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Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering. (Maskinteknik)
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 [en]
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: urn:nbn:se:lnu:diva-34736OAI: oai:DiVA.org:lnu-34736DiVA: diva2:722276
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
List of papers
1. Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multi-Harmonic Frequency Responses
Open this publication in new window or tab >>Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multi-Harmonic Frequency Responses
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
Keyword
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:nbn:se:lnu:diva-34671 (URN)10.1115/1.4033608 (DOI)000383104400023 ()
Available from: 2014-06-04 Created: 2014-06-04 Last updated: 2017-04-27Bibliographically approved
2. Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods
Open this publication in new window or tab >>Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods
2014 (English)In: Nonlinear Dynamics, Volume 2: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014 / [ed] Gaetan Kerschen, Springer, 2014, 35-44 p.Conference paper, Published paper (Refereed)
Abstract [en]

Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential 5 equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. 6 In many applications, among which model calibration can be one, steady-state frequency response functions are the desired 7 quantities to calculate. 8 The objective of this paper is to compare the performance of computations of nonlinear frequency response functions 9 (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain 10 methods Runge–Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state- 11 space based force feedback method that is shown to give efficient solutions. 12 The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a 13 non-linear spring at its free end.

Place, publisher, year, edition, pages
Springer, 2014
Keyword
Numerical methods, simulation, Nonlinear, Structural Dynamics, Harmonic Balancing, State Space
National Category
Engineering and Technology Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-33610 (URN)10.1007/978-3-319-04522-1_4 (DOI)000342929100004 ()978-3-319-04522-1 (ISBN)978-3-319-04522-1 (ISBN)
Conference
International Modal Analysis Conference (IMAC XXXII) A Conference and Exposition on Structural Dynamics, February 3–6, 2014, Orlando, Florida
Funder
Vinnova
Available from: 2014-04-04 Created: 2014-04-04 Last updated: 2015-05-24Bibliographically approved

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