Research On Optimal Water Level of Great Lakes Based on Dynamic Optimization Model and PID Control Algorithm

Abstract

This study aims to determine the optimal water levels of the Great Lakes by analyzing historical data from 2012 to 2022, including water levels of the lakes and flow rates of the rivers connecting them, to identify underlying trends. A multi-objective optimization model is developed, which holistically accounts for the welfare of local ecological, economic, and social stakeholders. By applying a genetic algorithm, the model calculates the optimal water levels for different times of the year. Furthermore, a dynamic relationship among the Great Lakes is modeled using differential equations, and a PID control algorithm is implemented to manage the optimal water levels under natural conditions. Compared with traditional algorithm, this approach not only enhances the precision of water level predictions but also introduces an adaptive control system that responds to real-time data. The integration of these methods allows for a more nuanced management of water levels, catering to the fluctuating demands of ecological, economic, and social stakeholders. A subsequent sensitivity analysis reveals that the proposed control algorithm demonstrates a high sensitivity to varying natural conditions and yields water levels more favorable than the actual recorded levels from the perspective of most stakeholders.