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

Abstract

Reduced-order modeling using the Volterra series approach has been successfully applied in the past decades to weakly nonlinear aerodynamic and aeroelastic systems. However, aspects regarding the identification of the kernels associated with the convolution integrals of Volterra series can profoundly affect the quality of the resulting reduced-order model (ROM). An alternative method for their identification based on artificial neural networks is evaluated in this work. This relation between the Volterra kernels and the internal parameters of a time-delay neural network is explored for the application in the reduced-order modeling of nonlinear unsteady aerodynamic loads. An impulse-type Volterra-based ROM is also under consideration for comparison. All aerodynamic data used for the construction of the reduced-order models are obtained from computational fluid dynamics (CFD) simulations of the NACA 0012 airfoil using the Euler equations. Prescribed inputs in pitch and in plunge degrees of freedom at different freestream Mach numbers are used to evaluate the range of applicability of the obtained models. For weakly nonlinear test cases, the modeling performance of the neural network Volterra ROM was comparable to the impulse-type ROM. Additional accuracy and adequate modeling of stronger nonlinearities, however, could only be attained with the inclusion of the neural network kernels of higher-order in the Volterra ROM. A generic expression is derived for the kernel function of p thorder from the internal parameters of a time-delay neural network.

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

“…In addition, a multi-kernel RBF neural network has been applied by Zhang et al [19] for modeling unsteady aerodynamics including varying flow conditions. 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.…”

Composite material structure optimization design and aeroelastic analysis on forward swept wing

“…Although CFD is a powerful tool for modeling complex flow features, especially those appearing in the transonic flight regime, the resulting models with thousands or millions of degrees of freedom are computationally demanding. 25 In order to decrease the massive computation time of aeroelastic analysis, reduced-order surrogate model is explored to describe the relationship between the composite variables and the deformations. Reducedorder methods are relatively more simple mathematical models that represent a viable alternative to more readily interpret a complex system behavior and to perform additional quantitative analysis and optimization more quickly.…”

Application of Principal Component Analysis-Assisted Neural Networks for the Rotor Blade Load Prediction

“…Elshafey et al researched on the use of neural networks to predict structural response on structures [12]. De Paula et al predicted nonlinear unsteady aerodynamic loads for NACA0012 airfoil using neural networks [13].…”