Conference Agenda

Data-Driven Computational Mechanics (DDCM) is a recent paradigm in continuum mechanics simulations

where the empirical material law that describes elasticity is replaced by a minimum-distance requirement with respect to raw measured data. We present function space formulations and finite element discretizations of the problem and analyze their properties, particularly the existence and uniqueness of solutions. We also discuss structure-exploiting algorithmic approaches for solving the problem in the function space setting and in the discretized setting.

Efficient set representation is the most relevant challenge of viability kernel numerical computation. Indeed, the classical Saint-Pierre (forward Euler) algorithm shows an accelerated explosion, even in reduced dimensions, attributed to its grid-based representation. On the other hand, in the context of the reachability problem, some authors have recently proposed the representation of (nonconvex) sets based on constrained polynomial zonotopes (CPZ). Since the issues of viability and reachability are closely related, the question arises about the effectiveness of the CPZ representation in computing the viability kernel. Therefore, we compare algorithms based on the CPZ representation with the classical Saint-Pierre representation. Additionally, we implemented the viability algorithm in its forward and backward versions using the CPZ representation. In this work, we found that the CPZ-based method is less demanding of computational resources. However, this comes at the cost of the accuracy of the results. Although our calculations are promising, we urgently propose investigating the error estimation of viable sets based on the CPZs representation.

Each wind turbine causes a wake with a reduced wind speed. This wake influences the mechanical loads and power of downstream turbines. Therefore, there is a strong interaction between the individual wind turbines in a wind farm. This interaction is an opportunity for optimal control to minimize the total load (e.g., tower activity) while increasing or keeping the total power of a wind farm, in particular in case of a wind gust as it requires a dynamic control reaction. We use the already known axial-induction-based control and investigate its potential using optimization in the case of a simply modeled wind gust in a turbulent wind field that passes through a simulated wind farm consisting of two turbines. First, for an initial guess, we modify the reaction of a standard controller by a heuristic. Second, knots and values of a cubic spline interpolation based on the initial guess offer the possibility to solve an optimization problem by sequential quadratic programming (SQP). We show that dynamic control of the upstream turbine significantly reduces the tower activity of the downstream wind turbine and finally reduces the total tower activity.