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
from sysidentpy.model_structure_selection import ER
from sysidentpy.basis_function._basis_function import Polynomial
from sysidentpy.parameter_estimation import RecursiveLeastSquares
from sysidentpy.metrics import root_relative_squared_error
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 from sysidentpy.model_structure_selection import ER from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.parameter_estimation import RecursiveLeastSquares from sysidentpy.metrics import root_relative_squared_error 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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df2[5000:80000].plot(figsize=(10, 4))
df2[5000:80000].plot(figsize=(10, 4))
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<Axes: >
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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)
estimator = RecursiveLeastSquares()
model = ER(
ylag=6,
xlag=6,
n_perm=2,
k=2,
skip_forward=True,
estimator=estimator,
basis_function=basis_function,
)
basis_function = Polynomial(degree=2) estimator = RecursiveLeastSquares() model = ER( ylag=6, xlag=6, n_perm=2, k=2, skip_forward=True, estimator=estimator, basis_function=basis_function, )
C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\utils\deprecation.py:40: FutureWarning: Passing a string to define the estimator will rise an error in v0.4.0. You'll have to use ER(estimator=LeastSquares()) instead. The only change is that you'll have to define the estimator first instead of passing a string like 'least_squares'. This change will make easier to implement new estimators and it'll improve code readability. warnings.warn(message, FutureWarning, stacklevel=1)
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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_20912\4260657624.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)
0.03276775133089435
Regressors Parameters ERR
0 1 -6.7052E+02 0.00000000E+00
1 y(k-1) 9.6022E-01 0.00000000E+00
2 y(k-5) -3.0769E-02 0.00000000E+00
3 x1(k-2) 7.3733E+02 0.00000000E+00
4 y(k-1)^2 1.5897E-04 0.00000000E+00
5 y(k-2)y(k-1) -2.2080E-04 0.00000000E+00
6 y(k-3)y(k-1) 2.9946E-06 0.00000000E+00
7 y(k-5)y(k-1) 4.9779E-06 0.00000000E+00
8 x1(k-1)y(k-1) -1.7036E-01 0.00000000E+00
9 x1(k-2)y(k-1) -2.0748E-01 0.00000000E+00
10 x1(k-4)y(k-1) 8.3724E-03 0.00000000E+00
11 y(k-2)^2 7.3635E-05 0.00000000E+00
12 x1(k-1)y(k-2) 1.2028E-01 0.00000000E+00
13 x1(k-2)y(k-2) 8.0270E-02 0.00000000E+00
14 x1(k-3)y(k-2) -3.0208E-03 0.00000000E+00
15 x1(k-4)y(k-2) -8.8307E-03 0.00000000E+00
16 x1(k-1)y(k-3) -4.9095E-02 0.00000000E+00
17 x1(k-1)y(k-4) 1.2375E-02 0.00000000E+00
18 x1(k-1)^2 1.1682E+02 0.00000000E+00
19 x1(k-3)x1(k-2) 5.2777E+00 0.00000000E+00
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