CAREER: Uncertainty Quantification and Big Data Analysis in Interconnected Systems: Algorithms, Computations, and Applications

近年来，不确定性量化（UQ）和大数据分析越来越受到关注。大量的研究工作已经致力于这些主题，和新的数值方法已经开发出有效地处理大规模的数据集和复杂的不确定性问题。UQ和大数据分析使我们能够更好地了解各种不确定输入（边界和初始数据，参数值，几何形状，网络等）的影响。数字预测。因此，UQ和大数据分析对许多重要的实际问题至关重要，例如气候建模，天气预报，海洋动力学和智能电网。随着参数空间的数据大小和维度的增加，UQ计算和大数据分析的最大挑战之一是分析数据和运行模拟的计算成本。对于大型复杂互联系统，确定性仿真可能非常耗时，并且进行UQ仿真进一步增加了仿真成本，并且可能非常昂贵。该项目旨在应对这些关键挑战。将开发一套新的高效UQ和大数据分析算法，使大数据分析和UQ模拟适用于大规模复杂互联系统。新算法将显著推进UQ和大数据分析方法的当前发展水平。该项目还整合了教育机会，包括让一系列本科生接触UQ和大数据，为研究生提供应用它们所需的高级技能，并指导博士生。学生成为昆士兰大学和大数据教育和研究的领导者。该研究项目正在开发的方法是基于多变量贝叶斯树高斯过程和电力网络简化的可扩展算法;高维UQ算法;非高斯噪声数据的动态状态估计和模型校准;以及高级随机应急分析。新算法将基于在网络模型和概率空间中建立多保真度模型。这样的算法可以在线性时间内容纳大数据。此外，虽然目前的应急分析只允许静态电网状态的评估，而不考虑不确定性，新的方法将允许动态和概率级联故障的应急分析。新算法将使研究人员能够建立一个有效的框架，严格量化不确定性，分析大数据，并赋予智能电网模拟一个复合误差条。

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.