Jeff D. Eldredge

Zhecheng Liu, Diederik Beckers, Jeff D. Eldredge

The intrinsic high dimension of fluid dynamics is an inherent challenge to control of aerodynamic flows, and this is further complicated by a flow's nonlinear response to strong disturbances. Deep reinforcement learning, which takes advantage of the exploratory aspects of reinforcement learning (RL) and the rich nonlinearity of a deep neural network, provides a promising approach to discover feasible control strategies. However, the typical model-free approach to reinforcement learning requires a significant amount of interaction between the flow environment and the RL agent during training, and this high training cost impedes its development and application. In this work, we propose a model-based reinforcement learning (MBRL) approach by incorporating a novel reduced-order model as a surrogate for the full environment. The model consists of a physics-augmented autoencoder, which compresses high-dimensional CFD flow field snaphsots into a three-dimensional latent space, and a latent dynamics model that is trained to accurately predict the long-time dynamics of trajectories in the latent space in response to action sequences. The accuracy and robustness of the model are demonstrated in the scenario of a pitching airfoil within a highly disturbed environment. Additionally, an application to a vertical-axis wind turbine in a disturbance-free environment is discussed in the Appendix Based on the model trained in the pitching airfoil problem, we realize an MBRL strategy to mitigate lift variation during gust-airfoil encounters. We demonstrate that the policy learned in the reduced-order environment translates to an effective control strategy in the full CFD environment.

Hanieh Mousavi, Jeff D. Eldredge

This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying response of sensors to gust-airfoil interactions, uncovering valuable insights into optimal sensor placement. To address uncertainties in deep learning predictions, we implement probabilistic regression strategies to model both epistemic and aleatoric uncertainties. Epistemic uncertainty, reflecting the model's confidence in its predictions, is modeled using Monte Carlo dropout, as an approximation to the variational inference in the Bayesian framework, treating the neural network as a stochastic entity. On the other hand, aleatoric uncertainty, arising from noisy input measurements, is captured via learned statistical parameters, which propagates measurement noise through the network into the final predictions. Our results showcase the efficacy of this dual uncertainty quantification strategy in accurately predicting aerodynamic behavior under extreme conditions while maintaining computational efficiency, underscoring its potential to improve online sensor-based flow estimation in real-world applications.

Zhecheng Liu, Jeff D. Eldredge

A linear flow control strategy designed for weak disturbances may not remain effective in sequences of strong disturbances due to nonlinear interactions, but it is sensible to leverage it for developing a better strategy. In the present study, we propose a transformer-based reinforcement learning (RL) framework to learn an effective control strategy for regulating aerodynamic lift in arbitrarily long gust sequences via pitch control. The random gusts produce intermittent, high-variance flows observed only through limited surface pressure sensors, making this control problem inherently challenging compared to stationary flows. The transformer addresses the challenge of partial observability from the limited surface pressures. We demonstrate that the training can be accelerated with two techniques -- pretraining with an expert policy (here, linear control) and task-level transfer learning (here, extending a policy trained on isolated gusts to multiple gusts). We show that the learned strategy outperforms the best proportional control, with the performance gap widening as the number of gusts increases. The control strategy learned in an environment with a small number of successive gusts is shown to effectively generalize to an environment with an arbitrarily long sequence of gusts. We investigate the pivot configuration and show that quarter-chord pitching control can achieve superior lift regulation with substantially less control effort compared to mid-chord pitching control. Through a decomposition of the lift, we attribute this advantage to the dominant added-mass contribution accessible via quarter-chord pitching.