Nonlinear updating method: a review

Bussetta, Philippe; Silva, Samuel da

doi:10.1007/s40430-017-0905-7

Cited by 13 publications

(6 citation statements)

References 108 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A Bayesian inference so updated the stochastic model over displacement amplitude of the fundamental harmonic component obtained in the function of the Bouc-Wen parameters through a piecewise HBM approach recently presented in the literature [21]. The methodology was proved to be quite efficient in represent the nonlinear behavior of the structure statistically, showing how practical and robust the proper formulation of a simple analytical tool such as HBM can be to identification purposes, even when dealing with more complex nonlinearities than those commonly identified through it in the literature, such as exemplified in the review made by Busseta et al [5].…”

Section: Final Remarksmentioning

confidence: 98%

Bayesian Model Identification Through Harmonic Balance Method For Hysteresis Prediction in Bolted Joints

Miguel

Teloli

Silva

2021

Preprint

View full text Add to dashboard Cite

Hysteresis is a nonlinear dissipative phenomenon present in many structures, such as those assembled by bolted joints. However, the approaches for identification are still limited in the literature due to their complexity. Additionally, there are also uncertainties held in bolted structures caused to fluctuations in tightening torque and pressure distribution along the contact surface. Thus, this paper yields a methodology for identifying a stochastic Bouc-Wen model for bolted joints based on the harmonic balance method. Unfortunately, some challenges are encountered when applying conventional series approximation to hysteresis, caused mainly by non-smooth behavior, which induces abrupt transitions between different motion regimes. In this work, previous adaptations were made to split the hysteresis loop in smooth paths and then use a piecewise harmonic balance approach. In this way, it was possible to deal with a deterministic Identification problem based on minimizing the error between the Fourier amplitudes of an experimental signal and those obtained through harmonic balance applying the Cross-Entropy optimization method. So, the results were extended to a stochastic model by applying the Bayesian paradigm, in which the maximized likelihood function was also based on the harmonic balance amplitudes. This methodology was demonstrated to identify Bouc-Wen parameters capable of predicting hysteresis in the BERT benchmark, composed of two aluminum beams jointed by a bolted joint in a cantilever boundary condition. Evaluating the results in the time and frequency domain and the nonlinear behavior through the hysteresis loop, it can be concluded that the method was able to identify an accurate stochastic Bouc-Wen model in predicting the dynamics of bolted structures even taking into account the probable uncertainties of the system.

show abstract

Section: Final Remarksmentioning

confidence: 98%

Bayesian Model Identification Through Harmonic Balance Method For Hysteresis Prediction in Bolted Joints

Miguel

Teloli

Silva

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Since the modeling process of the bridge submodel has been described in Chapter 2 (see (19)), it will not be repeated here.…”

Section: Bridge Submodelmentioning

confidence: 99%

“…In the TCV simulation, the accuracy of the bridge FE model has an important influence on the accuracy of the simulation results. However, the FE model is different from the actual structure due to the influence of mesh generation, boundary conditions, and uncertainty of structural physical parameters [19]. erefore, the FE model updating should be carried out to make it as close as possible to the actual structure, so as to conduct the vibration characteristics analysis of train-bridge system more accurately.…”

Section: Introductionmentioning

confidence: 99%

Train‐Bridge Dynamic Behaviour of Long‐Span Asymmetrical‐Stiffness Cable‐Stayed Bridge

Zhou

Zhang

et al. 2021

Shock and Vibration

View full text Add to dashboard Cite

Long-span cable-stayed bridge (LCB) with unequal-height towers is being designed and constructed in metro lines due to its better adaptability to environment and terrain conditions compared to traditional cable-stayed bridge with equal-height towers. However, the asymmetrical arrangement of towers leads to obvious nonuniformity of the structural stiffness along the longitudinal direction, which intensifies the wheel-rail coupled vibration behaviour, and affects the running safety of operating trains and ride comfort. Therefore, train-bridge dynamic behaviour of long-span asymmetrical-stiffness cable-stayed bridge is deeply investigated in this work. Primarily, considering the comprehensive index of frequency difference and modal assurance criterion (MAC), a nonlinear model updating technique (NMUT) based on penalty function theory is proposed, which can be used to optimize the bridge numerical model. Secondly, on the basis of the train-track-bridge dynamic interaction theory (TDIT), a train-track-bridge coupled dynamic model (TCDM) is established. Finally, a LCB with unequal-height towers is applied as a case to illustrate the influence of asymmetrical stiffness on the train-track-bridge dynamic characteristics. Results show that the proposed NMUT is efficacious and practical. For the LCB with unequal-height towers, a significant difference between the bridge vibration at low tower location and that at high tower location appears. The vertical displacement difference of the main beam on both sides of the bridge increases with the distance from the observation point to the bridge tower increasing. The variation of acceleration difference on both sides of the bridge is influenced by the speed of the train and the position of the observation point simultaneously. In general, vibrations of the main beam at low tower location are larger than those at high tower location.

show abstract

“…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.…”

Section: Updating Of a Nonlinear Finite Element Model Using Discrete-mentioning

confidence: 99%

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

Bussetta

Silva

2017

Lat. Am. j. solids struct.

Self Cite

View full text Add to dashboard Cite

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 ...

show abstract

Nonlinear updating method: a review

Cited by 13 publications

References 108 publications

Bayesian Model Identification Through Harmonic Balance Method For Hysteresis Prediction in Bolted Joints

Bayesian Model Identification Through Harmonic Balance Method For Hysteresis Prediction in Bolted Joints

Train‐Bridge Dynamic Behaviour of Long‐Span Asymmetrical‐Stiffness Cable‐Stayed Bridge

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

Contact Info

Product

Resources

About