Using the Accelerated Orthogonal Least-Squares algorithm for building Polynomial NARX models¶
Example created by Wilson Rocha Lacerda Junior
In [1]:
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import pandas as pd
from sysidentpy.utils.generate_data import get_siso_data
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.basis_function._basis_function import Polynomial
from sysidentpy.utils.display_results import results
from sysidentpy.utils.plotting import plot_residues_correlation, plot_results
from sysidentpy.residues.residues_correlation import (
compute_residues_autocorrelation,
compute_cross_correlation,
)
from sysidentpy.model_structure_selection import AOLS
# generating simulated data
x_train, x_test, y_train, y_test = get_siso_data(
n=1000, colored_noise=False, sigma=0.001, train_percentage=90
)
import pandas as pd from sysidentpy.utils.generate_data import get_siso_data from sysidentpy.metrics import root_relative_squared_error from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.utils.display_results import results from sysidentpy.utils.plotting import plot_residues_correlation, plot_results from sysidentpy.residues.residues_correlation import ( compute_residues_autocorrelation, compute_cross_correlation, ) from sysidentpy.model_structure_selection import AOLS # generating simulated data x_train, x_test, y_train, y_test = get_siso_data( n=1000, colored_noise=False, sigma=0.001, train_percentage=90 )
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basis_function = Polynomial(degree=2)
model = AOLS(xlag=3, ylag=3, k=5, L=1, basis_function=basis_function)
model.fit(X=x_train, y=y_train)
basis_function = Polynomial(degree=2) model = AOLS(xlag=3, ylag=3, k=5, L=1, basis_function=basis_function) model.fit(X=x_train, y=y_train)
Out[2]:
<sysidentpy.model_structure_selection.accelerated_orthogonal_least_squares.AOLS at 0x25cd3b406d0>
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yhat = model.predict(X=x_test, y=y_test)
rrse = root_relative_squared_error(y_test, yhat)
print(rrse)
r = pd.DataFrame(
results(
model.final_model,
model.theta,
model.err,
model.n_terms,
err_precision=8,
dtype="sci",
),
columns=["Regressors", "Parameters", "ERR"],
)
print(r)
yhat = model.predict(X=x_test, y=y_test) rrse = root_relative_squared_error(y_test, yhat) print(rrse) r = pd.DataFrame( results( model.final_model, model.theta, model.err, model.n_terms, err_precision=8, dtype="sci", ), columns=["Regressors", "Parameters", "ERR"], ) print(r)
0.0018996279285613828
Regressors Parameters ERR
0 y(k-1) 1.9999E-01 0.00000000E+00
1 x1(k-2) 9.0003E-01 0.00000000E+00
2 x1(k-1)y(k-1) 9.9954E-02 0.00000000E+00
3 x1(k-3)y(k-1) -2.1442E-04 0.00000000E+00
4 x1(k-1)^2 3.3714E-04 0.00000000E+00
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plot_results(y=y_test, yhat=yhat, n=1000)
ee = compute_residues_autocorrelation(y_test, yhat)
plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$")
x1e = compute_cross_correlation(y_test, yhat, x_test)
plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
plot_results(y=y_test, yhat=yhat, n=1000) ee = compute_residues_autocorrelation(y_test, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_test, yhat, x_test) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
