Grey-box identification of a non-linear solar array structure using cubic splines

Most identification methods in non-linear structural dynamics assume in advance a mathematical model of the non-linearities. This is however possible in specific situations only, since non-linear effects may be caused by numerous phenomena and a priori knowledge is generally limited. The present paper investigates the usefulness of piecewise third-order polynomials, termed cubic splines, to identify the complex non-linear dynamics of solar arrays in their stowed configuration. The estimation of the model parameters is achieved using the frequency-domain non-linear subspace identification (FNSI) method. A distinct advantage of the FNSI approach is its capability to calculate accurately a large number of parameters, while maintaining an acceptable computational burden. This makes tractable the use of cubic splines to represent non-linearity in real-life mechanical systems, as the dimensionality of the inverse problem is known to increase dramatically in this case. The experimental structure of interest consists of two parallel aluminium plates assembled with bolted connections. This application is challenging because of the existence of impacts between the two plates at high excitation amplitude, and of the activation of complicated stiffness and damping mechanisms within the bolted connections.