3.1. UQ: Uncertainty Quantification¶

The first selection panel the user must select from and enter data into is the UQ tab. It is in this panel that the user selects the UQ Engine to use for performing the uncertainty quantification calculations. The UQ Engine provides algorithms for solving various types of uncertainty analysis and optimization problems.

The UQ Engine options currently available are Dakota, SimCenterUQ, and UCSD-UQ. Users can also configure quoFEM app to use their own UQ methods and algorithms in the quoFEM app workflow by selecting the CustomUQ option.

3.1.1. UQ Features At-a-Glance¶

Forward propagation

Forward propagation generates sample realizations of input random variables (RVs) and output quantity of interests (QoIs) to provide statistics such as mean, variance, skewness, and kurtosis. See Dakota user manual for theory details.

▪ Forward Propagation in Dakota Example1 Example2

▪ Forward Propagation in SimCenterUQ Example

▪ Multi-fidelity Monte Carlo in SimCenterUQ

See Dakota user manual for theory details.

Global Sensitivity Analysis

Global sensitivity analysis is used to quantify the contribution of each input RV to the uncertainty in an output QoI. Dakota engine provides classical non-parametric estimation based on a smart sampling approach and the SimCenterUQ engine provides a probabilistic model-based approximation.

▪ Global Sensitivity Analysis in Dakota Example

▪ Global Sensitivity Analysis in SimCenterUQ Example1 Example2

See Dakota user manual and here for theory details.

Reliability Analysis

Reliability Analysis is performed to estimate the probability of failure, i.e. the probability that a system response (QoI) exceeds a certain threshold level.

▪ Reliability Analysis in Dakota Example

See Dakota user manual for theory details.

Bayesian Calibration

Bayesian Calibration is used to calibrate model parameters probabilistically based on Bayesian inference. The probability distributions of the input parameters (RVs) are updated by experimental data.

▪ Bayesian Calibration in Dakota

▪ Calibration of Non-hierarchical Model in UCSD-UQ Example1 Example2

Theory details can be found in Dakota user manual and here.

Deterministic Calibration

Deterministic Calibration estimates the best parameter values of a simulation model that best fit the experimental data, using deterministic optimization algorithms, e.g. Gauss-Newton least squares, pattern search, etc.

▪ Deterministic Calibration in Dakota Example1 Example2

▪ Gradient-free Parameter Estimation in Dakota

See Dakota user manual for theory details.

Surrogate Modeling

quoFEM app can be used to train a surrogate model that substitutes expensive computational simulation models or physical experiments.

▪ Gaussian Process (GP) Surrogate Modeling in SimCenterUQ Example1 Example2

▪ Probabilistic Learning on Manifolds (PLoM) in SimCenterUQ

Theory details can be found in here.

Custom UQ

Custom UQ helps the user plug in a user-defined UQ algorithm in SimCenter workflow.

▪ Configuring CustomUQ Engine in CustomUQ engine Example

3.1.2. Dakota UQ Engine¶

This UQ engine utilizes the Dakota Software, a state-of-the-art research application that is robust and provides many methods for optimization and UQ, a selection of which we utilize in this application. Dakota provides the user with a large number of methods for different kinds of analyses. For this reason, we have divided the methods into categories through a pull-down menu, as shown below. Once the category has been selected, a number of different methods are made available to the user.

By checking the Parallel Execution, the UQ analysis will be performed in parallel. It will try to use all the processors available on the machine.
By checking the Save Working dirs, individual working directories will be saved in the Local Jobs Directory. Local Jobs Directory is defined at File-Preference in the menubar. Otherwise, individual simulation files will be deleted after each simulation run. Users might uncheck this box when a large number of simulations is requested, to manage driver space.

Fig. 3.1.2.1 Dakota engine and category selection.¶

The following categories are available:

3.1.3. SimCenter UQ Engine¶

The SimCenterUQ engine is a UQ engine developed in-house at the SimCenter that accommodates different UQ methods, which are organized into categories that can be accessed through a pull-down menu, as shown below:

Fig. 3.1.3.1 SimCenterUQ engine and category selection.¶

The following category options are available:

3.1.4. UCSD UQ Engine¶

The UCSD-UQ engine is a module developed at the SimCenter in collaboration with UCSD. It provides algorithms for Bayesian estimation, which can be accessed through a pull-down menu, as shown in Fig. 3.1.4.1.

Fig. 3.1.4.1 UCSD-UQ engine and category selection.¶

This module currently offers support for Bayesian estimation of the parameters of a traditional (non-hierarchical) model using the Transitional Markov chain Monte Carlo (TMCMC) algorithm and of a hierarchical model using an adaptive Metropolis-within-Gibbs sampling algorithm.

3.1.5. Custom UQ Engine¶

The CustomUQ option enables users to switch out the UQ engine in the quoFEM app workflow such that different methods and tools can be applied within the SimCenter framework with minimal effort on the part of the user. The CustomUQ option can be accessed as shown below:

Fig. 3.1.5.1 CustomUQ engine selection.¶

In order to use the CustomUQ engine option, two steps are required:

Configuring the UQ tab to accept the required inputs
Adding UQ engine to customized UQ backend

These steps are described in more detail here:

3.1.5.1. Configuring CustomUQ Engine

3.1.6. Video Resources¶

Recorded in tool training, 2022.