SENSITIVITY ANALYSIS: DEPENDENT INPUT VARIABLES

In this example, the Kucherenko and ANCOVA sensitivity indices are computed and compared for the <https://www.sfu.ca/~ssurjano/shortcol short column function> with correlated input parameters.

Package imports

from uqpylab import sessions

Start a remote UQCloud session

# Start the session
mySession = sessions.cloud()
# (Optional) Get a convenient handle to the command line interface
uq = mySession.cli
# Reset the session
mySession.reset()

Processing .

.

 done!

 uqpylab.sessions :: INFO     :: This is UQ[py]Lab, version 1.00, running on https://uqcloud.ethz.ch. 
                                 UQ[py]Lab is free software, published under the open source BSD 3-clause license.
                                 To request special permissions, please contact:
                                  - Stefano Marelli (marelli@ibk.baug.ethz.ch).
                                 A new session (3b12439f2607429b9bbbf8d911d74a89) started.

 uqpylab.sessions :: INFO     :: Reset successful.

Set the random seed for reproducibility

uq.rng(101,'twister');

2 - COMPUTATIONAL MODEL

The short-column function is an analytical 3-dimensional function that models the limit state of a short steel column with a rectangular cross-section, subjected to a bending moment and an axial force. The short column function |uq_shortcol| is supplied with UQpyLab.

Create a MODEL object from the function file:

ModelOpts = {
    'Type': 'Model',
    'ModelFun': 'shortcol.model',
}

myModel = uq.createModel(ModelOpts)

3 - PROBABILISTIC INPUT MODEL

The probabilistic input model consists of three random variables with the following marginals:

Variable	Description	Distribution	Mean	Std. deviation
Y	Yield stress	Lognormal	5 MPa	0.5 MPa
M	Bending moment	Gaussian	2000 N.mm	400 N.mm
P	Axial force	Gaussian	500 N	100 N

Define the marginal distributions of the input model:

InputOpts = {
    'Marginals': [
        {
        'Name': 'Y', # yield stress
        'Type': 'Lognormal',
        'Moments': [5, 0.5] # (MPa)
        },
        {
        'Name': 'M', # bending moment
        'Type': 'Gaussian',
        'Moments': [2000, 400] # (N.mm)
        },
        {
        'Name': 'P', # axial force
        'Type': 'Gaussian',
        'Moments': [500, 100] # (N)
        }]
}

The parameters $P$ and $M$ are assumed to be correlated under Gaussian copula with a rank correlation of 0.72.

Define the Gaussian copula and its parameters:

InputOpts['Copula'] = {
    'Type': 'Gaussian',
    'RankCorr': [[1, 0, 0], [0, 1, 0.72], [0, 0.72, 1]]
}

Create an INPUT object based on the specified marginals and copula:

myInput = uq.createInput(InputOpts)

Show the correlated input:

uq.display(myInput);