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small change case1 5
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parduino committed Jun 10, 2024
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Expand Up @@ -26,7 +26,6 @@ The example problems in this project will utilize the scenario, soil profile, an
.. figure:: ./images/case1_settlementProblem.png
:scale: 45 %
:align: center
:figclass: align-center>

Fig. 1. Problem statement.

Expand Down Expand Up @@ -231,14 +230,18 @@ Example One - Forward Propagation
The results for Forward Propagation are outlined below:

.. figure:: ./images/case1_ForwardPropagationResults.png
:align: center

Fig. 4. Forward propagation results.


The results indicate that, given the mean parameters and standard deviation, a total settlement of 1.31 inches is expected with a standard deviation of 0.88 inches (CoV = 0.66). The corresponding histogram, based on Latin Hypercube Sampling (LHS), along with the associated normal distribution curve, is shown in the figure below:

.. figure:: ./images/case1_propagation_Normalized_Settl_histogram.png
:scale: 40%
:align: center

Fig. 1. QuoFEM propagation histogram.
Fig. 5. QuoFEM propagation histogram.


Example Two - Sensitivity Analysis
Expand All @@ -262,12 +265,14 @@ The results for the Sensitivity Analysis in QuoFEM are outlined below. Uncertain
.. figure:: ./images/case1_Sensitivity2.png
:scale: 60 %
:align: center
:figclass: align-center>

Fig. 6. QuoFEM sensitivity results.

.. figure:: ./images/case1_Sensitivity.png
:scale: 100 %
:align: center
:figclass: align-center>

Fig. 7. QuoFEM interface.


Example Three - Parameter Calibration
Expand All @@ -287,6 +292,8 @@ When testing the two different deterministic calibration algorithms supported in
:scale: 80%
:align: center

Fig. 8. Settlement field as a function of Cc and Precon pressure.

Bayesian Calibration
^^^^^^^^^^^^^^^^^^^^

Expand Down Expand Up @@ -314,6 +321,9 @@ The results for Bayesian Calibration are outlined below:
.. figure:: ./images/case1_BayesianResults1.png

.. figure:: ./images/case1_BayesianResults2.png
:align: center

Fig. 9. QuoFEM Bayesian calibration results.

The figure shows Cc and Precon pressure are the most relevant parameters.

Expand All @@ -323,6 +333,8 @@ A more in-depth analysis using prior and posterior distributions reveals that th
:scale: 80%
:align: center

Fig. 10. Prior and posterior distributions from Bayesian calibration.


Remarks
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