Identification of an electromechanical system¶
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 FROLS
from sysidentpy.basis_function._basis_function import Polynomial
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 import matplotlib.pyplot as plt from sysidentpy.model_structure_selection import FROLS from sysidentpy.basis_function._basis_function import Polynomial 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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<AxesSubplot:>
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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¶
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basis_function = Polynomial(degree=2)
model = FROLS(
order_selection=True,
n_info_values=40,
extended_least_squares=False,
ylag=2,
xlag=2,
info_criteria="bic",
estimator="recursive_least_squares",
basis_function=basis_function,
)
basis_function = Polynomial(degree=2) model = FROLS( order_selection=True, n_info_values=40, extended_least_squares=False, ylag=2, xlag=2, info_criteria="bic", estimator="recursive_least_squares", basis_function=basis_function, )
c:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\utils\deprecation.py:37: FutureWarning: Passing a string to define the estimator will rise an error in v0.4.0. You'll have to use FROLS(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)
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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\Desktop\projects\GitHub\sysidentpy\sysidentpy\model_structure_selection\forward_regression_orthogonal_least_squares.py:569: UserWarning: n_info_values is greater than the maximum number of all regressors space considering the chosen y_lag, u_lag, and non_degree. We set as 15 self.info_values = self.information_criterion(reg_matrix, y)
0.07912218629573997
Regressors Parameters ERR
0 y(k-1) 1.3016E+00 9.86000384E-01
1 x1(k-1)^2 1.0393E+02 7.94805130E-03
2 y(k-2)^2 1.6288E-05 2.50905908E-03
3 x1(k-1)y(k-1) -1.2567E-01 1.43301039E-03
4 y(k-2) -5.0784E-01 1.02781443E-03
5 x1(k-1)y(k-2) 5.6049E-02 5.35200312E-04
6 x1(k-2) 3.4986E+02 2.79648078E-04
7 x1(k-2)y(k-1) -8.4030E-02 1.12211942E-04
8 x1(k-2)x1(k-1) -7.8186E+00 4.54743448E-05
9 x1(k-2)y(k-2) 3.4050E-02 3.25346101E-05
