Identify important components in complex networks

What is sobol?

Which bridges are the most important to retrofit if we want to reduce the expected cost of the road network performance given a regional seismic hazard?

sobol is a repository that contains a set of methods and a sample data set with which to answer that and similar questions. Specifically, sobol comprises:

• A set of methods for quantifying the importance of individual components in complex networks by computing their

  first- and total-order Sobol' indices
• A sample data set on which to use those methods, comprising vector inputs (bridge fragility function

  parameters) and scalar outputs (the expected cost of road network performance over a set of earthquake rupture

  scenarios).

Retrofitting bridges based on their total-order Sobol' indices can be more cost efficient than selecting bridges according to other criteria (Bhattacharjee and Baker TBD).

These methods should be applicable to other networks and performance metrics of interest, provided they meet the criteria outlined in the paper associated with this repository (Bhattacharjee and Baker TBD).

What are Sobol' indices?

A Sobol' index approximates an exact sensitivity index that results from a global variance-based sensitivity analysis . The magnitude of a (normalized) Sobol' index indicates how much of the variance in an output quantity of interest can be attributed to variance in a particular input. The larger the Sobol' index, the more influential the input.

• For an basic introduction to Sobol' indices, head to the example.
• For a more detailed treatment, see Global Sensitivity Analysis: The Primer by Andrea Saltelli et al.
• For a detailed treatment of Sobol' indices for bridge retrofit (or component upgrade) prioritisation, see the paper

  associated with this repository (Bhattacharjee and Baker TBD).

How is sobol organized?

This repository includes all files (both scripts and results) necessary to reproduce the figures in Bhattacharjee and Baker TBD. Many of these figures have already been reproduced and stored in the directory figs.

• CONTENTS details the contents of each directory as well as the purpose of each script.
• CONFIG specifies which version of Python you should use to run the scripts included in this repository, as well as

  the packages you need to install.
• BENCHMARKS includes detailed outputs against which to verify the results you get when running certain scripts on

  your own machine.

How can I use sobol?

Try:

• Exploring the sample data set to better understand global variance-based sensitivity analysis or Sobol' indices.
• Replacing the sample data set with your own data, whether for bridges in road networks or for components in another

  system, and prioritising component-level interventions in your system of interest.
• Using the methods implemented for computing first- and total-order Sobol' indices for any function of your

  choosing -- it can be a simple polynomial or not expressible in closed form.

How can I install sobol?

In Terminal (on Mac), use the following, replacing [myDirectory] with your preferred directory, e.g. cd Desktop.

cd [myDirectory]

git clone https://github.com/gbhattacharjee/sobol.git

Before running any scripts in sobol, make sure you have all the required Python packages in config. Some

packages require specific (earlier) versions, so I recommend creating a virtual environment (e.g., venv) in which to install them. For example:

cd sobol

python2 -m venv sobol-venv

source sobol-venv/bin/activate

pip install networkx==1.8.1

pip install pp==1.6.5

pip install scipy

pip install numpy

pip install matplotlib

pip install plotly

To verify installation has worked, please compare the results of the specified function calls to those given in the benchmarks document.

How can I cite this repository?

Gitanjali Bhattacharjee. (2020, November 28). Sobol' index-based bridge retrofit prioritisation code (Version v1.0.0). Zenodo. http://doi.org/10.5281/zenodo.4294322

References

Gitanjali Bhattacharjee and Jack W. Baker. (2021) Using global variance-based sensitivity analysis to prioritise bridge retrofits in a regional road network subject to seismic hazard. Structure and Infrastructure Engineering (in press).

Andrea Saltelli, Stefano Tarantola, Francesca Campolongo, and Marco Ratto. (2004) Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. John Wiley & Sons, Ltd.

Andrea Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana, Stefano Tarantola. (2008) Global Sensitivity Analysis: The Primer. John Wiley & Sons, Ltd.

Contact

Gitanjali Bhattacharjee, Blume Earthquake Engineering Center Stanford University, gjee@stanford.edu