def run_sp_model_example(q, k, t, b, c, d, show_plot=False):
"""
Run the SP model example and the inverse to show how a synthetic curve can be obtained
:param q:
:param k:
:param t:
:param b:
:param c:
:param d:
:return:
"""
dT = sp_model_nominal(q, k, t, b, c, d)
dT_synth0, t0 = cut_to_zero(dT, t)
dt = t0[1] - t0[0]
kdet, bdet, tth, dT_sig_pro = sp_model_signal_inv(dT_synth0, t0, dt, q, output_model_array=True,
cutoff=0.5, filter=False)
dT_sig_pro_comp = dT_sp_model_signal(q, kdet, tth, bdet)
dT_sig_pro_comp_diff = dT_sig_pro - dT_sig_pro_comp
kd, bd, cd, dd = obtain_sp_vars_from_curve(q, t0, dT_synth0, kdet)
dT_comp = sp_model_nominal(q, kd, t0, bd, cd, dd)
dT_comp_diff = dT_synth0 - dT_comp
fig = plt.figure(num=None, figsize=SQUARE_FIGSIZE)
# (a)
ax = fig.add_subplot(2, 2, 1)
# ax.set_xlabel('Time (s)')
ticklabels_off_x()
ax.set_ylabel(create_label('$\Delta T$', 'K'))
ax.plot(t0, dT_synth0, color=MODELLED_COLOR, linewidth=4, label='Forward')
ax.plot(t0, dT_comp, color='grey', ls='dashed', label='Inverse')
ax.legend()
ax.set_title('(a)', loc='center')
# (b)
ax = fig.add_subplot(2, 2, 2)
# ax.set_xlabel('Time (s)')
ticklabels_off_x()
ax.set_ylabel(create_label('$\Delta T \hspace{1}$ Forward - Inverse', 'K'))
ax.plot(t0, dT_comp_diff, color=GREY_COLOR, label='Difference', ls='solid')
ax.legend()
ax.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
ax.set_title('(b)', loc='center')
# (c)
ax = fig.add_subplot(2, 2, 3)
ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta \Gamma _{5} \hspace{0.3} (\hspace{0.3} t \hspace{0.3})$', ''))
ax.plot(tth, dT_sig_pro_comp, color=MODELLED_COLOR, linewidth=4, label='Forward (Processed)')
ax.plot(tth, dT_sig_pro, color='grey', ls='dashed', label='Theoretical')
ax.set_title('(c)', loc='center')
ax.legend()
# (d)
ax = fig.add_subplot(2, 2, 4)
ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta \Gamma _{5} \hspace{0.3} (\hspace{0.3} t \hspace{0.3}) \hspace{1}$ '
'Forward - Inverse', 'K'))
ax.plot(tth, dT_sig_pro_comp_diff, color=GREY_COLOR, ls='solid')
ax.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
ax.set_title('(d)', loc='center')
plt.tight_layout()
plt.savefig(FIG_PATH + SP_SYNTH_FILENAME_EXAMPLE + PLOT_EXTENSION)
if show_plot:
plt.show()
def run_dp_model_inv_test(show_plot=False, run_full=False):
"""
Run the SP model inverse test to show an example of the reconstruction
:param show_plot: True to show the plot
:param run_full: True to run the reconstruction over the heating and cooling curve
False to run the reconstruction over only the heating curve
:return:
"""
################################################
# MAIN
################################################
q = 45
k = 5.2
theta_m = 0.59
theta_o = 9.2e-3
theta_w = 0.40
C = get_volumetric_heat_capacity(theta_m, theta_o, theta_w)
alpha = get_alpha_k_C(k, C)
r0 = 6e-3
fs = 12
t0 = 0
max_delta_r = 5.0e-3
timestep = 1 / fs
t_heat = 8 # 8 seconds for heating (when working with the full curve)
if run_full:
t1 = 60*3 # 3 minutes for heating and cooling
else:
t1 = 8 # 8 seconds for heating
# create the time vector
t = np.arange(t0, t1, timestep)
# required since t0 = 0 and this cannot be used since Ei(x=0) is not defined
rstep = length(t)-1
###########################################################
# LINEAR CHANGE (INCREASE)
###########################################################
print('Computing for linear increase in r(t)...')
r = r0 + np.linspace(0, max_delta_r, rstep)
dT_dual, dT_dual_fixed, r_det_mm, r_mm, r_t_det_diff, tt = \
run_plot_output(alpha, fs, k, q, r0, run_full, t_heat, t, r)
###########################################################
# LINEAR CHANGE (DECREASE)
###########################################################
print('Computing for linear decrease in r(t)...')
rdec = r[::-1]
r0_dec = rdec[0]
dT_dual_dec, dT_dual_fixed_dec, r_det_mm_dec, r_mm_dec, r_t_det_diff_dec, tt = \
run_plot_output(alpha, fs, k, q, r0_dec, run_full, t_heat, t, rdec)
###########################################################
# RANDOM WALK
###########################################################
print('Computing for Brownian random walk in r(t)...')
nr = length(r)
rb = brownian_noise_norm(nr, r0, r0 + max_delta_r)
rb0 = rb[0]
dT_dual_bn, dT_dual_fixed_bn, r_det_mm_bn, r_mm_bn, r_t_det_diff_bn, tt = \
run_plot_output(alpha, fs, k, q, rb0, run_full, t_heat, t, rb)
###########################################################
# FIGURES
###########################################################
print('DONE COMPUTING, RUNNING FIGURES')
fig = plt.figure(num=None, figsize=LARGE_SQUARE_FIGSIZE)
# INCREASE
# (a)
ax = fig.add_subplot(3, 3, 1)
ax.plot(tt, dT_dual_fixed, label='DP Fixed Radius', color='orange')
ax.plot(tt, dT_dual, label='DP Variable Radius', color="cornflowerblue")
# ax.set_xlabel('Time (s)')
ticklabels_off_x()
ax.set_ylabel(create_label('$\Delta T \hspace{1}$', 'K'))
ax.legend()
ax.set_title('(a)', loc='center')
# (b)
ax = fig.add_subplot(3, 3, 2)
ax.plot(tt, r_mm, color=MODELLED_COLOR, linewidth=4, label='Forward')
ax.plot(tt, r_det_mm, color='grey', ls='dashed', label='Inverse')
ax.set_ylabel(create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})$', 'mm'))
# ax.set_xlabel('Time (s)')
ticklabels_off_x()
ax.legend()
ax.set_title('(b)', loc='center')
# (c)
ax = fig.add_subplot(3, 3, 3)
ax.plot(tt, r_t_det_diff, color='grey', label='difference')
ax.set_ylabel(create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})\hspace{1}$ Forward -\n Inverse', 'mm'))
# ax.set_xlabel('Time (s)')
ticklabels_off_x()
ax.set_title('(c)', loc='center')
# DECREASE
# (d)
ax = fig.add_subplot(3, 3, 4)
ax.plot(tt, dT_dual_fixed_dec, label='DP Fixed Radius', color='orange')
ax.plot(tt, dT_dual_dec, label='DP Variable Radius', color="cornflowerblue")
ticklabels_off_x()
# ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta T \hspace{1}$', 'K'))
# ax.legend()
ax.set_title('(d)', loc='center')
# (e)
ax = fig.add_subplot(3, 3, 5)
ax.plot(tt, r_mm_dec, color=MODELLED_COLOR, linewidth=4, label='Forward')
ax.plot(tt, r_det_mm_dec, color='grey', ls='dashed', label='Inverse')
ax.set_ylabel(create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})$', 'mm'))
ticklabels_off_x()
# ax.set_xlabel('Time (s)')
# ax.legend()
ax.set_title('(e)', loc='center')
# (f)
ax = fig.add_subplot(3, 3, 6)
ax.plot(tt, r_t_det_diff_dec, color='grey', label='difference')
ax.set_ylabel(create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})\hspace{1}$ Forward -\n Inverse', 'mm'))
ticklabels_off_x()
# ax.set_xlabel('Time (s)')
ax.set_title('(f)', loc='center')
# RANDOM WALK
# (g)
ax = fig.add_subplot(3, 3, 7)
ax.plot(tt, dT_dual_fixed_bn, label='DP Fixed Radius', color='orange')
ax.plot(tt, dT_dual_bn, label='DP Variable Radius', color="cornflowerblue")
ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta T \hspace{1}$', 'K'))
# ax.legend()
ax.set_title('(g)', loc='center')
# (h)
ax = fig.add_subplot(3, 3, 8)
ax.plot(tt, r_mm_bn, color=MODELLED_COLOR, linewidth=4, label='Forward')
ax.plot(tt, r_det_mm_bn, color='grey', ls='dashed', label='Inverse')
ax.set_ylabel(create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})$', 'mm'))
ax.set_xlabel('Time (s)')
ylim = list(ax.get_ylim())
ylim[1] += 0.20*(ylim[1]-ylim[0])
ax.set_ylim(ylim)
ax.legend()
ax.set_title('(h)', loc='center')
# (i)
ax = fig.add_subplot(3, 3, 9)
ax.plot(tt, r_t_det_diff_bn, color='grey', label='difference')
ax.set_ylabel(create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})\hspace{1}$ Forward -\n Inverse', 'mm'))
ax.set_xlabel('Time (s)')
ax.set_title('(i)', loc='center')
# SHOW AND SAVE FIGURE
plt.tight_layout()
plt.savefig(FIG_PATH + DP_SYNTH_FILENAME_EXAMPLE + PLOT_EXTENSION)
if show_plot:
plt.show()
def plot_main_all_data(show_plot=False):
print('Loading data...')
experiments = pickle.load(open(DATA_PICKLE_FILE_VEC, "rb"))
theta_nom_sand, rho_nom_sand, theta_sig_sand, rho_sig_sand, \
alpha_det_sand, alpha_sig_sand, k_det_sand, kdet_sig_sand, kdet_linear_sand, \
qav_vec_sand, qknown_vec_sand = experiments[SAND_NAME]
theta_nom_peat, rho_nom_peat, theta_sig_peat, rho_sig_peat, \
alpha_det_peat, alpha_sig_peat, k_det_peat, kdet_sig_peat, kdet_linear_peat, \
qav_vec_peat, qknown_vec_peat \
= experiments[PEAT_NAME]
print('Done loading data...')
# first sequence of experiments
ns = length(theta_nom_sand)
xs = np.linspace(1, ns, ns)
# second sequence of experiments
nnp = length(theta_nom_peat)
xp = np.linspace(xs[-1] + 1, xs[-1] + nnp, nnp)
#################################################################
fig = plt.figure(num=None, figsize=SQUARE_FIGSIZE)
lim_theta = [0, 1.0]
lim_rho = [400, 2500]
# (a) theta_sand
ax = fig.add_subplot(2, 2, 1)
ax.plot(xs, theta_nom_sand, 's', label='Heating and Cooling DP')
ax.plot(xs, theta_sig_sand, 'o', label='Signal Processing SP and DP')
ax.axhline(THETA_NOMINAL_SAND,
linestyle='--',
label='Nominal Value',
color='gray')
ax.set_ylim(lim_theta)
set_x_axis_integer()
ax.set_ylabel(create_label(r'$\theta_w$', ''))
ticklabels_off_x()
ax.legend()
ax.set_title('(a)', loc='left')
# (b) theta_peat
ax = fig.add_subplot(2, 2, 2)
ax.plot(xp, theta_nom_peat, 's', label='Heating and Cooling DP')
ax.plot(xp, theta_sig_peat, 'o', label='Signal Processing SP and DP')
ax.axhline(THETA_NOMINAL_PEAT,
linestyle='--',
label='Nominal Value',
color='gray')
ax.set_ylim(lim_theta)
ticklabels_off_y()
ticklabels_off_x()
set_x_axis_integer()
ax.set_title('(b)', loc='left')
# (c) density of sand
ax = fig.add_subplot(2, 2, 3)
ax.plot(xs, rho_nom_sand, 's', label='Heating and Cooling DP')
ax.plot(xs, rho_sig_sand, 'o', label='Signal Processing SP and DP')
ax.axhline(DENSITY_NOMINAL_SAND,
linestyle='--',
label='Nominal Value',
color='gray')
ax.set_ylim(lim_rho)
set_x_axis_integer()
ax.set_ylabel(create_label(r'$\rho$', 'kg m^-3'))
ax.set_xlabel('Experiment #')
ax.set_title('(c)', loc='left')
# (d) density of peat
ax = fig.add_subplot(2, 2, 4)
ax.plot(xp, rho_nom_peat, 's', label='Heating and Cooling DP')
ax.plot(xp, rho_sig_peat, 'o', label='Signal Processing SP and DP')
ax.axhline(DENSITY_NOMINAL_PEAT,
linestyle='--',
label='Nominal Value',
color='gray')
ax.set_ylim(lim_rho)
ticklabels_off_y()
set_x_axis_integer()
ax.set_xlabel('Experiment #')
ax.set_title('(d)', loc='left')
plt.tight_layout()
plt.savefig(FIG_PATH + PLOTS_ALL_THETA_RHO_FILENAME + PLOT_EXTENSION)
if show_plot:
block = False
plt.show(block)
###########################################################################
lim_k = [0, 9]
lim_a = [1e-7, 6e-6]
fig = plt.figure(num=None, figsize=SQUARE_FIGSIZE)
# (a) k for sand
ax = fig.add_subplot(2, 2, 1)
ax.plot(xs, k_det_sand, 's', label='Heating and Cooling DP')
ax.plot(xs, kdet_sig_sand, 'o', label='Signal Processing SP')
ax.plot(xs, kdet_linear_sand, '^', label='Late-Time SP')
ax.set_ylim(lim_k)
set_x_axis_integer()
ax.set_ylabel(create_label(r'$k$', 'W m^-1 K^-1'))
ticklabels_off_x()
ax.legend()
ax.set_title('(a)', loc='center')
# (b) alpha for sand
ax = fig.add_subplot(2, 2, 3)
ax.plot(xs, alpha_det_sand, 's', label='Heating and Cooling DP')
ax.plot(xs, alpha_sig_sand, 'o', label='Signal Processing SP and DP')
ax.set_ylim(lim_a)
set_x_axis_integer()
set_y_scientific()
ax.set_ylabel(create_label(r'$\alpha$', 'm^2 s^-1'))
ax.set_xlabel('Experiment #')
ax.set_title('(c)', loc='center')
ax.legend()
# (c) k for peat
ax = fig.add_subplot(2, 2, 2)
ax.plot(xp, k_det_peat, 's', label='Heating and Cooling DP')
ax.plot(xp, kdet_sig_peat, 'o', label='Signal Processing SP')
ax.plot(xp, kdet_linear_peat, '^', label='Late-Time SP')
ax.set_ylim(lim_k)
set_x_axis_integer()
ticklabels_off_x()
ticklabels_off_y()
ax.set_title('(b)', loc='center')
# (d) alpha for peat
ax = fig.add_subplot(2, 2, 4)
ax.plot(xp, alpha_det_peat, 's', label='Heating and Cooling DP')
ax.plot(xp, alpha_sig_peat, 'o', label='Signal Processing SP')
set_x_axis_integer()
set_y_scientific()
ax.set_ylim(lim_a)
ticklabels_off_y()
ax.set_xlabel('Experiment #')
ax.set_title('(d)', loc='center')
plt.tight_layout()
plt.savefig(FIG_PATH + PLOTS_ALL_THERMAL_FILENAME + PLOT_EXTENSION)
if show_plot:
block = True
plt.show(block)
def run_test_calibration_k(show_plot):
path = '../hpp-data/hpp-formatted-data/calibration/July-12-2017/'
dec_places = 2 # number of decimal places to have result
t_cold = T_COLD_BEGIN # time at beginning which is cold
t_heat = T_HEAT_CAL # seconds heating (s)
t_total = TIME_TOTAL_CAL # 3 minutes for entire test
fs = FS_SAMPLE # sampling rate (Hz)
k_assumed = K_WATER # thermal conductivity of water (W m^-1 K^-1)
rho = RHO_WATER_AGAR # density of agar gel water (kg m^-3)
c = HEAT_CAPACITY_WATER # heat capacity of water (J kg^-1 K^-1)
filt = 'both' # filter both SP and DP
downsample = 'dp' # downsample DP
fs_down = DOWNSAMPLE_DP # 1 second downsample
filt_cutoff = DP_LOWPASS_FILTER_CUT # lowpass filter cutoff frequency
start_string = CAL_BEGIN # start calibration string
additional_text = NO_TEXT # additional text
Hstart = 80 # starting value for H
qlist = Q_VAL_CAL_LIST # list of q values during calibration
kout_dp_heating_vec = []
kout_dp_heating_cooling_vec = []
kout_sp_late_time_vec = []
kout_sp_all_vec = []
kout_signal_vec = []
kout_signal_curve_fit_vec = []
for q in qlist:
print('q = ', q)
kout_dp_heating, kout_dp_heating_cooling, kout_sp_late_time, _tlinear, kout_sp_all, \
kout_signal, bdet_signal, kout_signal_curve_fit = \
test_calibration_k(path, start_string, additional_text, downsample, filt, filt_cutoff, fs,
fs_down, q, t_cold, t_heat, t_total, k_assumed, Hstart)
kout_dp_heating_vec.append(kout_dp_heating)
kout_dp_heating_cooling_vec.append(kout_dp_heating_cooling)
kout_sp_late_time_vec.append(kout_sp_late_time)
kout_sp_all_vec.append(kout_sp_all)
kout_signal_vec.append(kout_signal)
kout_signal_curve_fit_vec.append(kout_signal_curve_fit)
# DONE
qlist = np.asarray(qlist)
kout_dp_heating_vec = np.asarray(kout_dp_heating_vec)
kout_dp_heating_cooling_vec = np.asarray(kout_dp_heating_cooling_vec)
kout_sp_late_time_vec = np.asarray(kout_sp_late_time_vec)
kout_sp_all_vec = np.asarray(kout_sp_all_vec)
kout_signal_vec = np.asarray(kout_signal_vec)
kout_signal_curve_fit_vec = np.asarray(kout_signal_curve_fit_vec)
ed = EasyDump(TABLE_PATH + K_PLOT_TABLE_FILENAME + TABLE_EXT, 2)
ed.open()
# COMPUTE RMSE AND MB FOR ALL EXPERIMENTS
rmse_kout_dp_heating = compute_rmse(k_assumed, kout_dp_heating_vec)
mb_kout_dp_heating = compute_mb(k_assumed, kout_dp_heating_vec)
pd_kout_dp_heating = compute_percentage_diff(k_assumed,
kout_dp_heating_vec)
ed.write(rmse_kout_dp_heating, 'rmse_kout_dp_heating')
ed.write(mb_kout_dp_heating, 'mb_kout_dp_heating')
ed.write(pd_kout_dp_heating, 'pd_kout_dp_heating')
rmse_kout_dp_heating_cooling = compute_rmse(k_assumed,
kout_dp_heating_cooling_vec)
mb_kout_dp_heating_cooling = compute_mb(k_assumed,
kout_dp_heating_cooling_vec)
pd_kout_dp_heating_cooling = compute_percentage_diff(
k_assumed, kout_dp_heating_cooling_vec)
ed.write(rmse_kout_dp_heating_cooling, 'rmse_kout_dp_heating_cooling')
ed.write(mb_kout_dp_heating_cooling, 'mb_kout_dp_heating_cooling')
ed.write(pd_kout_dp_heating_cooling, 'pd_kout_dp_heating_cooling')
rmse_kout_sp_late_time = compute_rmse(k_assumed, kout_sp_late_time_vec)
mb_kout_sp_late_time = compute_mb(k_assumed, kout_sp_late_time_vec)
pd_kout_sp_late_time = compute_percentage_diff(k_assumed,
kout_sp_late_time_vec)
ed.write(rmse_kout_sp_late_time, 'rmse_kout_sp_late_time')
ed.write(mb_kout_sp_late_time, 'mb_kout_sp_late_time')
ed.write(pd_kout_sp_late_time, 'pd_kout_sp_late_time')
rmse_kout_sp_all = compute_rmse(k_assumed, kout_sp_all_vec)
mb_kout_sp_all = compute_mb(k_assumed, kout_sp_all_vec)
pd_kout_sp_all = compute_percentage_diff(k_assumed, kout_sp_all_vec)
ed.write(rmse_kout_sp_all, 'rmse_kout_sp_all')
ed.write(mb_kout_sp_all, 'mb_kout_sp_all')
ed.write(pd_kout_sp_all, 'pd_kout_sp_all')
rmse_kout_signal = compute_rmse(k_assumed, kout_signal_vec)
mb_kout_signal = compute_mb(k_assumed, kout_signal_vec)
pd_kout_signal = compute_percentage_diff(k_assumed, kout_signal_vec)
ed.write(rmse_kout_signal, 'rmse_kout_signal')
ed.write(mb_kout_signal, 'mb_kout_signal')
ed.write(pd_kout_signal, 'pd_kout_signal')
rmse_kout_signal_curve_fit = compute_rmse(k_assumed,
kout_signal_curve_fit_vec)
mb_kout_signal_curve_fit = compute_mb(k_assumed, kout_signal_curve_fit_vec)
pd_kout_signal_curve_fit = compute_percentage_diff(
k_assumed, kout_signal_curve_fit_vec)
ed.write(rmse_kout_signal_curve_fit, 'rmse_kout_signal_curve_fit')
ed.write(mb_kout_signal_curve_fit, 'mb_kout_signal_curve_fit')
ed.write(pd_kout_signal_curve_fit, 'pd_kout_signal_curve_fit')
# close the file
ed.close()
# need to trim outliers
elem = kout_dp_heating_vec < 100
qq = qlist[elem]
kout_dp_heating_vec_trim = kout_dp_heating_vec[elem]
elem = kout_dp_heating_vec_trim > 0.01
qq = qq[elem]
kout_dp_heating_vec_trim = kout_dp_heating_vec_trim[elem]
fig = plt.figure(num=None)
nx = 6
ax = fig.add_subplot(1, 1, 1)
ax.plot(qq,
kout_dp_heating_vec_trim,
"o",
label='Heating DP',
color='orange')
ax.plot(qlist,
kout_dp_heating_cooling_vec,
"v",
label='Heating and Cooling DP')
ax.plot(qlist, kout_sp_late_time_vec, "s", label='Late-Time SP')
ax.plot(qlist, kout_sp_all_vec, "^", label='Late-Time SP (all data)')
ax.plot(qlist,
kout_signal_vec,
"*",
label='Signal Processing SP',
color="yellowgreen")
ax.plot(qlist,
kout_signal_curve_fit_vec,
"h",
label='Signal Processing SP with Curve-Fitting')
ax.set_ylim([-0.1, 7])
set_xlim_linear(qlist[0], qlist[-1], nx)
ax.set_xlim([qlist[0] - 3, qlist[-1] + 3])
ax.set_xlabel(create_label('$q$', 'W \hspace{0.1} m^-1'))
ax.set_ylabel(create_label('$k$', 'W \hspace{0.1} m^-1 \hspace{0.1} K^-1'))
ax.axhline(y=k_assumed,
color="silver",
linestyle='dashed',
label='Assumed Value')
ax.legend(loc='upper left')
plt.tight_layout()
plt.savefig(FIG_PATH + K_PLOT_FILENAME + PLOT_EXTENSION)
if show_plot: # show the plot for purposes of debugging
plt.show()
def plot_oat(show=False):
"""
Plot for sensitivity analysis
:return:
"""
# load in the data from the dictionary file
print('Loading in the data...')
dictionary = pickle.load(open(SENSITIVITY_ANALYSIS_VEC_FILE, "rb"))
print('DONE loading in the data.')
#######################################################################################
# RADIUS
rvec_sand, theta_nom_rmsd_vec_sand_radius, theta_nom_mb_vec_sand_radius, rho_nom_rmse_vec_sand_radius, \
rho_nom_mb_vec_sand_radius, theta_sig_rmsd_vec_sand_radius, theta_sig_mb_vec_sand_radius, \
rho_sig_rmse_vec_sand_radius, rho_sig_mb_vec_sand_radius = dictionary[SAND_RADIUS]
rvec_peat, theta_nom_rmsd_vec_peat_radius, theta_nom_mb_vec_peat_radius, rho_nom_rmse_vec_peat_radius, \
rho_nom_mb_vec_peat_radius, theta_sig_rmsd_vec_peat_radius, theta_sig_mb_vec_peat_radius, \
rho_sig_rmse_vec_peat_radius, rho_sig_mb_vec_peat_radius = dictionary[PEAT_RADIUS]
# ORGANIC CONTENT
dvec_sand_theta_o, theta_nom_rmsd_vec_sand_theta_o, theta_nom_mb_vec_sand_theta_o, rho_nom_rmse_vec_sand_theta_o, \
rho_nom_mb_vec_sand_theta_o, theta_sig_rmsd_vec_sand_theta_o, theta_sig_mb_vec_sand_theta_o, \
rho_sig_rmse_vec_sand_theta_o, rho_sig_mb_vec_sand_theta_o = dictionary[SAND_ORGANIC]
dvec_peat_theta_o, theta_nom_rmsd_vec_peat_theta_o, theta_nom_mb_vec_peat_theta_o, rho_nom_rmse_vec_peat_theta_o, \
rho_nom_mb_vec_peat_theta_o, theta_sig_rmsd_vec_peat_theta_o, theta_sig_mb_vec_peat_theta_o, \
rho_sig_rmse_vec_peat_theta_o, rho_sig_mb_vec_peat_theta_o = dictionary[PEAT_ORGANIC]
# MINERAL CONTENT
(dvec_sand_theta_m, theta_nom_rmsd_vec_sand_theta_m,
theta_nom_mb_vec_sand_theta_m, rho_nom_rmse_vec_sand_theta_m,
rho_nom_mb_vec_sand_theta_m, theta_sig_rmsd_vec_sand_theta_m,
theta_sig_mb_vec_sand_theta_m, rho_sig_rmse_vec_sand_theta_m,
rho_sig_mb_vec_sand_theta_m) = dictionary[SAND_MINERAL]
(dvec_peat_theta_m, theta_nom_rmsd_vec_peat_theta_m,
theta_nom_mb_vec_peat_theta_m, rho_nom_rmse_vec_peat_theta_m,
rho_nom_mb_vec_peat_theta_m, theta_sig_rmsd_vec_peat_theta_m,
theta_sig_mb_vec_peat_theta_m, rho_sig_rmse_vec_peat_theta_m,
rho_sig_mb_vec_peat_theta_m) = dictionary[PEAT_MINERAL]
# TIME SHIFT
(dvec_sand_time, theta_nom_rmsd_vec_sand_time, theta_nom_mb_vec_sand_time,
rho_nom_rmse_vec_sand_time, rho_nom_mb_vec_sand_time,
theta_sig_rmsd_vec_sand_time, theta_sig_mb_vec_sand_time,
rho_sig_rmse_vec_sand_time,
rho_sig_mb_vec_sand_time) = dictionary[SAND_TIME]
(dvec_peat_time, theta_nom_rmsd_vec_peat_time, theta_nom_mb_vec_peat_time,
rho_nom_rmse_vec_peat_time, rho_nom_mb_vec_peat_time,
theta_sig_rmsd_vec_peat_time, theta_sig_mb_vec_peat_time,
rho_sig_rmse_vec_peat_time,
rho_sig_mb_vec_peat_time) = dictionary[PEAT_TIME]
#######################################################################################
# There will be two plots:
# plot theta (3 x 2 = 6)
# plot rho (3 x 2 = 6)
#########################
# THETA ONLY
#########################
fig = plt.figure(num=None, figsize=VLONG_FIGSIZE)
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
# (a)
ax = fig.add_subplot(4, 2, 1)
ax.plot(rvec_sand,
theta_nom_rmsd_vec_sand_radius,
label='Heating and Cooling DP Sand')
ax.plot(rvec_sand,
theta_sig_rmsd_vec_sand_radius,
label='Signal Processing SP and DP Sand')
ax.plot(rvec_peat,
theta_nom_rmsd_vec_peat_radius,
label='Heating and Cooling DP Peat')
ax.plot(rvec_peat,
theta_sig_rmsd_vec_peat_radius,
label='Signal Processing SP and DP Peat')
ax.set_xlabel(create_label('$r$', 'mm'))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\theta$', ''))
ax.set_title('(a)', loc='center')
ax.set_ylim([0, 4])
ax.legend()
# (b)
# sand and peat MB for radius
ax = fig.add_subplot(4, 2, 2)
ax.plot(rvec_sand,
theta_nom_mb_vec_sand_radius,
label='Heating and Cooling DP Sand')
ax.plot(rvec_sand,
theta_sig_mb_vec_sand_radius,
label='Signal Processing SP and DP Sand')
ax.plot(rvec_peat,
theta_nom_mb_vec_peat_radius,
label='Heating and Cooling DP Peat')
ax.plot(rvec_peat,
theta_sig_mb_vec_peat_radius,
label='Signal Processing SP and DP Peat')
ax.set_xlabel(create_label('$r$', 'mm'))
ax.set_ylabel(create_label(r'MB$\hspace{1}\theta$', ''))
ax.set_title('(b)', loc='center')
# (c)
# sand and peat RMSD for theta_o
ax = fig.add_subplot(4, 2, 3)
ax.plot(dvec_sand_theta_o, theta_nom_rmsd_vec_sand_theta_o)
ax.plot(dvec_sand_theta_o, theta_sig_rmsd_vec_sand_theta_o)
ax.plot(dvec_peat_theta_o, theta_nom_rmsd_vec_peat_theta_o)
ax.plot(dvec_peat_theta_o, theta_sig_rmsd_vec_peat_theta_o)
ax.set_xlabel(create_label(r'$\theta_o$', ''))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\theta$', ''))
ax.set_title('(c)', loc='center')
# (d)
# sand and peat MB for theta_o
ax = fig.add_subplot(4, 2, 4)
ax.plot(dvec_sand_theta_o, theta_nom_mb_vec_sand_theta_o)
ax.plot(dvec_sand_theta_o, theta_sig_mb_vec_sand_theta_o)
ax.plot(dvec_peat_theta_o, theta_nom_mb_vec_peat_theta_o)
ax.plot(dvec_peat_theta_o, theta_sig_mb_vec_peat_theta_o)
ax.set_xlabel(create_label(r'$\theta_o$', ''))
ax.set_ylabel(create_label(r'MB$\hspace{1}\theta$', ''))
ax.set_title('(d)', loc='center')
# (e)
# sand and peat RMSD for theta_m
ax = fig.add_subplot(4, 2, 5)
ax.plot(dvec_sand_theta_m, theta_nom_rmsd_vec_sand_theta_m)
ax.plot(dvec_sand_theta_m, theta_sig_rmsd_vec_sand_theta_m)
ax.plot(dvec_peat_theta_m, theta_nom_rmsd_vec_peat_theta_m)
ax.plot(dvec_peat_theta_m, theta_sig_rmsd_vec_peat_theta_m)
ax.set_xlabel(create_label(r'$\theta_m$', ''))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\theta$', ''))
ax.set_title('(e)', loc='center')
# (f)
# sand and peat MB for theta_m
ax = fig.add_subplot(4, 2, 6)
ax.plot(dvec_sand_theta_m, theta_nom_mb_vec_sand_theta_m)
ax.plot(dvec_sand_theta_m, theta_sig_mb_vec_sand_theta_m)
ax.plot(dvec_peat_theta_m, theta_nom_mb_vec_peat_theta_m)
ax.plot(dvec_peat_theta_m, theta_sig_mb_vec_peat_theta_m)
ax.set_xlabel(create_label(r'$\theta_m$', ''))
ax.set_ylabel(create_label(r'MB$\hspace{1}\theta$', ''))
ax.set_title('(f)', loc='center')
# (g)
# time
ax = fig.add_subplot(4, 2, 7)
# ax.plot(dvec_sand_time, theta_nom_rmsd_vec_sand_time)
ax.plot(dvec_sand_time, theta_sig_rmsd_vec_sand_time, color=colors[1])
# ax.plot(dvec_sand_time, theta_nom_rmsd_vec_peat_time)
ax.plot(dvec_sand_time, theta_sig_rmsd_vec_peat_time, color=colors[3])
ax.set_xlabel(create_label(r'$t_a$', 's'))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\theta$', ''))
ax.set_title('(g)', loc='center')
# (h)
ax = fig.add_subplot(4, 2, 8)
# ax.plot(dvec_sand_time, theta_nom_mb_vec_sand_time)
ax.plot(dvec_sand_time, theta_sig_mb_vec_sand_time, color=colors[1])
# ax.plot(dvec_sand_time, theta_nom_mb_vec_peat_time)
ax.plot(dvec_sand_time, theta_sig_mb_vec_peat_time, color=colors[3])
ax.set_xlabel(create_label(r'$t_a$', 's'))
ax.set_ylabel(create_label(r'MB$\hspace{1}\theta$', ''))
ax.set_title('(h)', loc='center')
plt.tight_layout()
block = False
plt.savefig(OAT_SENSITIVITY_FIG_NAME_THETA)
if show:
plt.show(block)
#########################
# RHO ONLY
#########################
fig = plt.figure(num=None, figsize=VLONG_FIGSIZE)
# (a)
ax = fig.add_subplot(4, 2, 1)
ax.plot(rvec_sand,
rho_nom_rmse_vec_sand_radius,
label='Heating and Cooling DP Sand')
ax.plot(rvec_sand,
rho_sig_rmse_vec_sand_radius,
label='Signal Processing SP and DP Sand')
ax.plot(rvec_peat,
rho_nom_rmse_vec_peat_radius,
label='Heating and Cooling DP Peat')
ax.plot(rvec_peat,
rho_sig_rmse_vec_peat_radius,
label='Signal Processing SP and DP Peat')
ax.set_xlabel(create_label('$r$', 'mm'))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(a)', loc='center')
ax.legend()
# (b)
# sand and peat MB for radius
ax = fig.add_subplot(4, 2, 2)
ax.plot(rvec_sand,
rho_nom_mb_vec_sand_radius,
label='Heating and Cooling DP Sand')
ax.plot(rvec_sand,
rho_sig_mb_vec_sand_radius,
label='Signal Processing SP and DP Sand')
ax.plot(rvec_peat,
rho_nom_mb_vec_peat_radius,
label='Heating and Cooling DP Peat')
ax.plot(rvec_peat,
rho_sig_mb_vec_peat_radius,
label='Signal Processing SP and DP Peat')
ax.set_xlabel(create_label('$r$', 'mm'))
ax.set_ylabel(create_label(r'MB$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(b)', loc='center')
ax.set_ylim([None, 20000])
# (c)
# sand and peat RMSD for theta_o
ax = fig.add_subplot(4, 2, 3)
ax.plot(dvec_sand_theta_o, rho_nom_rmse_vec_sand_theta_o)
ax.plot(dvec_sand_theta_o, rho_sig_rmse_vec_sand_theta_o)
ax.plot(dvec_peat_theta_o, rho_nom_rmse_vec_peat_theta_o)
ax.plot(dvec_peat_theta_o, rho_sig_rmse_vec_peat_theta_o)
ax.set_xlabel(create_label(r'$\theta_o$', ''))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(c)', loc='center')
# (d)
# sand and peat MB for theta_o
ax = fig.add_subplot(4, 2, 4)
ax.plot(dvec_sand_theta_o, rho_nom_mb_vec_sand_theta_o)
ax.plot(dvec_sand_theta_o, rho_sig_mb_vec_sand_theta_o)
ax.plot(dvec_peat_theta_o, rho_nom_mb_vec_peat_theta_o)
ax.plot(dvec_peat_theta_o, rho_sig_mb_vec_peat_theta_o)
ax.set_xlabel(create_label(r'$\theta_o$', ''))
ax.set_ylabel(create_label(r'MB$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(d)', loc='center')
# (e)
# sand and peat RMSD for theta_m
ax = fig.add_subplot(4, 2, 5)
ax.plot(dvec_sand_theta_m, rho_nom_rmse_vec_sand_theta_m)
ax.plot(dvec_sand_theta_m, rho_sig_rmse_vec_sand_theta_m)
ax.plot(dvec_peat_theta_m, rho_nom_rmse_vec_peat_theta_m)
ax.plot(dvec_peat_theta_m, rho_sig_rmse_vec_peat_theta_m)
ax.set_xlabel(create_label(r'$\theta_m$', ''))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(e)', loc='center')
# (f)
# sand and peat MB for theta_m
ax = fig.add_subplot(4, 2, 6)
ax.plot(dvec_sand_theta_m, rho_nom_mb_vec_sand_theta_m)
ax.plot(dvec_sand_theta_m, rho_sig_mb_vec_sand_theta_m)
ax.plot(dvec_peat_theta_m, rho_nom_mb_vec_peat_theta_m)
ax.plot(dvec_peat_theta_m, rho_sig_mb_vec_peat_theta_m)
ax.set_xlabel(create_label(r'$\theta_m$', ''))
ax.set_ylabel(create_label(r'MB$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(f)', loc='center')
# (g)
# time
ax = fig.add_subplot(4, 2, 7)
# ax.plot(dvec_sand_time, rho_nom_rmse_vec_sand_time)
ax.plot(dvec_sand_time, rho_sig_rmse_vec_sand_time, color=colors[1])
# ax.plot(dvec_sand_time, rho_nom_rmse_vec_peat_time)
ax.plot(dvec_sand_time, rho_sig_rmse_vec_peat_time, color=colors[3])
ax.set_xlabel(create_label(r'$t_a$', 's'))
ax.set_ylabel(create_label(r'RMSD$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(g)', loc='center')
# (h)
# time
ax = fig.add_subplot(4, 2, 8)
# ax.plot(dvec_sand_time, rho_nom_mb_vec_sand_time)
ax.plot(dvec_sand_time, rho_sig_mb_vec_sand_time, color=colors[1])
# ax.plot(dvec_sand_time, rho_nom_mb_vec_peat_time)
ax.plot(dvec_sand_time, rho_sig_mb_vec_peat_time, color=colors[3])
ax.set_xlabel(create_label(r'$t_a$', 's'))
ax.set_ylabel(create_label(r'MB$\hspace{1}\rho$', 'kg m^-3'))
ax.set_title('(h)', loc='center')
plt.tight_layout()
block = True
plt.savefig(OAT_SENSITIVITY_FIG_NAME_RHO)
if show:
plt.show()
def run_example_signal_processing_figure(theta_known,
density_known,
path,
start_string,
additional_text,
q,
t_heat,
t_total,
end_trim_time,
fname,
show_plot=False):
"""
Run the example signal processing to construct a figure
:param path:
:param start_string:
:param additional_text:
:param q:
:param t_heat:
:param t_total:
:param end_trim_time:
:param fname:
:return:
"""
theta_w_nom, rho_nom, theta_w_sig, rho_sig, \
t2_trim1, delta_T2_trim1, dT_synth_nom, dT_synth_sig, \
cut_time, t2_trim1_cut, r_t_heating_cooling, \
alpha_det, alpha_sig, k_det, kdet_sig, \
t1_trim_heating1, delta_T1_trim_heating1, dT_synth_sp, \
delta_T1_trim, t1_trim, \
tlinear, kdet_linear, qav = \
recomp_theta_rho_additional(path, start_string, additional_text, q, t_heat, t_total, end_trim_time)
fig = plt.figure(num=None, figsize=HLONG_FIGSIZE_M)
# (a) Single Probe
ax = fig.add_subplot(1, 3, 1)
ax.plot(t1_trim, delta_T1_trim, label='Measured', color=MEASURED_COLOR)
ax.plot(t1_trim_heating1,
dT_synth_sp,
label='Modelled',
color=MODELLED_COLOR)
ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta T \hspace{1}$', 'K'))
ylim = list(ax.get_ylim())
ylim[1] += 0.20 * (ylim[1] - ylim[0])
ax.set_ylim(ylim)
ax.legend(loc='best')
ax.set_title('(a)', loc='left')
# (b) Dual Probe
ax = fig.add_subplot(1, 3, 2)
ax.plot(t2_trim1, delta_T2_trim1, label='Measured', color=MEASURED_COLOR)
ax.plot(t2_trim1, dT_synth_nom, label='Modelled', color=MODELLED_COLOR)
ax.axvline(cut_time,
linestyle='--',
label='Peak Time',
color=MODELLED_COLOR)
ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta T \hspace{1}$', 'K'))
ylim = list(ax.get_ylim())
ylim[1] += 0.20 * (ylim[1] - ylim[0])
ax.set_ylim(ylim)
ax.legend(loc='best')
ax.set_title('(b)', loc='left')
# (d) r(t)
ax = fig.add_subplot(1, 3, 3)
ax.plot(t2_trim1_cut,
r_t_heating_cooling / 1.0e-3,
label='Effective Radius',
color='grey')
ax.legend(loc='upper left')
ax.set_ylabel(
create_label('$r\hspace{0.3}(\hspace{0.3}t\hspace{0.3})$', 'mm'))
ax.set_xlabel('Time (s)')
ylim = list(ax.get_ylim())
ylim[1] += 0.20 * (ylim[1] - ylim[0])
ax.set_ylim(ylim)
ax.set_title('(c)', loc='left')
plt.tight_layout()
plt.savefig(FIG_PATH + fname + PLOT_EXTENSION)
# compute percentage differences
pd_theta_sig = float_round(
compute_percentage_diff(theta_known, theta_w_sig), NOM_DP)
pd_theta_nom = float_round(
compute_percentage_diff(theta_known, theta_w_nom), NOM_DP)
diff_theta_sig = float_round(theta_known - theta_w_sig, NOM_DP)
diff_theta_nom = float_round(theta_known - theta_w_nom, NOM_DP)
pd_rho_sig = float_round(compute_percentage_diff(density_known, rho_sig),
NOM_DP)
pd_rho_nom = float_round(compute_percentage_diff(density_known, rho_nom),
NOM_DP)
diff_rho_sig = float_round(density_known - rho_sig, NOM_DP)
diff_rho_nom = float_round(density_known - rho_nom, NOM_DP)
# create HTML table to show values
tab = PrettyTable()
tab.field_names = [
"Type", "Signal Hybrid SP and DP", "DP nominal", "late-time SP nominal"
]
tab.add_row([
"k",
float_round(kdet_sig, NOM_DP),
float_round(k_det, NOM_DP),
float_round(kdet_linear, NOM_DP)
])
tab.add_row([
"alpha",
float_round(alpha_sig, NOM_DP),
float_round(alpha_det, NOM_DP), None
])
tab.add_row([
"theta_w",
float_round(theta_w_sig, NOM_DP),
float_round(theta_w_nom, NOM_DP), None
])
tab.add_row([
"rho",
float_round(rho_sig, NOM_DP),
float_round(rho_nom, NOM_DP), None
])
print(tab)
# create HTML table with differences
tabd = PrettyTable()
tabd.field_names = [
"Type", "PD Signal (%)", "Diff signal", "PD nom (%)", "Diff nom"
]
tabd.add_row([
"theta_w",
float_round(pd_theta_sig, NOM_DP),
float_round(diff_theta_sig, NOM_DP),
float_round(pd_theta_nom, NOM_DP),
float_round(diff_theta_nom, NOM_DP)
])
tabd.add_row([
"rho",
float_round(pd_rho_sig, NOM_DP),
float_round(diff_rho_sig, NOM_DP),
float_round(pd_rho_nom, NOM_DP),
float_round(diff_rho_nom, NOM_DP)
])
print(tabd)
# save out the tables to HTML file
print('Saving tables....')
with open(TABLE_PATH + fname + '-table1' + HTML_EXT, 'w') as f:
f.write(tab.get_html_string())
f.close()
with open(TABLE_PATH + fname + '-table2' + HTML_EXT, 'w') as f:
f.write(tabd.get_html_string())
f.close()
print('DONE saving tables...')
if show_plot:
plt.show()
def run_k_q_example(start_string, additional_text, downsample, filt, filt_cutoff, fs, fs_down,
path, q, t_cold, t_heat, t_total, show, fn):
use_assumed_q = False
use_step_detector_q = True
I, Rw, T1, T2, Vout, dV, dac_code, delta_T1, delta_T1_trim, delta_T1_trim_heating, \
delta_T2, delta_T2_trim, num, qav, qprime, step_q_tfirst, step_q_tsecond, t1, t1_trim, \
t1_trim_heating, t2, t2_trim, ypk, t, rmse_q_calc, mb_q_calc, pd_q_calc, t2_trim_heating, \
delta_T2_trim_heating = \
initial_compute_hpp(start_string, additional_text,
downsample, filt, filt_cutoff, fs, fs_down, path, q, t_cold, t_heat, t_total,
use_assumed_q,
use_step_detector_q)
t1_trim_heating1, delta_T1_trim_heating1 = curve_time_trim(t1_trim_heating, delta_T1_trim_heating)
dt = t1_trim_heating1[1] - t1_trim_heating1[0]
# late-time model
entire = False
return_all = True
tlinear, kdet, bdet, t_tlinear0, dT_tlinear0 = sp_model_late_time_inv(delta_T1_trim_heating1,
t1_trim_heating1, dt, qav, entire, return_all)
tlog = np.log(t1_trim_heating1)
dT_sp_synth = sp_model_late_time(qav, kdet, t_tlinear0, bdet)
rmse_sp = compute_rmse(dT_tlinear0, dT_sp_synth)
mb_sp = compute_mb(dT_tlinear0, dT_sp_synth)
pd_sp = compute_percentage_diff(dT_tlinear0, dT_sp_synth)
# signal processing model
kdet_sig, bdet_sig, tth, dT2_h = sp_model_signal_inv(delta_T1_trim_heating1, t1_trim_heating1, dt, q,
output_model_array=True)
bout, cout, dout = sp_model_nominal_get_b_c_d(delta_T1_trim_heating1, t1_trim_heating1, q, kdet_sig)
print('SP output:')
print('kdet = ', kdet)
print('bout = ', bout)
print('cout = ', cout)
print('dout = ', dout)
# synthetic signal processing for comparison
dT_model_sig_synth = dT_sp_model_signal(qav, kdet_sig, tth, bdet_sig)
rmse_sp_sig = compute_rmse(dT2_h, dT_model_sig_synth)
mb_sp_sig = compute_mb(dT2_h, dT_model_sig_synth)
pd_sp_sig = compute_percentage_diff(dT2_h, dT_model_sig_synth)
fig = plt.figure(num=None, figsize=HSQUARE_FIGSIZE)
is_scientific = True
use_pd = True
# (a)
ax = fig.add_subplot(1, 2, 1)
ax.plot(tlog, delta_T1_trim_heating1, color=MEASURED_COLOR, label='Measured')
ax.plot(np.log(t_tlinear0), dT_sp_synth, color=MODELLED_COLOR, label='Modelled')
ax.axvline(x=np.log(tlinear), linestyle=':', color=MODELLED_COLOR, label='Linear\nSection')
place_rmse_mb_pd_on_plot(rmse_sp, mb_sp, pd_sp, 'K', 1, 'center left',
is_scientific,
use_pd)
ax.legend(loc='best')
ax.set_xlabel(r'$\mathrm{log}(t)$')
ax.set_ylabel(create_label('$\Delta T$', 'K'))
ylim = list(ax.get_ylim())
ylim[1] += 0.40*(ylim[1]-ylim[0])
ax.set_ylim(ylim)
ax.set_title('(a)', loc='left')
# (b)
ax = fig.add_subplot(1, 2, 2)
ax.plot(tth, dT2_h, color=MEASURED_COLOR, label='signal')
ax.plot(tth, dT_model_sig_synth, color=MODELLED_COLOR, label='model')
ax.set_xlabel('Time (s)')
ax.set_ylabel(create_label('$\Delta \Gamma_{5} \hspace{0.3} (\hspace{0.3}t\hspace{0.3})$', ''))
place_rmse_mb_pd_on_plot(rmse_sp_sig, mb_sp_sig, pd_sp_sig, 'K', 1, 'lower right',
is_scientific,
use_pd)
ax.set_title('(b)', loc='left')
plt.tight_layout()
plt.savefig(FIG_PATH + fn + PLOT_EXTENSION)
if show:
plt.show()