Gegenbauer orthogonal polynomial based small sample fault detection and diagnosis method for aircraft

In this study, a novel fault detection and diagnosis method based on Gegenbauer orthogonal polynomials is proposed for aircraft control surface system subject to uncertainties. Compared with deep learning methods that rely on large-scale training data, this method can still achieve effective fault diagnosis under small sample conditions, thus providing an important supplement to data constrained scenarios. First, a nonlinear model of the aircraft was developed, followed by an analysis of fault mechanisms and the formulation of a unified fault representation. Next, utilizing the parity and orthogonality properties of Gegenbauer polynomials, radial polynomials are constructed. By incorporating Fourier coefficients, two sets of Gegenbauer-Fourier orthogonal moments are defined in the polar coordinate system. This approach maps the signal onto a compact feature space using a limited set of basis functions. Subsequently, a nearest neighbor search algorithm is employed to build an index structure of the extracted fault features, and the high dimensional vector feature retrieval is achieved. The effectiveness of the proposed method is validated through simulations using the F-16 aircraft control surface fault dataset.