Stage Cost Formulations of Online Rainflow-counting for Model Predictive Control of Fatigue

The material fatigue cost formulation of Direct Online Rainflow-counting is reformulated to an Economic Stage Cost and a Tracking Stage Cost. This enables implementation in the majority of standard MPC frameworks, and even more importantly, this will enable further theoretical analysis. Key enablers for this reformulation are decoupling of fatigue cost in time, pre-simulation of the system-dynamics before the MPC, and periodic update of time-varying cost-parameters. Simulation-based tests of the cost calculation are shown which provide further insight and verify the correspondence to a classical moving-window a posteriori fatigue analysis. A brief theoretical discussion on the influence of presented approximations is provided. Finally, dynamic closed-loop simulations are presented which show the effectiveness of the formulations in attenuating oscillations of mechanical stress for a wind turbine model.