lower_bound=[0.006, 15000], upper_bound=[100, 30000], optimizationReport=True, parametersReport=False) #%% Evaluating the parameters uncertainty and coverage region # uncertaintyMethod: method for calculating the covariance matrix of the parameters; # objectiveFunctionMapping: Deals with mapping the objective function (True or False); # limite_inferior: Lower limit of parameters; # limite_superior: Upper limit of the parameters; # iterations: Number of iterations to perform the mapping of the objective function. The higher the better mapping, but it # increases the execution time # parametersReport: Informs whether the parameters report should be created. Estime.parametersUncertainty(uncertaintyMethod='Geral', objectiveFunctionMapping=True, lower_bound=[7.2e-3, 26400], upper_bound=[7.7e-3, 28600], parametersReport=True, iterations=200) #%% Evaluating model predictions # export_y: Exports the calculated data of y, its uncertainty, and degrees of freedom in a txt with comma separation (True or False); # export_y_xls: Exports the calculated data of y, its uncertainty, and degrees of freedom in a xls (True or False); # export_cov_y: Exports the covariance matrix of y (True or False); # export_x: Exports the calculated data of x, its uncertainty, and degrees of freedom in a txt with comma separation(True or False); # export_cov_x: Exports the covariance matrix of x (True or False). Estime.prediction(export_y=True, export_y_xls=True, export_cov_y=True, export_x=True, export_cov_x=True)
# Defining the previous data set to be used to parameter estimation Estime.setConjunto() #%% Optimization - estimating the parameters # initial_estimative: List with the initial estimates for the parameters; # algorithm: Informs the optimization algorithm that will be used. Each algorithm has its own keywords; # optimizationReport: Informs whether the optimization report should be created (True or False); Estime.optimize(initial_estimative=[18, 20000.000], optimizationReport=False, algorithm='ipopt') #%% Evaluating the parameters uncertainty and coverage region # uncertaintyMethod: method for calculating the covariance matrix of the parameters; # objectiveFunctionMapping: Deals with mapping the objective function (True or False); Estime.parametersUncertainty(uncertaintyMethod='2InvHessiana', objectiveFunctionMapping=True) #%%Running the charts without prediction. # using solely default options Estime.plots() #%% Evaluating model predictions # export_y: Exports the calculated data of y, its uncertainty, and degrees of freedom in a txt with comma separation (True or False); # export_y_xls: Exports the calculated data of y, its uncertainty, and degrees of freedom in a xls (True or False); # export_cov_y: Exports the covariance matrix of y (True or False); Estime.prediction( export_y=True, export_y_xls=True, export_cov_y=True, )
# parametersReport: Informs whether the parameters report should be created (True or False). Estimation.optimize(initial_estimative=[1, 1.5, 0.009], algorithm='bonmin', optimizationReport=True, parametersReport=False) #%% Evaluating the parameters uncertainty and coverage region # uncertaintyMethod: method for calculating the covariance matrix of the parameters: 2InvHessian, Geral, SensibilidadeModelo # Geral obtains the parameters uncertainty matrix without approximations (most accurate), while 2InvHessian and SensibilidadeModelo involves # some approximations. # objectiveFunctionMapping: Deals with mapping the objective function (True or False); # parametersReport: Informs whether the parameters report should be created (True or False). # iterations: Number of iterations to perform the mapping of the objective function. The higher the better mapping, but it # increases the execution time Estimation.parametersUncertainty(uncertaintyMethod='Geral', objectiveFunctionMapping=True, iterations=5000, parametersReport=False) #%% Evaluating model predictions # export_y: Exports the calculated data of y, its uncertainty, and degrees of freedom in a txt with comma separation (True or False); # export_y_xls: Exports the calculated data of y, its uncertainty, and degrees of freedom in a xls (True or False); # export_cov_y: Exports the covariance matrix of y (True or False); # export_x: Exports the calculated data of x, its uncertainty, and degrees of freedom in a txt with comma separation(True or False); Estimation.prediction(export_y=True, export_y_xls=True, export_cov_y=True, export_x=True) #%% Evaluating residuals and quality index # using solely default options Estimation.residualAnalysis()
# initial_estimative: List with the initial estimates for the parameters; # lower_bound: List with the lower bounds for the parameters; # upper_bound: List with the upper bounds for the parameters; # algorithm: Informs the optimization algorithm that will be used. Each algorithm has its own keywords; # optimizationReport: Informs whether the optimization report should be created (True or False); # parametersReport: Informs whether the parameters report should be created (True or False). Estime.optimize(initial_estimative=[3,0.1,5,0.4], algorithm='ipopt', lower_bound=[0.2,0.09,3.1,0.3], upper_bound=[3.6,0.3,5.6,0.6], optimizationReport = True, parametersReport = False) #%% Evaluating the parameters uncertainty and coverage region # uncertaintyMethod: method for calculating the covariance matrix of the parameters; # objectiveFunctionMapping: Deals with mapping the objective function (True or False); # lower_bound: Lower limit of parameters; # upper_bound: Upper limit of the parameters. # parametersReport: Informs whether the parameters report should be created. Estime.parametersUncertainty(uncertaintyMethod='2InvHessiana', objectiveFunctionMapping=True, lower_bound=[1,0.04,1.75,0.175], upper_bound=[4.5,0.16,6.75,1], parametersReport = True) #%% Evaluating model predictions # export_y: Exports the calculated data of y, its uncertainty, and degrees of freedom in a txt with comma separation (True or False); # export_y_xls: Exports the calculated data of y, its uncertainty, and degrees of freedom in a xls (True or False); # export_cov_y: Exports the covariance matrix of y (True or False); # export_x: Exports the calculated data of x, its uncertainty, and degrees of freedom in a txt with comma separation(True or False); # export_cov_x: Exports the covariance matrix of x (True or False). Estime.prediction(export_y=True,export_y_xls=True, export_cov_y=True, export_x=True, export_cov_x=True) #%% Evaluating residuals and quality index Estime.residualAnalysis(report=True) #%% Plotting the main results # using solely default options Estime.plots()
# initial_estimative: List with the initial estimates for the parameters; # lower_bound: List with the lower bounds for the parameters; # algorithm: Informs the optimization algorithm that will be used. Each algorithm has its own keywords; # optimizationReport: Informs whether the optimization report should be created (True or False); # parametersReport: Informs whether the parameters report should be created (True or False). Estimation.optimize(initial_estimative=[200, -80680.1], algorithm='ipopt', optimizationReport=True, parametersReport=False) #%% Evaluating the parameters uncertainty and coverage region # uncertaintyMethod: method for calculating the covariance matrix of the parameters; # objectiveFunctionMapping: Deals with mapping the objective function (True or False); # parametersReport: Informs whether the parameters report should be created. Estimation.parametersUncertainty(uncertaintyMethod='SensibilidadeModelo', objectiveFunctionMapping=True, parametersReport=True) #%% Evaluating model predictions # export_y: Exports the calculated data of y, its uncertainty, and degrees of freedom in a txt with comma separation (True or False); # export_y_xls: Exports the calculated data of y, its uncertainty, and degrees of freedom in a xls (True or False); # export_cov_y: Exports the covariance matrix of y (True or False); # export_x: Exports the calculated data of x, its uncertainty, and degrees of freedom in a txt with comma separation(True or False); # export_cov_x: Exports the covariance matrix of x (True or False). Estimation.prediction(export_y=True, export_y_xls=True, export_cov_y=True, export_x=True, export_cov_x=True) #%% Evaluating residuals and quality index
#%% Setting the observed data set # Independent variables Estime.setDados(0,(time,uxtime),(temperature,uxtemperature)) # Dependent variable Estime.setDados(1,(y,uy)) # Defining the previous data set to be used to parameter estimation Estime.setConjunto() #%% Optimization - estimating the parameters # initial_estimate: list containing initial estimate for optimization algorithm Estime.optimize(initial_estimative=[0.5,25000]) #%% Evaluating the parameters uncertainty and coverage region # using solely default options Estime.parametersUncertainty() #%% Evaluating model predictions # using solely default options Estime.prediction() #%% Evaluating residuals and quality index # using solely default options Estime.residualAnalysis() #%% Plotting the main results # using solely default options Estime.plots() #%% Reference of this case study # SCHWAAB, M.M.;PINTO, J.C. Análise de Dados Experimentais I: Fundamentos da Estátistica e Estimação de Parâmetros. Rio de Janeiro: e-papers, 2007.