Volterra Kernel Extrapolation for Modeling Nonlinear Aeroelastic Systems at Novel Flight Conditions

摘要

This paper investigates the modeling of parameter-varying nonlinear aeroelastic systems using Volterra theory. With this approach, the system dynamics are expressed in terms of a set of Volterra kernels. It is well known that the parameters of aeroelastic systems, such as natural frequencies and damping ratios, change with flight condition. Therefore, a system is characterized by a different set of Volterra kernels at each flight condition. These kernels must be extracted from the flight data at each flight condition of interest: a relatively costly procedure. This paper presents a kernel extrapolation method designed to model first- and second-order kernels as functions of a single varying parameter, such as altitude or Mach number. First, using a multiwavelet-based algorithm, a set of Volterra kernels is identified from the input/output data at a number of flight conditions. In this manner, each kernel is represented in terms of a set of multiwavelet basis functions. An extrapolation model is then obtained by using a polynomial curve-fit to express the magnitude of each basis coefficient as a function of the varying parameter. The performance of this kernel extrapolation method is studied in detail for a simulated nonlinear aeroelastic system, demonstrating the validity of the approach. Then, the algorithm is applied to flight data from the F/A-18 Active Aeroelastic Wing. This example illustrates some of the difficulties associated with extrapolating kernels from noisy flight data.