Chapter17 Tutorial on Nonlinear System Identification G. Kerschen Abstract Because nonlinearity is now a frequent occurrence in real-life applications, the practitioner should understand the resulting dynamical phenomena and account for them in the design process. This tutorial focuses on nonlinear system identification, which extracts relevant information about nonlinearity directly from experimental measurements. Specifically, the identification process is a progression through three steps, namely detection, characterization and parameter estimation. The tutorial presents these steps in detail and illustrates them using real aerospace structures. Keywords Nonlinear vibrations • System identification • Detection • Characterization • Parameter estimation 17.1 Introduction Mathematical modeling refers to the use of mathematical language to simulate the behavior of a ‘real world’ (practical) system. Its role is to provide a better understanding and characterization of the system. Theory is useful for drawing general conclusions from simple models, and computers are useful for drawing specific conclusions from complicated models. In the theory of mechanical vibrations, mathematical models—termed structural models—are helpful for the analysis of the dynamic behavior of the structure being modeled. The demand for enhanced and reliable performance of vibrating structures in terms of weight, comfort, safety, noise and durability is ever increasing while, at the same time, there is a demand for shorter design cycles, longer operating life, minimization of inspection and repair needs, and reduced costs. With the advent of powerful computers, it has become less expensive both in terms of cost and time to perform numerical simulations, than to run a sophisticated experiment. The consequence has been a considerable shift toward computer-aided design and numerical experiments, where structural models are employed to simulate experiments, and to perform accurate and reliable predictions of the structure’s future behavior. Even if we are entering the age of virtual prototyping [1], experimental testing and system identification still play a key role because they help the structural dynamicist to reconcile numerical predictions with experimental investigations. The term ‘system identification’ is sometimes used in a broader context in the technical literature and may also refer to the extraction of information about the structural behavior directly from experimental data, i.e., without necessarily requesting a model (e.g., identification of the number of active modes or the presence of natural frequencies within a certain frequency range). In this tutorial, system identification refers to the development (or the improvement) of structural models from input and output measurements performed on the real structure using vibration sensing devices. Linear system identification is a discipline that has evolved considerably during the last 30 years [2, 3]. Modal parameter estimation—termedmodal analysis—is indubitably the most popular approach to performing linear system identification in structural dynamics. The model of the system is known to be in the form of modal parameters, namely the natural frequencies, mode shapes and damping ratios. The popularity of modal analysis stems from its great generality; modal parameters can describe the behavior of a system for any input type and any range of the input. Numerous approaches have been developed for this purpose: Ibrahim time domainmethod [4], eigensystem realization algorithm[5], stochastic subspace identification method [6], polyreference least-squares complex frequency domain method [7] to name a few. It is, however, important to note that modal identification of highly damped structures or complex industrial structures with high modal density and G. Kerschen ( ) Department of Aerospace and Mechanical Engineering, Space Structures and Systems Laboratory (S3L), Structural Dynamics Research Group, University of Liège, Liège, Belgium e-mail: g.kerschen@ulg.ac.be © The Society for Experimental Mechanics, Inc. 2016 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29739-2_17 185
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