Reduced-order modeling of dynamic stall using neuro-fuzzy inference system and orthogonal functions

Abstract

To consider stall flutter in the design procedure of a blade, accurate models of flow loading are needed. This paper first presents a numerical simulation of an airfoil undergoing a deep dynamic stall employing a computational fluid dynamics code. Overset and polyhedral grid techniques are adopted to accurately simulate the flow field at high angles of attack. Having validated the simulation, the occurrence of stall flutter over a pitching airfoil with an increase in amplitude and frequency of oscillations is examined. The results express that the amplitude of the lift and pitching moment depends on the amplitude of the forced oscillation and there are higher harmonics of the pitching moment compared to the forced oscillation frequency content, both indicating the nonlinearity of aerodynamic lift and pitching moment. Subsequently, a nonlinear reduced model of the dynamic stall is derived using a fuzzy inference system (FIS) and the adaptive network-based FIS (ANFIS). Due to the unsatisfactory results of modeling, especially at post-stall angles of attack, the Gram–Schmidt orthogonalization technique is used to construct a more complex structure of the input variables. The new higher-order input variables have been re-employed by FIS and ANFIS. The results show that excellent modeling is achieved by ANFIS between the new structure of the inputs and the corresponding aerodynamic coefficients using only 10% of input–output data. Having found an appropriate relation, the proposed reduced-order model could properly predict the aerodynamic response of the pitching airfoil at two reduced frequencies.

Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning

“…29,30 The resulting deep reinforcement learning (DRL) paradigm has been successfully deployed to resolve several high-profile, complex problems, such as playing a wide range of Atari game without hardcoding strategies, 31 generating realistic dialogs, 32 or controlling the dynamics of complex robots. 33 Compared with data-driven and supervised learning approaches, which have also found some applications in fluid mechanics within particle image velocimetry (PIV) measurement, [34][35][36] reduced-order modeling, 37,38 or predictions of flow features, [39][40][41] DRL allows us to find a solution through trial-anderror, even when no solution is known a priori. One can observe that challenging systems successfully controlled by DRL have remarkably similar properties of nonlinearity and high-dimension, similar to the features of flow phenomena that make AFC challenging.…”

A WaveNet-based fully stochastic dynamic stall model

“…Neural networks are used by Glaz et al (2012) and Spentzos et al (2006) to predict unsteady RANS data. Tatar and Sabour (2020) created a nonlinear reducedorder dynamic stall model using a fuzzy inference system (FIS) and adaptive network-based FIS (ANFIS) to fit simulated RANS data as well. All of these publications have in common that their models are based on simulation data that roughly correspond to the phase-averaged data from the measurements discussed earlier.…”

Neuro-Fuzzy Network-Based Reduced-Order Modeling of Transonic Aileron Buzz

“…Further, Volterra and basic neural networks applied by Paula et al [20] and Faller et al [18] yield sufficient results concerning three-dimensional flow field and unsteady aerodynamic load prediction. Moreover, ROMs based on fuzzy logic [21,22] yield accurate and reliable results for capturing weak aerodynamic nonlinearities as well as small perturbation flow characteristics.…”