Multi-fidelity surrogate modeling for the optimization of vertical-axis hydrokinetic turbines via Bayesian methods

Abstract

A multi-fidelity Bayesian optimization framework is presented for the design of vertical-axis turbines, which necessitates cost-effective computational methods due to their unsteady flow character. Compared to CFD-based optimization, surrogate-based design optimization offers a more effective strategy, provided that adaptive sampling is handled with caution and care. Bayesian optimization is implemented for this purpose, which enables adaptive sampling to ensure that the uncertainty of the optimal point and its value is minimized. The computational cost of the optimization process is reduced using a multi-fidelity scheme that blends information from a low-fidelity model and high-fidelity simulations. Different multi-fidelity modeling approaches are investigated through the Bayesian optimization framework. In the present optimization framework, two distinct optimization tasks are performed using the nonlinear auto-regressive Gaussian process, each integrating a different low-fidelity numerical model with a high-fidelity one. The adaptive sampling is executed by the max-value entropy search function, and its advantages in multi-fidelity Bayesian optimization are also shown and discussed. The present Bayesian optimization process is monitored by using specific metrics that quantify the convergence of the model. Both the genetic algorithm and the Broyden-Fletcher-Goldfarb-Shanno algorithm are employed in different stages of the present optimization. The optimization process achieves a reasonable optimum for a three-bladed turbine with a significantly low computer cost and reduced uncertainty.