def transfer_same_dist(test_list, train_list, com_comp, test_rem):
if len(test_rem) == 0:
return test_list, train_list, com_comp
sizes = [len(line) for line in test_rem]
mean_test_size = np_mean(sizes)
sd = sqrt(np_var(sizes))
if sd != 0:
test_rem_dist = norm_dist(mean_test_size, sd)
p_dist = [test_rem_dist.pdf(len(line)) for line in train_list]
norm_ct = sum(p_dist)
if norm_ct != 0:
p_dist = [val / norm_ct for val in p_dist]
train_rem = rand_choice(train_list,
size=com_comp,
replace=False,
p=p_dist)
else:
train_rem = [
line for line in train_list if len(line) == mean_test_size
][:com_comp]
test_list = test_list + train_rem
for line in train_rem:
train_list.remove(line)
return test_list, train_list
def central_limit(rvs, n, length):
rv_mean = np.zeros(length)
for i in range(n):
rv = rvs(size=length)
rv_mean = rv_mean + rv
rv_mean = rv_mean / n
gaussian_params = norm_dist.fit(rv_mean)
gaussian = norm_dist(gaussian_params[0], gaussian_params[1])
return rv_mean, gaussian
def run_case(dummy, fuel, P_0, T_0, P_C, mfuel, T_a, mix):
# Set the Cantera Solution with the thermo data from the xml file.
# Get the molecular weight of the fuel and set the unit basis for
# the Solution to molar basis.
gas = ct.Solution('therm-data.xml')
fuel_mw = gas.molecular_weights[gas.species_index(fuel)]
gas.basis = 'molar'
# Set the ambient temperature and distribution. Convert the ambient
# temperature to °C to match the spec but use absolute temperature
# for the distribution.
sigma_Ta = max(2.2, (T_a - 273.15) * 0.0075) / 2
Ta_dist = norm_dist(loc=T_a, scale=sigma_Ta)
# Ta_dist = uniform(loc=T_a-sigma_Ta, scale=sigma_Ta*2)
# Ta_dist = triang(loc=T_a-sigma_Ta, scale=sigma_Ta*2, c=0.5)
# Set the tank volume and distribution.
nom_tank_volume = 0.01660
sigma_volume = 0.00001
vol_dist = norm_dist(loc=nom_tank_volume, scale=sigma_volume)
# Create the normal distributions for the initial temperature,
# initial pressure, and compressed pressure. Convert the initial
# temperature to °C to match the spec. Use the appropriate
# distribution for the desired analysis (normal, uniform,
# triangular).
sigma_T0 = max(2.2, (T_0 - 273) * 0.0075) / 2
T0_dist = norm_dist(loc=T_0, scale=sigma_T0)
# T0_dist = uniform(loc=T_0-sigma_T0, scale=sigma_T0*2)
# T0_dist = triang(loc=T_0-sigma_T0, scale=sigma_T0*2, c=0.5)
sigma_P0 = 346.6 / 2
P0_dist = norm_dist(loc=P_0, scale=sigma_P0)
sigma_PC = 5000 / 2
PC_dist = norm_dist(loc=P_C, scale=sigma_PC)
# Set the nominal injected mass of the fuel. Compute the nominal
# moles of fuel and corresponding nominal required number of moles
# of the gases.
nom_mass_fuel = mfuel
nom_mole_fuel = nom_mass_fuel / fuel_mw
nom_mole_o2 = nom_mole_fuel * mix[0]
nom_mole_n2 = nom_mole_fuel * mix[1]
nom_mole_ar = nom_mole_fuel * mix[2]
# Create the normal distribution for the fuel mass.
sigma_mass = 0.03 / 2
fuel_mass_dist = norm_dist(loc=nom_mass_fuel, scale=sigma_mass)
# Calculate the nominal pressure required for each gas to match the
# desired molar proportions. Note that the gas constant from
# Cantera is given in units of J/kmol-K, hence the factor of 1000.
nom_o2_pres = nom_mole_o2 * ct.gas_constant * T_a / (1000 *
nom_tank_volume)
nom_n2_pres = nom_mole_n2 * ct.gas_constant * T_a / (1000 *
nom_tank_volume)
nom_ar_pres = nom_mole_ar * ct.gas_constant * T_a / (1000 *
nom_tank_volume)
# Compute the pressures of each component as they are filled into
# the mixing tank. The mean of the distribution of the pressure of
# each subsequent gas is the sum of the sampled value of the
# pressure of the previous gas plus the nominal value of the
# current gas. Note that these are thus not partial pressures, but
# the total pressure in the tank after filling each component.
sigma_pressure = 346.6 / 2
o2_dist = norm_dist(loc=nom_o2_pres, scale=sigma_pressure)
o2_pres_rand = o2_dist.ppf(np.random.random_sample())
n2_pressure = o2_pres_rand + nom_n2_pres
n2_dist = norm_dist(loc=n2_pressure, scale=sigma_pressure)
n2_pres_rand = n2_dist.ppf(np.random.random_sample())
ar_pressure = n2_pres_rand + nom_ar_pres
ar_dist = norm_dist(loc=ar_pressure, scale=sigma_pressure)
ar_pres_rand = ar_dist.ppf(np.random.random_sample())
# Sample random values of the ambient temperature, tank volume, and
# fuel mass from their distributions.
Ta_rand = Ta_dist.ppf(np.random.random_sample())
tank_volume_rand = vol_dist.ppf(np.random.random_sample())
mole_fuel_rand = fuel_mass_dist.ppf(np.random.random_sample()) / fuel_mw
# Compute the number of moles of each gaseous component based on
# the sampling from the various distributions. Note that the gas
# constant from Cantera is given in units of J/kmol-K, hence the
# factor of 1000.
mole_o2_rand = o2_pres_rand * tank_volume_rand * 1000 / (ct.gas_constant *
Ta_rand)
mole_n2_rand = (n2_pres_rand - o2_pres_rand) * tank_volume_rand * 1000 / (
ct.gas_constant * Ta_rand)
mole_ar_rand = (ar_pres_rand - n2_pres_rand) * tank_volume_rand * 1000 / (
ct.gas_constant * Ta_rand)
# Compute the mole fractions of each component and set the state of
# the Cantera solution.
total_moles = sum(
[mole_fuel_rand, mole_o2_rand, mole_n2_rand, mole_ar_rand])
mole_fractions = '{fuel_name}:{fuel_mole},o2:{o2},n2:{n2},ar:{ar}'.format(
fuel_name=fuel,
fuel_mole=mole_fuel_rand / total_moles,
o2=mole_o2_rand / total_moles,
n2=mole_n2_rand / total_moles,
ar=mole_ar_rand / total_moles)
gas.TPX = None, None, mole_fractions
# Initialize the array of temperatures over which the C_p should be fit.
# The range is [first input, second input) with increment set by the third
# input. Loop through the temperatures and compute the non-dimensional
# specific heats.
temperatures = np.arange(300, 1105, 5)
gas_cp = np.zeros(len(temperatures))
for j, temp in enumerate(temperatures):
gas.TP = temp, None
gas_cp[j] = gas.cp / ct.gas_constant
# Compute the linear fit to the specific heat.
(gas_b, gas_a) = np.polyfit(temperatures, gas_cp, 1)
# Sample the values for the initial temperature, initial pressure, and
# compressed pressure.
T0_rand = T0_dist.ppf(np.random.random_sample())
P0_rand = P0_dist.ppf(np.random.random_sample())
PC_rand = PC_dist.ppf(np.random.random_sample())
# Compute the compressed temperature and return it.
lam_rand = gas_b / gas_a * np.exp(
gas_b * T0_rand / gas_a) * T0_rand * (PC_rand / P0_rand)**(1 / gas_a)
TC_rand = np.real(gas_a * lambertw(lam_rand) / gas_b)
return TC_rand
def run_case(dummy, fuel, P_0, T_0, P_C, mfuel, T_a, mix):
# Set the Cantera Solution with the thermo data from the xml file.
# Get the molecular weight of the fuel and set the unit basis for
# the Solution to molar basis.
gas = ct.Solution('therm-data.xml')
fuel_mw = gas.molecular_weights[gas.species_index(fuel)]
gas.basis = 'molar'
# Set the ambient temperature and distribution. Convert the ambient
# temperature to °C to match the spec but use absolute temperature
# for the distribution.
sigma_Ta = max(2.2, (T_a - 273.15)*0.0075)/2
Ta_dist = norm_dist(loc=T_a, scale=sigma_Ta)
# Ta_dist = uniform(loc=T_a-sigma_Ta, scale=sigma_Ta*2)
# Ta_dist = triang(loc=T_a-sigma_Ta, scale=sigma_Ta*2, c=0.5)
# Set the tank volume and distribution.
nom_tank_volume = 0.01660
sigma_volume = 0.00001
vol_dist = norm_dist(loc=nom_tank_volume, scale=sigma_volume)
# Create the normal distributions for the initial temperature,
# initial pressure, and compressed pressure. Convert the initial
# temperature to °C to match the spec. Use the appropriate
# distribution for the desired analysis (normal, uniform,
# triangular).
sigma_T0 = max(2.2, (T_0 - 273)*0.0075)/2
T0_dist = norm_dist(loc=T_0, scale=sigma_T0)
# T0_dist = uniform(loc=T_0-sigma_T0, scale=sigma_T0*2)
# T0_dist = triang(loc=T_0-sigma_T0, scale=sigma_T0*2, c=0.5)
sigma_P0 = 346.6/2
P0_dist = norm_dist(loc=P_0, scale=sigma_P0)
sigma_PC = 5000/2
PC_dist = norm_dist(loc=P_C, scale=sigma_PC)
# Set the nominal injected mass of the fuel. Compute the nominal
# moles of fuel and corresponding nominal required number of moles
# of the gases.
nom_mass_fuel = mfuel
nom_mole_fuel = nom_mass_fuel/fuel_mw
nom_mole_o2 = nom_mole_fuel*mix[0]
nom_mole_n2 = nom_mole_fuel*mix[1]
nom_mole_ar = nom_mole_fuel*mix[2]
# Create the normal distribution for the fuel mass.
sigma_mass = 0.03/2
fuel_mass_dist = norm_dist(loc=nom_mass_fuel, scale=sigma_mass)
# Calculate the nominal pressure required for each gas to match the
# desired molar proportions. Note that the gas constant from
# Cantera is given in units of J/kmol-K, hence the factor of 1000.
nom_o2_pres = nom_mole_o2*ct.gas_constant*T_a/(1000*nom_tank_volume)
nom_n2_pres = nom_mole_n2*ct.gas_constant*T_a/(1000*nom_tank_volume)
nom_ar_pres = nom_mole_ar*ct.gas_constant*T_a/(1000*nom_tank_volume)
# Compute the pressures of each component as they are filled into
# the mixing tank. The mean of the distribution of the pressure of
# each subsequent gas is the sum of the sampled value of the
# pressure of the previous gas plus the nominal value of the
# current gas. Note that these are thus not partial pressures, but
# the total pressure in the tank after filling each component.
sigma_pressure = 346.6/2
o2_dist = norm_dist(loc=nom_o2_pres, scale=sigma_pressure)
o2_pres_rand = o2_dist.ppf(np.random.random_sample())
n2_pressure = o2_pres_rand + nom_n2_pres
n2_dist = norm_dist(loc=n2_pressure, scale=sigma_pressure)
n2_pres_rand = n2_dist.ppf(np.random.random_sample())
ar_pressure = n2_pres_rand + nom_ar_pres
ar_dist = norm_dist(loc=ar_pressure, scale=sigma_pressure)
ar_pres_rand = ar_dist.ppf(np.random.random_sample())
# Sample random values of the ambient temperature, tank volume, and
# fuel mass from their distributions.
Ta_rand = Ta_dist.ppf(np.random.random_sample())
tank_volume_rand = vol_dist.ppf(np.random.random_sample())
mole_fuel_rand = fuel_mass_dist.ppf(np.random.random_sample())/fuel_mw
# Compute the number of moles of each gaseous component based on
# the sampling from the various distributions. Note that the gas
# constant from Cantera is given in units of J/kmol-K, hence the
# factor of 1000.
mole_o2_rand = o2_pres_rand*tank_volume_rand*1000/(ct.gas_constant*Ta_rand)
mole_n2_rand = (n2_pres_rand - o2_pres_rand)*tank_volume_rand*1000/(ct.gas_constant*Ta_rand)
mole_ar_rand = (ar_pres_rand - n2_pres_rand)*tank_volume_rand*1000/(ct.gas_constant*Ta_rand)
# Compute the mole fractions of each component and set the state of
# the Cantera solution.
total_moles = sum([mole_fuel_rand, mole_o2_rand, mole_n2_rand, mole_ar_rand])
mole_fractions = '{fuel_name}:{fuel_mole},o2:{o2},n2:{n2},ar:{ar}'.format(
fuel_name=fuel, fuel_mole=mole_fuel_rand/total_moles, o2=mole_o2_rand/total_moles,
n2=mole_n2_rand/total_moles, ar=mole_ar_rand/total_moles)
gas.TPX = None, None, mole_fractions
# Initialize the array of temperatures over which the C_p should be fit.
# The range is [first input, second input) with increment set by the third
# input. Loop through the temperatures and compute the non-dimensional
# specific heats.
temperatures = np.arange(300, 1105, 5)
gas_cp = np.zeros(len(temperatures))
for j, temp in enumerate(temperatures):
gas.TP = temp, None
gas_cp[j] = gas.cp/ct.gas_constant
# Compute the linear fit to the specific heat.
(gas_b, gas_a) = np.polyfit(temperatures, gas_cp, 1)
# Sample the values for the initial temperature, initial pressure, and
# compressed pressure.
T0_rand = T0_dist.ppf(np.random.random_sample())
P0_rand = P0_dist.ppf(np.random.random_sample())
PC_rand = PC_dist.ppf(np.random.random_sample())
# Compute the compressed temperature and return it.
lam_rand = gas_b/gas_a * np.exp(gas_b*T0_rand/gas_a) * T0_rand * (PC_rand/P0_rand)**(1/gas_a)
TC_rand = np.real(gas_a * lambertw(lam_rand)/gas_b)
return TC_rand
learning_rate=args.lr,
natural_gradient=args.natural,
minibatch_frac=args.minibatch_frac,
verbose=args.verbose,
)
ngb.fit(X_trainall, y_trainall)
# the final prediction for this fold
forecast = ngb.pred_dist(X_test, max_iter=best_itr)
forecast_val = ngb.pred_dist(X_val, max_iter=best_itr)
# set the appropriate scale if using a homoskedastic Normal
if args.distn == "NormalFixedVar":
scale = (forecast.var *
((forecast_val.loc - y_val.flatten())**2).mean()**0.5)
forecast = norm_dist(loc=forecast.loc, scale=scale)
ngb_rmse += [np.sqrt(mean_squared_error(forecast.mean(), y_test))]
ngb_nll += [-forecast.logpdf(y_test.flatten()).mean()]
print("[%d/%d] BestIter=%d RMSE: Val=%.4f Test=%.4f NLL: Test=%.4f" % (
itr + 1,
args.n_splits,
best_itr,
np.sqrt(val_rmse[best_itr - 1]),
np.sqrt(mean_squared_error(forecast.mean(), y_test)),
ngb_nll[-1],
))
print(
"== RMSE GBM=%.4f +/- %.4f, NGB=%.4f +/- %.4f, NLL NGB=%.4f +/ %.4f" %
def run_case(dummy, fuel, P_0, T_0, P_C, mix):
# Set the Cantera Solution with the thermo data from the xml file.
# Set the unit basis for the Solution to molar basis.
gas = ct.Solution('therm-data.xml')
gas.basis = 'molar'
# Create the normal distributions for the initial temperature,
# initial pressure, and compressed pressure. Convert the initial
# temperature to °C to match the spec. Use the appropriate
# distribution for the desired analysis (normal, uniform,
# triangular).
sigma_T0 = max(2.2, (T_0 - 273)*0.0075)/2
T0_dist = norm_dist(loc=T_0, scale=sigma_T0)
# T0_dist = triang(loc=T_0-sigma_T0, scale=2*sigma_T0, c=0.5)
# T0_dist = uniform(loc=T_0-sigma_T0, scale=2*sigma_T0)
sigma_P0 = 346.6/2
P0_dist = norm_dist(loc=P_0, scale=sigma_P0)
sigma_PC = 5000/2
PC_dist = norm_dist(loc=P_C, scale=sigma_PC)
sigma_pressure = 346.6/2
# For the experiments studied here, if there was no argon added,
# the nitrogen was added first. Otherwise, the order was o2, n2,
# ar, fuel. Compute the pressures of each component as they are
# filled into the mixing tank.
if mix['ar'] > 0:
nom_o2_pres = mix['o2']*ct.one_atm/760
nom_n2_pres = (mix['n2'] - mix['o2'])*ct.one_atm/760
nom_ar_pres = (mix['ar'] - mix['n2'])*ct.one_atm/760
nom_fuel_pres = (mix['fuel'] - mix['ar'])*ct.one_atm/760
o2_dist = norm_dist(loc=nom_o2_pres, scale=sigma_pressure)
o2_pres_rand = o2_dist.ppf(np.random.random_sample())
n2_pressure = o2_pres_rand + nom_n2_pres
n2_dist = norm_dist(loc=n2_pressure, scale=sigma_pressure)
n2_pres_rand = n2_dist.ppf(np.random.random_sample())
ar_pressure = n2_pres_rand + nom_ar_pres
ar_dist = norm_dist(loc=ar_pressure, scale=sigma_pressure)
ar_pres_rand = ar_dist.ppf(np.random.random_sample())
fuel_pressure = ar_pres_rand + nom_fuel_pres
fuel_dist = norm_dist(loc=fuel_pressure, scale=sigma_pressure)
fuel_pres_rand = fuel_dist.ppf(np.random.random_sample())
o2_par_pres = o2_pres_rand
n2_par_pres = n2_pres_rand - o2_pres_rand
ar_par_pres = ar_pres_rand - n2_pres_rand
fuel_par_pres = fuel_pres_rand - ar_pres_rand
else:
nom_n2_pres = mix['n2']*ct.one_atm/760
nom_o2_pres = (mix['o2'] - mix['n2'])*ct.one_atm/760
nom_fuel_pres = (mix['fuel'] - mix['o2'])*ct.one_atm/760
nom_ar_pres = 0
n2_dist = norm_dist(loc=nom_n2_pres, scale=sigma_pressure)
n2_pres_rand = n2_dist.ppf(np.random.random_sample())
o2_pressure = n2_pres_rand + nom_o2_pres
o2_dist = norm_dist(loc=o2_pressure, scale=sigma_pressure)
o2_pres_rand = o2_dist.ppf(np.random.random_sample())
fuel_pressure = o2_pres_rand + nom_fuel_pres
fuel_dist = norm_dist(loc=fuel_pressure, scale=sigma_pressure)
fuel_pres_rand = fuel_dist.ppf(np.random.random_sample())
n2_par_pres = n2_pres_rand
o2_par_pres = o2_pres_rand - n2_pres_rand
fuel_par_pres = fuel_pres_rand - o2_pres_rand
ar_par_pres = 0
# Compute the mole fractions of each component and set the state of
# the Cantera solution.
total_pres = sum([o2_par_pres, n2_par_pres, ar_par_pres, fuel_par_pres])
mole_fractions = '{fuel_name}:{fuel_mole},o2:{o2},n2:{n2},ar:{ar}'.format(
fuel_name=fuel, fuel_mole=fuel_par_pres/total_pres,
o2=o2_par_pres/total_pres, n2=n2_par_pres/total_pres,
ar=ar_par_pres/total_pres)
gas.TPX = None, None, mole_fractions
# Initialize the array of temperatures over which the C_p should be
# fit. The range is [first input, second input) with increment set
# by the third input. Loop through the temperatures and compute the
# non-dimensional specific heats.
temperatures = np.arange(300, 1105, 5)
gas_cp = np.zeros(len(temperatures))
for j, temp in enumerate(temperatures):
gas.TP = temp, None
gas_cp[j] = gas.cp/ct.gas_constant
# Compute the linear fit to the specific heat.
(gas_b, gas_a) = np.polyfit(temperatures, gas_cp, 1)
# Sample the values for the initial temperature, initial pressure, and
# compressed pressure.
T0_rand = T0_dist.ppf(np.random.random_sample())
P0_rand = P0_dist.ppf(np.random.random_sample())
PC_rand = PC_dist.ppf(np.random.random_sample())
# Compute the compressed temperature and return it.
lam_rand = gas_b/gas_a * np.exp(gas_b*T0_rand/gas_a) * T0_rand * (PC_rand/P0_rand)**(1/gas_a)
TC_rand = np.real(gas_a * lambertw(lam_rand)/gas_b)
return TC_rand