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
pip install sysidentpy
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.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
df1 = pd.read_csv('examples/datasets/x_cc.csv')
df2 = pd.read_csv('examples/datasets/y_cc.csv')
df2[5000:80000].plot(figsize=(10, 4))
<AxesSubplot:>

# 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¶
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
)
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:472: 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)
0.08011571455967419
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



Testing different autoregressive models¶
from sklearn.neighbors import KNeighborsRegressor
from sklearn.svm import SVC, LinearSVC, NuSVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor, AdaBoostRegressor, GradientBoostingRegressor
from sklearn.naive_bayes import GaussianNB
from catboost import CatBoostRegressor
from sklearn.linear_model import BayesianRidge, ARDRegression
from sysidentpy.general_estimators import NARX
basis_function = Polynomial(degree=2)
estimators = [
('KNeighborsRegressor', NARX(
base_estimator=KNeighborsRegressor(),
xlag=10,
ylag=10)),
('NARX-DecisionTreeRegressor', NARX(
base_estimator=DecisionTreeRegressor(),
xlag=10,
ylag=10)),
('NARX-RandomForestRegressor', NARX(
base_estimator=RandomForestRegressor(
n_estimators=200),
xlag=10,
ylag=10,
)),
('NARX-Catboost', NARX(
base_estimator=CatBoostRegressor(
iterations=800,
learning_rate=0.1,
depth=8),
xlag=10,
ylag=10,
non_degree=1,
fit_params={'verbose': False}
)),
('NARX-ARD', NARX(
base_estimator=ARDRegression(),
xlag=10,
ylag=10,
non_degree=2
)),
('FROLS-Polynomial_NARX', FROLS(
order_selection=True,
n_info_values=50,
extended_least_squares=False,
ylag=10, xlag=10,
info_criteria='bic',
estimator='recursive_least_squares',
basis_function=basis_function
)
),
]
resultados = {}
for nome_do_modelo, modelo in estimators:
resultados['%s' % (nome_do_modelo)] = []
modelo.fit(X=x_train, y=y_train)
yhat = modelo.predict(X=x_valid, y=y_valid)
result = root_relative_squared_error(y_valid[modelo.max_lag:], yhat[modelo.max_lag:])
resultados['%s' % (nome_do_modelo)].append(result)
print(nome_do_modelo, '%.3f' % np.mean(result))
10-14 20:35:42 - INFO - Training the model
10-14 20:35:42 - INFO - Creating the regressor matrix
10-14 20:35:42 - INFO - The regressor matrix have 21 features
10-14 20:35:42 - INFO - Done! Model is built!
c:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\utils\deprecation.py:27: FutureWarning: Function __init__ has been deprecated since v0.1.7.
Use NARXNN(ylag=2, xlag=2, basis_function='Some basis function') instead.This module was deprecated in favor of NARXNN(ylag=2, xlag=2, basis_function='Some basis function') module into which all the refactored classes and functions are moved.
This feature will be removed in version v0.2.0.
warnings.warn(message, FutureWarning)
KNeighborsRegressor 1.871
10-14 20:35:42 - INFO - Training the model
10-14 20:35:42 - INFO - Creating the regressor matrix
10-14 20:35:42 - INFO - The regressor matrix have 21 features
10-14 20:35:42 - INFO - Done! Model is built!
NARX-DecisionTreeRegressor 0.137
10-14 20:35:43 - INFO - Training the model
10-14 20:35:43 - INFO - Creating the regressor matrix
10-14 20:35:43 - INFO - The regressor matrix have 21 features
c:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\general_estimators\narx.py:161: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples,), for example using ravel().
self.base_estimator.fit(X, y, **self.fit_params)
10-14 20:35:43 - INFO - Done! Model is built!
NARX-RandomForestRegressor 0.167
10-14 20:35:47 - INFO - Training the model
10-14 20:35:47 - INFO - Creating the regressor matrix
10-14 20:35:47 - INFO - The regressor matrix have 21 features
10-14 20:35:49 - INFO - Done! Model is built!
NARX-Catboost 0.182
10-14 20:35:50 - INFO - Training the model
10-14 20:35:50 - INFO - Creating the regressor matrix
10-14 20:35:50 - INFO - The regressor matrix have 231 features
10-14 20:35:50 - INFO - Done! Model is built!
C:\Users\wilso\miniconda3\envs\sysidentpy\lib\site-packages\sklearn\utils\validation.py:63: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
return f(*args, **kwargs)
NARX-ARD 0.075
FROLS-Polynomial_NARX 0.047
for aux_results, results in sorted(resultados.items(), key=lambda x: np.mean(x[1]), reverse=False):
print(aux_results, np.mean(results))
FROLS-Polynomial_NARX 0.04663897799085836
NARX-ARD 0.07507698375814373
NARX-DecisionTreeRegressor 0.1370352822444405
NARX-RandomForestRegressor 0.16746617689296395
NARX-Catboost 0.1818567377511571
KNeighborsRegressor 1.8710938813353852