In this paper, we propose an approximation method for the well-known fatigue-damage estimation of rainflow counting (RFC) using the dissipativity property of hysteresis operators that can be embedded in model predictive control (MPC) frameworks. Firstly, we revisit results that establish the equivalence between RFC to an energy dissipation property of an infinite-dimensional operator of the Preisach hysteresis model. Subsequently, we approximate the Preisach model using a finite-dimensional differential Duhem hysteresis model and propose an extended MPC scheme that takes into account the dissipated energy of Duhem hysteresis model as a damage proxy in the optimization problem formulation. Lastly, we present an example of control design for damage minimization in the shaft of a wind turbine where we illustrate the proposed strategy.

在本文中，我们提出了一种利用滞后算子的耗散特性，可以将其嵌入模型预测控制（MPC）框架中的著名的雨流计数疲劳损伤估计（RFC）的近似方法。首先，我们重新审视在RFC与Preisach磁滞模型的无穷维算子的能量耗散特性之间建立等效性的结果。随后，我们使用有限维差分Duhem磁滞模型对Preisach模型进行了近似，并提出了扩展的MPC方案，该方案考虑了Duhem磁滞模型的耗散能量作为优化问题公式中的损伤代用品。最后，我们展示了一个用于最小化风轮机轴中的损伤的控制设计示例，在此我们说明了所提出的策略。