Uncertainty quantification (UQ) and big data analysis have received increasing attention in recent years. Extensive research effort has been devoted to these topics, and novel numerical methods have been developed to efficiently deal with large-scale data sets and complex problems with uncertainty. Both UQ and big data analysis enable us to better understand the impacts of various uncertain inputs (boundary and initial data, parameter values, geometry, network etc.) to numerical predictions. UQ and big data analysis are thus critical to many important practical problems such as climate modeling, weather prediction, ocean dynamics, and smart grids. As the data size and dimensions of parameter space increase, one of the biggest challenges in UQ computations and big data analysis is the computational cost for analyzing the data and running the simulations. For large-scale complex interconnected systems, deterministic simulations can be very time-consuming, and conducting UQ simulations further increases the simulation cost and can be prohibitively expensive. This project aims to address these critical challenges. A novel set of highly efficient UQ and big data analysis algorithms will be developed to make big data analysis and UQ simulations amenable for large-scale complex interconnected systems. The new algorithms will significantly advance the current state of the art of UQ and big data analysis methods. The project also integrates educational opportunities, including exposing a range of undergraduate students to UQ and big data, giving graduate students the advanced skills needed to apply them, and mentoring Ph.D. students to be leaders in UQ and big data education and research.
The approach under development in this research project is based on scalable algorithms for multivariate Bayesian-treed Gaussian process and power network reduction; high-dimensional UQ algorithms; dynamic state estimation and model calibration for non-Gaussian noisy data; and advanced stochastic contingency analysis. The new algorithms will be based on building multi-fidelity models in both network models and probability space. Such algorithms can accommodate big data in linear time. In addition, while current contingency analysis allows only assessment of a static power grid status without considering uncertainty, the new approaches will allow analysis of contingency dynamically and probabilistically for cascade failures. The new algorithms will allow investigators to establish an efficient framework to rigorously quantify the uncertainty, analyze big data, and endow smart grid simulations with a composite error bar.
