A New Substitution Based Recursive B-Splines Method for Aerodynamic Model Identification

A new substitution based (SB) recursive identification method, using multivariate simplex B-splines (MVSBs), has been developed for the purpose of reducing the computational time in updating the spline B-coefficients. Once the structure selected, the recursive identification problem using the MVSBs turns to be a constrained recursive identification problem. In the proposed approach, the constrained identification problem is converted into an unconstrained problem through a transformation using the orthonormal bases of the kernel space associated with the constraint equations. The main advantage of this algorithm is that the required computational time is greatly reduced due to the fact that the scale of the identification problem, as well as the scale of the global covariance matrix, is reduced by the transformation. For validation purpose, the SB-RMVSBs algorithm has been applied to approximate a wind tunnel data set of the F-16 fighter aircraft. Compared with the batch MVSBs method and the equality constrained recursive least squares (ECRLS) MVSBs method, the computational load of the proposed SB-RMVSBs method is much lower than that of the batch type method while it is comparable to that of the ECRLS-MVSBs method. Moreover, the higher the continuity order is, the less computational time the SB-RMVSBs method requires compared with the ECRLS-MVSBs method.