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small change case1 6
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parduino committed Jun 10, 2024
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4 changes: 3 additions & 1 deletion source/case_1.rst
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Expand Up @@ -30,6 +30,8 @@ The example problems in this project will utilize the scenario, soil profile, an
Fig. 1. Problem statement.




.. list-table:: Soil Profile Parameters
:widths: 25 25 50
:header-rows: 1
Expand Down Expand Up @@ -330,7 +332,7 @@ The figure shows Cc and Precon pressure are the most relevant parameters.
A more in-depth analysis using prior and posterior distributions reveals that the posterior distributions from the Bayesian calibration process result in more accurate and less uncertain settlement estimations. The figure below illustrates these distributions.

.. figure:: ./images/case1_calibration_PriorPost.png
:scale: 80%
:scale: 70%
:align: center

Fig. 10. Prior and posterior distributions from Bayesian calibration.
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22 changes: 17 additions & 5 deletions source/case_1.rst~
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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 @@ -314,15 +321,20 @@ 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.

A more in-depth analysis using prior and posterior distributions reveals that the posterior distributions from the Bayesian calibration process result in more accurate and less uncertain settlement estimations. The figure below illustrates these distributions.

.. figure:: ./images/case1_calibration_PriorPost.png
:scale: 80%
:scale: 70%
:align: center

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


Remarks
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