lnu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multi-Harmonic Frequency Responses
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering. (Maskinteknik)
Chalmers University of Technology. (Strukturdynamik)
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering. (Maskinteknik)ORCID iD: 0000-0002-4404-5708
Chalmers University of Technology. (Strukturdynamik)
2016 (English)In: Journal of Computational and Nonlinear Dynamics, ISSN 1555-1415, E-ISSN 1555-1423, Vol. 11, no 5, 051023Article in journal (Refereed) Published
Abstract [en]

In industry, linear FE-models commonly serve as baseline models to represent the global structural dynamics behavior. However, available test data may show evidence of significant nonlinear dynamic characteristics. In such a case, the baseline linear model may be insufficient to represent the dynamics of the structure. The causes of the nonlinear characteristics may be local in nature and the remaining parts of the structure may be satisfactorily represented by linear descriptions. Although the baseline model can then serve as a good foundation, the physical phenomena needed to substantially increase the model's capability of representing the real structure are most likely not modelled in it. Therefore, a set of candidate nonlinear property parameters to control the nonlinear effects have to be added and subjected to calibration to form a credible model. The selection of the calibration parameters and the choice of data for a calibration metric form a coupled problem. An over-parameterized model for calibration may result in parameter value estimates that do not survive a validation test. The parameterization is coupled to the test data and should be chosen so that the expected co-variances of the chosen parameter's estimates are made small. Accurate test data, suitable for calibration, is often obtained from sinusoidal testing. Because a pure mono-sinusoidal excitation is difficult to achieve during a test of a nonlinear structure, the excitation is here designed to contain sub and super harmonics besides the fundamental harmonic. The steady-state responses at the side frequencies are shown to contain valuable information for the calibration process that can improve the accuracy of the parameter estimates. The nonlinear steady-state solutions can be found efficiently using the multi-harmonic balance method. In this paper, synthetic test data from a model of a nonlinear benchmark structure are used for illustration. The model calibration and an associated K-fold cross-validation are based on the Levenberg-Marquardt and the undamped Gauss-Newton algorithm, respectively. Starting seed candidates for calibration are found by the Latin hypercube sampling method. The realization that gives the smallest deviation to test data is selected as a starting point for the iterative search for a calibration solution. The calibration result shows good agreement with the true parameter setting, and the K-fold cross validation result shows that the variance of the estimated parameters shrinks when adding sub and super harmonics to the nonlinear frequency response functions.

Place, publisher, year, edition, pages
ASME Press, 2016. Vol. 11, no 5, 051023
Keyword [en]
model calibration, Fisher information matrix, identifiability, multi-harmonic response, cross-validation
National Category
Applied Mechanics
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
URN: urn:nbn:se:lnu:diva-34671DOI: 10.1115/1.4033608ISI: 000383104400023OAI: oai:DiVA.org:lnu-34671DiVA: diva2:721669
Available from: 2014-06-04 Created: 2014-06-04 Last updated: 2017-04-27Bibliographically approved
In thesis
1. Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
Open this publication in new window or tab >>Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In industry, linear finite element models are commonly employed to represent global structural behavior. It is crucial that the computational models are able to accurately represent the structures’ behavior. This cannot always be achieved by the use of linear models.

When vibrational test data show significant nonlinear characteristics, an initial linear finite element model may be judged insufficient in representing the structural behavior. Although an initial model can give a good foundation for the understanding of the dynamic behavior of the structure, the parameters that capture the nonlinear effects are most likely not included. Therefore, a set of candidate parameters controlling the nonlinear effect have to be added. The selection of such candidates is a delicate task which solution is preferably supported by engineering insight into the characteristics of the structure.

One part of this work is on the selection of parameters, among all possibly uncertain properties, together with the forming of the objective function to be used for calibration. To obtain precise estimates of the parameters, the objective function data have to be informative with respect to the selected parameters. Further the parameters have to be identifiable. To improve these qualities, a multi-harmonic sinusoidal excitation was designed since the corresponding steady-state responses at the sub- and super- harmonics were shown to contain valuable information for the calibration process. Model calibration of nonlinear systems made by minimizing the differences between predicted and measured multi-harmonic frequency response functions.

Further, in the calibration, multi-harmonic frequency response functions need to be calculated recurrently in order to reach convergence; therefore a fast simulation scheme was required. The performance of computations of multi-harmonic frequency response functions calculated using time domain as well as frequency domain simulation techniques were studied and compared.

Finally, the proposed calibration method was validated by use of experimental testing on a replica of the Ecole de Lyon nonlinear benchmark structure. It was shown in the validation results that the predictions stemming from the calibrated model matched the experimental data well.

Place, publisher, year, edition, pages
Växjö: Linnaeus University, 2014. 75 p.
Keyword
finite element model calibration, multi-harmonic frequency response function, Fisher information matrix, nonlinear structural dynamics, identifiability, data informativeness
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-34736 (URN)
Presentation
2014-06-12, 13:32 (English)
Opponent
Supervisors
Funder
Vinnova
Available from: 2014-06-09 Created: 2014-06-06 Last updated: 2015-05-24Bibliographically approved
2. 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

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Chen, YoushengLinderholt, Andreas
By organisation
Department of Mechanical Engineering
In the same journal
Journal of Computational and Nonlinear Dynamics
Applied Mechanics

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 402 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf