Volterra Kernels Assessment via Time-Delay Neural Networks for Nonlinear Unsteady Aerodynamic Loading Identification

Area of Science:

• Aerospace Engineering
• Computational Fluid Dynamics
• Nonlinear Dynamics

Background:

• Reduced-order modeling (ROM) using Volterra series is established for weakly nonlinear aerodynamic systems.
• Accurate identification of Volterra kernels is crucial for ROM quality.
• Existing kernel identification methods can be a bottleneck in developing effective ROMs.

Purpose of the Study:

• To evaluate artificial neural networks (ANNs) as an alternative method for identifying Volterra kernels.
• To explore the relationship between Volterra kernels and time-delay neural network parameters for ROM of nonlinear unsteady aerodynamic loads.
• To compare ANN-based Volterra ROMs with traditional impulse-type Volterra ROMs.

Main Methods:

• Utilized computational fluid dynamics (CFD) simulations of the NACA 0012 airfoil with Euler equations to generate aerodynamic data.
• Employed time-delay neural networks to identify Volterra kernels.
• Developed and compared ANN-based Volterra ROMs against impulse-type Volterra ROMs.
• Investigated model performance across various Mach numbers and degrees of freedom (pitch and plunge).

Main Results:

• ANN-based Volterra ROMs demonstrated comparable performance to impulse-type ROMs for weakly nonlinear cases.
• Higher-order ANN kernels were necessary to achieve additional accuracy and model stronger nonlinearities.
• A generic expression for pth-order kernel functions was derived from time-delay neural network parameters.

Conclusions:

• Artificial neural networks offer a viable and effective approach for identifying Volterra kernels in ROM.
• The ANN-based method provides a pathway to improved modeling of stronger nonlinear aerodynamic phenomena.
• This research contributes a generalized method for kernel identification applicable to various orders.