Advertisement

A Bayesian Framework for Optimal Experimental Design in Structural Dynamics

  • Costas Argyris
  • Costas PapadimitriouEmail author
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

A Bayesian framework for optimal experimental design in structural dynamics is presented. The optimal design is based on an expected utility function that measures the value of the information arising from alternative experimental designs and takes into account the uncertainties in model parameters and model prediction error. The evaluation of the expected utility function requires a large number of structural model simulations. Asymptotic techniques are used to simplify the expected utility functions under small model prediction error uncertainties, providing insight into the optimal design and drastically reducing the computation effort involved in the evaluation of the multi-dimensional integrals that arise. The framework is demonstrated using the design of sensors for modal identification and is applied to the design of a small number of reference sensors for experiments involving multiple sensor configuration setups accomplished with reference and moving sensors. In contrast to previous formulations, the Bayesian optimal experimental design overcomes the problem of the ill-conditioned Fisher information matrix for small number of reference sensors by exploiting the information in the prior distribution.

Keywords

Bayesian inference Information entropy Relative entropy Kullback–Leibler divergence Structural dynamics 

Notes

Acknowledgement

This research has been implemented under the “ARISTEIA” Action of the “Operational Programme Education and Lifelong Learning” and was co-funded by the European Social Fund (ESF) and Greek National Resources.

References

  1. 1.
    Huan, X., Marzouk, Y.M.: Simulation-based optimal Bayesian experimental design for nonlinear systems. J. Comput. Phys. 232(1), 288–317 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Papadimitriou, C., Beck, J.L., Au, S.K.: Entropy-based optimal sensor location for structural model updating. J. Vib. Control. 6(5), 781–800 (2000)CrossRefGoogle Scholar
  3. 3.
    Papadimitriou, C.: Optimal sensor placement methodology for parametric identification of structural systems. J. Sound Vib. 278(4), 923–947 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Papadimitriou, C., Lombaert, G.: The effect of prediction error correlation on optimal sensor placement in structural dynamics. Mech. Syst. Signal Process. 28, 105–127 (2012)CrossRefGoogle Scholar
  5. 5.
    Kammer, D.C.: Sensor placements for on orbit modal identification and correlation of large space structures. J. Guid. Control. Dyn. 14, 251–259 (1991)CrossRefGoogle Scholar
  6. 6.
    Lindley, D.V.: On a measure of the information provided by an experiment. Ann. Math. Stat. 27, 986–1005 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hansen, N., Muller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11(1), 1–18 (2003)CrossRefGoogle Scholar
  8. 8.
    Bleistein, N., Handelsman, R.: Asymptotic Expansions for Integrals. Dover, New York (1986)zbMATHGoogle Scholar
  9. 9.
    Gerstner, T., Griebel, M.: Numerical integration using sparse grids. Numer. Algorithms 18, 209–232 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bungartz, H.J., Griebel, M.: Sparse grids. Acta Numer. 13, 147–269 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Papadimitriou, D.I., Papadimitriou, C.: Optimal sensor placement for the estimation of turbulence model parameters in CFD. Int. J. Uncertain. Quantif. 5, 1 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Papadimitriou, C., Papadioti, D.C.: Component mode synthesis techniques for finite element model updating. Comput. Struct. 126, 15–28 (2013)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of ThessalyVolosGreece

Personalised recommendations