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.