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Accurately determining system order plays a vital role in system identification directly related to the accuracy of identification results, especially for nonlinear system identification. Due to the need for human subjective judgment, the traditional sequence determination method easily causes uncertainty in the results; and the phenomenon of the virtual mode or omission occurs. An automatic nonlinear subspace identification method is proposed to address the aforementioned problems. When the eigenvalue decomposition of the constructed Hankel matrix is performed, the calculation range of the modal order of the system is estimated. The similarity coefficient and distance function are introduced to cluster the identified modal results, the poles of the false modes are removed to obtain the cluster stabilization diagram, and the best order of the system is received. Then, the modal parameters and nonlinear coefficients are obtained. Simulation examples are carried out to verify the effectiveness and robustness of the proposed method. An experimental study is carried out on a multilayer building with nonlinear characteristics. Compared with the traditional stabilization graph, the accuracy of the automatic order determination proposed in this paper is proven.

In nonlinear system identification, one of the main challenges is how to select a nonlinear model. The accuracy of nonlinear subspace identification depends on the accuracy of the nonlinear feedbac...

This paper deals with the nonlinear system identification of structures exhibiting distributed nonlinearities, which has become of great interest recently, due to the continuous interest to improve the performance of structures. This brings the need for designing lighter and more flexible structural elements, which are usually characterized by moderate and large deformation, resulting in a distributed nonlinear behavior. In this framework, system identification remains a particularly challenging problem, especially when experimental measurements are considered. This work proposes a method to perform such a task, based on a convenient model order reduction of the considered structure, followed by a nonlinear system identification algorithm. The methodology is validated on a very thin beam undergoing large-amplitude oscillations, firstly using numerical data and then considering an experimental test bench. On the experimental side, the nonlinearity is first characterized using just the measured data, in order to acquire information that would help the identification process. Eventually, nonlinear system identification is performed in the reduced-order domain. An ad-hoc version of the nonlinear subspace identification (NSI) algorithm is used, but the presented methodology can also be applied with other nonlinear identification tools. Results confirm the goodness of the identification strategy in obtaining a reliable model which takes into account the distributed nonlinear behavior.

International audience; A smartphone is a low-cost pocket wireless multichannel multiphysical data acquisition system: the use of such a device for noise and vibration analysis is a challenging task. To what extent is it possible to carry out relevant analysis from it? The Survishno conference, held in Lyon in July 2019, proposed a contest to participants based on this subject. Two challenges were proposed, wherein each a mute video showing an object moving/excited at different frequencies was provided. Due to the frequencies set and the video sampling characteristics, special effects occurred and are visible on both videos. From the first video, participants were asked to estimate the Instantaneous Angular Speed (IAS) of a rotating fan. From the second video, they were asked to perform the modal analysis of a cantilever beam. This paper gathers the interesting ideas proposed by the contestants and proposes a global method to solve these two problems. One major point of the paper might be the advantageous use of the rolling shutter effect, a well-known artefact of smartphone videos, to perform advanced mechanical analyses: the consideration of the unavoidable slight phase shift between the acquisition of each pixel opens up the possibility to perform a dynamic analysis at frequencies that are much higher than the video frame rate.

Robustly identifying nonlinear mechanical systems is generally a challenging task, and this is particularly true when the structure under test exhibits nonlinear behaviors related to both stiffness...

Nonlinear dissipative phenomena are common features of many dynamical systems and engineering applications, and their experimental characterization has always been a challenge among the research community. Within the wide range of nonlinear damping mechanisms, friction is surely one of the most common, and with a high impact on the dynamical behavior of structures. In this paper, the nonlinear identification of friction in a negative stiffness oscillator is pursued. The structure exhibits a strong nonlinear behavior, mainly due to its polynomial elastic restoring force with a negative stiffness region. This leads to an asymmetric double-well potential with two stable equilibrium positions, and the possibility of switching between them in a chaotic way. Friction plays a crucial role in this context, as it derives from the continuous sliding between the central guide and the moving mass. The system is driven through harmonic tests with several input amplitudes, in order to estimate the variations in the energy dissipated per cycle. The identification of the frictional behavior is then pursed by minimizing the errors between the experimental measurements and the model predictions, using the harmonic balance method in conjunction with a continuation technique on the forcing amplitudes.

The need of lightweight design in structural engineering is steadily growing due to economic and ecological reasons. This usually causes the structure to exhibit moderate to large displacements and rotations, resulting in a distributed nonlinear behavior. However, the characterization of geometrical nonlinearities is challenging and sensitive to structural boundaries and loading. It is commonly performed with numerical simulations, utilizing particularly finite element formulations. This study comprises simulations of a clamped-clamped beam with moderate to large amplitude oscillations. Four different (commercial and noncommercial) numerical approaches are considered: three finite element representations and one assumed-modes approach. A first comparison is conducted when the system is under a sine sweep excitation over one single mode. Subsequently, a modified model featuring nonlinear internal resonance is considered, to disclose differences in the modeling of the nonlinearity when coupling between modes occurs. The results show some expected features for geometrical nonlinearities in all methods, but also some important differences, especially when the modal interaction is activated.

In this paper an analytical method for studying the free response of continuous vibrating systems with distributed and possibly non-proportional viscous damping is proposed. The most general case the method refers to is a piece-wise homogeneous Euler-Bernoulli beam, with lumped elastic and inertial elements and subjected to tensile load. The practical application of the method to a contact wire is also presented, aiming at analysing its dynamic response. Contact wires are typically used in the overhead contact line of the railway electrification system but, despite their wide diffusion, their damping properties have not been exhaustively studied. This study aims at experimentally validate the analytical method to define a reliable dynamic model of overhead contact lines. The wire is modelled as an axially loaded homogeneous beam, with lumped elastic and inertial elements (i.e. droppers and clamps). A state-form expansion applied in conjunction with a transfer matrix technique is adopted to extract the eigenvalues and to express the eigenfunctions in analytical form. Experimental measurements have been carried out in the Dynamics & Identification Research Group (DIRG) laboratory of Politecnico di Torino considering two different damping scenarios, and the modal properties of the test bench have been extracted by using a linear subspace identification technique. The damping distribution is finally investigated starting from the experimental data, in order to seek for the most appropriate damping model.

Nonlinear system identification has become of great interest during the last decades. However, a common and shared framework is not present yet, and the identification may be challenging, especially when real engineering structures are considered with strong nonlinearities. Subspace methods have proved to be effective when dealing with local nonlinearities, both in time domain (TNSI method) and in frequency domain (FNSI method). This study reports an improvement for both methods, as a first attempt to account for distributed nonlinearities, which is still an open question in the research community. A numerical beam under moderately large oscillations that exhibits geometric nonlinearity is considered. The object of the identification process is to exploit its behavior through the correct identification of the parameters that define the nonlinearity. Results show a high level of confidence between the two methods, and suggest that a more complete analysis of distributed nonlinear phenomena can be conducted based on these approaches.