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Admittance Identification from Point-wise Sound Pressure Measurements Using Reduced-order Modelling

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Abstract

In this work an acoustic application is studied. The goal is to estimate the complex-valued admittance from given point measurements of the sound pressure. This parameter identification problem is formulated in terms of an infinite-dimensional optimization problem. First- and second-order optimality conditions are discussed. For the numerical realization a reduced-order model based on proper orthogonal decomposition is used. Numerical examples illustrate the efficiency of the proposed approach.

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References

  1. Hepberger, A., Diwoky, F., Priebsch, H.-H., Volkwein, S.: Impedance identification out of pressure datas with a hybrid measurement-simulation methodology up to 1 kHz. In: Proceedings of International Conference on Noise and Vibration Engineering, Leuven, Belgium (2006)

  2. Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.: Optimization with PDE Constraints. Mathematical Modelling: Theory and Applications. Springer, Berlin (2009)

    MATH  Google Scholar 

  3. Volkwein, S., Hepberger, A.: Impedance identification by POD model reduction techniques. Automatisierungstechnik 8, 437–446 (2008)

    Article  Google Scholar 

  4. Fukuda, K.: Introduction to Statistical Recognition. Academic Press, New York (1990)

    Google Scholar 

  5. Holmes, P., Lumley, J.L., Berkooz, G.: Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  6. Sirovich, L.: Turbulence and the dynamics of coherent structures, parts I–III. Q. Appl. Math. XLV, 561–590 (1987)

    MathSciNet  Google Scholar 

  7. Hinze, M., Volkwein, S.: Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control. In: Benner, P., Mehrmann, V., Sorensen, D.C. (eds.) Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, vol. 45, pp. 261–306. Springer, Berlin (2005)

    Chapter  Google Scholar 

  8. Desmet, W.: A Wave Based Prediction Technique for Coupled Vibro-Acoustic Analysis. Ph.D. Thesis, K. U. Leuven (2002)

  9. Hepberger, A.: Mathematical Methods for the Prediction of the Interior Car Noise in the Middle Frequency Range. Ph.D. Thesis, TU Graz (2002)

  10. Tröltzsch, F., Volkwein, S.: POD a-posteriori error estimates for linear-quadratic optimal control problems. Comput. Optim. Appl. 44, 83–115 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cao, Y., Hussaini, M.Y., Yang, H.: Estimation of optimal acoustic linear impedance factor for reduction of radiated noise. Int. J. Numer. Anal. Model. 4, 116–126 (2007)

    MathSciNet  MATH  Google Scholar 

  12. Bermúdez, A., Gamallo, P., Rodríguez, R.: Finite element methods in local active control of sound. SIAM J. Control Optim. 43, 437–465 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Evans, L.C.: Partial Differential Equations. American Math. Society, Providence (2002)

    Google Scholar 

  14. Casas, E.: Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31, 993–1006 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  15. Agranovich, M.S.: Regularity of variational solutions to linear boundary value problems. Funct. Anal. Appl. 40, 323–329 (2006)

    Article  MathSciNet  Google Scholar 

  16. Tröltzsch, F.: Optimal Control of Partial Differential Equations. Theory, Methods and Applications. Graduate Studies in Mathematics, vol. 112. American Mathematical Society, Providence (2010)

    MATH  Google Scholar 

  17. Kunisch, K., Volkwein, S.: Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 40, 492–515 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Raymond, J.P., Zidani, H.: Hamiltonian Pontryagin’s principles for control problems governed by semilinear parabolic equations. Appl. Math. Optim. 39, 143–177 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Luenberger, D.G.: Optimization by Vector Space Methods. Wiley, New York (1969)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Mathematics and Statistics, University of Constance, Universitätsstraße 10, 78464, Konstanz, Germany

    S. Volkwein

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  1. S. Volkwein
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Correspondence to S. Volkwein.

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Communicated by H.-J. Pesch.

The author gratefully acknowledges support by the Austrian Science Fund FWF under grant no. P19588-N18 and by the SFB Research Center “Mathematical Optimization in Biomedical Sciences” (SFB F32). The author would also like to thank Benjamin Gotthardt who did parts of the coding.

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Volkwein, S. Admittance Identification from Point-wise Sound Pressure Measurements Using Reduced-order Modelling. J Optim Theory Appl 147, 169–193 (2010). https://doi.org/10.1007/s10957-010-9704-3

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  • DOI: https://doi.org/10.1007/s10957-010-9704-3

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