def test_dimensionReduction(self):
systemsize = 4
eigen_decayrate = 2.0
# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)
# Create stochastic collocation object
collocation = StochasticCollocation(3, "Normal")
# Create dimension reduction object
threshold_factor = 0.9
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=True)
# Initialize chaospy distribution
std_dev = 0.2 * np.ones(QoI.systemsize)
x = np.ones(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))
# Get the eigenmodes of the Hessian product and the dominant indices
dominant_space.getDominantDirections(QoI, jdist)
true_eigenvals = np.array([0.08, 0.02, 0.005, 0.00888888888888889])
err_eigenvals = abs(dominant_space.iso_eigenvals - true_eigenvals)
true_eigenvecs = np.array([[0.5, 0.5, -0.5, -0.5],
[0.5, -0.5, 0.5,
-0.5], [0.5, 0.5, 0.5, 0.5],
[0.5, -0.5, -0.5, 0.5]])
err_eigenvecs = abs(dominant_space.iso_eigenvecs - true_eigenvecs)
self.assertTrue((err_eigenvals < 1.e-15).all())
self.assertTrue((err_eigenvecs < 1.e-15).all())
self.assertEqual(dominant_space.dominant_indices, [0, 1])
def run_hadamard(systemsize, eigen_decayrate, std_dev, n_eigenmodes):
n_collocation_pts = 2
# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)
# # Create stochastic collocation object
# collocation = StochasticCollocation(n_collocation_pts, "Normal")
# Initialize chaospy distribution
x = np.random.rand(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))
threshold_factor = 0.5
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=False,
n_arnoldi_sample=71,
min_eigen_accuracy=1.e-2)
dominant_space.getDominantDirections(QoI,
jdist,
max_eigenmodes=n_eigenmodes)
# if systemsize == 64:
# print('x = \n', repr(x))
# print('std_dev = \n', repr(std_dev))
# print('iso_eigenvals = ', dominant_space.iso_eigenvals)
# print("dominant_indices = ", dominant_space.dominant_indices)
# Collocate
# collocation = StochasticCollocation(n_collocation_pts, "Normal")
# mu_j = collocation.normal.reduced_mean(QoI.eval_QoI, jdist, dominant_space)
# print "mu_j = ", mu_j
QoI_dict = {
'Hadamard': {
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
},
}
sc_obj = StochasticCollocation2(jdist,
n_collocation_pts,
'MvNormal',
QoI_dict,
include_derivs=False,
reduced_collocation=True,
dominant_dir=dominant_space.dominant_dir)
sc_obj.evaluateQoIs(jdist)
mu_j_dict = sc_obj.mean(of=['Hadamard'])
mu_j = mu_j_dict['Hadamard']
# Evaluate the analytical value of the Hadamard Quadratic
covariance = cp.Cov(jdist)
mu_analytic = QoI.eval_analytical_QoI_mean(x, covariance)
# print "mu_analytic = ", mu_analytic
relative_error = np.linalg.norm((mu_j - mu_analytic) / mu_analytic)
# print "relative_error = ", relative_error
return relative_error
def run_hadamard(systemsize, eigen_decayrate, std_dev, n_sample):
# n_collocation_pts = 2
# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)
# Create stochastic collocation object
# collocation = StochasticCollocation(n_collocation_pts, "Normal")
# Initialize chaospy distribution
x = np.random.randn(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))
threshold_factor = 0.5
dominant_space_exact = DimensionReduction(
threshold_factor=threshold_factor, exact_Hessian=True)
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=False,
n_arnoldi_sample=n_sample)
dominant_space.getDominantDirections(QoI, jdist, max_eigenmodes=20)
dominant_space_exact.getDominantDirections(QoI, jdist)
# Sort the exact eigenvalues in descending order
sort_ind = dominant_space_exact.iso_eigenvals.argsort()[::-1]
# Compare the eigenvalues of the 10 most dominant spaces
lambda_exact = dominant_space_exact.iso_eigenvals[sort_ind]
error_arr = dominant_space.iso_eigenvals[0:10] - lambda_exact[0:10]
# print 'error_arr = ', error_arr
rel_error_norm = np.linalg.norm(error_arr) / np.linalg.norm(
lambda_exact[0:10])
return rel_error_norm
def test_dominant_directions(self):
uq_systemsize = 5
mean_v = 248.136 # Mean value of input random variable
mean_alpha = 5 #
mean_Ma = 0.84
mean_re = 1.e6
mean_rho = 0.38
mean_cg = np.zeros((3))
std_dev = np.diag([1.0, 0.2, 0.01, 1.e2,
0.01]) # np.eye(uq_systemsize)
mu_init = np.array([mean_v, mean_alpha, mean_Ma, mean_re, mean_rho])
rv_dict = {
'v': mean_v,
'alpha': mean_alpha,
'Mach_number': mean_Ma,
're': mean_re,
'rho': mean_rho,
}
QoI = examples.OASAerodynamicWrapper(uq_systemsize, rv_dict)
jdist = cp.MvNormal(mu_init, std_dev)
dominant_space = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
exact_Hessian=False)
dominant_space.getDominantDirections(QoI, jdist, max_eigenmodes=3)
expected_eigenvals = np.array([0.00001345, -0.00000043, 0., 0., -0.])
expected_eigenvecs = np.array([[-0.00000003, 0.00000002],
[-1., 0.00000001],
[-0.00000001, -0.99999992],
[0., -0.00039715], [0.00000004, 0.]])
# We will only test the first 2 eigenvectors since the remaining 4 eigenvalues
# are 0.
np.testing.assert_array_almost_equal(dominant_space.iso_eigenvals,
expected_eigenvals,
decimal=6)
np.testing.assert_array_almost_equal(dominant_space.iso_eigenvecs[:,
0:2],
expected_eigenvecs,
decimal=6)
def test_reducedCollocation(self):
systemsize = 4
eigen_decayrate = 2.0
# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)
# Create stochastic collocation object
collocation = StochasticCollocation(3, "Normal")
# Create dimension reduction object
threshold_factor = 0.9
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=True)
# Initialize chaospy distribution
std_dev = 0.2 * np.ones(QoI.systemsize)
x = np.ones(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))
# Get the eigenmodes of the Hessian product and the dominant indices
dominant_space.getDominantDirections(QoI, jdist)
QoI_func = QoI.eval_QoI
# Check the mean
mu_j = collocation.normal.reduced_mean(QoI_func, jdist, dominant_space)
true_value_mu_j = 4.05
err = abs(mu_j - true_value_mu_j)
self.assertTrue(err < 1.e-13)
# Check the variance
red_var_j = collocation.normal.reduced_variance(
QoI_func, jdist, dominant_space, mu_j)
# var_j = collocation.normal.variance(QoI_func, jdist, mu_j)
analytical_var_j = QoI.eval_analytical_QoI_variance(x, cp.Cov(jdist))
err = abs(analytical_var_j - red_var_j)
self.assertTrue(err < 1.e-4)
def test_angles_2QoI(self):
systemsize = 2
theta = np.pi / 3
mu = np.random.randn(systemsize)
std_dev = np.eye(systemsize) # np.diag(np.random.rand(systemsize))
jdist = cp.MvNormal(mu, std_dev)
QoI1 = examples.Paraboloid2D(systemsize, (theta, ))
QoI2 = examples.PolyRVDV()
QoI_dict = {
'paraboloid2': {
'quadrature_degree': 3,
'reduced_collocation': False,
'QoI_func': QoI1.eval_QoI,
'output_dimensions': 1,
'include_derivs': False,
},
'PolyRVDV': {
'quadrature_degree': 3,
'reduced_collocation': False,
'QoI_func': QoI2.eval_QoI,
'output_dimensions': 1,
'include_derivs': False,
}
}
# Create the dominant space for the 2 dominant directions
threshold_factor = 0.8
QoI1_dominant_space = DimensionReduction(
threshold_factor=threshold_factor, exact_Hessian=True)
QoI2_dominant_space = DimensionReduction(
threshold_factor=threshold_factor, exact_Hessian=True)
QoI1_dominant_space.getDominantDirections(QoI1, jdist)
QoI2_dominant_space.getDominantDirections(QoI2, jdist)
S1 = QoI1_dominant_space.iso_eigenvecs[:, QoI1_dominant_space.
dominant_indices]
S2 = QoI2_dominant_space.iso_eigenvecs[:, QoI2_dominant_space.
dominant_indices]
# Finally, compute the angles
angles = utils.compute_subspace_angles(S1, S2)
self.assertTrue(abs(angles[0] - theta) < 1.e-14)
def test_dimensionReduction_arnoldi_enlarge(self):
systemsize = 128
eigen_decayrate = 1.0
# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)
# Create stochastic collocation object
collocation = StochasticCollocation(3, "Normal")
# Create dimension reduction object
threshold_factor = 0.9
dominant_space_exactHess = DimensionReduction(
threshold_factor=threshold_factor, exact_Hessian=True)
dominant_space_arnoldi = DimensionReduction(exact_Hessian=False,
n_arnoldi_sample=71)
# Initialize chaospy distribution
std_dev = np.random.rand(QoI.systemsize)
x = np.random.rand(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))
# Get the eigenmodes of the Hessian product and the dominant indices
dominant_space_exactHess.getDominantDirections(QoI, jdist)
dominant_space_arnoldi.getDominantDirections(QoI, jdist)
# Print iso_eigenvals
sort_ind1 = dominant_space_exactHess.iso_eigenvals.argsort()[::-1]
sort_ind2 = dominant_space_arnoldi.iso_eigenvals.argsort()[::-1]
lambda_exact = dominant_space_exactHess.iso_eigenvals[sort_ind1]
lambda_arnoldi = dominant_space_arnoldi.iso_eigenvals[sort_ind2]
energy_err = np.linalg.norm(lambda_arnoldi[0:10] -
lambda_exact[0:10]) / np.linalg.norm(
lambda_exact[0:10])
self.assertTrue(energy_err < 1.e-8)
def test_nonrv_derivatives_reduced_collocation(self):
# This test checks the analytical derivative w.r.t complex step
systemsize = 2
n_parameters = 2
mu = mean_2dim # np.random.randn(systemsize)
std_dev = std_dev_2dim # abs(np.diag(np.random.randn(systemsize)))
jdist = cp.MvNormal(mu, std_dev)
QoI = examples.PolyRVDV(data_type=complex)
dv = np.random.randn(systemsize) + 0j
QoI.set_dv(dv)
# Create dimension reduction object
threshold_factor = 0.9
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=True)
# Get the eigenmodes of the Hessian product and the dominant indices
dominant_space.getDominantDirections(QoI, jdist)
dominant_dir = dominant_space.iso_eigenvecs[:, dominant_space.
dominant_indices]
# Create the Stochastic Collocation object
deriv_dict = {
'dv': {
'dQoI_func': QoI.eval_QoIGradient_dv,
'output_dimensions': n_parameters
}
}
QoI_dict = {
'PolyRVDV': {
'quadrature_degree': 3,
'reduced_collocation': True,
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
'dominant_dir': dominant_dir,
'include_derivs': True,
'deriv_dict': deriv_dict
}
}
sc_obj = StochasticCollocation3(jdist,
'MvNormal',
QoI_dict,
data_type=complex)
sc_obj.evaluateQoIs(jdist)
dmu_j = sc_obj.dmean(of=['PolyRVDV'], wrt=['dv'])
dvar_j = sc_obj.dvariance(of=['PolyRVDV'], wrt=['dv'])
dstd_dev = sc_obj.dStdDev(of=['PolyRVDV'], wrt=['dv'])
# Lets do complex step
pert = complex(0, 1e-30)
dmu_j_complex = np.zeros(n_parameters, dtype=complex)
dvar_j_complex = np.zeros(n_parameters, dtype=complex)
dstd_dev_complex = np.zeros(n_parameters, dtype=complex)
for i in range(0, n_parameters):
dv[i] += pert
QoI.set_dv(dv)
sc_obj.evaluateQoIs(jdist)
mu_j = sc_obj.mean(of=['PolyRVDV'])
var_j = sc_obj.variance(of=['PolyRVDV'])
std_dev_j = np.sqrt(var_j['PolyRVDV'][0, 0])
dmu_j_complex[i] = mu_j['PolyRVDV'].imag / pert.imag
dvar_j_complex[i] = var_j['PolyRVDV'].imag / pert.imag
dstd_dev_complex[i] = std_dev_j.imag / pert.imag
dv[i] -= pert
err1 = dmu_j['PolyRVDV']['dv'] - dmu_j_complex
self.assertTrue((err1 < 1.e-13).all())
err2 = dvar_j['PolyRVDV']['dv'] - dvar_j_complex
self.assertTrue((err2 < 1.e-10).all())
err3 = dstd_dev['PolyRVDV']['dv'] - dstd_dev_complex
self.assertTrue((err2 < 1.e-12).all())
return mu_j, var_j
if __name__ == "__main__":
# Step 1: Instantiate all objects needed for test
uq_systemsize = 6
UQObj = UQScanEagleOpt(uq_systemsize, all_rv=True)
UQObj.QoI.p['oas_scaneagle.wing.thickness_cp'] = 1.e-3 * np.array(
[5.5, 5.5, 5.5])
UQObj.QoI.p['oas_scaneagle.wing.twist_cp'] = 2.5 * np.ones(3)
UQObj.QoI.p.final_setup()
# Dominant dominant
dominant_space = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
exact_Hessian=False,
sample_radius=1.e-2)
dominant_space.getDominantDirections(UQObj.QoI,
UQObj.jdist,
max_eigenmodes=4)
# # Full collocation
# sc_obj = StochasticCollocation2(UQObj.jdist, 3, 'MvNormal', UQObj.QoI_dict,
# include_derivs=False)
# sc_obj.evaluateQoIs(UQObj.jdist, include_derivs=False)
# REduced collocation
dominant_dir = dominant_space.iso_eigenvecs[:, dominant_space.
dominant_indices]
sc_obj = StochasticCollocation2(UQObj.jdist,
3,
'MvNormal',
'surrogate info full path':
os.environ['HOME'] +
'/UserApps/pyStatReduce/pystatreduce/optimize/dymos_interceptor/quadratic_surrogate/'
+ fname,
'surrogate_type':
'kriging',
'kriging_theta':
1.e-4,
'correlation function':
'squar_exp',
}
surrogate_QoI = InterceptorSurrogateQoI(systemsize, surrogate_input_dict)
# Get the dominant directions
dominant_space = DimensionReduction(n_arnoldi_sample=systemsize + 1,
exact_Hessian=False,
sample_radius=1.e-1)
dominant_space.getDominantDirections(surrogate_QoI, jdist, max_eigenmodes=10)
# Get the Active Subspace
active_subspace = ActiveSubspace(surrogate_QoI,
n_dominant_dimensions=20,
n_monte_carlo_samples=1000,
read_rv_samples=False,
use_svd=True,
use_iso_transformation=True)
active_subspace.getDominantDirections(surrogate_QoI, jdist)
# Now get the two angles
n_bases = 2
eigenvecs_dom = dominant_space.iso_eigenvecs[:, 0:n_bases]
def run_hadamard(systemsize, eigen_decayrate, std_dev, n_eigenmodes):
n_collocation_pts = 3
# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)
# Initialize chaospy distribution
x = np.random.rand(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))
threshold_factor = 1.0
use_exact_Hessian = False
if use_exact_Hessian:
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=True)
dominant_space.getDominantDirections(QoI, jdist)
dominant_dir = dominant_space.iso_eigenvecs[:, 0:n_eigenmodes]
else:
dominant_space = DimensionReduction(threshold_factor=threshold_factor,
exact_Hessian=False,
n_arnoldi_sample=71,
min_eigen_accuracy=1.e-2)
dominant_space.getDominantDirections(QoI,
jdist,
max_eigenmodes=n_eigenmodes)
dominant_dir = dominant_space.dominant_dir
# print "dominant_indices = ", dominant_space.dominant_indices
# Create stochastic collocation object
# collocation = StochasticCollocation(n_collocation_pts, "Normal")
QoI_dict = {
'Hadamard': {
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
},
}
sc_obj = StochasticCollocation2(jdist,
n_collocation_pts,
'MvNormal',
QoI_dict,
include_derivs=False,
reduced_collocation=True,
dominant_dir=dominant_dir)
sc_obj.evaluateQoIs(jdist)
# Collocate
# mu_j = collocation.normal.reduced_mean(QoI, jdist, dominant_space)
mu_j = sc_obj.mean(of=['Hadamard'])
var_j = sc_obj.variance(of=['Hadamard'])
std_dev_j = np.sqrt(var_j['Hadamard'])
# print "mu_j = ", mu_j
# Evaluate the analytical value of the Hadamard Quadratic
covariance = cp.Cov(jdist)
mu_analytic = QoI.eval_analytical_QoI_mean(x, covariance)
var_analytic = QoI.eval_analytical_QoI_variance(x, covariance)
std_dev_analytic = np.sqrt(var_analytic)
# print "mu_analytic = ", mu_analytic
relative_error_mu = np.linalg.norm(
(mu_j['Hadamard'] - mu_analytic) / mu_analytic)
relative_err_var = np.linalg.norm(
(var_j['Hadamard'] - var_analytic) / var_analytic)
relative_err_std_dev = np.linalg.norm(
(std_dev_j - std_dev_analytic) / std_dev_analytic)
# print "relative_error = ", relative_error
return relative_error_mu, relative_err_var, relative_err_std_dev
def __init__(self,
rv_dict,
design_point,
rdo_factor=2.0,
krylov_pert=1.e-1,
active_subspace=False,
max_eigenmodes=2,
n_as_samples=1000):
self.rdo_factor = rdo_factor
# Total number of nodes to use in the spanwise (num_y) and
# chordwise (num_x) directions. Vary these to change the level of fidelity.
num_y = 21
num_x = 3
mesh_dict = {
'num_y': num_y,
'num_x': num_x,
'wing_type': 'rect',
'symmetry': True,
'span_cos_spacing': 0.5,
'span': 3.11,
'root_chord': 0.3,
}
self.uq_systemsize = len(rv_dict)
dv_dict = {
'n_twist_cp': 3,
'n_thickness_cp': 3,
'n_CM': 3,
'n_thickness_intersects': 10,
'n_constraints': 1 + 10 + 1 + 3 + 3,
'ndv': 3 + 3 + 2,
'mesh_dict': mesh_dict,
'rv_dict': rv_dict
}
mu, std_dev = self.get_input_rv_statistics(rv_dict)
self.jdist = cp.MvNormal(mu, std_dev)
self.QoI = examples.oas_scaneagle2.OASScanEagleWrapper2(
self.uq_systemsize, dv_dict)
self.QoI.p['oas_scaneagle.wing.thickness_cp'] = design_point[
'thickness_cp']
self.QoI.p['oas_scaneagle.wing.twist_cp'] = design_point['twist_cp']
self.QoI.p['oas_scaneagle.wing.sweep'] = design_point['sweep']
self.QoI.p['oas_scaneagle.alpha'] = design_point['alpha']
self.QoI.p.final_setup()
# Figure out which dimension reduction technique to use
start_time = time.time()
if active_subspace == False:
self.dominant_space = DimensionReduction(
n_arnoldi_sample=self.uq_systemsize + 1,
exact_Hessian=False,
sample_radius=krylov_pert)
self.dominant_space.getDominantDirections(
self.QoI, self.jdist, max_eigenmodes=max_eigenmodes)
else:
self.dominant_space = ActiveSubspace(
self.QoI,
n_dominant_dimensions=max_eigenmodes,
n_monte_carlo_samples=n_as_samples,
read_rv_samples=False,
use_svd=True,
use_iso_transformation=True)
self.dominant_space.getDominantDirections(self.QoI, self.jdist)
# Reset the design point
self.QoI.p['oas_scaneagle.wing.thickness_cp'] = design_point[
'thickness_cp']
self.QoI.p['oas_scaneagle.wing.twist_cp'] = design_point[
'twist_cp']
self.QoI.p['oas_scaneagle.wing.sweep'] = design_point['sweep']
self.QoI.p['oas_scaneagle.alpha'] = design_point['alpha']
self.QoI.p.final_setup()
# Reset the random variables
self.QoI.update_rv(mu)
time_elapsed = time.time() - start_time
print('time_elapsed =', time_elapsed)
dfuelburn_dict = {
'dv': {
'dQoI_func': self.QoI.eval_ObjGradient_dv,
'output_dimensions': dv_dict['ndv'],
}
}
dcon_dict = {
'dv': {
'dQoI_func': self.QoI.eval_ConGradient_dv,
'output_dimensions': dv_dict['ndv']
}
}
dcon_failure_dict = {
'dv': {
'dQoI_func': self.QoI.eval_ConFailureGradient_dv,
'output_dimensions': dv_dict['ndv'],
}
}
self.QoI_dict = {
'fuelburn': {
'QoI_func': self.QoI.eval_QoI,
'output_dimensions': 1,
'deriv_dict': dfuelburn_dict
},
'constraints': {
'QoI_func': self.QoI.eval_AllConstraintQoI,
'output_dimensions': dv_dict['n_constraints'],
'deriv_dict': dcon_dict
},
'con_failure': {
'QoI_func': self.QoI.eval_confailureQoI,
'output_dimensions': 1,
'deriv_dict': dcon_failure_dict
}
}
print('mu_j_mc = ', mu_j['fuelburn'][0])
print('var_j_mc = ', var_j['fuelburn'][0])
print("time for sampling = ", t_sampling - start_time)
print('time mu = ', time_elapsed_mu)
print('time var = ', time_elapsed_var)
elif sys.argv[1] == 'reduced':
# mu_j_full = 5.341619712754059 # RV :- Ma, CT, W0, R, load_factor, mrho
# var_j_full = 3.786547863834123 #
mu_j_full = 5.342395801650296 # RV :- Ma, CT, W0, R, load_factor, mrho, altitude
var_j_full = 3.790677219208799 # (3 collocation pts per ditection)
# Create dimension reduction based on system arguments
dominant_space = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
exact_Hessian=False,
sample_radius=sample_radii[int(
sys.argv[2])])
dominant_space.getDominantDirections(QoI,
jdist,
max_eigenmodes=int(sys.argv[3]))
print('iso_eigenvals = ', dominant_space.iso_eigenvals)
print('iso_eigenvecs = \n', dominant_space.iso_eigenvecs)
# Create a stochastic collocation object
sc_obj = StochasticCollocation2(jdist,
2,
'MvNormal',
QoI_dict,
include_derivs=False,
reduced_collocation=True,
dominant_dir=dominant_space.dominant_dir)
sc_obj.evaluateQoIs(jdist, include_derivs=False)
'rv_dict': rv_dict
}
# Create the base openaerostruct problem wrapper that will be used by the
# different quantity of interests
oas_obj = OASScanEagleWrapper(uq_systemsize, input_dict, include_dict_rv=True)
# Create the QoI objects
obj_QoI = Fuelburn(uq_systemsize, oas_obj)
failure_QoI = StressConstraint(uq_systemsize, oas_obj)
lift_con_QoI = LiftConstraint(uq_systemsize, oas_obj)
moment_con_QoI = MomentConstraint(uq_systemsize, oas_obj)
# Create the dimension reduction objects for all of the different quantity of interest
# Get the dominant directions of the different QoIs here
dominant_space_obj = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
exact_Hessian=False,
sample_radius=1.e-2)
dominant_space_obj.getDominantDirections(obj_QoI, jdist, max_eigenmodes=4)
dominant_space_failure = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
exact_Hessian=False,
sample_radius=1.e-2)
dominant_space_failure.getDominantDirections(failure_QoI,
jdist,
max_eigenmodes=4)
dominant_space_liftcon = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
exact_Hessian=False,
sample_radius=1.e-2)
dominant_space_liftcon.getDominantDirections(lift_con_QoI,
jdist,
max_eigenmodes=4)
dominant_space_CM = DimensionReduction(n_arnoldi_sample=uq_systemsize + 1,
def __init__(self, uq_systemsize, all_rv=False):
self.rdo_factor = 2.0
# Total number of nodes to use in the spanwise (num_y) and
# chordwise (num_x) directions. Vary these to change the level of fidelity.
num_y = 21
num_x = 3
mesh_dict = {'num_y' : num_y,
'num_x' : num_x,
'wing_type' : 'rect',
'symmetry' : True,
'span_cos_spacing' : 0.5,
'span' : 3.11,
'root_chord' : 0.3,
}
rv_dict = {'Mach_number' : mean_Ma,
'CT' : mean_TSFC,
'W0' : mean_W0,
'E' : mean_E, # surface RV
'G' : mean_G, # surface RV
'mrho' : mean_mrho, # surface RV
}
dv_dict = {'n_twist_cp' : 3,
'n_thickness_cp' : 3,
'n_CM' : 3,
'n_thickness_intersects' : 10,
'n_constraints' : 1 + 10 + 1 + 3 + 3,
'ndv' : 3 + 3 + 2,
'mesh_dict' : mesh_dict,
'rv_dict' : rv_dict
}
mu = np.array([mean_Ma, mean_TSFC, mean_W0, mean_E, mean_G, mean_mrho])
std_dev = np.diag([0.005, 0.00607/3600, 0.2, 5.e9, 1.e9, 50])
self.jdist = cp.MvNormal(mu, std_dev)
self.QoI = examples.OASScanEagleWrapper(uq_systemsize, dv_dict)
# This setup is according to the one in the scaneagle paper
self.QoI.p['oas_scaneagle.wing.thickness_cp'] = 1.e-3 * np.array([5.5, 5.5, 5.5])
self.QoI.p['oas_scaneagle.wing.twist_cp'] = 2.5*np.ones(3)
self.QoI.p.final_setup()
# Compute the dominant directions
self.dominant_space = DimensionReduction(n_arnoldi_sample=uq_systemsize+1,
exact_Hessian=False,
sample_radius=1.e-2)
self.dominant_space.getDominantDirections(self.QoI, self.jdist, max_eigenmodes=2)
dfuelburn_dict = {'dv' : {'dQoI_func' : self.QoI.eval_ObjGradient_dv,
'output_dimensions' : dv_dict['ndv'],
}
}
dcon_dict = {'dv' : {'dQoI_func' : self.QoI.eval_ConGradient_dv,
'output_dimensions' : dv_dict['ndv']
}
}
dcon_failure_dict = {'dv' : {'dQoI_func' : self.QoI.eval_ConFailureGradient_dv,
'output_dimensions' : dv_dict['ndv'],
}
}
self.QoI_dict = {'fuelburn' : {'QoI_func' : self.QoI.eval_QoI,
'output_dimensions' : 1,
'deriv_dict' : dfuelburn_dict
},
'constraints' : {'QoI_func' : self.QoI.eval_AllConstraintQoI,
'output_dimensions' : dv_dict['n_constraints'],
'deriv_dict' : dcon_dict
},
'con_failure' : {'QoI_func' : self.QoI.eval_confailureQoI,
'output_dimensions' : 1,
'deriv_dict' : dcon_failure_dict
}
}
0.02550976, 0.01783919, 0.0125073, 0.01226541
])
jdist = cp.MvNormal(mu, np.diag(std_dev[:-1]))
# Create the QoI object
QoI = InterceptorSurrogateQoI(systemsize, input_dict)
QoI_dict = {
'time_duration': {
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
}
}
# Get the dominant directions
dominant_space = DimensionReduction(n_arnoldi_sample=int(sys.argv[1]),
exact_Hessian=False,
sample_radius=1.e-1)
dominant_space.getDominantDirections(QoI, jdist, max_eigenmodes=15)
n_dominant_dir = 10 # int(sys.argv[2])
dominant_dir = dominant_space.iso_eigenvecs[:, 0:n_dominant_dir]
# Do the monte carlo integration
nsample = 10000
mc_obj = MonteCarlo(nsample,
jdist,
QoI_dict,
reduced_collocation=False,
include_derivs=False)
mc_obj.getSamples(jdist, include_derivs=False)
mu_j = mc_obj.mean(jdist, of=['time_duration'])