Uncertainty Quantification
In uncertainty quantification (UQ), the impact of randomness on the behavior of the responses is assessed. In reality, various sources of uncertainties affect the response such as inherent randomness, modeling error, and lack of knowledge. The sources of uncertainties and how they influence the response should be studied appropriately to have a proper confidence in the prediction of stochastic responses. However, performing UQ is challenging and computationally exhaustive even with state-of-the-art computational power. Hence, efficient algorithms should be utilized while performing UQ of expensive functions. Furthermore, since there are many software available for deterministic simulations, the priority is to use the available software for finite element analysis, computational fluid dynamics, with less number of calls.
Our research group mainly specializes in a spectral approach called Polynomial Chaos Expansion (PCE) for UQ, which is known for its mean-square convergence. However, like other computational approaches for UQ, it is also affected by the "Curse of dimensionality". To tackle this problem, some of our recently proposed works include adaptive PCE and adaptive sampling using regression based PCE. More recently, L1-minimization approaches for sparse PCE has been implemented, and Karhunen-Loeve Expansion (KLE) is used to randomness provided as random field. The PCE approximation thus built can be used for estimation of the statistics of the stochastic responses or used for reliability estimation.
Global Sensitivity Analysis
In uncertainty analysis, it is paramount to understand the influence or contribution of random parameters on the stochastic response. To this end, global sensitivity analysis (GSA) can be utilized. Two of the main approaches are: variance-based (Sobol Indices), and moment-independent (Borgonov Indices).
The variance-based GSA can be obtained as a post-processing once the PCE of the stochastic responses. So, it has been widely popular in finding the significant random parameters that will guide the dimension reduction and help in calibration process.
The variance-based GSA can be obtained as a post-processing once the PCE of the stochastic responses. So, it has been widely popular in finding the significant random parameters that will guide the dimension reduction and help in calibration process.
Several algorithms and programs for UQ using PCE and GSA have been developed at the lab and can be provided upon a suitable request for collaboration.