A Sparse Set Membership approach to interval estimation of nonlinear functions and application to fault detection

In the paper, the problems of approximating an unknown function from data and deriving reliable interval estimates are first considered. An algorithm is proposed to solve these problems, based on a sparsification technique and a nonparametric Set Membership optimality analysis. Assuming that the noise affecting the data is bounded and that the unknown function satisfies a mild regularity assumption, it is shown that the algorithm provides an almost-optimal approximation (in a worst-case sense), and tight interval estimates are evaluated. An innovative approach to fault detection for nonlinear systems is then proposed, based on the derived interval estimates, overcoming some relevant problems proper of the standard techniques. The proposed algorithm is applied in a simulation study to solve the challenging problem of fault detection for a new class of wind energy generators, which use kites to capture the power from high-altitude winds.