Skip to main content
SpringerLink
Log in

State-space Modeling of Large Domain Wave Propagation Systems by Partitioned C-matrices

  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

Reduced-order models represent an enabling technology in the representation of large-scale dynamic systems. This technology often involves identification of linear state-space models with system matrix A, input matrix B, and output matrix C. Our focus is partitioned C-matrices that facilitate creation of reduced-order discrete-time state-space models appropriate for simulation of large-output wave propagation systems. The C y-partition method, used to generate the partitioned C-matrices, is suitable when the output dimension is orders of magnitude higher than the number of discrete time samples specifying the time duration of interest. The resulting state-space model is characterized by a relatively small C-matrix component relating a small number of “anchored” or basis outputs to the inputs, and a large C-matrix component relating all remaining outputs to the anchored outputs. The partitioned C-matrix and the associated A, B matrices can be identified from input-output data directly using time-domain signals, without the necessity of identifying or computing transfer functions. The resulting models can be used for accurate and rapid prediction of wave-field responses. The theory is general for modeling short-duration dynamics and the applications include modeling of vibrations propagating through a large flexible structure (for damage assessment for example).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Balas, M.: Active control of flexible systems. J. Optim. Theory Appl. 25(3), 415–436 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  2. Antoulas, A., Sorenson, D., Gugercin, S.: A survey of model reduction methods for large-scale systems. Structured matrices in operator theory. Numer. Anal. Control, Sig. Image Process. Contemp. Math. 280, 193–219 (2001)

    Google Scholar 

  3. Haykin, S., Moulines, E.: Large-scale dynamic systems. Proc. IEEE 95(5), 849–852 (2007)

    Article  Google Scholar 

  4. Ketcham, S., Phan, M., Cudney, H.: Reduced-order wave propagation modeling using the eigensystem realization algorithm, Modeling. In: Bock, H., Phu, H., Rannacher, R., Schloder, J. (eds.) simulation, and optimization of complex process, pp 183–193. Springer-Verlag (2012)

  5. Phan, M., Ketcham, S., Darling, R., Cudney, H.: Superstable models for short-duration large domain wave propagation. In: Bock, H., Phu, H., Rannacher, R., Schloder, J. (eds.) Modeling, simulation, and optimization of complex process, pp 257–269. Springer-Verlag (2012)

  6. Seed, H.B., Idriss, I. M.: Soil moduli and damping factors for dynamic response analyses. Earthquake Engrg. Res. Ctr., College of Engrg., Univ. of California, EERC 70-10 (1970)

  7. Lin, P., Phan, M.Q., Ketcham, S.A.: State-space model and Kalman filter gain identification by a superspace method. In: Bock, H.G., Phu, H.X., Rannacher, R., Schloder, J.P. (eds.) Modeling, Simulation, and Optimization of Complex Processes, pp. 121–132. Springer (2014)

  8. Phan, M.: Interaction matrices in system identification and control. In: Proceedings of the 15th Yale Workshop on Adaptive and Learning Systems, New Haven, CT (2011)

  9. Juang, J.-N.: Applied System Identification. Upper Saddle River, NJ: Prentice-Hall (2001)

    Google Scholar 

  10. Juang, J.-N., Phan, M., Horta, L., Longman, R.: Identification of observer/kalman filter markov parameters - theory and experiments. J. Guid. Control. Dyn. 16(2), 320–329 (1993)

    Article  MATH  Google Scholar 

  11. Phan, M., Juang, J.-N., Longman, R.: Identification of linear multivariable systems by identification of observers with assigned real eigenvalues. J. Astronaut. Sci. 15(1), 88–95 (1992)

    MathSciNet  Google Scholar 

  12. Qin, S.: An overview of subspace identification. Comput. Chem. Eng. 30 (10-12), 1502–1513 (2006)

    Article  Google Scholar 

  13. Van Overchee, P., De Moor, B.: Subspace identification for linear systems. Kluwer Academic Publishers (1996)

  14. Van Overchee, P., De Moor, B.: N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems. Automatica 30(1), 75–93 (1994)

    Article  MathSciNet  Google Scholar 

  15. Verhaegen, M., DeWilde, P.: Subspace model identification part 1: the output error state-space model identification class of algorithms. Int. J. Control 56(5), 1187–1210 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  16. Darling, R., Phan, M., Ketcham, S.: A hybrid model for short-duration large domain wave propagation (in preparation)

Download references

Acknowledgments

This study was in support of the Enhanced Linear Sensors for Persistent Intelligence, Surveillance, and Reconnaissance project performed at the U.S. Army Engineer Research and Development Center. Computational support was from the U.S. Department of Defense High Performance Computing Modernization Program. Support to Thayer School at Dartmouth was from a Small Business Technology Transfer grant by the U.S. Department of the Army.

Author information

Authors and Affiliations

  1. Signature Physics Branch, Cold Regions Research and Engineering Laboratory, U.S. Army Engineer Research and Development Center, 72 Lyme Rd., Hanover, NH, 03755, USA

    Richard S. Darling & Stephen A. Ketcham

  2. Thayer School of Engineering, Dartmouth College, 14 Engineering Drive, Hanover, NH, 03755, USA

    Minh Q. Phan

Authors
  1. Richard S. Darling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Minh Q. Phan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephen A. Ketcham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minh Q. Phan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Darling, R.S., Phan, M.Q. & Ketcham, S.A. State-space Modeling of Large Domain Wave Propagation Systems by Partitioned C-matrices. J of Astronaut Sci 60, 541–558 (2013). https://doi.org/10.1007/s40295-015-0069-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-015-0069-6

Keywords

Search

Navigation