def create_rbf(_independent_variables, _dependent_variables):
rbf_stress_list = []
for _dependent_var in _dependent_variables:
# kriging_stress = Kriging()
rbf_stress = RBF()
rbf_stress.fit(_independent_variables, _dependent_var.reshape(-1, 1))
rbf_stress_list.append(rbf_stress)
return rbf_stress_list
def create_rbf(_independent_variables, _dependent_variables):
rbf_deformation_list = []
for _dependent_var in _dependent_variables:
# kriging_deformation = Kriging()
rbf_deformation = RBF()
rbf_deformation.fit(_independent_variables,
_dependent_var.reshape(-1, 1))
rbf_deformation_list.append(rbf_deformation)
return rbf_deformation_list
def fit(self, x_low, y_low, x_high, y_high, bf_type="MQ"):
self.x_high = x_high
self.y_high = y_high
self.low_model = RBF(rbf="gs")
self.low_model.fit(x_low, y_low)
# print(np.asarray([12.5, 0]).reshape(1, -1))
# print(self.low_model.predict(np.asarray([12.5, 0]).reshape(1, -1)))
self.y_x_high_by_low_model = self.low_model.predict(x_high)
n_train = len(self.x_high)
dist = np.zeros((n_train, n_train))
for i in range(n_train):
# 两个变量之差的平方
dist1 = (x_high - np.tile(x_high[i, :], (n_train, 1)))**2
# 对上述的平方和求开方，如果是多维变量，则相加后再开方
dist[i, :] = np.sqrt(np.sum(dist1, axis=1))
if bf_type == 'LN':
bf_sigma = 0
phi = dist
elif bf_type == 'CB':
bf_sigma = 0
phi = dist**3
elif bf_type == 'TPS':
bf_sigma = 0
phi = dist**2. * np.log(dist)
elif bf_type == 'G':
bf_sigma = np.max(np.max(dist / np.sqrt(2 * n_train)))
phi = np.exp(-dist**2. /
(2 * np.tile(bf_sigma**2, [n_train, n_train])))
elif bf_type == 'MQ':
bf_sigma = np.max(np.max(dist / np.sqrt(2 * n_train)))
phi = np.sqrt(dist**2 + np.tile(bf_sigma**2, [n_train, n_train]))
elif bf_type == 'IMQ':
bf_sigma = np.max(np.max(dist / np.sqrt(2 * n_train)))
phi = np.ones(n_train) / np.sqrt(
dist**2 + np.tile(bf_sigma**2, [n_train, n_train]))
else:
raise AttributeError(
"please input follow values: 'LN', 'CB', 'TSP', 'G', 'MQ', 'IMQ'."
)
Mphi = np.hstack((self.y_x_high_by_low_model, phi))
omega = Mphi.T.dot(np.linalg.inv(Mphi.dot(Mphi.T))).dot(y_high)
self.omega = omega
self.rbf_type = bf_type
self.bf_sigma = bf_sigma
self.phi = phi
def create_rbf(_independent_variables, _dependent_variables,
deformation_or_stress, high_or_low):
rbf_list = []
list_w_stress = []
stds = None
rbf_type = 'mq'
_i_point = 0
for _dependent_var in _dependent_variables:
rbf = RBF()
rbf.fit(_independent_variables, _dependent_var.reshape(-1, 1))
rbf_list.append(rbf)
list_w_stress.append(rbf.w.tolist())
if _i_point == 0:
stds = rbf.std
_i_point += 1
dict_rbf_model = {
"stds_" + high_or_low: stds,
"x_train_" + high_or_low: _independent_variables.flatten().tolist(),
"w_" + deformation_or_stress + "_" + high_or_low: list_w_stress,
"rbf_type_" + deformation_or_stress + "_" + high_or_low: rbf_type,
}
return dict_rbf_model
class MF_RBF(object):
def __init__(self):
self.omega = None
self.rbf_type = None
self.bf_sigma = None
self.phi = None
self.phis = None
self.y_x_low_by_low_model = None
self.low_model = None
self.y_x_high_by_low_model = None
self.x_high = None
self.y_high = None
def fit(self, x_low, y_low, x_high, y_high, bf_type="MQ"):
self.x_high = x_high
self.y_high = y_high
self.low_model = RBF(rbf="gs")
self.low_model.fit(x_low, y_low)
# print(np.asarray([12.5, 0]).reshape(1, -1))
# print(self.low_model.predict(np.asarray([12.5, 0]).reshape(1, -1)))
self.y_x_high_by_low_model = self.low_model.predict(x_high)
n_train = len(self.x_high)
dist = np.zeros((n_train, n_train))
for i in range(n_train):
# 两个变量之差的平方
dist1 = (x_high - np.tile(x_high[i, :], (n_train, 1)))**2
# 对上述的平方和求开方，如果是多维变量，则相加后再开方
dist[i, :] = np.sqrt(np.sum(dist1, axis=1))
if bf_type == 'LN':
bf_sigma = 0
phi = dist
elif bf_type == 'CB':
bf_sigma = 0
phi = dist**3
elif bf_type == 'TPS':
bf_sigma = 0
phi = dist**2. * np.log(dist)
elif bf_type == 'G':
bf_sigma = np.max(np.max(dist / np.sqrt(2 * n_train)))
phi = np.exp(-dist**2. /
(2 * np.tile(bf_sigma**2, [n_train, n_train])))
elif bf_type == 'MQ':
bf_sigma = np.max(np.max(dist / np.sqrt(2 * n_train)))
phi = np.sqrt(dist**2 + np.tile(bf_sigma**2, [n_train, n_train]))
elif bf_type == 'IMQ':
bf_sigma = np.max(np.max(dist / np.sqrt(2 * n_train)))
phi = np.ones(n_train) / np.sqrt(
dist**2 + np.tile(bf_sigma**2, [n_train, n_train]))
else:
raise AttributeError(
"please input follow values: 'LN', 'CB', 'TSP', 'G', 'MQ', 'IMQ'."
)
Mphi = np.hstack((self.y_x_high_by_low_model, phi))
omega = Mphi.T.dot(np.linalg.inv(Mphi.dot(Mphi.T))).dot(y_high)
self.omega = omega
self.rbf_type = bf_type
self.bf_sigma = bf_sigma
self.phi = phi
def predict(self, x_test):
# x_test = np.asarray([[12.5, 0]])
self.y_x_low_by_low_model = self.low_model.predict(x_test)
n_train = len(self.x_high)
n_test = len(x_test)
dists = np.zeros((n_test, n_train))
# print(x_test)
# print(np.tile(x_test[0, :], (n_train, 1)))
for i in range(n_test):
dists1 = (self.x_high - np.tile(x_test[i, :], (n_train, 1)))**2
dists[i, :] = np.sqrt(np.sum(dists1, axis=1))
# Choose different basis function to generate Euclidean distance matrix
if self.rbf_type == 'LN':
phis = dists
elif self.rbf_type == 'CB':
phis = dists**3
elif self.rbf_type == 'TPS':
phis = dists**2. * np.log(dists)
elif self.rbf_type == 'G':
phis = np.exp(-dists**2. /
(2 * np.tile(self.bf_sigma**2, [n_test, n_train])))
elif self.rbf_type == 'MQ':
phis = np.sqrt(dists**2 +
np.tile(self.bf_sigma**2, [n_test, n_train]))
elif self.rbf_type == 'IMQ':
phis = np.ones(n_train) / np.sqrt(
dists**2 + np.tile(self.bf_sigma**2, [n_test, n_train]))
else:
raise AttributeError(
"please input follow values: 'LN', 'CB', 'TSP', 'G', 'MQ', 'IMQ'."
)
# 求得测试点在低保真模型处的预测值 动态预测
self.phis = phis
# 只需要知道 yyL phis omega 就可以进行预测
# 而在这之前，XL,YL,XH yL_H YH 'MQ' 可固化 xtest yyL 动态
# print(self.y_x_low_by_low_model)
# print(self.phis)
Mphis = np.hstack((self.y_x_low_by_low_model, self.phis))
# print(Mphis)
y_MFRBF = Mphis.dot(self.omega)
# print(y_MFRBF)
return y_MFRBF