WLPCM Approach for Great Lakes Regulation (2504.04761v1)

Abstract: This study develops a water-level management model for the Great Lakes using a predictive control framework. Requirement 1: Historical data (pre-2019) revealed consistent monthly water-level patterns. A simulated annealing algorithm optimized flow control via the Moses-Saunders Dam and Compensating Works to align levels with multi-year benchmarks. Requirement 2: A Water Level Predictive Control Model (WLPCM) integrated delayed differential equations (DDEs) and model predictive control (MPC) to account for inflow/outflow dynamics and upstream time lags. Natural variables (e.g., precipitation) were modeled via linear regression, while dam flow rates were optimized over 6-month horizons with feedback adjustments for robustness. Requirement 3: Testing WLPCM on 2017 data successfully mitigated Ottawa River flooding, outperforming historical records. Sensitivity analysis via the Sobol method confirmed model resilience to parameter variations. Requirement 4: Ice-clogging was identified as the most impactful natural variable (via RMSE-based sensitivity tests), followed by snowpack and precipitation. Requirement 5: Stakeholder demands (e.g., flood prevention, ecological balance) were incorporated into a fitness function. Compared to Plan 2014, WLPCM reduced catastrophic high levels in Lake Ontario and excessive St. Lawrence River flows by prioritizing long-term optimization. Key innovations include DDE-based predictive regulation, real-time feedback loops, and adaptive control under extreme conditions. The framework balances hydrological dynamics, stakeholder needs, and uncertainty management, offering a scalable solution for large freshwater systems.