A Hybrid Data-Model Fusion Approach to Calibrate a Flush Air Data Sensing System

A hybrid data-model fusion approach has been devised to calibrate a Flush Air Data Sensing system. Numerical simulation and artificial neural network based approaches have been previously applied to predict airdata state from flush pressure measurements. However both approaches have their shortcomings. Numerical simulations rely on approximations to model the truth while learning algorithms do not incorporate the physics of the problem and often need a large set of data for training. A principled approach has been devised to fuse experimental FADS data and numerical solutions in an optimal manner. The purpose of this approach is to improve the prediction accuracies of the airdata state obtained by a pure neural network based approach. Other objectives of this approach include better noise tolerance and a need for fewer experimental data. Nomenclature bn, b1n, b2n = n bias in the approximation cn, c1n, c2n = n linear coefficient in the approximation Cp = coefficient of pressure = P/q d = input dimension f = arbitrary function fps = feet per second F = forward mapping function G = inverse mapping function n = number of bases , P q = static gauge pressure and dynamic pressure n r = n th stage of the function residual = real coordinate space d = ddimensional vector space s = number of training samples ( ) u ξ = target function ( ) a n u ξ = n stage of the target function approximation V∞ = freestream wind speed 1 Graduate Student, Mechanical Engineering, Mail Stop 321, AIAA Member. 2 Professor, Mechanical Engineering, Mail Stop 321, AIAA Associate Fellow. 3 Undergraduate Student, Mechanical Engineering , AIAA Member. AIAA Infotech@Aerospace 2010 20 22 April 2010, Atlanta, Georgia AIAA 2010-3347 Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. , D f v = = discrete inner product of f and v ( s i i i f v ∑ ) f = absolute value of f 2 f = ( = L )1/ 2 2 f dξ Ω ∫ 2 norm of f 2,D f = = discrete L ( ) ( 1/ 2 2 s i i f ∑ ) 2 norm of f Greek Symbols β = yaw angle η = set of nonlinear optimization parameters ε = objective function θ = polar coordinate λ = width parameter of Gaussian basis function ξ = d-dimensional input of the target function i ξ = i th sample input of the target function * n ξ = sample input with component index j * at the n stage τ = user specified tolerance φ = basis function ν = arbitrary function δ = input sensitivity ρ = density Subscripts i = dummy index j = component index of r(n-1) with the maximum magnitude n = associated with the number of bases s = associated with the number of samples ∞ = associated with freestream conditions Superscripts a = associated with the approximation d = associated with the input dimension