#plt.plot(time_s, uExc[1], time_s, v[1], time_s, fb[1], time_s, pqrDist[1])
#%% Estimate the frequency response function
optSpec = FreqTrans.OptSpect(dftType='czt',
freqRate=freqRate_rps,
smooth=('box', 3),
winType=('tukey', 0.0),
detrendType='Linear',
interpType='linear')
# Excited Frequencies per input channel
optSpec.freq = freqChan_rps
# FRF Estimate
freq_rps, Teb, Ceb, Pee, Pbb, Peb = FreqTrans.FreqRespFuncEst(
uExc, fb, optSpec)
_, Tev, Cev, _, Pvv, Pev = FreqTrans.FreqRespFuncEst(uExc, v, optSpec)
freq_hz = freq_rps * rps2hz
# Form the Frequency Response, T = Teb @ Tev^-1
T = np.zeros_like(Tev, dtype=complex)
C = np.zeros_like(Tev, dtype=float)
for i in range(T.shape[-1]):
T[..., i] = (Teb[..., i].T @ np.linalg.inv(Tev[..., i].T)).T
sigmaNom_mag, _ = FreqTrans.Sigma(T) # Singular Value Decomp
# Coherence
C = Ceb
freqGap_rps = optSpec.freq.flatten()[0:-1] + 0.5 * np.diff(
optSpec.freq.flatten())
optSpec.freqNull = freqGap_rps
optSpec.freqNullInterp = True
# FRF Estimate
freq_rps = []
freq_hz = []
T = []
TUnc = []
C = []
for iSeg, seg in enumerate(oDataSegs):
freq, Tey, Cey, Pee, Pyy, Pey, TeyUnc, Pee_N, Pyy_N = FreqTrans.FreqRespFuncEstNoise(
eList[iSeg], outList[iSeg], optSpec)
freq, Teu, Ceu, _, Puu, Peu = FreqTrans.FreqRespFuncEst(
eList[iSeg], uList[iSeg], optSpec)
# Form the Frequency Response
freq_hz = freq * rps2hz
# Form the Frequency Response
T_seg = np.zeros_like(Tey)
TUnc_seg = np.zeros_like(Tey)
for i in range(T_seg.shape[-1]):
T_seg[..., i] = (Tey[..., i] @ np.linalg.inv(Teu[..., i]))
TUnc_seg[..., i] = (TeyUnc[..., i] @ np.linalg.inv(Teu[..., i]))
T.append(T_seg)
TUnc.append(np.abs(TUnc_seg))
C.append(Cey)
#%% Estimate the frequency response function
# Define the excitation frequencies
freqRate_hz = 50
freqRate_rps = freqRate_hz * hz2rps
optSpec = FreqTrans.OptSpect(dftType = 'czt', freqRate = freqRate_rps, smooth = ('box', 3), winType = ('tukey', 0.2), detrendType = 'Linear')
# Excited Frequencies per input channel
optSpec.freq = np.asarray(freqExc_rps)
# FRF Estimate
T = []
C = []
for iSeg, seg in enumerate(oDataSegs):
freq_rps, Teb, Ceb, Pee, Pbb, Peb = FreqTrans.FreqRespFuncEst(vExcList[iSeg], vFbList[iSeg], optSpec)
_ , Tev, Cev, _ , Pvv, Pev = FreqTrans.FreqRespFuncEst(vExcList[iSeg], vCmdList[iSeg], optSpec)
freq_hz = freq_rps * rps2hz
# Form the Frequency Response
T_seg = np.empty_like(Tev)
for i in range(T_seg.shape[-1]):
T_seg[...,i] = Teb[...,i] @ np.linalg.inv(Tev[...,i])
T.append( T_seg )
# C.append(Cev)
C.append(Ceb)
time_s,
ampInit,
ampFinal,
freqType='linear',
ampType='linear',
initZero=1)
# Simulate the excitation through the system
time_s, y, _ = signal.lsim(sys, x, time_s)
y = np.atleast_2d(y)
# Estimate the transfer function
optSpec = FreqTrans.OptSpect(freqRate=freqRate_rps,
smooth=('box', 1),
winType=('tukey', 0.0))
freq_rps, Txy, Cxy, Pxx, Pyy, Pxy = FreqTrans.FreqRespFuncEst(x, y, optSpec)
gain_dB, phase_deg = FreqTrans.GainPhase(Txy)
freq_hz = freq_rps * rps2hz
freq_hz = np.squeeze(freq_hz)
gain_dB = np.squeeze(gain_dB)
phase_deg = np.unwrap(np.squeeze(phase_deg) * deg2rad) * rad2deg
Cxy = np.squeeze(Cxy)
#%% Multisine signal with CZT
numChan = 1
numCycles = 1
freqMinDes_rps = freqInit_rps * np.ones(numChan)
freqMaxDes_rps = freqFinal_rps * np.ones(numChan)
freqStepDes_rps = (10 / freqRate_hz) * hz2rps
freqRate=freqRate_rps,
smooth=('box', 3),
winType=('tukey', 0.2),
detrendType='Linear')
# Excited Frequencies per input channel
optSpec.freq = np.asarray(freqExc_rps)
# FRF Estimate
freq_rps = []
freq_hz = []
T = []
C = []
for iSeg, seg in enumerate(oDataSegs):
freq, Tey, Cey, Pee, Pyy, Pey = FreqTrans.FreqRespFuncEst(
eList[iSeg], outList[iSeg], optSpec)
freq, Teu, Ceu, _, Puu, Peu = FreqTrans.FreqRespFuncEst(
eList[iSeg], uList[iSeg], optSpec)
# Form the Frequency Response
freq_hz = freq * rps2hz
# Form the Frequency Response
T_seg = np.zeros_like(Tey)
for i in range(T_seg.shape[-1]):
T_seg[..., i] = Tey[..., i] @ np.linalg.inv(Teu[..., i])
T.append(T_seg)
C.append(Cey)
plt.figure(1)
plt.plot(time_s, pCmd, time_s, pOut)
#%% Plot the Excitation Spectrum
optSpec = FreqTrans.OptSpect(dftType = 'czt', freqRate = freqRate_hz * hz2rps, freq = freqExc_rps, smooth = ('box', 3), winType = 'rect')
plt.figure(2)
TxyList = []
CxyList = []
PxxList = []
PyyList = []
PxyList = []
for i, pOut in enumerate(pOutList):
pCmd = pCmdList[i]
freq_rps, Txy, Cxy, Pxx, Pyy, Pxy = FreqTrans.FreqRespFuncEst(pCmd, pOut, optSpec)
gain_dB, phase_deg = FreqTrans.GainPhase(Txy)
freq_hz = freq_rps * rps2hz
freq_hz = np.squeeze(freq_hz)
gain_dB = np.squeeze(gain_dB)
phase_deg = np.squeeze(phase_deg)
Cxy = np.squeeze(Cxy)
# Cxy = np.squeeze(np.abs(Cxy)**2)
TxyList.append(Txy)
CxyList.append(Cxy)
PxxList.append(Pxx)
PyyList.append(Pyy)
PxyList.append(Pxy)
optSpec = FreqTrans.OptSpect(dftType='czt',
freqRate=freqRate_rps,
smooth=('box', 3),
winType=('tukey', 0.2),
detrendType='Linear')
# Excited Frequencies per input channel
optSpec.freq = np.asarray(freqExc_rps)
# FRF Estimate
LiEstNomList = []
LiEstCohList = []
svLiEstNomList = []
for iSeg, seg in enumerate(oDataSegs):
freq_rps, Teb, Ceb, Pee, Pbb, Peb = FreqTrans.FreqRespFuncEst(
vExcList[iSeg], vExcList[iSeg] + vFbList[iSeg], optSpec)
# _ , Tev, Cev, _ , Pvv, Pev = FreqTrans.FreqRespFuncEst(vExcList[iSeg], vCmdList[iSeg], optSpec)
freq_hz = freq_rps * rps2hz
I3 = np.repeat([np.eye(3)], Teb.shape[-1], axis=0).T
SaEstNom = Teb # Sa = I + Teb
SaEstCoh = Ceb # Cxy = np.abs(Sxy)**2 / (Sxx * Syy) = (np.abs(Sxy) / Sxx) * (np.abs(Sxy) / Syy)
# T = TNom = (uCtrl + uExc) / uExc - uNull / uExc
# Li = inv(TNom + TUnc) - I = LiEstNom + LiEstUnc
# LiEstNom = -I + TNom^-1
# LiEstUnc = -(I + TNom^-1 * TUnc)^-1 * TNom^-1 * TUnc * TNom^-1
LiEstNom = np.zeros_like(SaEstNom, dtype=complex)
LiEstCoh = np.zeros_like(SaEstCoh)
