]
# output uncertainty
uy1 = [1] * 29
#%% Setting the observed data set
# inputs
Estime.setDados(0, (time, uxtime), (temperature, uxtemperature))
# output
Estime.setDados(1, (y, uy1))
# Defining the previous data set to be used to parameter estimation
# dataType: Defines the purpose of the informed data set: estimacao, predicao.
# glx: Degrees of freedom of quantity x;
# gly: Degrees of freedom of quantity y;
Estime.setConjunto(dataType='estimacao', glx=[], gly=[])
#%% Optimization - estimating the parameters
# 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=[0.005, 20000.000],
algorithm='ipopt',
lower_bound=[0.006, 15000],
upper_bound=[100, 30000],
optimizationReport=True,
parametersReport=False)
0.696, 0.582, 0.795, 0.800, 0.790, 0.883, 0.712, 0.576, 0.715, 0.673,
0.802, 0.802, 0.804, 0.794, 0.804, 0.799, 0.764, 0.688, 0.717, 0.802,
0.695, 0.808, 0.655, 0.309, 0.689, 0.437, 0.425, 0.638, .659, 0.449
]
# output uncertainty
uy = [1] * 41
#%% Setting the observed data set
# inputs
Estime.setDados(0, (time, uxtime), (temperature, uxtemperature))
# outputs
Estime.setDados(1, (y, uy))
# 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)
631.0, 631.0, 639.0, 639.0, 639.0, 639.0, 639.0, 639.0, 639.0, 639.0, 639.0
]
uy = [1] * 41
uxtempo = [1] * 41
uxtemperatura = [1] * 41
#Execução do MT_PEU
Estime = EstimacaoNaoLinear(Modelo,
simbolos_x=['t', 'T'],
simbolos_y=['y'],
simbolos_param=['ko', 'E'],
Folder='Exemplo1')
Estime.setDados(0, (tempo, uxtempo), (temperatura, uxtemperatura))
Estime.setDados(1, (y, uy))
Estime.setConjunto(tipo='estimacao')
Estime.optimize(initial_estimative=[0.5, 25000], algoritmo='ipopt')
Estime.incertezaParametros(metodoIncerteza='Geral' '')
Estime.predicao()
# Valores originais
hessian = array([[5.46625676e+00, -7.50116238e-03],
[-7.50116238e-03, 1.02960714e-05]])
sensibilidade = array([[-1.06335451e-01, 1.52826132e-04],
[-5.59353653e-02, 8.03907392e-05],
[-1.28132438e-01, 1.80542088e-04],
[-2.26100338e-01, 3.18581523e-04],
[-2.26100338e-01, 3.18581523e-04],
[-1.28132438e-01, 1.80542088e-04],
[-2.07847997e-01, 2.89084593e-04],
[-1.16257751e-01, 1.61696650e-04],
]
# Output data uncertainty
uP = [
0.08, 0.09, 0.09, 0.11, 0.17, 0.21, 0.25, 0.35, 0.40, 0.47, 0.48, 0.58,
0.70, 0.89, 1.05, 1.28, 1.61, 2.00, 2.37, 2.90, 3.53, 4.32, 5.23
]
#%% Setting the observed data set
# inputs
Estimation.setDados(0, (T, uxT))
# outputs
Estimation.setDados(1, (P, uP))
# Defining the previous data set to be used to parameter estimation.
# dataType: Defines the purpose of the informed data set: estimacao, predicao.
Estimation.setConjunto(dataType='estimacao')
#%% 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);
# 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.
uP = [
0.08, 0.09, 0.09, 0.11, 0.17, 0.21, 0.25, 0.35, 0.40, 0.47, 0.48, 0.58,
0.70, 0.89, 1.05, 1.28, 1.61, 2.00, 2.37, 2.90, 3.53, 4.32, 5.23
]
#%% Setting the observed data set
# inputs
Estimation.setDados(0, (T, uT))
# outputs
Estimation.setDados(1, (P, uP))
# Defining the previous data set to be used to parameter estimation
# dataType: Defines the purpose of the informed data set: estimacao, predicao.
# glx: Degrees of freedom of quantity x;
# gly: Degrees of freedom of quantity y;
Estimation.setConjunto(dataType='estimacao', glx=[], gly=[])
#%% Optimization - estimating the parameters
# 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);