Advertisement

Hybrid Substructure Assembly Techniques for Efficient and Robust Optimization of Additional Structures in Late Phase NVH Design: A Comparison

  • Benjamin KammermeierEmail author
  • Johannes Mayet
  • Daniel J. Rixen
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

In certain circumstances, not all desired NVH properties of a given mechanical structure, e.g. a vehicle, are satisfied at the end of a development process. In this situation, NVH properties of an existing structure must be improved while extensive changes of this structure are not practicable. Consequently, additional components such as mass dampers are included to improve the NVH properties. The arising task is to determine the optimal configuration of these additional components. If one assumes that no valid or accurate simulation model of the underlying structure exists, a hybrid substructuring approach is essential. The existing structure is measured at the required positions, the additional structures are modeled virtually, subsequently they are combined to a hybrid assembly. The optimization includes the repeated evaluation of such an hybrid assembly. In this contribution two major strategies are regarded: frequency based substructuring (FBS) and state-space substructuring (SSS). The possibly large number of evaluations imposes a greater demand on the computational efficiency compared to onetime assemblies. Furthermore, properties concerning the robustness towards measurement noise of the assembly technique play an important role. Based on a common notation for both assembly techniques, the relevant properties—efficiency and robustness—are compared on a numerical example.

Keywords

Hybrid substructuring Frequency-based substructuring State-space substructuring System identification Frequency response estimation 

References

  1. 1.
    Alvin, K., Robertson, A., Reich, G., Park, K.: Structural system identification: from reality to models. Comput. Struct. 81(12), 1149–1176 (2003). ISSN: 00457949. https://doi.org/10.1016/S0045-7949(03)00034-8. http://linkinghub.elsevier.com/retrieve/pii/S0045794903000348 CrossRefGoogle Scholar
  2. 2.
    Blackman, R.B., Tukey, J.W.: The measurement of power spectra from the point of view of communications engineering — Part I. Bell Syst. Tech. J. 37(1), 185–282 (1958). ISSN: 0005-8580. https://doi.org/10.1002/j.1538-7305.1958.tb03874.x. http://dx.doi.org/10.1002/j.1538-7305.1958.tb01530.x%20http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6773415%20http://ieeexplore.ieee.org/document/6768513/MathSciNetCrossRefGoogle Scholar
  3. 3.
    Blackman, R.B., Tukey, J.W.: The measurement of power spectra from the point of view of communications engineering - part II. Bell Syst. Tech. J. 37(2), 485–569 (1958). ISSN: 00058580. https://doi.org/10.1002/j.1538-7305.1958.tb01530.x. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6773415 MathSciNetCrossRefGoogle Scholar
  4. 4.
    Favoreel, W., De Moor, B., Van Overschee, P.: Subspace state space system identification for industrial processes. J. Process Control 10(2–3), 149–155 (2000). ISSN: 09591524. https://doi.org/10.1016/S0959-1524(99)00030-X. http://linkinghub.elsevier.com/retrieve/pii/S095915249900030X CrossRefGoogle Scholar
  5. 5.
    Jansson, M.: Subspace identification and ARX modeling. In: IFAC Proceedings Volumes, Sept. 2003, vol. 36(16), pp. 1585–1590 (2003). ISSN: 14746670. https://doi.org/10.1016/S1474-6670(17)34986-8. https://linkinghub.elsevier.com/retrieve/pii/S1474667017349868 CrossRefGoogle Scholar
  6. 6.
    Kammer, D.C., Krattiger, D.: Propagation of uncertainty in substructured spacecraft using frequency response. AIAA J. 51(2), 353–361 (2013). ISSN: 0001-1452. https://doi.org/10.2514/1.J051771. http://arc.aiaa.org/doi/10.2514/1.J051771 CrossRefGoogle Scholar
  7. 7.
    Kammer, D.C., Nimityongskul, S.: Propagation of uncertainty in test-analysis correlation of substructured spacecraft. J. Sound Vib. (2011). ISSN: 0022460X. https://doi.org/10.1016/j.jsv.2010.09.029 CrossRefGoogle Scholar
  8. 8.
    Klerk, D.D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review and classification of techniques. AIAA J. 46(5), 1169–1181 (2008). ISSN:0001-1452. https://doi.org/10.2514/1.33274. http://arc.aiaa.org/doi/10.2514/1.33274 CrossRefGoogle Scholar
  9. 9.
    Larimore, W.: Canonical variate analysis in identification, filtering, and adaptive control. In: 29th IEEE Conference on Decision and Control, vol. 2, pp. 596–604. IEEE, New York (1990).  https://doi.org/10.1109/CDC.1990.203665. http://ieeexplore.ieee.org/document/203665/
  10. 10.
    Ljung, L.: System Identification: Theory for the User. Prentice Hall, Upper Saddle River (1998). ISBN: 9780132441933Google Scholar
  11. 11.
    Nicgorski, D., Avitabile, P.: Conditioning of FRF measurements for use with frequency based substructuring. In: Mechanical Systems and Signal Processing (2010). ISSN: 08883270. https://doi.org/10.1016/j.ymssp.2009.07.013 CrossRefGoogle Scholar
  12. 12.
    Nicgorski, D., Avitabile, P.: Experimental issues related to frequency response function measurements for frequencybased substructuring. Mech. Syst. Signal Process. 24(5), 1324–1337 (2010). ISSN: 08883270. https://doi.org/10.1016/j.ymssp.2009.09.006. http://linkinghub.elsevier.com/retrieve/pii/S0888327009002660 CrossRefGoogle Scholar
  13. 13.
    Rixen, D.J.: How measurement inaccuracies induce spurious peaks in Frequency Based Substructuring. In: Proceedings of the XXVI International Modal Analysis Conference. Society for Experimental Mechanics, Orlando (2008)Google Scholar
  14. 14.
    Sjövall, P., Abrahamsson, T.: Component system identification and state-space model synthesis. Mech. Syst. Signal Process. 21(7), 2697–2714 (2007). ISSN: 08883270. https://doi.org/10.1016/j.ymssp.2007.03.002. http://linkinghub.elsevier.com/retrieve/pii/S088832700700043X CrossRefGoogle Scholar
  15. 15.
    Sjövall, P., McKelvey, T., Abrahamsson, T.: Constrained state–space system identification with application to structural dynamics. Automatica 42(9), 1539–1546 (2006). ISSN: 00051098. https://doi.org/10.1016/j.automatica.2006.04.021. http://linkinghub.elsevier.com/retrieve/pii/S0005109806001725 MathSciNetCrossRefGoogle Scholar
  16. 16.
    Su, T.-J., Juang, J.-N.: Substructure system identification and synthesis. J. Guid. Control Dynam. 17(5), 1087–1095 (1994). ISSN: 0731-5090. https://doi.org/10.2514/3.21314. http://arc.aiaa.org/doi/10.2514/3.21314 CrossRefGoogle Scholar
  17. 17.
    Tangirala, A.K.: Principles of System Identification: Theory and Practice, 1st edn. CRC Press, Boca Raton (2014). ISBN: 9781439895993CrossRefGoogle Scholar
  18. 18.
    van der Seijs, M.V., de Klerk, D., Rixen, D.J.: General framework for transfer path analysis: history, theory and classification of techniques. Mech. Syst. Signal Process. 68–69, 217–244 (2016). ISSN: 08883270. https://doi.org/10.1016/j.ymssp.2015.08.004. http://dx.doi.org/10.1016/j.ymssp.2015.08.004%20https://linkinghub.elsevier.com/retrieve/pii/S0888327015003647CrossRefGoogle Scholar
  19. 19.
    Verhaegen, M.: Identification of the deterministic part of MIMO state space models given in innovations form from input-output data. Automatica 30(1), 61–74 (1994). ISSN: 00051098. https://doi.org/10.1016/0005-1098(94)90229-1. http://linkinghub.elsevier.com/retrieve/pii/0005109894902291 MathSciNetCrossRefGoogle Scholar
  20. 20.
    Welch, P. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15(2), 70–73 (1967). ISSN: 0018-9278.  https://doi.org/10.1109/TAU.1967.1161901. http://ieeexplore.ieee.org/document/1161901/ CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  • Benjamin Kammermeier
    • 1
    • 2
    Email author
  • Johannes Mayet
    • 2
  • Daniel J. Rixen
    • 1
  1. 1.Faculty of Mechanical EngineeringTechnical University of MunichGarchingGermany
  2. 2.Forschungs- und Innovationszentrum FIZBMW GroupMünchenGermany

Personalised recommendations