PDE-Based Dynamic Data-Driven Monitoring of Atmospheric Dispersion Processes

Atmospheric dispersion of pollutants highly affects human health and well-being. For disaster surveillance and response in such catastrophic scenarios, repeated estimation of the current process state and of relevant process parameters is essentially required. The respective estimates can be obtained by repeatedly integrating measurements from a sensor network into a process model capable of forecasting current estimates to future times. Networks of mobile sensors are increasingly considered in this context since they offer the possibility to move along trajectories, which provide a high expected information gain concerning the current dispersion state. In related work, these trajectories are mostly determined offline prior to the application by solving a complex optimal control problem subject to process, vehicle and uncertainty dynamics. However, the trajectories depend on the process state and parameters to be determined. Hence, it is much more desirable to apply a dynamic data-driven approach, in which the available measurements are directly integrated into the process model and control inputs for the sensor-carrying vehicles are determined online based thereupon. The dynamic data-driven application belongs to the domain of cyber-physical systems and is characterized by real-time requirements so that lightweight process models with rather inaccurate prediction abilities have been predominantly used in related work. On the other hand, models based on partial differential equations (PDEs) are typically related to the computationally expensive solution of a high-dimensional problem. However, due to their ability to provide physically realistic forecasts, PDE-models are a key feature of this thesis and simplifications are introduced to cope with them. In this work, three new PDE-based dynamic data-driven monitoring strategies for state and parameter estimation of dispersion processes are proposed based on a coordinated fleet of sensor-carrying vehicles processing models and estimations online. The first monitoring strategy is based on a sub-optimal procedural structure consisting of multiple loosely coupled building blocks to increase the efficiency compared to sophisticated optimal control problems. Forecasts stemming from a process simulation based on the finite element method are combined with the sensors' measurements using an efficient ensemble-based data assimilation method. A sequential procedure is proposed to identify informative measurement locations that are based on the current estimates as well as on their uncertainty. The identified locations are handed to a cooperative optimization-based vehicle controller, which is in charge of guiding the vehicles to the suggested locations. Furthermore, an estimation method to jointly estimate current process state vectors and the source function is presented and the handling of a model error covariance matrix depending on the process state is described. In contrast to the first approach, the second approach is based on a decentralized computation and communication structure. In order to explicitly account for limited communication ranges and to increase scalability, a central computing node is waived and computations are performed only locally on-board the vehicles, exchanging local information with vehicles in their vicinity. While the general procedural structure of the centralized approach is preserved, modifications are necessary to account for the limited onboard computing capability, potentially different models maintained on different vehicles, and limited communication ranges. To simplify the process model, Proper Orthogonal Decomposition is used to generate reduced order models. A suitable choice of the snapshot set, required to generate the reduced order model, is proposed. Furthermore, a two-step reduced data assimilation method is developed updating the own local state with the local measurement first and fusing state information with neighbors in a second step. A decentralized version of the identification procedure for suitable measurement locations is described and an existing decentralized variant of the vehicle controller is employed. The third approach represents a partitioned decentralized dynamic data-driven monitoring strategy. To further pursue decentrality, the global problem domain is decomposed into several subdomains with vehicles being assigned to subdomains they are currently located in. In this way, only a local process and multi-vehicle model has to be maintained by each sensor-carrying vehicle, while communication with vehicles on directly adjacent subdomains ensures convergence of the whole problem. A new ensemble-based prediction and update method is proposed that is based on an efficient domain decomposition method and that requires only minimal exchange between vehicles on neighboring subdomains. For more flexibility, target point generation and vehicle trajectories are adapted to allow vehicles to move to other subdomains, where they might be even more useful. The respective approaches are applied in a number of test case scenarios and are evaluated regarding their estimation results and computing time. While the centralized monitoring approach provides the best estimation results, significantly outperforming other basic monitoring strategies, limited communication ranges, a large number of mobile sensors and higher dimensional problems could become problematic. In the latter case, the decentralized approach offers a more efficient alternative at the cost of minor losses in estimation quality. The same applies to the application of the partitioned approach, which, while being less flexible, provides even more scalability with respect to the number of sensor-carrying vehicles