Polynomial approximations for fast predictive analysis of infrastructure systems: Applications to power and transportation systems

Infrastructure systems are complex networks with inherent sources of uncertainty. Optimal operation of these systems directly affects the welfare of society. Accurate analysis and predictions for infrastructure systems are vital to achieve optimal management and operation. Data for predictive analysis can be from different sources, including computationally expensive system simulations or sensors placed within the system. For a reliable predictive analysis, it is necessary to (a) incorporate significant uncertainty in behavior of the system induced by inherent variability of system components, and (b) capture the changes within the system and adjust the predictions accordingly. This study aims to address some of the main challenges regarding these two pillars of a reliable predictive analysis for infrastructure systems. Specifically, consider power transmission or distribution systems, where computationally expensive power flow simulations must be run to evaluate the future state of the system. Conventionally, uncertain variables, such as power consumption, are treated as deterministic variables. This can result in unreliable predictions and consequently suboptimal decisions. On the other hand, quantifying the uncertainty in the system's state using sampling approaches may require thousands of simulations and can be computationally intractable. To reduce the computational burden, full scale simulations should be replaced with analytical surrogates such as polynomial functions, radial basis functions, and Gaussian processes. Accuracy of these surrogates directly affects the accuracy of system analysis and the optimality of the decisions made based on the analysis. In this dissertation, we focus on polynomial surrogates and develop innovative methodologies to improve the accuracy of the polynomial surrogates. We use several numerical examples to validate the efficiency and accuracy of the proposed methodologies. Also, as demonstration on the application side, we apply the developed methodologies to a power distribution system with various uncertainty, such as power generation and consumption uncertainty. The results demonstrate that our proposed approaches substantially reduce the computational cost associated with probabilistic power flow analysis and probabilistic system control. Additionally, for the cases that data is constantly streaming from the sensors within the system, a computationally fast online predictive model is introduced, that is capable of adjusting the predictions once system faces significant disruptions. The efficiency and accuracy of the proposed approach is demonstrated using a real-world extreme scenario, namely the Woolsey wildfire in California, following which traffic patterns significantly changed. Specifically, we study traffic conditions in locations close to the wildfire and show that the proposed approach can capture and accurately predict the post-disaster changes.LimitedAuthor requested closed access (OA after 2yrs) in Vireo ETD syste