Multi-kernel neural networks for nonlinear unsteady aerodynamic reduced-order modeling

This paper proposes the multi-kernel neural networks and applies them to model the nonlinear unsteady aerodynamics at constant or varying flow conditions. Different from standard radial basis function (RBF) networks with a single Gaussian hidden kernel, the multi-kernel neural networks improve the accuracy and generalization capability through linearly combining the Gaussian and wavelet basis functions as the hidden basis functions. In order to capture the complex nonlinear characteristics under noisy or multiple flow conditions, a novel asymmetric wavelet kernel is also introduced. The training of network parameters is achieved by incorporating proper orthogonal decomposition and particle swarm optimization algorithm, where the former process is adopted to decide the representative hidden centers and the latter technique is introduced to calculate the remaining parameters, including the widths of each multi-kernel and the linear weighting values. The proposed aerodynamic reduced-order models based on symmetric or asymmetric multi-kernel neural networks are tested by three groups of cases. Firstly, a routine reduced-order modeling task of predicting the aerodynamic loads at a constant Mach number is performed. Then the measurement noise is added to test the models under noise conditions. Finally, these models are utilized to identify the aerodynamic loads across a range of transonic Mach numbers. Results indicate that the proposed multi-kernel neural networks outperform the single-kernel RBF neural networks in modeling noise-free and noisy aerodynamics at a constant Mach number, as well as predicting the aerodynamic loads with varying Mach numbers.