Efficient derivative computation for unsteady fatigue-constrained nonlinear aero-structural wind turbine blade optimization

Abstract. Gradient-based optimization offers significant efficiency advantages for wind turbine blade design, but its application has often been limited by the cost and accuracy of finite difference derivative calculations, especially when fatigue constraints are considered. In this work, we systematically compare and evaluate four differentiation techniques, namely algorithmic differentiation, implicit differentiation, sparsity exploitation, and parallelization, to determine their effectiveness in computing accurate gradients through time-domain aero-structural simulations. By integrating these techniques with unsteady nonlinear aerodynamic and structural models, we develop software designed for accurate gradient computation. We show that combining these techniques addresses memory and runtime challenges associated with long simulations required by design load cases. Specifically, the most effective combination reduces derivative computation wall time by over an order of magnitude compared to finite differencing while maintaining superior accuracy. We demonstrate this approach in a proof-of-concept aero-structural optimization of a wind turbine blade that improves the cost of energy by 11.4 %. This comparative study establishes a viable approach for fatigue-aware blade design that balances computational efficiency with modeling accuracy.