Control theory-based data assimilation for open channel hydraulic models: tuning PID controllers using multi-objective optimization

Abstract

Reliable water resources management requires decision support tools to successfully forecast hydraulic data (stage and flow hydrographs). Even though data-driven methods are nowadays trendy to apply, they still fail to provide reliable forecasts during extreme periods due to a lack of training data. Therefore, model-driven forecasting is still needed. However, the model-driven forecasting approach is affected by numerous uncertainties in initial and boundary conditions. To improve the real-time model's operation, it can be regularly updated using measured data in the data assimilation (DA) procedure. Widely used DA techniques are computationally expensive, which reduce their real-time applications. Previous research shows that tailor-made, time-efficient DA methods based on the control theory could be used instead. This paper presents further insights into the control theory-based DA for 1D hydraulic models. This method uses Proportional–Integrative–Derivative (PID) controllers to assimilate computed water levels and observed data. This paper describes the two-stage PID controllers’ tuning procedure. Multi-objective optimization by Nondominated Sorting Genetic Algorithm II (NSGA-II) was used to determine optimal parameters for PID controllers. The proposed tuning procedure is tested on a hydraulic model used as a decision support tool for the transboundary Iron Gate 1 hydropower system on the Danube River, showing that the average discrepancy between modeled and observed water levels can be less than 0.05 m for more than 97% of assimilation window.