Topologically assisted optimization for rotor design

TL;DR

This paper introduces a topologically assisted optimization method for rotor design, combining global evolutionary algorithms with topological data analysis to identify optimal and near-optimal rotor shapes based on simulation data.

Contribution

The paper presents a novel two-step optimization approach that integrates topological analysis with genetic algorithms to improve rotor shape optimization processes.

Findings

Global maximum identified within the data suggests potential for further optimization.

Topological analysis effectively distinguishes between true optima and local errors.

Data can be approximated by a smooth surrogate model, simplifying optimization.

Abstract

We develop and apply a novel shape optimization exemplified for a two-blade rotor with respect to the figure of merit ($FM$). This topologically assisted optimization (TAO) contains two steps. First a global evolutionary optimization is performed for the shape parameters and then a topological analysis reveals the local and global extrema of the objective function directly from the data. This non-dimensional objective function compares the achieved thrust with the required torque. Rotor blades have a decisive contribution to the performance of quadcopters. A two-blade rotor with pre-defined chord length distribution is chosen as the baseline model.The simulation is performed in a moving reference frame with a $k-\omega$ turbulence model for the hovering condition.The rotor shape is parameterized by the twist angle distribution.The optimization of this distribution employs a genetic algorithm. The local maxima are distilled from the data using a novel topological analysis inspired by discrete scalar-field topology. We identify one global maximum to be located in the interior of the data and five further local maxima related to errors from non-converged simulations.The interior location of the global optimum suggests that small improvements can be gained from further optimization.The local maxima have a small persistence, i.e., disappear under a small $\varepsilon$ perturbation of the figure of merit values. In other words, the data may be approximated by a smooth mono-modal surrogate model. Thus, the topological data analysis provides valuable insights for optimization and surrogate modeling.