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Bias errors of different simulation methods for linear and nonlinear systems
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
Xielalin Consulting, Sweden.
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.ORCID iD: 0000-0002-4404-5708
2015 (English)In: Nonlinear Dynamics, Volume 1: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015 / [ed] Gaetan Kerschen, Springer, 2015, 505-520 p.Conference paper, Published paper (Other academic)
Abstract [en]

Responses of mechanical systems are often studied using numerical time-domain methods. Discrete excitation forces require a transformation of the dynamic system from continuous time into discrete time. Such a transformation introduces an aliasing error. To reduce the aliasing error, different discretization techniques are used. The bias errors introduced by some discretization techniques are studied in this paper.

Algebraic expressions of the bias error obtained for some discretization methods are presented. The bias error depends on the assumption of the characteristics of the load between two subsequent time steps; here the zero-order, first-order and Lagrange second-order assumptions are studied. Different simulation methods are also studied for numerical evaluation of the derived theoretical bias errors. The discretization techniques are implemented for Runge-Kutta, the Digital Filter method and for the Pseudo Force in State Space method.

The study is carried out for both a linear and a nonlinear system; two numerical examples assist in evaluating the theory. Perfect matches between the numerically estimated bias errors and the theoretical ones are shown. The results also show that, for the nonlinear example, the fourth order Runge-Kutta method is less accurate than the Digital Filter and the used single step Pseudo Force in State Space method.

Place, publisher, year, edition, pages
Springer, 2015. 505-520 p.
Series
Conference Proceedings of the Society for Experimental Mechanics Series, ISSN 2191-5644
Keyword [en]
Bias error, numerical methods, digital filter, state space, frequency response function
National Category
Mechanical Engineering Other Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
URN: urn:nbn:se:lnu:diva-40230DOI: 10.1007/978-3-319-15221-9_44ISI: 000381753700044ISBN: 978-3-319-15220-2 (print)OAI: oai:DiVA.org:lnu-40230DiVA: diva2:800293
Conference
The 33rd IMAC Conference and Exposition on Structural Dynamics, February 2–5, 2015, Orlando, Florida
Available from: 2015-04-02 Created: 2015-02-18 Last updated: 2017-01-10Bibliographically approved
In thesis
1. Model calibration methods for mechanical systems with local nonlinearities
Open this publication in new window or tab >>Model calibration methods for mechanical systems with local nonlinearities
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Most modern product development utilizes computational models. With increasing demands on reducing the product development lead-time, it becomes more important to improve the accuracy and efficiency of simulations. In addition, to improve product performance, a lot of products are designed to be lighter and more flexible, thus more prone to nonlinear behaviour. Linear finite element (FE) models, which still form the basis of numerical models used to represent mechanical structures, may not be able to predict structural behaviour with necessary accuracy when nonlinear effects are significant. Nonlinearities are often localized to joints or boundary conditions. Including nonlinear behaviour in FE-models introduces more sources of uncertainty and it is often necessary to calibrate the models with the use of experimental data. This research work presents a model calibration method that is suitable for mechanical systems with structural nonlinearities. The methodology concerns pre-test planning, parameterization, simulation methods, vibrational testing and optimization.

The selection of parameters for the calibration requires physical insights together with analyses of the structure; the latter can be achieved by use of simulations. Traditional simulation methods may be computationally expensive when dealing with nonlinear systems; therefore an efficient fixed-step state-space based simulation method was developed. To gain knowledge of the accuracy of different simulation methods, the bias errors for the proposed method as well as other widespread simulation methods were studied and compared. The proposed method performs well in comparison to other simulation methods.

To obtain precise estimates of the parameters, the test data should be informative of the parameters chosen and the parameters should be identifiable. Test data informativeness and parameter identifiability are coupled and they can be assessed by the Fisher information matrix (FIM). To optimize the informativeness of test data, a FIM based pre-test planning method was developed and a multi-sinusoidal excitation was designed. The steady-state responses at the side harmonics were shown to contain valuable information for model calibration of FE-models representing mechanical systems with structural nonlinearities.

In this work, model calibration was made by minimizing the difference between predicted and measured multi-harmonic frequency response functions using an efficient optimization routine. The steady-state responses were calculated using the extended multi-harmonic balance method. When the parameters were calibrated, a k-fold cross validation was used to obtain parameter uncertainty.

The proposed model calibration method was validated using two test-rigs, one with a geometrical nonlinearity and one with a clearance type of nonlinearity. To attain high quality data efficiently, the amplitude of the forcing harmonics was controlled at each frequency step by an off-line force feedback algorithm. The applied force was then measured and used in the numerical simulations of the responses. It was shown in the validation results that the predictions from the calibrated models agree well with the experimental results.

In summary, the presented methodology concerns both theoretical and experimental aspects as it includes methods for pre-test planning, simulations, testing, calibration and validation. As such, this research work offers a complete framework and contributes to more effective and efficient analyses on mechanical systems with structural nonlinearities.

Place, publisher, year, edition, pages
Linnaeus University Press, 2016. 145 p.
Series
Linnaeus University Dissertations, 262
Keyword
model calibration, finite element modelling, nonlinear structural dynamics, pre-test planning, multi-sinusoidal excitation, vibrational testing, cross validation
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-57638 (URN)978-91-88357-37-3 (ISBN)
Public defence
2016-10-25, N1017, Växjö, 09:30 (English)
Opponent
Supervisors
Available from: 2016-11-10 Created: 2016-10-26 Last updated: 2016-11-22Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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