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Assembled structures are nonlinear. The sources of this nonlinearity could include the jointed interfaces, damage and wear, non-idealized boundary conditions, or other features inherent in real parts. To study these systems and to ascertain if they will be operating in a regime in which the nonlinearity is prominent, nonlinear system identification techniques are needed to assess and characterize the nature of the nonlinearity in the structure. Significant progress over the last few years has focused on using nonlinear system identification to identify damage and other deviations from idealized structures. This research reviews nine different methods for nonlinear system identification (restoring force surface, Hilbert transform, direct quadrature, zero-crossing, short-time Fourier transform, Gabor wavelet, Morlet wavelet, Morse wavelet, and a neural network-based algorithm) in order to assess their accuracy. The methods are compared by identifying characteristics of two systems: a single degree of freedom model of a Duffing oscillator and measured data from a jointed structure. As neural networks are not commonly used for system identification, multiple variations of the method are investigated to study its effectiveness. Perturbation analysis is conducted to see the efficacy of the different methods for identifying parameters across a large range of design spaces, and the advantages and disadvantages of each method are discussed. The primary contribution of this paper is a comparison on both analytical and experimental data of multiple widely used system identification methods, and an assessment of when each method is most and least applicable, specifically in the context of jointed structures. [ABSTRACT FROM AUTHOR]

The dynamic responses of assembled structures are greatly affected by the mechanical joints, which are often the cause of nonlinear behavior. To better understand and, in the future, tailor the nonlinearities, accurate methods are needed to characterize the dynamic properties of jointed structures. In this paper, the nonlinear characteristics of a jointed beam is studied with the help of multiple identification methods, including the Hilbert Transform method, Peak Finding and Fitting method, Dynamic Mode Decomposition method, State-Space Spectral Submanifold, and Wavelet-Bounded Empirical Mode Decomposition method. The nonlinearities are identified by the responses that are measured via accelerometers in a series of experiments that consist of hammer testing, shaker ringdown testing, and response/force-control stepped sine testing. In addition to accelerometers, two high-speed cameras are used to capture the motion of the whole structure during the shaker ringdown testing. Digital Image Correlation (DIC) is then adopted to obtain the displacement responses and used to determine the mode shapes of the jointed beam. The accuracy of the DIC data is validated by the comparison between the identification results of acceleration and displacement signals. As enabled by full-field data, the energy-dependent characteristics of the structure are also presented. The setup of the different experiments is described in detail in Part I (Chen et al., 2021) of this research. The focus of this paper is to compare nonlinear system identification methods applied to different measurement techniques and to exploit the use of high spatial resolution data. • The results of several nonlinear system identification methods are compared. • Backbone and damping curves of a jointed beam are identified. • Free decay and forced responses data reveal consistent nonlinear characteristics. • The amplitude-dependent mode shape is reconstructed using digital image correlation. • Digital image correlation allows the computation of the kinetic energy of the beam. [ABSTRACT FROM AUTHOR]

Jointed structures are ubiquitous constituents of engineering systems; however, their dynamic properties (e.g., natural frequencies and damping ratios) are challenging to identify correctly due to the complex, nonlinear nature of interfaces. This research seeks to extend the efficacy of traditional experimental methods for linear system identification (such as impact testing, shaker ringdown testing, random excitation, and force or amplitude-control stepped sine testing) on nonlinear jointed systems, e.g., the half Brake–Reuß beam, by augmenting them with full-field data collected by high-speed videography. The full-field response is acquired using high-speed cameras combined with Digital Image Correlation (DIC), which enables studying the spatial–temporal dynamic characteristics of the system. As this is a video-based experiment, additional constraints are attached to the beam at the node points to remove the rigid body motion, which ensures that the beam is in the view of the camera during the entire test. The use of a video-based method introduces new sources of experimental error, such as noise from the high-speed camera's fan and electrical noise, and so the measurement accuracy of DIC is validated using accelerometer data. After validating the DIC data, the measurements are recorded for several types of excitation, including hammer testing, shaker ringdown testing, fixed sine testing, and stepped sine testing. Using the DIC data to augment standard nonlinear system identification techniques, modal coupling and the mode shapes' evolution are investigated. The suitability of videography methods for nonlinear system identification of nonlinear beams is explored for the first time in this paper, and recommendations for techniques to facilitate this process are made. This article focuses on developing an accurate data collection methodology as well as recommendations for nonlinear testing with DIC, which paves the way for video-based investigation of nonlinear system identification. In Part-II (Jin et al., 2021) of this work, the same data set is used for a rigorous assessment of nonlinear system identification with full-field DIC data. • Nonlinear system identification strategies are applied to a jointed structure. • The use of Digital Image Correlation for nonlinear system identification is assessed. • A novel shaker ringdown excitation method is proposed. • Hardening-softening behavior is observed in the frequency response of the structure. • Modal interactions between the first and third mode are observed. [ABSTRACT FROM AUTHOR]