def coh_palm(p0_ind, p1_ind, t_para, tSeq, varSeq, tL):
t_start = t_para[0]
t_end = t_para[1]
t_delta = t_para[2]
fs = 1 / t_delta # sampling frequency
t_num = int((t_end - t_start) / t_delta + 1)
t_seq = np.linspace(t_start, t_end, t_num)
u0 = varSeq[:, p0_ind[2], p0_ind[1], p0_ind[0]]
u1 = varSeq[:, p1_ind[2], p1_ind[1], p1_ind[0]]
f0 = interp1d(tSeq, u0, kind='linear', fill_value='extrapolate')
f1 = interp1d(tSeq, u1, kind='linear', fill_value='extrapolate')
u0_ = f0(t_seq)
u1_ = f1(t_seq)
segNum = tL * fs
freq, coh, co_coh, phase = funcs.coherence(u0_, u1_, fs, segNum)
return t_seq, u0_, u1_, freq, coh, co_coh, phase
def coh_sowfa(p0_ind, p1_ind, xNum, yNum, t_para, tSeq, varSeq, tL):
"""
Calculate coherence, co-coherence, phase based on interpolated data
INPUT
p0_ind: indice of the probe0
p1_ind: indice of the probe1
xNum: length of xSeq
yNum: length of ySeq
t_para: parameters of the interpolated time array, tuple, (start time, end time, time step)
tSeq: original time array
varSeq: variable array
tL: length of subsegment (s)
OUTPUT
t_seq: interpolated time array
u0_: 1st velocity array
u1_: 2nd velocity array
freq: frequency array
coh: coherence array
co_coh: co-coh array
quad_coh: quad-coh array
phase: phase array
"""
p0_id = p0_ind[2] * xNum * yNum + p0_ind[1] * xNum + p0_ind[0]
p1_id = p1_ind[2] * xNum * yNum + p1_ind[1] * xNum + p1_ind[0]
t_start = t_para[0]
t_end = t_para[1]
t_delta = t_para[2]
fs = 1 / t_delta # sampling frequency
t_num = int((t_end - t_start) / t_delta + 1)
t_seq = np.linspace(t_start, t_end, t_num)
u0 = varSeq[p0_id]
u1 = varSeq[p1_id]
f0 = interp1d(tSeq, u0, kind='linear', fill_value='extrapolate')
f1 = interp1d(tSeq, u1, kind='linear', fill_value='extrapolate')
u0_ = f0(t_seq)
u1_ = f1(t_seq)
segNum = tL * fs
freq, coh, co_coh, quad_coh, phase = funcs.coherence(u0_, u1_, fs, segNum)
return t_seq, u0_, u1_, freq, coh, co_coh, quad_coh, phase
def coh_sowfa(p0_ind, p1_ind, xNum, yNum, t_para, tSeq, varSeq, tL):
p0_id = p0_ind[2] * xNum * yNum + p0_ind[1] * xNum + p0_ind[0]
p1_id = p1_ind[2] * xNum * yNum + p1_ind[1] * xNum + p1_ind[0]
t_start = t_para[0]
t_end = t_para[1]
t_delta = t_para[2]
fs = 1 / t_delta # sampling frequency
t_num = int((t_end - t_start) / t_delta + 1)
t_seq = np.linspace(t_start, t_end, t_num)
u0 = varSeq[p0_id]
u1 = varSeq[p1_id]
f0 = interp1d(tSeq, u0, kind='linear', fill_value='extrapolate')
f1 = interp1d(tSeq, u1, kind='linear', fill_value='extrapolate')
u0_ = f0(t_seq)
u1_ = f1(t_seq)
segNum = tL * fs
# freq, coh, co_coh, phase = funcs.coherence(u0_, u1_, fs, segNum)
tmp = funcs.coherence(u0_, u1_, fs, segNum)
return t_seq, u0_, u1_, tmp[0], tmp[1], tmp[2], tmp[4]
coh = []
yInd = yInd_start
while yInd <= yInd_end:
coh_temp = []
xInd0 = xInd_start
xInd1 = xInd0 + dInd
while xInd1 < xNum:
u0 = data_org['u'][:, yInd, xInd0]
u1 = data_org['u'][:, yInd, xInd1]
# time interpolation
f0 = interp1d(tSeq, u0, kind='cubic', fill_value='extrapolate')
f1 = interp1d(tSeq, u1, kind='cubic', fill_value='extrapolate')
u0 = f0(t_seq)
u1 = f1(t_seq)
# calculate coherence and phase
freq, coh_, phase_ = funcs.coherence(u0, u1, fs, segNum)
coh_temp.append(coh_)
xInd0 += 1
xInd1 += 1
coh_temp = sum(coh_temp) / len(coh_temp)
coh.append(coh_temp)
yInd += 1
coh = sum(coh) / len(coh)
cohList.append(coh)
ax.text(0.56,
1.02,
'dx = ' + str(np.round(dx, 1)) + 'm' + ', ' + 'h = ' +
str(np.round(p0_coor[2])) + 'm',
transform=ax.transAxes,
fontsize=12)
plt.grid()
plt.legend()
saveName = 'u_ts_120' + '_dx_' + str(np.round(dx, 1)) + '_h_' + str(
np.round(p0_coor[2])) + '_pr.png'
plt.savefig(ppDir + '/' + saveName)
plt.show()
plt.close()
# calculate coherence and phase_
freq, coh, co_coh, phase = funcs.coherence(u0, u1, fs, segNum)
def fitting_func(x, a, alpha):
return a * np.exp(-alpha * x)
""" plot coherence """
f_out = 0.15
tmp = abs(freq - f_out)
ind_in, ind_out = 1, np.where(tmp == tmp.min())[0][0]
fig, ax = plt.subplots(figsize=(6, 6))
ax.plot(freq, coh, linestyle='', marker='x', markersize=3, color='k')
popt, pcov = curve_fit(fitting_func,
freq[ind_in:ind_out],
1.02,
'dx = ' + str(np.round(dx, 1)) + 'm' + ', ' + 'h = ' +
str(np.round(p0_coor[2])) + 'm',
transform=ax.transAxes,
fontsize=12)
plt.grid()
plt.legend()
saveName = 'u_ts_120' + '_dx_' + str(np.round(dx, 1)) + '_h_' + str(
np.round(p0_coor[2])) + '_pr.png'
plt.savefig(ppDir + '/' + saveName)
plt.show()
plt.close()
segNum = 120 * fs
# calculate coherence and phase
freq, coh01, co_coh01, phase01 = funcs.coherence(u0, u1, fs, segNum)
freq, coh02, co_coh02, phase02 = funcs.coherence(u0, u2, fs, segNum)
freq, coh03, co_coh03, phase03 = funcs.coherence(u0, u3, fs, segNum)
""" plot coherence and fitting curve """
def fitting_func(x, a, alpha):
return a * np.exp(-alpha * x)
f_out = 1
tmp = abs(freq - f_out)
ind_in, ind_out = 1, np.where(tmp == tmp.min())[0][0]
# dx = 40m
fig, ax = plt.subplots(figsize=(6, 4))
