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.
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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
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/
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
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
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
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
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
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
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/
Ljung, L.: System Identification: Theory for the User. Prentice Hall, Upper Saddle River (1998). ISBN: 9780132441933
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
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
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)
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
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
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
Tangirala, A.K.: Principles of System Identification: Theory and Practice, 1st edn. CRC Press, Boca Raton (2014). ISBN: 9781439895993
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/S0888327015003647
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
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/
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Kammermeier, B., Mayet, J., Rixen, D.J. (2020). Hybrid Substructure Assembly Techniques for Efficient and Robust Optimization of Additional Structures in Late Phase NVH Design: A Comparison. In: Linderholt, A., Allen, M., Mayes, R., Rixen, D. (eds) Dynamic Substructures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12184-6_4
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DOI: https://doi.org/10.1007/978-3-030-12184-6_4
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