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The optimal design of a wind farm which maximizes energy production depends on the spatially variable wind flow field. However, due to the complexity associated with modeling atmospheric winds, especially in the presence of complex terrain, the wind field is inherently uncertain. Uncertainty in the wind field during the design stage reduces the likelihood that the constructed wind farm achieves maximum energy production for a given number of turbines. As such, contemporary wind farms are designed through a two step process. First, experimental data collected from simultaneously constructed meteorological towers are used, along with simplified engineering flow models, to estimate the flow field. Then, the estimated flow field is used to place wind turbines to maximize an objective function, such as wind farm energy production. To increase wind farm energy production and reduce its uncertainty, we propose a farm design methodology that combines both the sensor placement and wind turbine location selection steps into a single sequential decision-making process. Future sensor placements sequentially leverage information gained from previous ones. Rather than placing sensors to attempt to reduce wind field uncertainty, we select sensor locations to maximize wind farm profit. Using profit as the objective function balances the increased revenue, from the increased energy production associated with improved wind field knowledge, against the higher costs from additional sensors. In this proof-of-concept study, we use idealized numerical case studies to demonstrate that sequential wind field sensor placement, compared to concurrent placement, improves the robustness of the resulting wind farm design to imperfect initial knowledge of the wind field. The numerical results suggest a wind farm annual energy output (lifetime profit) increase of approximately 6.55% (16.78%), equaling roughly 0.7 GWh/year (0.35 million USD) per turbine, compared to a typical, two-step wind farm design process which first places sensors concurrently then designs the farm thereafter. Our results also indicate that using a far-sighted sequential method as proposed in this paper outperforms standard metrics, such as entropy, that solely focus on wind field uncertainty minimization. These proof-of-concept findings suggest that future research should be dedicated to improving the wind farm design process through sequential decision-making under uncertainty. [Display omitted] [ABSTRACT FROM AUTHOR]

• Groundwater remediation planning and decision problem formulated as a partially observable Markov decision process (POMDP). • Comparison between POMDP and the conventional state-of-the-art optimization approaches, such as one-shot optimization and model predictive control (closed loop) optimization. • DESPOT, a state-of-the-art POMDP solver, outperforms optimization solution methods using PSO and hand-crafted heuristic solutions. • Optimizing the trade-off between information gathering and the performance of possible future scenarios via POMDP formulation. • Importance of belief updates, also known as inversion problems or history matching, in groundwater problems. Groundwater contamination causes significant groundwater supply risks that severely affect humans and livestock, especially in the era of climate change. Consequently, the need to develop and optimize remediation strategies such as pump and treat is indispensable. An effective and efficient strategy can reduce the spread of contaminants and cost of clean-up. However, developing such a strategy is challenging due to the inherent uncertainty and sequential nature of the problem. For example, taking actions such as drilling wells is interwoven with information gathering over time. In this paper, we formulate the groundwater remediation planning and decision problem as a partially observable Markov decision process (POMDP). A POMDP formulation allows planning by optimizing the trade-off between information gathering and the performance of possible future scenarios. We use a state-of-the-art POMDP solver called DESPOT for planning remediation strategies. The results show that DESPOT can yield much better remediation strategies than hand crafted heuristics and optimization methods. The superior performance of DESPOT is due to the incorporation of both previous information and future reward into the current decision. We also demonstrate the robustness of the POMDP formulation to measurement error. [ABSTRACT FROM AUTHOR]