# %% graph = calibrationResult.drawParameterDistributions() view = viewer.View(graph) # %% # The two distributions are different, which shows that the calibration is sensible to the observations (if the observations were not sensible, the two distributions were superimposed). Moreover, the two distributions are quite close, which implies that the prior distribution has played a roled in the calibration (otherwise the two distributions would be completely different, indicating that only the observations were taken into account). # %% # Gaussian nonlinear calibration # ------------------------------ # %% # The `GaussianNonLinearCalibration` class performs Gaussian nonlinear calibration. # %% algo = ot.GaussianNonLinearCalibration(mycf, Qobs, Hobs, thetaPrior, sigma, errorCovariance) # %% # The `run` method computes the solution of the problem. # %% algo.run() # %% calibrationResult = algo.getResult() # %% # Analysis of the results # ----------------------- # %%
view = viewer.View(graph)
# %%
# For the :math:`R` variable, the observations are much more important than the prior: this is shown by the fact that the posterior and prior distribution of the :math:`R` variable are very different.
#
# We see that the prior and posterior distribution are close to each other for the :math:`\gamma` variable: the observations did not convey much information for this variable.
# %%
# Gaussian nonlinear calibration
# ------------------------------
# %%
# The `GaussianNonLinearCalibration` class performs the gaussian nonlinear calibration.
# %%
algo = ot.GaussianNonLinearCalibration(mycf, observedStrain, observedStress,
thetaPrior, sigma, errorCovariance)
# %%
# The `run` method computes the solution of the problem.
# %%
algo.run()
# %%
calibrationResult = algo.getResult()
# %%
# Analysis of the results
# -----------------------
# %%
priorCovariance[i, i] = 3.0 + (1.0 + i) * (1.0 + i)
for j in range(i):
priorCovariance[i, j] = 1.0 / (1.0 + i + j)
errorCovariance = ot.CovarianceMatrix(2)
for i in range(2):
errorCovariance[i, i] = 2.0 + (1.0 + i) * (1.0 + i)
for j in range(i):
errorCovariance[i, j] = 1.0 / (1.0 + i + j)
globalErrorCovariance = ot.CovarianceMatrix(2 * m)
for i in range(2 * m):
globalErrorCovariance[i, i] = 2.0 + (1.0 + i) * (1.0 + i)
for j in range(i):
globalErrorCovariance[i, j] = 1.0 / (1.0 + i + j)
bootstrapSizes = [0, 100]
for bootstrapSize in bootstrapSizes:
algo = ot.GaussianNonLinearCalibration(modelX, x, y, candidate,
priorCovariance, errorCovariance)
algo.setBootstrapSize(bootstrapSize)
algo.run()
# To avoid discrepance between the plaforms with or without CMinpack
print("result (Auto)=", algo.getResult().getParameterMAP())
algo.setOptimizationAlgorithm(
ot.MultiStart(
ot.TNC(),
ot.LowDiscrepancyExperiment(
ot.SobolSequence(),
ot.Normal(
candidate,
ot.CovarianceMatrix(ot.Point(candidate).getDimension())),
ot.ResourceMap.GetAsUnsignedInteger(
"GaussianNonLinearCalibration-MultiStartSize")).generate())
)
errorCovariance = ot.CovarianceMatrix(3) errorCovariance[0,0] = sigmaObservation[0]**2 errorCovariance[1,1] = sigmaObservation[1]**2 errorCovariance[2,2] = sigmaObservation[2]**2 # %% calibrationFunction.setParameter(thetaPrior) predictedOutput = calibrationFunction(observedInput) predictedOutput[0:5] # %% # Calibration with gaussian non linear least squares # -------------------------------------------------- # %% algo = ot.GaussianNonLinearCalibration(calibrationFunction, observedInput, observedOutput, thetaPrior, parameterCovariance, errorCovariance) # %% algo.run() # %% calibrationResult = algo.getResult() # %% # Analysis of the results # ----------------------- # %% thetaMAP = calibrationResult.getParameterMAP() thetaMAP