numCycles = 6 ampInit = 1 ampFinal = 1 freqMinDes_rps = 0.1 * hz2rps * np.ones(numExc) freqMaxDes_rps = 10.3 * hz2rps * np.ones(numExc) freqStepDes_rps = (20 / freqRate_hz) * hz2rps methodSW = 'zip' # "zippered" component distribution # Generate MultiSine Frequencies freqExc_rps, sigIndx, time_s = GenExcite.MultiSineComponents(freqMinDes_rps, freqMaxDes_rps, freqRate_hz, numCycles, freqStepDes_rps, methodSW) # Generate Schroeder MultiSine Signal ampExcit_nd = np.linspace(ampInit, ampFinal, len(freqExc_rps)) / np.sqrt(len(freqExc_rps)) rExc, phaseElem_rad, sigExcit = GenExcite.MultiSine(freqExc_rps, ampExcit_nd, sigIndx, time_s, phaseInit_rad = 0, boundPhase = 1, initZero = 1, normalize = 'peak', costType = 'Schroeder') rExc = rExc / np.std(rExc) rPeak = np.mean(GenExcite.PeakFactor(rExc) * np.std(rExc))**2 # Excited Frequencies per input channel freqChan_rps = freqExc_rps[sigIndx] freqChan_hz = freqChan_rps * rps2hz # Null Frequencies freqGap_rps = freqExc_rps[0:-1] + 0.5 * np.diff(freqExc_rps) freqGap_hz = freqGap_rps * rps2hz #%% Simulate the excitation through the system np.random.seed(0) # Time Response p = np.random.normal([0.0, 0.0], pSigma, size = (len(time_s), 2)).T
#freqMaxDes_rps = (freqRate_hz/2) * hz2rps * np.ones(numChan)
freqMaxDes_rps = 10 * hz2rps * np.ones(numChan)
freqStepDes_rps = (10 / freqRate_hz) * hz2rps
methodSW = 'zip' # "zippered" component distribution
## Generate MultiSine Frequencies
freqElem_rps, sigIndx, time_s = GenExcite.MultiSineComponents(freqMinDes_rps, freqMaxDes_rps, freqRate_hz, numCycles, freqStepDes_rps, methodSW)
timeDur_s = time_s[-1] - time_s[0]
## Generate Schroeder MultiSine Signal
ampElem_nd = np.ones_like(freqElem_rps) ## Approximate relative signal amplitude, create flat
sigList, phaseElem_rad, sigElem = GenExcite.MultiSine(freqElem_rps, ampElem_nd, sigIndx, time_s, costType = 'Norm2', phaseInit_rad = 0, boundPhase = 1, initZero = 1, normalize = 'peak');
## Results
peakFactor = GenExcite.PeakFactor(sigList)
peakFactorRel = peakFactor / np.sqrt(2)
print(peakFactorRel)
# Signal Power
sigPowerRel = (ampElem_nd / max(ampElem_nd))**2 / len(ampElem_nd)
if True:
fig, ax = plt.subplots(ncols=1, nrows=numChan, sharex=True)
for iChan in range(0, numChan):
ax[iChan].plot(time_s, sigList[iChan])
ax[iChan].set_ylabel('Amplitude (nd)')
ax[iChan].grid(True)
ax[iChan].set_xlabel('Time (s)')
freqMaxDes_rps = 10.1 * hz2rps * np.ones(numExc)
freqStepDes_rps = (10/freqRate_hz) * hz2rps
methodSW = 'zip' # "zippered" component distribution
# Generate MultiSine Frequencies
freqExc_rps, sigIndx, time_s = GenExcite.MultiSineComponents(freqMinDes_rps, freqMaxDes_rps, freqRate_hz, numCycles, freqStepDes_rps, methodSW)
freqGap_rps = freqExc_rps[0:-1] + 0.5 * np.diff(freqExc_rps)
#time_s = time_s[0:-5]
# Generate Schroeder MultiSine Signal
ampExcit_nd = np.linspace(ampInit, ampFinal, len(freqExc_rps)) / np.sqrt(len(freqExc_rps))
uExc, phaseElem_rad, sigExcit = GenExcite.MultiSine(freqExc_rps, ampExcit_nd, sigIndx, time_s, phaseInit_rad = 0, boundPhase = 1, initZero = 1, normalize = 'rms', costType = 'Schroeder')
uExc = (uExc.T * (1 / np.std(uExc, axis = -1))).T
uStd = np.std(uExc, axis = -1)
uPeak = np.mean(GenExcite.PeakFactor(uExc) * uStd)**2
# Excited Frequencies per input channel
freqChan_rps = freqExc_rps[sigIndx]
freqChan_hz = freqChan_rps * rps2hz
# Simulate the excitation through the system
_, y, _ = control.forced_response(sysPlant, T = time_s, U = uExc)
# Plant-Output Noise
noiseK11 = (2/8) * np.abs(sysPlant.dcgain())[0, 0]; noiseWn11 = 6 * hz2rps; noiseD11 = 0.1;
noiseK22 = (8/8) * np.abs(sysPlant.dcgain())[1, 1]; noiseWn22 = 4 * hz2rps; noiseD22 = 1.0;
sysN = control.tf([[[-noiseK11, 0, noiseK11 * noiseWn11**2], [0]],
[[0], [-noiseK22, 0, noiseK22 * noiseWn22**2]]],
#time_s = time_s[0:-5]
# Generate Schroeder MultiSine Signal
ampExcit_nd = np.linspace(ampInit, ampFinal, len(freqExc_rps)) / np.sqrt(
len(freqExc_rps))
exc, phaseElem_rad, sigExcit = GenExcite.MultiSine(freqExc_rps,
ampExcit_nd,
sigIndx,
time_s,
phaseInit_rad=0,
boundPhase=1,
initZero=1,
normalize='peak',
costType='Schroeder')
exc = exc / np.std(exc)
uPeak = np.mean(GenExcite.PeakFactor(exc) * np.std(exc, axis=-1))**2
# Excited Frequencies per input channel
freqChan_rps = freqExc_rps[sigIndx]
freqChan_hz = freqChan_rps * rps2hz
#%%
N = 2**8
fBin = np.linspace(0, 10, num=N)
D = FreqTrans.Dirichlet(fBin, N)
Dmag = np.abs(D)
Dmax = np.nanmax(Dmag)
Dnorm_mag = Dmag / Dmax
Dnorm_dB = mag2db(Dnorm_mag)