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Calibri 83ffff̙̙3f3fff3f3f33333f33333.)TU Delft Repositoryg v0uuidrepository linktitleauthorcontributorpublication yearabstract
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departmentresearch group programmeprojectcoordinates)uuid:fa68d1b6623649b8819fc76452ddab3bDhttp://resolver.tudelft.nl/uuid:fa68d1b6623649b8819fc76452ddab3bdOnline Aerodynamic Model Identification using a Recursive Sequential Method for Multivariate Splines3Sun, L.G.; De Visser, C.C.; Chu, Q.P.; Mulder, J.A.6Avoiding high computational loads is essential to online aerodynamic model identi fication algorithms, which are at the heart of any modelbased adaptive flight control system. Multivariate simplex Bspline (MVSB) methods are excellent function approximation tools for modeling the nonlinear aerodynamics of high performance aircraft. However, the computational efficiency of the MVSB method must be improved in order to enable realtime onboard applications, for example in adaptive nonlinear flight control systems. In this paper, a new recursive sequential identification strategy is proposed for the MVSB method aimed at increasing its computational efficiency, thereby allowing its use in onboard system identification applications. The main contribution of this new method is a significant reduction of computational load for large scale online identification problems as compared to the existing MVSB methods. The proposed method consists of two sequential steps for each time interval, and makes use of a decomposition of the global problem domain into a number of subdomains, called modules. In the first step the Bcoefficients for each module are estimated using a least squares estimator. In the second step the local Bcoefficients for each module are then smoothened into a single global Bcoefficient vector using a linear minimum mean square errors (LMMSE) estimation. The new method is compared to existing batch and recursive MVSB methods in a numerical experiment in which an aerodynamic model is recursively identified based on data from an NASA F16 windtunnel model.Precursive identification; aerodynamic model identification; multivariate splinesenjournal articleAIAAAerospace EngineeringControl & Operations)uuid:926233cbd99941f586a64ce19965dce5Dhttp://resolver.tudelft.nl/uuid:926233cbd99941f586a64ce19965dce5WDifferential constraints for bounded recursive identification with multivariate splines(De Visser, C.C.; Chu, Q.P.; Mulder, J.A.The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive modelbased control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able to perform online model identification and bounded model extrapolation in the framework of a modelbased control system. A new type of linear constraints, the differential constraints, are used as differential boundary conditions within the recursive estimator which limit polynomial divergence when extrapolating data. The differential constraints are derived with a new, onestep matrix form of the de Casteljau algorithm, which reduces their formulation into a single matrix multiplication. The recursive estimator is demonstrated on a bivariate dataset, where it is shown to provide a speedup of two orders of magnitude over an ordinary least squares batch method. Additionally, it is demonstrated that inclusion of differential constraints in the least squares optimization scheme can prevent polynomial divergence close to edges of the model domain where local data coverage may be insufficient, a situation often encountered with global recursive data approximation.Rmultivariate splines; parameter estimation; scattered data; function approximatorsElsevier
20140501)uuid:f2b6bdbd5d114ec5ac7ed2c2ce21144cDhttp://resolver.tudelft.nl/uuid:f2b6bdbd5d114ec5ac7ed2c2ce21144c=A new approach to linear regression with multivariate splinesA new methodology for <creating highly accurate, static nonlinear maps from scattered, multivariate data is presented. This new methodology uses the Bform polynomials of multivariate simplex splines in a new linear regression scheme. This allows the use of standard parameter estimation techniques for estimating the Bcoefficients of the multivariate simplex splines. We present a generalized least squares estimator for the Bcoefficients, and show how the estimated Bcoefficient variances lead to a new model quality assessment measure in the form of the Bcoefficient variance surface. The new modeling methodology is demonstrated on a nonlinear scattered bivariate dataset.Csplines; parameter estimation; scattered data; multivariate splines
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