New Approach to Designing Multilayer Feedforward Neural Network Architecture for Modeling Nonlinear Restoring Forces. I: Formulation
Publication: Journal of Engineering Mechanics
Volume 132, Issue 12
Abstract
This paper addresses the modeling problem of nonlinear and hysteretic dynamic behaviors through a constructive modeling approach which exploits existing mathematical concepts in artificial neural network modeling. In contrast with many neural network applications, which often result in large and complex “black-box” models, here, the writers strive to produce phenomenologically accurate model behavior starting with network architecture of manageable/small sizes. This affords the potential of creating relationships between model parameter values and observed phenomenological behaviors. Here a linear sum of basis functions is used in modeling nonlinear hysteretic restoring forces. In particular, nonlinear sigmoidal activation functions are chosen as the core building block for their robustness in approximating arbitrary functions. The appropriateness and effectiveness of this set of basis function in modeling a wide variety of nonlinear dynamic behaviors observed in structural mechanics are depicted from an algebraic and geometric perspective.
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Acknowledgments
This study was supported in part by the National Science Foundation under Grant No. NSFSGER CMS-0332350 for the first writer and CAREER Award No. NSFCMS-0134333 for the second writer. Professor Joseph P. Wright at the Applied Science Division, Weidlinger Associates Inc. is deeply acknowledged by the writers for numerous valuable discussions, detailed reading, and feedback on the manuscript when this work was initially developed.
References
Adams, D., and Allemang, R. (2000). “Non-linear vibrations classnotes, course 20-263-781.” ⟨http://www.sdrl.uc.edu/ucme781/ucme781.html⟩.
Al-Hadid, M., and Wright, J. (1989). “Developments in the force-state mapping technique for non-linear systems and the extension to the location of non-linear elements in a lumped-parameter system.” Mech. Syst. Signal Process., 3(3), 269–290.
Applied Technology Council. (2001). “Evaluation and improvement of inelastic seismic analysis procedures: Phase ii work plan.” ⟨www.atcouncil.org⟩.
Benedettini, F., Capecchi, D., and Vestroni, F. (1995). “Identification of hysteretic oscillators under earthquake loading by nonparametric models.” J. Eng. Mech., 121(5), 606–612.
Chassiakos, A., Masri, S., Smyth, A., and Caughey, T. (1998). “On-line identification of hysteretic systems.” ASME Trans. J. Appl. Mech., 65, 194–203.
Crawley, E., and O’Donnell, K. (1986). “Force-state mapping identification of nonlinear joints.” AIAA/ASME/ASCE/AHS Proc., 27th Structures, Structural Dynamics and Materials Conf., San Antonio, Tex., 1003–1010.
Cybenko, G. (1989). “Approximation by superpositions of sigmoidal function.” Math. Control, Signals, Syst., 2, 303–314.
Demuth, H., and Beale, M. (1998). Neural network toolbox for use with MATLAB, The MathWorks, Inc.
Ghaboussi, J., and Wu, X. (1998). “Soft computing with neural networks for engineering applications: Fundamental issues and adaptive approaches.” Struct. Eng. Mech., 6(8), 955–969.
Gumey, K. (1997). An introduction to neural networks, UCL Press.
Hagan, M., Demuth, H., and Beale, M. (1995). Neural network design, PWS Publishing Company.
Haykin, S. (1998). Neural networks: A comprehensive foundation, 2nd Ed., Prentice-Hall, Upper Saddle River, N.J.
Hornik, K., Stinchcombe, M., and White, H. (1989). “Multilayer feedforward networks are universal approximators.” Neural Networks, 2, 359–366.
Jennings, P. (1964). “Periodic response of a general yielding structure.” J. Engrg. Mech. Div., 90(2), 131–166.
Jones, L. (1990). “Constructive approximations for neural networks by sigmoidal functions.” Proc. IEEE, 78(10), 1586–1589.
Kosmatopoulos, E., Smyth, A., Masri, S., and Chassiakos, A. (2001). “Robust adaptive neural estimation of restoring forces in nonlinear structures.” J. Appl. Mech., 68(6), 880–893.
Lapedes, A., and Farber, R. (1988). Neural information processing systems, D. Anderson, ed., American Institute of Physics, New York, 442–456.
Lippmann, R. (1987). “An introduction to computing with neural nets.” IEEE ASSP Magazine, 4–22.
Lippmann, R. (1989). “Pattern classification using neural networks.” IEEE Commun. Mag., 27(11), 47–64.
Masri, S., and Caughey, T. (1979). “A nonparametric identification technique for nonlinear dynamic problems.” J. Appl. Mech., 46, 433–447.
Masri, S., Smyth, A., Chassiakos, A., Caughey, T., and Hunter, N. (2000). “Application of neural networks for detection of changes in nonlinear systems.” J. Eng. Mech., 126(7), 666–676.
Masri, S., Smyth, A., Chassiakos, A., Nakamura, M., and Caughey, T. (1999). “Training neural networks by adaptive random search techniques.” J. Eng. Mech., 125(2), 123–132.
Mehrotra, K., Mohan, C., and Ranka, S. (1997). Elements of artificial neural networks, MIT Press, Cambridge, Mass.
Nelles, O. (2000). Nonlinear system identification: From classical approaches to neural networks and fuzzy models, Springer, New York.
O’Donnell, K., and Crawley, E. (1985). “Identification of nonlinear system parameters in space structure joints using the force-state mapping technique.” Report No. SSL#16-85, MIT Space Systems Lab., Cambridge, Mass.
Pei, J.-S. (2001). “Parametric and nonparametric identification of nonlinear systems,” Ph.D. dissertation, Columbia Univ., New York.
Pei, J.-S., Smyth, A., and Kosmatopoulos, E. (2004). “Analysis and modification of volterra/wiener neural networks for identification of nonlinear hysteretic dynamic systems.” J. Sound Vib., 275(3–5), 693–718.
Pei, J.-S., Wright, J., and Smyth, A. (2005). “Mapping polynomial fitting into feedforward neural networks for modeling nonlinear dynamic systems and beyond.” Comput. Methods Appl. Mech. Eng., 194(42–44), 4481–4505.
Rumelhart, D., McClelland, J., and the PDP Research Group (1986). Parallel distributed processing explorations in the microstructure of cognition: Foundations, Vol. 1, MIT Press, Cambridge, Mass.
Sandberg, I., Lo, J., Fancourt, C., Principe, J., Katagiri, S., and Haykin, S. (2001). Nonlinear dynamical systems: Feedforward neural network perspectives, Wiley-Interscience, New York.
Smyth, A. (1998). “Analytical and experimental studies in nonlinear system identification and modeling for structural control.” Ph.D. dissertation, Univ. of Southern California, Los Angeles.
Smyth, A., Masri, S., Chassiakos, A., and Caughey, T. (1999). “On-line parametric identification of mdof nonlinear hysteretic systems.” J. Eng. Mech., 125(2), 133–142.
Sohn, H., Worden, K., and Farrar, C. (2003). “Statistical damage classification under changing environmental and operational conditions.” J. Intell. Mater. Syst. Struct., 13(9), 561–574.
Wen, Y. (1989). “Methods of random vibration for inelastic structures.” Appl. Mech. Rev., 42(2), 39–52.
Worden, K. (1990). “Data processing and experiment design for the restoring force surface method. Part II: Choice of excitation signal.” Mech. Syst. Signal Process., 4(4), 321–344.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 12 • December 2006
Pages: 1290 - 1300
Copyright
© 2006 ASCE.
History
Received: Oct 15, 2003
Accepted: Apr 26, 2005
Published online: Dec 1, 2006
Published in print: Dec 2006
Notes
Note. Associate Editor: Gerhart I. Schueller
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