Cantilever Beam (Uncertainty Quantification)

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This page shows how to perform Uncertainty Quantification of the Cantilever Beam with COSSAN-X.

Please refer to Cantilever Beam (Problem definition) to the definition of the problem.

Uncertainty Quantification Analysis

After saving the data, the simulation is ready to start. 
Different simulations can be started by pressing at the small white triangle within a green circle at top right.
Start analysis.png


Run the Analysis


The next window allows to choose among different analysis types such as: 'Design of Experiments', 'Sensitivity Analysis', 'Uncertainty Quantification'  and 'Userdefined Analysis'. In this tutorial 'Uncertainty Quantification' is selected.


Type of analysis.png

After pressing 'Next' the following page appears and the method simulation is selected:


UQbeam.png

After pressing 'Next' in the above window, various options for simulation are provided. The well known Monte Carlo sampling procedure is selected. At the right, the number of independent samples can be declared. It is possible to split the computation into several batches which might be processed by different computers using parallel computing.

Bulbgraph.png It is recommended to keep the number of sample per simulation smaller than 10000
The computational performance degradate with the increase of the batch size


In this simple example with little computational effort, only a single batch is used. Choosing a zero maximum runtime, means that no limit for the runtime is given.


Simulation method.png

Pressing Next it is possible to specify the Grid Settings (i.e. how to perform the analysis). In this example the analysis will be performed on the local machine and it is not necessary to change the default values in the mask. 


GridSetting.png

The actual computations starts after pressing the 'Finish' button. Then, the the following window appears.


Running MCSimulation.png

When completed, a message of successful completion is provided:


Successful completion.png

Show the Results

All results are accessible in the section "Analysis". The results are stored in sub-folders according to the performed analysis. In the present case only Uncertainty Quantification has been performed. This can be recognized by the value '(1)' in the folder 'Uncertainty Quantification'

ResultTypes.png

For more information about the structure of the results (outputs), please refer to the following page Category:Outputs.

Uncertainty Quantification

Expanding the folder 'Results' of the Uncertainty Quantification shows the following sub folders and all the involved variables defined in the input. 

Subfolders simu.png

In order to facilitate the visualization of the results the Perspectives 'Output view' can be selected. Alternatively, the 'Output view' can also be selected from the menu 'Window'>'Open Perspective'>'Output'. 

Output view.png


Scatter Plots

The following shows the 'Scatter View' and the 'Parallel Coordinates' view:


Scatter view.png

To visualize all 1000 realizations of the density rho and the Youngs modulus E, the variables can be selected using the mouse, and drags to the 'Scatter View':


Drag rho E.png

This leads to the following:


Scatter rho E.png

A scatter of the load P and the tip displacement w_out is shown in the following scatter plot:


Scatter P w out.png



Parallel Coordinates

The 'Parallel Coordinates View' allows to show correlations between several variables:


Parallel Coord 1.png

Table View

Open a new table view, by clicking on the icon on the toolbar and then drag and drop the quantity of interest on the table. 

ResultsTable.png

Histogram

Open a new table view, by clicking on the icon on the toolbar and then drag and drop the quantity of interest on the Histogram view. 

ResultsIstogram.png

See Also