def partion_data(data, Rest=2, Ntr=1, Ntr_steady=1):
y = data['y']
u = data['u']
lines = data['lines']
fs = data['fs']
npp, p, R, P = y.shape
freq = np.arange(npp) / npp * fs
# partitioning the data. Use last period of two last realizations.
# test for performance testing and val for model selection
utest = u[:, :, -1, -1]
ytest = y[:, :, -1, -1]
uval = u[:, :, -1, -1]
yval = y[:, :, -1, -1]
# all other realizations are used for estimation
uest = u[..., :Rest, Ntr_steady:]
yest = y[..., :Rest, Ntr_steady:]
# noise estimate over periods. This sets the performace limit for the
# estimated model
covY = covariance(yest)
# create signal object
sig = Signal(uest, yest, fs=fs)
sig.lines = lines
# plot periodicity for one realization to verify data is steady state
# sig.periodicity()
# Calculate BLA, total- and noise distortion. Used for subspace
# identification
sig.bla()
# average signal over periods. Used for training of PNLSS model
um, ym = sig.average()
return Data(sig, uest, yest, uval, yval, utest, ytest, um, ym, covY, freq,
lines, npp, Ntr)
def simulate(true_model, npp=1024, Ntr=1, Rest=2, add_noise=False):
print()
print(f'Nonlinear parameters:',
f'{len(true_model.nlx.active) + len(true_model.nly.active)}')
print(f'Parameters to estimate: {true_model.npar}')
# set non-active coefficients to zero. Note order of input matters
idx = np.setdiff1d(np.arange(true_model.E.size), true_model.nlx.active)
idy = np.setdiff1d(np.arange(true_model.F.size), true_model.nly.active)
true_model.E.flat[idx] = 0
true_model.F.flat[idy] = 0
# get predictable random numbers. https://dilbert.com/strip/2001-10-25
np.random.seed(10)
# shape of u from multisine: (R,P*npp)
u, lines, freq = multisine(N=npp, P=P, R=R, lines=kind, rms=RMSu)
# Transient: Add Ntr periods before the start of each realization. To
# generate steady state data.
T1 = np.r_[npp * Ntr, np.r_[0:(R - 1) * P * npp + 1:P * npp]]
_, yorig, _ = true_model.simulate(u.ravel(), T1=T1)
u = u.reshape((R, P, npp)).transpose((2, 0, 1))[:, None] # (npp,m,R,P)
y = yorig.reshape((R, P, npp, p)).transpose((2, 3, 0, 1))
# Add colored noise to the output. randn generate white noise
if add_noise:
np.random.seed(10)
noise = 1e-3 * np.std(y[:, -1, -1]) * np.random.randn(*y.shape)
# Do some filtering to get colored noise
noise[1:-2] += noise[2:-1]
y += noise
## START of Identification ##
# partitioning the data. Use last period of two last realizations.
# test for performance testing and val for model selection
utest = u[:, :, -1, -1]
ytest = y[:, :, -1, -1]
uval = u[:, :, -2, -1]
yval = y[:, :, -2, -1]
# all other realizations are used for estimation
uest = u[..., :Rest, :]
yest = y[..., :Rest, :]
# noise estimate over periods. This sets the performace limit for the
# estimated model
covY = covariance(yest)
# create signal object
sig = Signal(uest, yest, fs=fs)
sig.lines = lines
# plot periodicity for one realization to verify data is steady state
# sig.periodicity()
# Calculate BLA, total- and noise distortion. Used for subspace
# identification
sig.bla()
# average signal over periods. Used for training of PNLSS model
um, ym = sig.average()
return Data(sig, uest, yest, uval, yval, utest, ytest, um, ym, covY, freq,
lines, npp, Ntr)
ytest = y[:, :, -1, -1]
uval = u[:, :, -2, -1]
yval = y[:, :, -2, -1]
# all other realizations are used for estimation
uest = u[..., :-2, :]
yest = y[..., :-2, :]
# noise estimate over periods. This sets the performace limit for the estimated
# model
covY = covariance(yest)
npp, p, Rest, Pest = yest.shape
npp, m, Rest, Pest = uest.shape
Ptr = 5 # number of periods to use for transient handling during simulation
# create signal object
sig = Signal(uest, yest, fs=fs)
sig.lines = lines
# plot periodicity for one realization to verify data is steady state
# sig.periodicity()
# Calculate BLA, total- and noise distortion. Used for subspace identification
sig.bla()
# average signal over periods. Used for training of PNLSS model
um, ym = sig.average()
# model orders and Subspace dimensioning parameter
nvec = [3]
maxr = 10
if 'linmodel' not in locals() or True:
linmodel = Subspace(sig)
linmodel.estimate(2, maxr, weight=weight)
linmodel.optimize(weight=weight)
# test for performance testing and val for model selection utest = u[:, :, -1, -1] ytest = y[:, :, -1, -1] uval = u[:, :, -2, -1] yval = y[:, :, -2, -1] # all other realizations are used for estimation u = u[..., :-2, :] y = y[..., :-2, :] # model orders and Subspace dimensioning parameter nvec = [2, 3] maxr = 5 # create signal object sig = Signal(u, y) sig.lines(lines) # average signal over periods. Used for training of PNLSS model um, ym = sig.average() npp, F = sig.npp, sig.F R, P = sig.R, sig.P linmodel = linss() # estimate bla, total distortion, and noise distortion linmodel.bla(sig) # get best model on validation data models, infodict = linmodel.scan(nvec, maxr) l_errvec = linmodel.extract_model(yval, uval) # estimate PNLSS # transient: Add one period before the start of each realization. Note that # this for the signal averaged over periods
covY = covariance(yest[:, :, None])
# Validation data. 50 different realizations of 3 periods. Use the last
# realization and last period
uval_raw, _, _, Pval = load('u', 100, fnsi=False)
yval_raw = load('y', 100, fnsi=False)
uval_raw = uval_raw.reshape(npp, Pval, 50, order='F').swapaxes(1, 2)[:, None]
yval_raw = yval_raw.reshape(npp, Pval, 50, order='F').swapaxes(1, 2)[:, None]
uval = uval_raw[:, :, -1, -1]
yval = yval_raw[:, :, -1, -1]
utest = uval_raw[:, :, 1, -1]
ytest = yval_raw[:, :, 1, -1]
Rval = uval_raw.shape[2]
sig = Signal(uest, yest, fs=fs)
sig.lines = lines
um, ym = sig.average()
# sig.periodicity()
# for subspace model (from BLA)
sig2 = Signal(uest[:, :, None], yest[:, :, None], fs=fs)
sig2.lines = lines
sig2.bla()
# model orders and Subspace dimensioning parameter
n = 2
maxr = 20
dof = 0
iu = 0
xpowers = np.array([[2], [3]])