# 4. ExamplesΒΆ

The following are a few examples showing the usage of quoFEM. Video companions showing these examples are also provided for selected problems. The files for the examples are available on Github.

This example illustrates how quoFEM interacts with the Tcl interpreter for OpenSees. A simple forward propagation procedure is run to estimate the first and second central moments of a FE model's response, given the marginal distributions of various random parameters.

This example illustrates how quoFEM interacts with OpenSeesPy. A simple forward propagation procedure is run to estimate the first and second central moments of a FE model's response, given the marginal distributions of various random parameters.

This example illustrates how Python scripting can be used with quoFEM to express general mathematical models without the use of a dedicated finite element analysis engine.

In this example, a parameter estimation routine is used to estimate column stiffnesses of a simple steel frame, given data about its mode shapes and mass distribution.

A global sensitivity analysis is conducted with correlated random variables using the SimCenterUQ engine for sensitivity analysis.

In this example, Bayesian estimation is used to estimate the lateral story stiffnesses of the two stories of a simple steel frame, given data about its mode shapes and frequencies. The transitional Markov chain Monte Carlo algorithm is used to obtain samples from the posterior probability distribution of the lateral story stiffnesses

This example constructs a Gaussian process-based surrogate model for the response of a building structure given a ground motion time history. We are interested in the maximum inter-story drift/acceleration response determined in 14 structural parameters.

This example constructs a Gaussian process-based surrogate model for the mean and variance of building responses subjected to ten different ground motions. A floor response of a six-story shear building model is investigated.

In this example, the parameters of the STEEL02 material model in OpenSees are calibrated by Bayesian inference. Experimental data is passed in to quoFEM from an external file, and the output is the time-history of stress - a non-scalar response quantity.

Consider the problem simulating response of a two-dimensional truss structure with uncertain material properties. The goal of the exercise is to demonstrate the use of ``PLoM model`` method under ``SimCenterUQ`` to predict the response of the truss under the given load.

In this example, the parameters of the STEEL02 material model in OpenSees are calibrated by Bayesian inference. Experimental data is passed in to quoFEM from an external file, and the output is the time-history of stress - a non-scalar response quantity.

In this example, demonstrates the heteroscedastic Gaussian process model

Two models of a 6-story structure are used to predict the maximum base shear experienced during a nonlinear time history analysis of the structure subjected to seismic excitation

A hierarchical model is used to model the uncertainty in the parameters of a material model and data from multiple experiments is used to calibrate the hierarchical model