Identification of piecewise linear aeroelastic systems

The work presented in this paper is concerned with the identification of a piecewise linear aeroelastic system from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems such that one does not know a prior which subsystem has generated which data, that is, the switching points of the freeplay nonlinearity. The linear part of the nonlinear aeroelastic system is represented by the orthonormal basis functions constructed by the physical poles of the linear part, and the nonlinear part is represented by a Hammerstein model. By a simple rearrangement of the data corresponding to the degree-of-freedom of freeplay and selecting a segment of the data, the identification of the physical poles could be reduced to a linear parametric problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. The iterative sequence of the switching points is constructed, and solved by a method synthesizing the non-iterative and iterative algorithms. Then the parameters of the linear and nonlinear parts of the nonlinear system including the switching points are successfully obtained. A two-dimensional airfoil with nonlinear structural freeplay in the pitch degree-of-freedom is presented to demonstrate the validity of the proposed identification algorithm