Aerodynamic reduced-order models based on observer techniques

A new approach for constructing reduced-order models (ROM) of unsteady aerodynamics is presented using observer techniques. The aerodynamic system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by eigenvalue assignment. The Markov parameters of the observer are identified from training data. The Markov parameters of the actual system are then recovered from those of the observer, and employed to realize a state space model of the system with an Eigensystem Realization Algorithm. The formulation is applied to a two-dimensional airfoil undergoing pitch and plunge motions. AGARD test CT6 is included as one of validation examples, and the result agrees well with published data. The ROM obtained by the observer method captures the essence of an aerodynamic system. Furthermore, an interpolation procedure is proposed for the purpose of improving the robustness of ROMs with respect to parameters variations which change the appropriate nonlinear flow mean solution. The research on varying parameters is concentrated on Mach number. A Mach-varying ROM adapting to the change in Mach number is generated using the linear interpolation of Markov parameters. Numerical examples are presented to illustrate the usefulness of Mach-varying ROMs based on the observer method and its accuracy to computational fluid dynamics simulation is quantified via relative error and time history matching. The results demonstrate that the observer approach is suitable for building the Mach-varying ROM.