Polynomial nonlinear state space identification of an aero-engine structure

Abstract

Most nonlinear identification problems often require prior knowledge or an initial assumption of the mathematical law (model structure) and data processing to estimate the nonlinear parameters present in a system, i.e. they require the functional form or depend on a proposition that the measured data obey a certain nonlinear function. However, obtaining prior knowledge or performing nonlinear characterisation can be difficult or impossible for certain identification problems due to the individualistic nature of practical nonlinearities. For example, joints between substructures of large aerospace design frequently feature complex physics at local regions of the structure, making a physically motivated identification in terms of nonlinear stiffness and damping impossible. As a result, black-box models which use no prior knowledge can be regarded as an effective method. This paper explores the pragmatism of a black-box approach based on Polynomial Nonlinear State Space (PNLSS) models to identify the nonlinear dynamics observed in a large aerospace component. As a first step, the Best Linear Approximation (BLA), noise and nonlinear distortion levels are estimated over different amplitudes of excitation using the Local Polynomial Method (LPM). Next, a linear state space model is estimated on the non-parametric BLA using the frequency domain subspace identification method. Nonlinear model terms are then constructed in the form of multivariate polynomials in the state variables while the parameters are estimated through a nonlinear optimisation routine. Further analyses were also conducted to determine the most suitable monomial degree and type required for the nonlinear identification procedure. Practical application is carried out on an Aero-Engine casing assembly with multiple joints, while model estimation and validation is achieved using measured sine-sweep and broadband data obtained from the experimental campaign.