Nonlinear features identified by Volterra series for damage detection in a buckled beam

Lat. Am. j. solids struct.

2017

In this study, the discrete-time Volterra series are used to update parameters in a nonlinear finite element model. The main idea of the Volterra series is to describe the discrete-time output of a nonlinear system using multidimensional convolutions between the Volterra kernels represented in a Kautz orthogonal basis and the excitations. A metric based on the residue between the experimental and the numerical Volterra kernels is used to identify the parameters of the numerical model. First, the identification of the linear parameters is performed using a metric based only on the first order Volterra kernels. Then the nonlinear parameters are identified through a metric based on the higher-order kernels. The originality of this nonlinear updating method stems from the decoupling of linear and nonlinear parameters and the use of global nonlinear model. In order to put in light the applicability of this technique, this work focus on the identification of the parameters in a nonlinear finite element model of a beam that was preloaded by compression mechanism. This work shows that the updated numerical model was able to represent the behaviour observed in the experimental measurements.Keywords Discrete-time Volterra series, Kautz filters, model updating, nonlinear finite element model, nonlinear identification, sensitivity. Updating of a Nonlinear Finite Element Model Using Discrete-Time Volterra Series 1 INTRODUCTIONIn many cases, the dynamical behaviour is needed to design a mechanical system. Moreover, the knowledge of the dynamical behaviour of a structure is important to control its integrity and to predict its service life. In the practical systems, nonlinear effects due to large displacements, gaps, jumps, discontinuities, etc. are very common (e.g. Worden and Tomlinson (2001)). The nonlinear finite element method is a very powerful tool to study the nonlinear vibrations. Nevertheless, it is not easy to identify the parameters of the nonlinear model due to the uncertainties in the modelling of the experimental system (e.g. the mechanical properties, the boundary conditions). Despite of the important number of investigations, the nonlinear model updating techniques are not mature as the classical linear ones.A bibliography review on the state of the art nonlinear system identification techniques in structure dynamics is presented by Noël and Kerschen (2017). Furthermore, a bibliography review of the nonlinear updating methods is exposed by Bussetta et al. (2017). Generally, the updating methods are based on the minimisation of an objective function or a metric that represents the difference between the numerical results and the experimental data. This objective function can use data in the frequency domain or in the time domain. The Volterra series can be used to defined this objective function (e.g. Wu and Kareem (2014); Guo et al. (2013)). In the paper of Shiki et al. (2012) the authors made a numerical comparison of a nonlinear model updating technique based on Volterra series and proper orthogonal ...

Section: Methodsmentioning

confidence: 97%

“…This experimental setup was already used by Scussel and da Silva (2016) to experimentally identify the value of the first three Volterra kernels and by Shiki et al (2014a) for damage detection. It has been the subject of experimental study to identify cubic stiffness non-linearity of single degree-offreedom Duffing system Tang et al (2015).…”

Section: Methodsmentioning

confidence: 99%

Updating of a Nonlinear Finite Element Model Using Discrete-Time Volterra Series

Bussetta

Lat. Am. j. solids struct.

2017

“…Volterra series expanded in Kautz filters is a powerfull technique to identify nonlinear systems due to several reasons (Shiki et al, 2013b;da Silva, 2011a). Several papers as Shiki et al (2013a), da Silva et al (2010), Shiki et al (2014), Hansen et al (2014a) e Hansen et al (2014b) have shown the practical application of this approach.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis in Volterra Series Applied in a Nonlinear System.

Villani

23rd ABCM International Congress of Mechanical Engineering

Cunha

2015

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Output-Only Identification of Nonlinear Systems Via Volterra Series

Scussel

Journal of Vibration and Acoustics

2016

The operational modal analysis methods based on output-only measurements are well-known and applied in linear systems. However, they are not so well developed for nonlinear systems. Thus, this paper proposes an approach for nonlinear system identification using output-only data. In the conventional Volterra series, the outputs of the system are computed by multiple convolutions between the excitation force and the Volterra kernels. However, in this paper at least two time series measured in different placements are used to compute the multiple convolutions and the excitation signals are not required. The novel kernels identified can be used to characterize nonlinear behavior through a model using only output data. A numerical example based on a Duffing oscillator with two degrees-of-freedom (2DOF) and experimental vibration data from a buckled beam with hardening nonlinearities are used to illustrate the proposed method. The prediction results using output-only data are similar to the conventional Volterra kernels based on input and output data.