An empirical study on decoupling PNLSS models illustrated on an airplane

This paper illustrates a combined nonparametric and parametric system identification framework for modeling nonlinear vibrating structures. First step is the analysis: multiple-input multiple-output measurements are (semi-automatically) preprocessed, and a nonparametric Best Linear Approximation (BLA) method is performed. The outcome of the BLA analysis results in nonparametric frequency response function, noise and nonlinear distortion estimates. Based on this information, a linear parametric (state-space) model is built. This model is used to initialize a high complexity Polynomial Nonlinear State-Space PNLSS model. The nonlinear part of a PNLSS model is manifested as a combination of high-dimensional multivariate polynomials. The last step in the proposed approach is the decoupling: transforming multivariate polynomials into a simplified, alternative basis, thereby dramatically reducing the number of parameters. In this work a novel filtered canonical polyadic decomposition (CPD) is used. The proposed methodology is illustrated on, but of course not limited to, a ground vibration testing measurement of an air fighter.