8. Nonlinear Modelling of an F16 Benchmark Measurement

Engineers and scientists want mathematical models of the observed system for understanding, design, and control. Many mechanical and civil structures are nonlinear. This paper illustrates a combined nonparametric and parametric system identification framework for modelling a nonlinear vibrating structure. First step of the process is the analysis: measurements are (semiautomatically) preprocessed, and a nonparametric best linear approximation (BLA) method is applied. The outcome of the BLA analysis results in nonparametric frequency response function, noise and nonlinear distortion estimates. Second, based on the information obtained from the BLA process, a linear parametric (state-space) model is built. Third, the parametric model is used to initialize a complex 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 significantly 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 F16 aircraft.