Bayesian Uncertainty Quantification in the Development of a New Vibration Absorber Technology

Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


The engineer starts with paper and pencil. From the basic idea to the axiomatic model, this is all he or she needs. If the axiomatic model does not reproduce the results of the experiment due to too many simplifications, the axiomatic model shall be extended. The aim is to guarantee the desired functionality at an early design stage and thus ensure a safe design. Mathematical models of a new vibration absorber technology of different complexity are utilized in order to predict its dynamic response under different operation conditions. Such a prediction of the dynamic response is subject to model uncertainty.

The focus of this paper is on model’s uncertainty resulting from model’s complexity. The model’s complexity is designed to be as simple as possible for an efficient optimisation approach. Since development is domain-specific, system and boundaries must first be defined. For this purpose, the modules are cut out of the overall system. The system boundaries, of the Fluid Dynamic Vibration Absorber have first to be found for a mathematical model but also for an experimental setup to get reliable empiric data. After this the proposed dynamic response of mathematical model is investigated. At a hydraulic transmission in an oscillating system, there are several approaches to modelling the oscillating flow and damping. Damping plays a decisive role in vibration absorbers. The occurring uncertainty of prediction of the dynamic response of the different models has to be quantified, especially if it represents a risk for vehicle occupants. Therefore, a Bayesian interval hypothesis-based method is used to quantify this uncertainty. It turns out that the choice of model boundary is a crucial one for model confidence.


Bayesian interval hypothesis Model validation Vibration absorber Uncertainty 



Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 57157498 – SFB 805. The authors especially would like to thank the project cooperation partner ZF Friedrichshafen AG for supporting this project.


  1. 1.
    Hedrich, P., Brötz, N., Pelz, P.F.: Resilient product development – a new approach for controlling uncertainty. AMM. 885, 88–101 (2018)CrossRefGoogle Scholar
  2. 2.
    Kennedy, M.C., O’hagan, A.: Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B. 63(3), 425–464 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Roy, C.J., Oberkampf, W.L.: A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Comput. Methods Appl. Mech. Eng. 200(25–28), 2131–2144 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Jiang, X., Mahadevan, S.: Bayesian wavelet method for multivariate model assessment of dynamic systems. J. Sound Vib. 312(4–5), 694–712 (2008)CrossRefGoogle Scholar
  5. 5.
    Brötz, N., Hedrich, P., Pelz, P.F.: Integrated fluid dynamic vibration absorber for mobile applications. In: 11th International Fluid Power Conference (11th Ifk), pp. 14–25, Aachen (2018)Google Scholar
  6. 6.
    Corneli, T., Pelz, P.F.: Employing hydraulic transmission for light weight dynamic absorber. In: 9th International Fluid Power Conference (9th Ifk), pp. 198–209, Aachen (2014)Google Scholar
  7. 7.
    Den Hartog, J.P.: Mechanical Vibrations. Dover Publications, New York (1985)zbMATHGoogle Scholar
  8. 8.
    Markert, R.: Strukturdynamik: Skript Zur Vorlesung “Strukturdynamik Für Maschinenbauer”, 1st edn. Technische Universität, Fachgebiet Strukturdynamik, Darmstadt (2011)Google Scholar
  9. 9.
    Zhan, Z., Fu, Y., Yang, R.-J., Peng, Y.: Bayesian based multivariate model validation method under uncertainty for dynamic systems. J. Mech. Des. 134(3), 2408 (2012)CrossRefGoogle Scholar
  10. 10.
    Mallapur, S., Platz, R.: Quantification of uncertainty in the mathematical modelling of a multivariable suspension strut using Bayesian interval hypothesis-based approach. AMM. 885, 3–17 (2018)CrossRefGoogle Scholar
  11. 11.
    Bailer-Jones, C.A.L.: Practical Bayesian Inference. Cambridge University Press, Cambridge (2017)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  1. 1.Chair of FluidsystemsTechnische Universität DarmstadtDarmstadtGermany

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