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]])