau_scale = [0.85377504364710732, 1.0754895775375046, 1.3336402595345596, 1.6285211551178209, 1.9598281655654299, 2.3273933214348754]
# p = np.linspace(1e-5, 1., 1000)
x = np.linspace(0., 0.5, 1000)
for i, k in enumerate(tau_shape):
tau = RV('gamma', shape=k, scale=tau_scale[i], loc=0.)
# x = tau.ppf(p)
plt.plot(x, tau.pdf(x), label=str(i))
plt.legend()
plt.show()
# rv1 = fibers_MC(m = 7.0, sV0=0.0095)
#
#
# pdf = rv.pdf(x)
#
# plt.plot(x, pdf, lw=2)
#
