SysIdentPy offers State of the Art techniques to build your NARMAX models, including it's variantsNARX,NARMA,NAR,NFIR,ARMAX,ARX,ARMA and others. It also includes tons of interesting examples to help you build nonlinear forecasting models using SysIdentPy.

What is SysIdentPy?

How do I install SysIdentPy?

pip install sysidentpy

Requirements

What are the main features of SysIdentPy?

Why does SysIdentPy exist?

How do I use sysIdentPy?

Examples

fromtorchimportnnimportnumpyasnpimportpandasaspdimportmatplotlib.pyplotaspltfromsysidentpy.metricsimportroot_relative_squared_errorfromsysidentpy.utils.generate_dataimportget_siso_data# Generate a dataset of a simulated dynamical systemx_train,x_valid,y_train,y_valid=get_siso_data(n=1000,colored_noise=False,sigma=0.001,train_percentage=80)

Building Polynomial NARX models with FROLS algorithm

fromsysidentpy.model_structure_selectionimportFROLSfromsysidentpy.basis_functionimportPolynomialfromsysidentpy.utils.display_resultsimportresultsfromsysidentpy.utils.plottingimportplot_residues_correlation,plot_resultsfromsysidentpy.residues.residues_correlationimportcompute_residues_autocorrelationfromsysidentpy.residues.residues_correlationimportcompute_cross_correlationbasis_function=Polynomial(degree=2)model=FROLS(order_selection=True,n_info_values=10,extended_least_squares=False,ylag=2,xlag=2,info_criteria='aic',estimator='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)RegressorsParametersERR0x1(k-2)0.90000.955565741y(k-1)0.19990.041079432x1(k-1)y(k-1)0.10000.00335113plot_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,x2_val)plot_residues_correlation(data=x1e,title="Residues",ylabel="$x_1e$")

NARX Neural Network

fromsysidentpy.neural_networkimportNARXNNfromsysidentpy.basis_functionimportPolynomialfromsysidentpy.utils.plottingimportplot_residues_correlation,plot_resultsfromsysidentpy.residues.residues_correlationimportcompute_residues_autocorrelationfromsysidentpy.residues.residues_correlationimportcompute_cross_correlationclassNARX(nn.Module):def__init__(self):super().__init__()self.lin=nn.Linear(4,10)self.lin2=nn.Linear(10,10)self.lin3=nn.Linear(10,1)self.tanh=nn.Tanh()defforward(self,xb):z=self.lin(xb)z=self.tanh(z)z=self.lin2(z)z=self.tanh(z)z=self.lin3(z)returnzbasis_function=Polynomial(degree=1)narx_net=NARXNN(net=NARX(),ylag=2,xlag=2,basis_function=basis_function,model_type="NARMAX",loss_func='mse_loss',optimizer='Adam',epochs=200,verbose=False,optim_params={'betas': (0.9,0.999),'eps':1e-05}# optional parameters of the optimizer)narx_net.fit(X=x_train,y=y_train)yhat=narx_net.predict(X=x_valid,y=y_valid)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="$x_1e$")

Catboost-narx

fromcatboostimportCatBoostRegressorfromsysidentpy.general_estimatorsimportNARXfromsysidentpy.basis_functionimportPolynomialfromsysidentpy.utils.plottingimportplot_residues_correlation,plot_resultsfromsysidentpy.residues.residues_correlationimportcompute_residues_autocorrelationfromsysidentpy.residues.residues_correlationimportcompute_cross_correlationbasis_function=Polynomial(degree=1)catboost_narx=NARX(base_estimator=CatBoostRegressor(iterations=300,learning_rate=0.1,depth=6),xlag=2,ylag=2,basis_function=basis_function,fit_params={'verbose':False})catboost_narx.fit(X=x_train,y=y_train)yhat=catboost_narx.predict(X=x_valid,y=y_valid)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="$x_1e$")

Catboost without NARX configuration

defplot_results_tmp(y_valid,yhat):_,ax=plt.subplots(figsize=(14,8))ax.plot(y_valid[:200],label='Data',marker='o')ax.plot(yhat[:200],label='Prediction',marker='*')ax.set_xlabel("$n$",fontsize=18)ax.set_ylabel("$y[n]$",fontsize=18)ax.grid()ax.legend(fontsize=18)plt.show()catboost=CatBoostRegressor(iterations=300,learning_rate=0.1,depth=6)catboost.fit(x_train,y_train,verbose=False)plot_results_tmp(y_valid,catboost.predict(x_valid))

Communication

Citation

@article{Lacerda2020,  doi = {10.21105/joss.02384},  url = {https://doi.org/10.21105/joss.02384},  year = {2020},  publisher = {The Open Journal},  volume = {5},  number = {54},  pages = {2384},  author = {Wilson Rocha Lacerda Junior and Luan Pascoal Costa da Andrade and Samuel Carlos Pessoa Oliveira and Samir Angelo Milani Martins},  title = {SysIdentPy: A Python package for System Identification using NARMAX models},  journal = {Journal of Open Source Software}}

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