Chapter 27 Nonlinear Identification of an Aero-Engine Component Using Polynomial Nonlinear State Space Model Samson B. Cooper, Koen Tiels, and Dario DiMaio Abstract In non-linear structural dynamics, the identification of nonlinearity often requires prior knowledge or an initial assumption of the mathematical law (model) of the type of nonlinearity present in a system. However, applying such assumptions to large structures with several sources and types of nonlinearities can be difficult or practically impossible due to the individualistic nature of nonlinear systems. This paper presents the identification of an aerospace component using polynomial nonlinear state space models. As a first step, the best linear approximation (BLA), noise and nonlinear distortion levels are estimated over different amplitudes of excitation. Next, a linear state space model is estimated on the nonparametric BLA using the frequency domain subspace identification method. The nonlinear model is constructed using a set of multivariate polynomial terms in the state variables and the parameters are estimated through a nonlinear optimisation routine. The polynomial nonlinear state space models are tested and validated on measured data obtained from the experimental investigation of the Aero-Engine component. Keywords Nonlinear systems · System identification · Black-box model · Aircraft Structures 27.1 Introduction The levels of nonlinearities encountered during the vibration test of aerospace structures is ever increasing and becoming more significant as attested by the literature [1]. Over the last few years, evidence of nonlinear phenomena has been reported during the Ground Vibration Testing (GVT) of large aircraft structures [2–4] and it is now evident that these cases require profound investigation to understand and identify the nonlinearities observed in such test data. In addition, the use of developed linear tools and theories to perform identification on nonlinear test data often produces undesirable results or in most cases fail to predict the structural response within the acceptable levels which are required for validation and industrial certification purpose. Hence the development of effective system identification techniques applicable to nonlinear systems is a major demand by many structural dynamic engineers and researchers. In most cases, the detection of nonlinearity from measured data can easily be achieved by using simple techniques such as the superposition principle, observation of distorted peaks at the resonances and recognition of jumps between low and high response amplitudes. After nonlinearity has been detected in measured data, identification of parametric or nonparametric models from such data is a challenging task. The last two decades have witnessed the development of several procedures and techniques for nonlinear system identification, in [5] the white-box identification process namely (Detection, Characterisation and Quantification) was revealed. The white-box approach has a great progression procedure with the advantage of implementing and integrating two or more developed techniques such as the Wavelet Transform (WT), Hilbert Transform (HT) [6], Restoring Force Surface (RFS) [7] and the Frequency Nonlinear Subspace Identification (FNSI) [8]. A drawback to this approach is that the functional forms and mathematical representation of the nonlinearities must be known in advance based on the physics law governing the dynamics of the system. In addition, this application can be difficult for large aircraft structures with multiple nonlinear sources and different individualistic nonlinear phenomena. Another successful way of tackling nonlinear system identification is to consider black-box approaches, in this case the only available information about the system is given by the measured inputs and outputs. A black-box approach uses model structures that are adequate and rich to capture all the appropriate physics and dynamics governing the nonlinearities S. B. Cooper ( ) · D. DiMaio University of Bristol, Department of Mechanical Engineering, Queen’s Building, University Walk, Bristol, UK e-mail: sc14784@bristol.ac.uk K. Tiels Vrije Universiteit Brussel (VUB), Department of Fundamental Electricity and Instrumentation (ELEC), Brussels, Belgium © The Society for Experimental Mechanics, Inc. 2019 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-319-74280-9_27 261
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