Linking Nonlinear System Identification with Nonlinear Dynamic Simulation under OpenSees: Some Justifications and Implementations
Publication: Journal of Engineering Mechanics
Volume 135, Issue 11
Abstract
This study seeks to bridge the gap between nonlinear system identification and nonlinear dynamic finite-element analysis. Motivated by the needs in earthquake simulation, it is first investigated under which conditions and to what degree the prediction of maximum lateral drift and base shear requires accurate nonlinear hysteretic moment-rotation joint models. A series of simulations is carried out using a simple but typical steel frame under two different earthquake ground motion time histories scaled up to various levels. As one of the two major classes of models in nonlinear system identification, nonparametric models are proposed to be implemented into OpenSees. A methodology with details is provided to effectively implement feedforward neural networks with one hidden layer as a new one-dimensional nonlinear smooth material model directly from a MATLAB environment to OpenSees. The same methodology can be applied to benefit the implementation of other parametric and nonparametric models with linear parameterization. Numerical examples are provided. Challenges are discussed and future work is identified.
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Acknowledgments
The second writer acknowledges Dr. Jerome P. Lynch at University of Michigan, Ann Arbor, for a collaborative NSF NEES Research (NEESR) proposal that has initiated and eventually led to the development of this work. The many helpful discussions provided by Dr. Lynch are greatly appreciated. The invaluable detailed review provided by Dr. Joel P. Conte, Associate Editor for the ASCE Journal of Engineering Mechanics, is greatly appreciated for significantly reshaping and improving the presentation of this work. Several discussions with Dr. Andrew W. Smyth on the state-of-the-art online identification using parametric models are greatly appreciated.
References
Adeli, H. (2001). “Neural networks in civil engineering: 1989–2000.” Comput. Aided Civ. Infrastruct. Eng., 16, 126–142.
Al-Hadid, M. A., and Wright, J. R. (1989). “Developments in the force-state mapping technique for non-linear systems and the extension to the location of nonlinear elements in a lumped-parameter system.” Mech. Syst. Signal Process., 3(3), 269–290.
Ashrafi, S. A., and Smyth, A. W. (2007). “Generalized masing approach to modeling hysteretic deteriorating behavior.” J. Eng. Mech., 133(5), 495–505.
Ashrafi, S. A., and Smyth, A. W. (2008). “Adaptive parametric identification scheme for a class of nondeteriorating and deteriorating nonlinear hysteretic behavior.” J. Eng. Mech., 134(6), 482–494.
Baber, T. T., and Noori, M. N. (1985). “Random vibration of degrading, pinching systems.” J. Eng. Mech., 111(8), 1010–1026.
Bani-Hani, K., and Ghaboussi, J. (1998). “Nonlinear structural control using neural networks.” J. Eng. Mech., 124(3), 319–327.
Bass, B. J., and Christenson, R. E. (2007). “System identification of a 200 kn magneto-rheological fluid damper for structural control in large-scale smart structures.” Proc., American Control Conf. (ACC), IEEE Control Systems Society, New York, 2690–2695.
Bathe, K. J. (1996). Finite element procedures, Prentice-Hall, Upper Saddle River, N.J.
Bouc, R. (1967). “Forced vibration of mechanical systems with hysteresis.” Proc., 4th Conf. on Nonlinear Oscillations, Prague, Czechoslovakia.
Chadwell, C. B., Fenves, G. L., and A., M. S. (2003). “Near source earthquake effects on the ji lu cable-stayed bridge in the 21 September 1999 chi-chi taiwan earthquake.” Community workshop on computational simulation and visualization environment for NEES, W. Roddis, ed., National Science Foundation, Univ. of Kansas, Lawrence, Kan.
Chopra, A. (2000). Dynamics of structures: Theory and applications to earthquake engineering, Prentice-Hall, Upper Saddle River, N.J.
Computers & Engineering. (2005). SAP2000 English manuals, v10 Ed., ⟨http://www.comp-engineering.com/contact.htm⟩.
Conte, J. P., Elgamal, A., Yang, Z., Zhang, Y., Acero, G., and Seible, F. (2002). “Nonlinear seismic analysis of a bridge ground system.” Proc., 15th ASCE Engineering Mechanics Conf., Columbia Univ., New York.
Crisfield, M. A. (1991). Non-linear finite element analysis of solids and structures, Vol. 2, Wiley, New York.
Cybenko, G. (1989). “Approximation by superpositions of sigmoidal function.” Math. Control, Signals, Syst., 2, 303–314.
El-Metwally, S. E., and Chen, W. F. (1988). “Moment-rotation modeling of reinforced concrete beam-column connections.” ACI Struct. J., 85(4), 384–394.
Farrar, C. R., Worden, K., Todd, M. D., Park, G., Nichols, J., Adams, D. E., Bement, M. T., and Fairnholt, K. (2007). “Nonlinear system identification for damage detection.” Rep. No. LA-14353, Los Alamos National Laboratory, ⟨http://www.osti.gov/bridge/product.biblio.jsp?osti_id=922532⟩.
Fenves, G. L., Mazzoni, S., McKenna, F., and Scott, M. H. (2004). Open system for earthquake engineering simulation examples primer, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Filippou, F. C., Ambrisi, A. D., and Issa, A. (1992). “Nonlinear static and dynamic analysis of reinforced concrete subassemblage.” Rep. No. UCB/EERC-92/08, Univ. of California, Berkeley, Calif.
Filippou, F. C., and Issa, A. (1988). “Nonlinear analysis of reinforced concrete frames under cyclic load reversals.” Rep. No. UCB/EERC-88/12, Univ. of California, Berkeley, Calif.
Filippou, F. C., Popov, E. P., and Bertero, V. V. (1983). “Effects of bond deterioration on hysteretic behavior of reinforced concrete joints.” Rep. No. UCB/EERC-83/19, Univ. of California, Berkeley, Calif.
Flood, I. (2002). “Neural networks in civil engineering: A review.” Civil and structural engineering computing: 2001, B. H. V. Topping, ed., Saxe-Coburg, 185–209.
Foliente, G. C. (1995). “Hysteresis modeling of wood joints and structural systems.” J. Struct. Eng., 121(6), 1013–1022.
Ghaboussi, J., Garrett, J. H., and Wu, X. (1991). “Knowledge-based modeling of material behavior with neural networks.” J. Eng. Mech., 117(1), 132–153.
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.
Hagan, M. T., Demuth, H. B., and Beale, M. (1995). Neural network design, PWS, Boston.
Haykin, S. S. (1998). Neural networks: A comprehensive foundation, 2nd Ed., Prentice-Hall, Upper Saddle River, N.J.
He, X.,Moaveni, B., Conte, J. P., Elgamal, A., Masri, S. F., Caffrey, J. P., Wahbeh, M., Tasbihgoo, F., and Whang, D. H. (2005). “System identification of new Carquinez Bridge using ambient vibration data.” Proc., Conf. on Experimental Vibration Analysis for Civil Engineering Structures (EVACES’05), Bordeaux, France.
Heine, C. P. (2001). “Simulated response of degrading hysteretic joints with slack behavior.” Ph.D. dissertation, Virginia Polytechnic Institute and State Univ., Va.
Hornik, K., Stinchcombe, M., and White, H. (1989). “Multilayer feedforward networks are universal approximators.” Neural Networks, 2, 359–366.
Housner, G., Bergman, L., Caughey, T., Chassiakos, A., Claus, R., Masri, S., Skelton, R., Soong, T., Spencer, B., and Yao, J. P. (1997). “Structural control: Past, present, and future.” J. Eng. Mech., 123(9), 897–971.
Jeremic, B., Kunnath, S., and Xiong, F. (2004). “Influence of soil-foundation-structure interaction on seismic response of the i-880 viaduct.” Eng. Struct., 26, 391–402.
Kerschen, G., Worden, K., Vakakis, A. F., and Golinval, J.-C. (2006). “Past, present and future of nonlinear system identification in structural dynamics.” Mech. Syst. Signal Process., 20(3), 505–592.
Kosmatopoulos, E. B., Smyth, A. W., Masri, S. F., and Chassiakos, A. G. (2001). “Robust adaptive neural estimation of restoring forces in nonlinear structures.” J. Appl. Mech., 68, 880–893.
Kreyszig, E. (1993). Advanced engineering mathematics, 8th Ed., Wiley, New York.
Ljung, L. (1999). System identification theory for the user, 2nd Ed., Prentice-Hall, Upper Saddle River, N.J.
Lowes, L. N., Mitra, N., and Altoontash, A. (2004). “A beam-column joint model for simulating the earthquake response of reinforced concrete frames.” Rep. No. PEER 2003/10, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Masri, S. F., Caffrey, J. P., Caughey, T. K., Smyth, A. W., and Chassiakos, A. G. (2004). “Identification of the state equation in complex non-linear systems.” Int. J. Non-Linear Mech., 39, 1111–1127.
Masri, S. F., and Caughey, T. K. (1979). “A nonparametric identification technique for nonlinear dynamic problems.” J. Appl. Mech., 46, 433–447.
Masri, S. F., Nakamura, M., Chassiakos, A. G., and Caughey, T. K. (1996). “Neural network approach to detection of changes in structural parameters.” J. Eng. Mech., 122(4), 350–360.
Masri, S. F., Smyth, A. W., Chassiakos, A. G., Caughey, T. K., and Hunter, N. F. (2000). “Application of neural networks for detection of changes in nonlinear systems.” J. Eng. Mech., 126(7), 666–676.
Mazzoni, S., Fenves, G. L., and Smith, J. B. (2004). “Effects of local deformations on lateral response of bridge frames.” California Department of Transportation, ⟨http://www.dot.ca.gov/hq/esc/earthquake_engineering/Research/LOCAL_DEFORMATIONS_PAPER.pdf⟩.
Menegotto, M., and Pinto, P. (1973). “Method of analysis for cyclically loaded rc plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending.” Proc., Symp. Resistance and Ultimate Deformability of Struct. Acted on by Well-Defined Repeated Loads, IABSE Reports.
Narayanan, R. (1989). Structural connections: Stability and strength, Elsevier, New York.
NEES. (2007). “Issues and research needs in simulation development.” Workshop on Simulation Development Sponsored by the National Science Foundation through NEES Consortium, Inc., ⟨http://www.nehrp.gov/pdf/issues_research_2007.pdf⟩.
Nelles, O. (2000). Nonlinear system identification: From classical approaches to neural networks and fuzzy models, Springer, New York.
O’Donnell, K. J., and Crawley, E. F. (1985). “Identification of nonlinear system parameters in space structure joints using the force-state mapping technique.” Rep. No. SSL#16-85, MIT Space Systems Lab.
Ozcelik, O., Luco, J. E., and Conte, J. P. (2008). “Identification of the mechanical subsystem of the NEES-UCSD shake table by a least-squares approach.” J. Eng. Mech., 134(1), 23–34.
Ozdemir, H. (1976). “Nonlinear transient dynamic analysis of yielding structures.” Ph.D. thesis, Univ. of California, Berkeley, Calif.
Pei, J. S., and Mai, E. C. (2008). “Constructing multilayer feedforward neural networks to approximate nonlinear functions in engineering mechanics applications.” J. Appl. Mech., 75(6), 061002–1–8.
Pei, J. S., Mai, E. C., Wright, J. P., and Smyth, A. W. (2007). “Neural network initialization with prototypes—Function approximation in engineering mechanics application.” 2007 Int. Joint Conf. on Neural Networks (IJCNN2007), Orlando, Fla., IEEE.
Pei, J. S., and Piyawat, K. (2008). “Deterministic excitation forces for simulation and identification of nonlinear hysteretic sdofsystems.” J. Eng. Mech., 15(4), 471–504.
Pei, J. S., and Smyth, A. W. (2006a). “A new approach to design multilayer feedforward neural network architecture in modeling nonlinear restoring forces. I: Formulation.” J. Eng. Mech., 132(12), 1290–1300.
Pei, J. S., and Smyth, A. W. (2006b). “A new approach to design multilayer feedforward neural network architecture in modeling nonlinear restoring forces. II: Applications.” J. Eng. Mech., 132(12), 1301–1312.
Pei, J. S., Smyth, A. W., and Kosmatopoulos, E. B. (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. P., and Smyth, A. W. (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.
Piyawat, K. (2005). “Understanding nonlinear dynamic simulation using opensees.” MS thesis, Univ. of Oklahoma, Okla.
Priesley, M. J. N., Seible, F., and Calvi, G. M. (1996). Seismic design and retrofit of bridges, Wiley, New York.
Roddis, W. M. K. (2003). “Community workshop on computational simulation and visualization environment for the network for earthquake engineering simulation (nees).” NSF Directorate for Engineering CMS Division SSE, Arlington, Va., ⟨https://www.nees.org/images/uploads/2am/docs/NEESinc-SimVis-report.pdf⟩.
SAC. (2000). “Cyclic response of rbs moment connections: Loading sequence and lateral bracing effects.” Rep. No. SSR-99/13.
Sandberg, I. W., Lo, J. T., Fancourt, C. L., Principe, J. C., Katagiri, S., and Haykin, S. (2001). Nonlinear dynamical systems: Feedforward neural network perspectives, Wiley-Interscience, New York.
Scott, M. H., and Fenves, G. L. (2001). How to introduce a new material into OpenSees, version 1.1 Ed., PEER, Univ. of California, Berkeley, Calif.
Shames, I. H., and Cozzarelli, F. A. (1997). Elastic and inelastic stress analysis, Taylor and Francis, London.
Simeonov, V. K., Sivaselvan, M. V., and Reinhorn, A. M. (2000). “Nonlinear analysis of structural frame systems by the state-space approach.” Comput. Aided Civ. Infrastruct. Eng., 15(2), 76–89.
Sivaselvan, M. V., and Reinhorn, A. M. (2000). “Hysteretic models for deteriorating inelastic structures.” J. Eng. Mech., 126(6), 633–640.
Smyth, A. W., Kosmatopoulos, E. B., Masri, S. F., Chassiakos, A. G., and Caughey, T. K. (2002). “Development of adaptive modeling techniques for nonlinear hysteretic systems.” Int. J. Non-Linear Mech., 37, 1435–1451.
Sohn, H., Farrar, C. R., Hemez, F. M., Shunk, D. D., Stinemates, D. W., and Nadler, B. R. (2003). “A review of structural health monitoring literature: 1996–2001.” Rep. No. LA-13976-MS, Los Alamos National Laboratory, ⟨http://www.lanl.gov/damage_id/reports/LA_13976_MS_Final.pdf⟩.
Sohn, H., Worden, K., and Farrar, C. R. (2002). “Statistical damage classification under changing environmental and operational conditions.” J. Intell. Mater. Syst. Struct., 13(9), 561–574.
Spacone, E., Ciampi, V., and Filippou, F. C. (1992). “A beam element for seismic damage analysis.” Rep. No. UCB/EERC-92/07, Univ. of California, Berkeley, Calif.
Swanson Analysis Systems. (1992). ANSYS user’s manual, Swanson Analysis Systems, Houston.
Taucer, F. F., Spacone, E., and Filippou, F. C. (1991). “A fiber beam-column element for seismic response analysis of reinforced concrete structures.” Rep. No. UCB/EERC-91/17, Univ. of California, Berkeley, Calif.
Taylor, R. L., Filippou, F. C., Saritas, A., and Auricchio, F. (2003). “A mixed finite element method for beam and frame problems.” Comput. Mech., 31(1–2), 192–203.
Wen, Y. K. (1976). “Method of random vibration of hysteretic systems.” J. Eng. Mech., 102(2), 249–263.
Wen, Y. K. (1989). “Methods of random vibration for inelastic structures.” Appl. Mech. Rev., 42(2), 39–52.
Worden, K., and Tomlinson, G. R. (1988). “Developments in force state mapping for nonlinear systems.” Proc., 6th Int. Modal Analysis Conf., Society of Experimental Mechanics, Kissimmee, Fla., 1471–1479.
Wu, M., and Smyth, A. W. (2008). “Real-time parameter estimation for degrading and pinching hysteretic models.” Int. J. Non-Linear Mech., 43, 822–833.
Yang, J. N., and Lin, S. (2005). “Identification of parametric variations of structures based on least squares estimation and adaptive tracking technique.” J. Eng. Mech., 131(9), 290–298.
Yang, Y. S., Hsieh, S. H., Wang, K. J., Wang, S. J., Hsu, C. W., and Tsai, K. C. (2002). “Numerical analysis framework for distributed pseudo-dynamic tests.” 2nd Int. Conf. on Structural Stability and Dynamics.
Yang, Z., He, L., Bielak, J., Zhang, Y. A. E., and Conte, J. P. (2003). “Nonlinear seismic response of a bridge site subjected to spatially varying ground motion.” Proc., 16th ASCE Engineering Mechanics Conf., Univ. of Washington, Seattle.
Zhang, Y., Yang, Z., Bielak, J., Conte, J. P., and Elgamal, A. (2003). “Treatment of seismic input and boundary conditions in nonlinear seismic analysis of a bridge ground system.” 16th ASCE Engineering Mechanics Conf., Univ. of Washington, Seattle.
Zhou, L., Wu, S., and Yang, J. N. (2008). “Experimental study of an adaptive extended kalman filter for structural damage identification.” J. Infrastruct. Syst., 14(1), 42–51.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 11 • November 2009
Pages: 1213 - 1226
Copyright
© 2009 ASCE.
History
Received: Dec 19, 2005
Accepted: Jun 5, 2009
Published online: Oct 15, 2009
Published in print: Nov 2009
Notes
Note. Associate Editor: Lambros S. Katafygiotis
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