Identification of an electromechanical system using Entropic Regression¶
Example created by Wilson Rocha Lacerda Junior
More details about this data can be found in the following paper (in Portuguese): https://www.researchgate.net/publication/320418710_Identificacao_de_um_motorgerador_CC_por_meio_de_modelos_polinomiais_autorregressivos_e_redes_neurais_artificiais
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pip install sysidentpy
pip install sysidentpy
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sysidentpy.model_structure_selection import ER
from sysidentpy.basis_function._basis_function import Polynomial
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.utils.generate_data import get_siso_data
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
import numpy as np import pandas as pd import matplotlib.pyplot as plt from sysidentpy.model_structure_selection import ER from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.metrics import root_relative_squared_error from sysidentpy.utils.generate_data import get_siso_data 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
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df1 = pd.read_csv('examples/datasets/x_cc.csv')
df2 = pd.read_csv('examples/datasets/y_cc.csv')
df1 = pd.read_csv('examples/datasets/x_cc.csv') df2 = pd.read_csv('examples/datasets/y_cc.csv')
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# we will decimate the data using d=500 in this example
x_train, x_valid = np.split(df1.iloc[::500].values, 2)
y_train, y_valid = np.split(df2.iloc[::500].values, 2)
# we will decimate the data using d=500 in this example x_train, x_valid = np.split(df1.iloc[::500].values, 2) y_train, y_valid = np.split(df2.iloc[::500].values, 2)
Building a Polynomial NARX model using Entropic Regression Algorithm¶
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basis_function = Polynomial(degree=2)
model = ER(
ylag=6,
xlag=6,
n_perm=2,
k=2,
skip_forward=True,
estimator='recursive_least_squares',
basis_function=basis_function
)
basis_function = Polynomial(degree=2) model = ER( ylag=6, xlag=6, n_perm=2, k=2, skip_forward=True, estimator='recursive_least_squares', basis_function=basis_function )
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model.fit(X=x_train, y=y_train)
yhat = model.predict(X=x_valid, y=y_valid)
rrse = root_relative_squared_error(y_valid, 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)
plot_results(y=y_valid, yhat = yhat, n=1000)
ee = compute_residues_autocorrelation(y_valid, yhat)
plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$")
x1e = compute_cross_correlation(y_valid, yhat, x_valid)
plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
model.fit(X=x_train, y=y_train) yhat = model.predict(X=x_valid, y=y_valid) rrse = root_relative_squared_error(y_valid, 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) plot_results(y=y_valid, yhat = yhat, n=1000) ee = compute_residues_autocorrelation(y_valid, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_valid, yhat, x_valid) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
C:\Users\wilso\AppData\Local\Temp/ipykernel_12756/1917592845.py:1: UserWarning: Given the higher number of possible regressors (91), the Entropic Regression algorithm may take long time to run. Consider reducing the number of regressors model.fit(X=x_train, y=y_train)
0.0403103654397461 Regressors Parameters ERR 0 1 -4.7284E+02 0.00000000E+00 1 y(k-1) 1.2177E+00 0.00000000E+00 2 y(k-2) -3.8216E-01 0.00000000E+00 3 y(k-4) 2.4306E-01 0.00000000E+00 4 y(k-5) -2.3846E-01 0.00000000E+00 .. ... ... ... 65 x1(k-5)x1(k-2) 3.2336E-01 0.00000000E+00 66 x1(k-6)x1(k-2) 3.4907E-01 0.00000000E+00 67 x1(k-4)x1(k-3) -1.9440E+00 0.00000000E+00 68 x1(k-5)x1(k-3) 1.9960E-01 0.00000000E+00 69 x1(k-6)x1(k-5) -1.9914E+00 0.00000000E+00 [70 rows x 3 columns]