Double Fourier Applications for Real Time Aerodynamic Load Recovery

This work examines application of an inverse interpolation method coupled with Finite Element Analysis (FEA) to recover the Double Fourier coefficients for continuous polynomial functions representative of historical or theoretical flight loads. Additionally, the factors that determine the optimum locations for strain gages along a lifting surface that will allow an applied load distribution to be recovered most accurately are investigated. Functions are approximated by their Fourier series terms in order to create a database of strains produced by applying each individual Fourier term as a load function. Strain data from an applied unknown load coupled with FEM data from the Fourier loads allow prediction of the Fourier coefficients of the actual load. Ultimately the flight loads are identified by comparing the strains from the database Fourier loads to the strains obtained from application of the unknown function using “least squares” minimization. Successful load predictions are made for polynomial surface functions. It is also shown that the variance of the strain data arising from application of the individual Fourier loads plays a key role in the accuracy of the method. The variance of the measured strain is shown to depend on the position and amount of the strain measurements and the nature of the applied load function. This relationship is explored by varying strain gage locations along the surface for specific linear and quadratic load function cases.