def get_material_list(db_filename, first_id, last_id, interp_opt=None):
"""Return a list of TEProp classes.
:param db_filename: database filename containing the thermoelectric material properties
:param first_id: smallest id of a TEP.
:param last_id: largest id of a TEP.
:param interp_opt: interpolation option to be used in TEProp.
:return: (list of materials, list of material ids).
"""
material_list = [None] * (last_id + 1)
material_id_list = []
for id_num in range(first_id, last_id + 1):
try:
material = TEProp(db_filename=db_filename, id_num=id_num)
except ValueError:
pass
else:
if interp_opt is not None:
material.set_interp_opt(interp_opt)
material_list[id_num] = material
material_id_list.append(id_num)
return material_list, material_id_list
def main(num_cheb_nodes, noise_percent):
RESULT_SUBDIR = "noise_{}%".format(noise_percent)
RESULT_FILENAME_WO_PATH = "accuracy_cheb_{}_nodes_with_{}%_noise.csv".format(
num_cheb_nodes, noise_percent)
RESULT_FILENAME = os.path.join(RESULT_DIR, RESULT_SUBDIR,
RESULT_FILENAME_WO_PATH)
print("{} Chebyshev Nodes; {}% Noise; File = {}".format(
num_cheb_nodes, noise_percent, RESULT_FILENAME))
info_df = pd.read_csv(INFO_FILENAME, index_col=0)
result_df = pd.DataFrame(columns=RESULT_COLUMNS)
result_df.index.name = 'id'
for id_num in info_df.index:
print("processing id={}...".format(id_num))
mat = TEProp(db_filename=DB_FILENAME, id_num=id_num)
Seebeck_xy_data = np.asarray(mat.Seebeck.raw_data())
elec_resi_xy_data = np.asarray(mat.elec_resi.raw_data())
thrm_cond_xy_data = np.asarray(mat.thrm_cond.raw_data())
# make unique, sorted on temperature
_, Seebeck_unique_indices = np.unique(Seebeck_xy_data[:, 0],
return_index=True)
Seebeck_xy_data = Seebeck_xy_data[Seebeck_unique_indices, :]
_, elec_resi_unique_indices = np.unique(elec_resi_xy_data[:, 0],
return_index=True)
elec_resi_xy_data = elec_resi_xy_data[elec_resi_unique_indices, :]
_, thrm_cond_unique_indices = np.unique(thrm_cond_xy_data[:, 0],
return_index=True)
thrm_cond_xy_data = thrm_cond_xy_data[thrm_cond_unique_indices, :]
Seebeck_interp_func, Seebeck_exact_func, Seebeck_cheb_nodes = \
interpolate_barycentric_cheb_with_noise(Seebeck_xy_data[:, 0], Seebeck_xy_data[:, 1],
num_cheb_nodes, spline_order=SEEBECK_SPLINE_ORDER,
noise_percent=noise_percent)
elec_resi_interp_func, elec_resi_exact_func, elec_resi_cheb_nodes = \
interpolate_barycentric_cheb_with_noise(elec_resi_xy_data[:, 0], elec_resi_xy_data[:, 1],
num_cheb_nodes, spline_order=ELEC_RESI_SPLINE_ORDER,
noise_percent=noise_percent)
thrm_cond_interp_func, thrm_cond_exact_func, thrm_cond_cheb_nodes = \
interpolate_barycentric_cheb_with_noise(thrm_cond_xy_data[:, 0], thrm_cond_xy_data[:, 1],
num_cheb_nodes, spline_order=THRM_COND_SPLINE_ORDER,
noise_percent=noise_percent)
# compute the curves
Seebeck_T = np.linspace(Seebeck_xy_data[:, 0][0],
Seebeck_xy_data[:, 0][-1],
num=10000)
elec_resi_T = np.linspace(elec_resi_xy_data[:, 0][0],
elec_resi_xy_data[:, 0][-1],
num=10000)
thrm_cond_T = np.linspace(thrm_cond_xy_data[:, 0][0],
thrm_cond_xy_data[:, 0][-1],
num=10000)
Seebeck_interp_curve = Seebeck_interp_func(Seebeck_T)
Seebeck_exact_curve = Seebeck_exact_func(Seebeck_T)
dSeebeck_dT_interp_curve = Seebeck_interp_func.derivative()(Seebeck_T)
dSeebeck_dT_exact_curve = Seebeck_exact_func.derivative()(Seebeck_T)
elec_resi_interp_curve = elec_resi_interp_func(elec_resi_T)
elec_resi_exact_curve = elec_resi_exact_func(elec_resi_T)
thrm_cond_interp_curve = thrm_cond_interp_func(thrm_cond_T)
thrm_cond_exact_curve = thrm_cond_exact_func(thrm_cond_T)
# RMAE (Relative Maximum Absolute Error), divided by maximum exact value
Seebeck_RMAE = np.max(
np.abs(Seebeck_interp_curve - Seebeck_exact_curve)) / np.max(
np.abs(Seebeck_exact_curve))
dSeebeck_dT_RMAE = np.max(
np.abs(dSeebeck_dT_interp_curve -
dSeebeck_dT_exact_curve)) / np.max(
np.abs(dSeebeck_dT_exact_curve))
elec_resi_RMAE = np.max(
np.abs(elec_resi_interp_curve - elec_resi_exact_curve)) / np.max(
np.abs(elec_resi_exact_curve))
thrm_cond_RMAE = np.max(
np.abs(thrm_cond_interp_curve - thrm_cond_exact_curve)) / np.max(
np.abs(thrm_cond_exact_curve))
# RL2E (Relative L^2-Error)
Seebeck_RL2E = np.sqrt(
np.trapz(
(Seebeck_interp_curve - Seebeck_exact_curve)**2, Seebeck_T) /
np.trapz(Seebeck_exact_curve**2, Seebeck_T))
dSeebeck_dT_RL2E = np.sqrt(
np.trapz(
(dSeebeck_dT_interp_curve - dSeebeck_dT_exact_curve)**2,
Seebeck_T) / np.trapz(dSeebeck_dT_exact_curve**2, Seebeck_T))
elec_resi_RL2E = np.sqrt(
np.trapz(
(elec_resi_interp_curve - elec_resi_exact_curve)**2,
elec_resi_T) / np.trapz(elec_resi_exact_curve**2, elec_resi_T))
thrm_cond_RL2E = np.sqrt(
np.trapz(
(thrm_cond_interp_curve - thrm_cond_exact_curve)**2,
thrm_cond_T) / np.trapz(thrm_cond_exact_curve**2, thrm_cond_T))
# RL1E (Relative L^1-Error)
Seebeck_RL1E = np.trapz(
np.abs(Seebeck_interp_curve - Seebeck_exact_curve),
Seebeck_T) / np.trapz(np.abs(Seebeck_exact_curve), Seebeck_T)
dSeebeck_dT_RL1E = np.trapz(
np.abs(dSeebeck_dT_interp_curve - dSeebeck_dT_exact_curve),
Seebeck_T) / np.trapz(np.abs(dSeebeck_dT_exact_curve), Seebeck_T)
elec_resi_RL1E = np.trapz(
np.abs(elec_resi_interp_curve - elec_resi_exact_curve),
elec_resi_T) / np.trapz(np.abs(elec_resi_exact_curve), elec_resi_T)
thrm_cond_RL1E = np.trapz(
np.abs(thrm_cond_interp_curve - thrm_cond_exact_curve),
thrm_cond_T) / np.trapz(np.abs(thrm_cond_exact_curve), thrm_cond_T)
# save the result
result_df.loc[id_num] = [
Seebeck_RMAE, dSeebeck_dT_RMAE, elec_resi_RMAE, thrm_cond_RMAE,
Seebeck_RL2E, dSeebeck_dT_RL2E, elec_resi_RL2E, thrm_cond_RL2E,
Seebeck_RL1E, dSeebeck_dT_RL1E, elec_resi_RL1E, thrm_cond_RL1E
]
result_df.to_csv(RESULT_FILENAME)
def main(num_cheb_nodes, noise_percent):
result_subdir = "noise_{}%".format(noise_percent)
result_filename_wo_path = "performance_cheb_{}_nodes_with_{}%_noise.csv".format(num_cheb_nodes, noise_percent)
result_filename = os.path.join(RESULT_DIR, result_subdir, result_filename_wo_path)
print("{} Chebyshev Nodes; {}% Noise; File = {}".format(num_cheb_nodes, noise_percent, result_filename))
info_df = pd.read_csv(INFO_FILENAME, index_col=0)
result_df = pd.DataFrame(columns=RESULT_COLUMNS)
result_df.index.name = 'id'
for id_num in info_df.index:
print("processing id={}...".format(id_num))
mat = TEProp(db_filename=DB_FILENAME, id_num=id_num)
Tc = mat.min_raw_T
Th = mat.max_raw_T
Seebeck_xy_data = np.asarray(mat.Seebeck.raw_data())
elec_resi_xy_data = np.asarray(mat.elec_resi.raw_data())
thrm_cond_xy_data = np.asarray(mat.thrm_cond.raw_data())
# make unique on temperature
_, Seebeck_unique_indices = np.unique(Seebeck_xy_data[:, 0], return_index=True)
Seebeck_xy_data = Seebeck_xy_data[Seebeck_unique_indices, :]
_, elec_resi_unique_indices = np.unique(elec_resi_xy_data[:, 0], return_index=True)
elec_resi_xy_data = elec_resi_xy_data[elec_resi_unique_indices, :]
_, thrm_cond_unique_indices = np.unique(thrm_cond_xy_data[:, 0], return_index=True)
thrm_cond_xy_data = thrm_cond_xy_data[thrm_cond_unique_indices, :]
num_Seebeck_samples = len(Seebeck_xy_data)
num_elec_resi_samples = len(elec_resi_xy_data)
num_thrm_cond_samples = len(thrm_cond_xy_data)
Seebeck_interp_func, Seebeck_exact_func, Seebeck_cheb_nodes = \
interpolate_barycentric_cheb_with_noise(Seebeck_xy_data[:, 0], Seebeck_xy_data[:, 1],
num_cheb_nodes, spline_order=SEEBECK_SPLINE_ORDER,
noise_percent=noise_percent)
elec_resi_interp_func, elec_resi_exact_func, elec_resi_cheb_nodes = \
interpolate_barycentric_cheb_with_noise(elec_resi_xy_data[:, 0], elec_resi_xy_data[:, 1],
num_cheb_nodes, spline_order=ELEC_RESI_SPLINE_ORDER,
noise_percent=noise_percent)
thrm_cond_interp_func, thrm_cond_exact_func, thrm_cond_cheb_nodes = \
interpolate_barycentric_cheb_with_noise(thrm_cond_xy_data[:, 0], thrm_cond_xy_data[:, 1],
num_cheb_nodes, spline_order=THRM_COND_SPLINE_ORDER,
noise_percent=noise_percent)
# compute the max zT
T_grid = np.linspace(Tc, Th, num=10000)
Seebeck_curve = Seebeck_interp_func(T_grid)
elec_resi_curve = elec_resi_interp_func(T_grid)
thrm_cond_curve = thrm_cond_interp_func(T_grid)
zT_curve = Seebeck_curve ** 2 / elec_resi_curve / thrm_cond_curve * T_grid
index_for_max_zT = np.argmax(zT_curve)
max_zT = zT_curve[int(index_for_max_zT)]
T_for_max_zT = T_grid[index_for_max_zT]
# compute the maximum power density and efficiency
solver = ThermoelctricEquationSolver(L, A)
solver.set_bc(Tc, Th)
solver.set_te_mat_func(thrm_cond_interp_func,
elec_resi_interp_func,
Seebeck_interp_func, Seebeck_interp_func.derivative())
res = solver.compute_max_power_density()
if not res.success:
print("computation of max. power density failed for id={}".format(id_num))
continue
I_for_max_power_density = res.x
max_power_density = -res.fun
num_eval_for_max_power_density = res.nfev
res = solver.compute_max_efficiency()
if not res.success:
print("computation of max. efficiency failed for id={}".format(id_num))
continue
I_for_max_efficiency = res.x
max_efficiency = -res.fun
num_eval_for_max_efficiency = res.nfev
# test the validity
Carnot_efficiency = (Th - Tc) / Th * 100
assert (max_efficiency < Carnot_efficiency)
print("\tmax. power density= {} [W/cm^2] at I= {} [A] (nfev={})".format(max_power_density,
I_for_max_power_density,
num_eval_for_max_power_density))
print("\tmax. efficiency= {} [%] at I= {} [A] (nfev={})".format(max_efficiency, I_for_max_efficiency,
num_eval_for_max_efficiency))
# save the result
result_df.loc[id_num] = [max_zT, T_for_max_zT,
max_power_density, I_for_max_power_density,
max_efficiency, I_for_max_efficiency,
num_Seebeck_samples, num_elec_resi_samples, num_thrm_cond_samples,
]
result_df = result_df.astype({"num_Seebeck_samples": "int32",
"num_elec_resi_samples": "int32",
"num_thrm_cond_samples": "int32"})
result_df.to_csv(result_filename)
"num_elec_resi_samples",
"num_thrm_cond_samples",
]
RESULT_FILENAME = os.path.join(RESULT_DIR, "performance_exact.csv")
print("Performance for exact curves (splines); File = {}".format(
RESULT_FILENAME))
info_df = pd.read_csv(INFO_FILENAME, index_col=0)
result_df = pd.DataFrame(columns=RESULT_COLUMNS)
result_df.index.name = 'id'
for id_num in info_df.index:
print("processing id={}...".format(id_num))
mat = TEProp(db_filename=DB_FILENAME, id_num=id_num)
Tc = mat.min_raw_T
Th = mat.max_raw_T
Seebeck_xy_data = np.asarray(mat.Seebeck.raw_data())
elec_resi_xy_data = np.asarray(mat.elec_resi.raw_data())
thrm_cond_xy_data = np.asarray(mat.thrm_cond.raw_data())
# make unique on temperature
_, Seebeck_unique_indices = np.unique(Seebeck_xy_data[:, 0],
return_index=True)
Seebeck_xy_data = Seebeck_xy_data[Seebeck_unique_indices, :]
_, elec_resi_unique_indices = np.unique(elec_resi_xy_data[:, 0],
return_index=True)
elec_resi_xy_data = elec_resi_xy_data[elec_resi_unique_indices, :]
_, thrm_cond_unique_indices = np.unique(thrm_cond_xy_data[:, 0],