V0.1.6 - Multiple Inputs usage¶
Example created by Wilson Rocha Lacerda Junior
Generating 2 input 1 output sample data¶
The data is generated by simulating the following model:
\(y_k = 0.4y_{k-1}^2 + 0.1y_{k-1}x1_{k-1} + 0.6x2_{k-1} -0.3x1_{k-1}x2_{k-2} + e_{k}\)
If colored_noise is set to True:
\(e_{k} = 0.8\nu_{k-1} + \nu_{k}\)
where \(x\) is a uniformly distributed random variable and \(\nu\) is a gaussian distributed variable with \(\mu=0\) and \(\sigma=0.001\)
pip install sysidentpy
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Note: you may need to restart the kernel to use updated packages.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sysidentpy.polynomial_basis import PolynomialNarmax
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.utils.generate_data import get_miso_data, get_siso_data
x_train, x_valid, y_train, y_valid = get_miso_data(n=1000,
colored_noise=False,
sigma=0.001,
train_percentage=90)
There is specific diferences for multiple input data.
You have to set the number of inputs (n_inputs=2 in this example)
You have to pass the lags for each input in a nested list (e.g., [[1, 2], [1, 2]])
The remainder settings remains the same.
Build the model¶
model = PolynomialNarmax(non_degree=2,
order_selection=True,
n_info_values=15,
n_terms=4,
extended_least_squares=False,
ylag=2, xlag=[[1, 2], [1, 2]],
n_inputs=2,
info_criteria='lilc',
estimator='least_squares',
)
model.fit(x_train, y_train)
<sysidentpy.polynomial_basis.narmax.PolynomialNarmax at 0x27672c85820>
Model evaluation¶
yhat = model.predict(x_valid, y_valid)
rrse = root_relative_squared_error(y_valid, yhat)
print(rrse)
results = pd.DataFrame(model.results(err_precision=8,
dtype='dec'),
columns=['Regressors', 'Parameters', 'ERR'])
print(results)
ee, ex, extras, lam = model.residuals(x_valid, y_valid, yhat)
model.plot_result(y_valid, yhat, ee, ex)
0.0025720880126656447
Regressors Parameters ERR
0 x2(k-1) 0.6001 0.90504940
1 x2(k-2)x1(k-1) -0.3000 0.05060522
2 y(k-1)^2 0.3999 0.04398562
3 x1(k-1)y(k-1) 0.1001 0.00035238
xaxis = np.arange(1, model.n_info_values + 1)
plt.plot(xaxis, model.info_values)
plt.xlabel('n_terms')
plt.ylabel('Information Criteria')
Text(0, 0.5, 'Information Criteria')
