An Inverse Vibration Problem Solved by an Artificial Neural Network

Authors

  • E.H. Shiguemori
  • L.D. Chiwiacowsky
  • H.F. de Campos Velho
  • J.D.S. da Silva

DOI:

https://doi.org/10.5540/tema.2005.06.01.0163

Abstract

Inverse problems in vibration is a process of determining parameters based on numerical analysis from a comparison between measured vibration data and its predicted values provided by a mathematical model. In this work the dis- placement data have been chosen in order to identify the stiffness matrix which will cause a changing in the time-history of the system displacement. This is an inverse problem, since the stiffness matrix evaluation is obtained through the de- termination of the modified stiffness coefficients. In this work, the artificial neural network technique is applied to the inverse vibration problem where the goal is to estimate the unknown time-dependent stiffness coefficients simultaneously in a two degree-of-freedom structure, using a Multilayer Perceptron Neural Network model. Numerical experiments have been carried out with synthetic experimental data considering a noise level of 1%. Good recoveries have been achieved with this methodology.

References

[1] S.V. Barai and P.C. Pandey, Time-delay neural networks in damage detection of railway bridges, Advances in Engineering Software, 28 (1997), 1-10.

E.P. Carden and P. Fanning, Vibration Based Condition Monitoring: A Review, Structural Health Monitoring, 3, No. 4 (2004), 355-377.

L.D. Chiwiacowsky and H.F. Campos Velho, Different Approaches for the Solution of a Backward Heat Conduction Problem, Inverse Problems in Engineering, 11, No. 6 (2003), 471-494.

L.D. Chiwiacowsky, H.F. Campos Velho and P. Gasbarri, The Damage Identification Problem: A Hybrid Approach, em “Anais do II Congresso Temático de Dinâmica, Controle e Aplicações (DINCON)” (J.M. Balthazar, G.N. da Silva, M. Tsuchida, M. Boaventura, L.C.S. Góes e J.D.S. Silva, eds.), pp. 1393-1402, São José dos Campos, SP, Brazil, 2003.

S.W. Doebling, C.R. Farrar, M.B. Prime and D.W. Shevitz, “Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review”, Los Alamos National Laboratory, Technical Report LA-13070-MS, USA, 1996.

J. Hadamard, “Lectures on the Cauchy problem in linear partial differential equations”, Yale University Press, New Haven, 1923.

S. Haykin, “Neural Networks: A Comprehensive Foundation”, Macmillan, New York, 1993.

C. H. Huang, A non-linear inverse vibration problem of estimating the timedependent stiffness coefficients by conjugate gradient method, International Journal of Numerical Methods in Engineering, 50 (2001), 1545-1558.

C.H. Huang, An inverse vibration problem for simultaneously estimating the time-dependent stiffness coefficients, in “Proceedings of the 4th International Conference on Inverse Problems in Engineering: Theory and Practice”, pp. 123-131, Rio de Janeiro, RJ, Brazil, 2002.

M. Nadler and E.P. Smith, “Pattern Recognition Engineering”, John Wiley & Sons, New York, 1993.

N.M. Newmark, A method of computation for structural dynamics, ASCE -Journal of the Engineering Mechanics Division, 85 (1959), 67-94.

E.H. Shiguemori, H.F. de Campos Velho, J.D.S. da Silva, Estimation of Initial Condition in Heat Conduction by Neural Network, Inverse Problems in Science and Engineering, 12, No. 3 (2004), 317-328.

H. Sohn, C.R. Farrar, F.M. Hemez, D.D. Shunk, D.W. Stinemates, B.R. Nadler, “A Review of Structural Health Monitoring Literature: 1996-2001”, Los Alamos National Laboratory, Technical Report LA-13976-MS, USA, 2003.

K.Worden and J.M. Dulieu-Barton, An Overview of Intelligent Fault Detection in Systems and Structures, Structural Health Monitoring, 3, No. 1 (2004), 85-98.

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Published

2005-06-01

How to Cite

Shiguemori, E., Chiwiacowsky, L., de Campos Velho, H., & da Silva, J. (2005). An Inverse Vibration Problem Solved by an Artificial Neural Network. Trends in Computational and Applied Mathematics, 6(1), 163–175. https://doi.org/10.5540/tema.2005.06.01.0163

Issue

Vol. 6 No. 1 (2005)

Section

Original Article

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