Structural Identification of Nonlinear Systems Subjected to Quasistatic Loading

  • A. Nappi
Part of the International Centre for Mechanical Sciences book series (CISM, volume 296)


During the last decade the mathematical methods developed within the context of System Identification [1–2] have been applied to the solution of ‘inverse problems’ in structural engineering. Most of the research activity in this field has primarily concerned dynamic systems, with the purpose of identifying, on the basis of experimental data, parameters hardly susceptible to be measured directly, such as damping characteristics and local stiffness [3–14]. In certain civil engineering situations, however, measurements have to be made in static conditions on systems which exhibit non-linear behaviour under external actions. An interesting example is provided by models concerned with the flexural behaviour of reinforced concrete beams under cyclic loading [15]. Another case is represented by the parameters related to the local strength of rock masses (e.g.: cohesion and friction angle). Such parameters are hardly measurable ‘in situ’ and sometimes may be estimated through nonlinear response measurements [16–17]. Indeed, the application of system identification to geotechnical problems seems to be very promising and parameter estimation techniques have been the object of remarkable research activity [16–22]. This is mainly due to the importance of ‘in situ’ measurements, which can often provide much more information about large rock masses than laboratory tests.


Nonlinear System Kalman Filter External Action Concrete Beam Linear Complementarity Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pister, K.S.,” Constitutive modelling and numerical solution of field problems”, Nucl. Eng. Design, 1974, 28, 137CrossRefGoogle Scholar
  2. 2.
    Eikhoff, P., System identification, John Wiley, Chichester, 1979Google Scholar
  3. 3.
    Ibanez, P., “Identificaion of dynamic parameters of linear and nonlinear structural models from experimental data”, Nucl. Eng. Design, 1972, 25, 30.CrossRefGoogle Scholar
  4. 4.
    Collins, J.D., Hart, G.C., Hasselmann, T.K., Kennedy B. “Statistical identification of structures”, AIAA J., 12, 1974, 185–190.CrossRefMATHGoogle Scholar
  5. 5.
    Beliveau, J.G., “Identification of viscous damping in structures from modal information”, J. Appl. Mech., 98, 2, 1976, 335–339.CrossRefGoogle Scholar
  6. 6.
    Goodwin, G.C., Payne, R.T., Dynamic system identification. Experiment design and data analysis, Academic Press, New York 1977.MATHGoogle Scholar
  7. 7.
    Hart, G.C., Torkamani, M.A.M., “Structural system identification”, in Stochastic problems in mechanics, Eds. Ariaratuam S.T., Leipholz M.M.E., Univ. of Waterloo Canada, 1977, 207–228.Google Scholar
  8. 8.
    Hart, G.C., Yao, J.T.P., “System identification in structural dynamics”, J. Eng. mech. Div., Proc. ASCE, 103, 6, 1977, 1089–1104.Google Scholar
  9. 9.
    Natke, H.G., “Die Korrectur des Rechnenmodelles eines Elastomechanischen systems mittels gemessener erzungener Schwingungen”, Ing. Arch., 46, 1977, 169.CrossRefMATHGoogle Scholar
  10. 10.
    Liu, S.C., Yao, J.T.P., “Structural identification concept”, J. Struct. Div., Proc. ASCE, 1978, 104, (12), 1845.Google Scholar
  11. 11.
    Fillod, R., Piranda, J., “Identification of eigensolution by Galerkin techniques”, 79-DET-35, Design Engineering Techn. Conference, ASME, 79-DET-75, 1979.Google Scholar
  12. 12.
    Isenberg, J., Collins, J.D., Kavarna, J., “Statistical estimations of geotechnical material model parameters from in situ test data”, Proc. ASCE Spec. Conf. on Probabilistic Mechanics and Structural Reliability, Tucson, 1979, 348–352.Google Scholar
  13. 13.
    Wedig, W., “Anwendung einer Spektralfiltertechnik zur Identifikation linearer und nichtlinearer Systeme”, Ing. Arcg., 1980, 49, 413.MATHGoogle Scholar
  14. 14.
    Yun, C.B., Shinozuka M., “Identification of non-linear structural dynamic systems”, J. Struct. Mech., 8, 2, 1980, 187–203.CrossRefGoogle Scholar
  15. 15.
    Stanton, J.F., McNiven, H.D., “The development of a mathematical model to predict the flexural reponse of reinforced concrete beams to cyclic loads, using system identification”, Rep. UCB/EERC-79/02, Univ of California, Berkeley, 1979.Google Scholar
  16. 16.
    Gioda, G., Maier, G., “Direct search solution of an inverse problem in elastoplasticity: Identification of cohesionm friction angle and ‘in situ’ stress by pressure tunnel tests”, Int. J. Num. Meth. Eng., 15, 1980, 1823–1848.CrossRefMATHGoogle Scholar
  17. 17.
    Jurina, L., Maier, G., Podolak, K., “On model identification problems in rock mechanics”, Proc. Int. Symp. on Geotechnics of Structurally Complex Foundations, Capri, Vol. 1, AGI 1977.Google Scholar
  18. 18.
    Asoako, A., Matsuo, M., “Bayesian approach to inverse problem in consolidation and its application to settlement prediction”, Proc. 3rd Int. Conf. on Numerical Methods in Geomechanics, Aachen 1979.Google Scholar
  19. 19.
    Tomizawa, M., “Identification of a one-dimensional model for a soil-layer system during an earthquake”, Earthq. Engng. Struct. Dynam., 8, 1980.Google Scholar
  20. 20.
    Gioda, G., Jurina, L., “Numerical identification of soil structure interaction pressure”, Int. J. Num. Analyt. Meth. Geomech., 5, 1981, 33–56.CrossRefMATHGoogle Scholar
  21. 21.
    Maier, G., Gioda, G., “Optimization methods for parametric identification of geotechnical systems”, in Numerical Methods in Geomechanics, Ed. J.B. Martins., Reidel, Dordrecht 1982.Google Scholar
  22. 22.
    Cividini, A., Jurina, L., Gioda, G., “Some aspects of ‘characterization’ problems in geomechanics”, Int. J. Rock Mech. Min. Sci., 18, 1981, 487–503.CrossRefGoogle Scholar
  23. 23.
    Maier, G., Nappi, A., Cividini, A., “Statistical identification of yield limits in piecewiselinear structural models”, In Proc. Int. Conf. on Computational Methods and Experimental Measurements, ISCME (Washington, D.C. July 1982 ) Eds. G.C. Keramidas, C.A. Brebbia, Springer, Berlin, 1982, 812–829.CrossRefGoogle Scholar
  24. 24.
    Bittanti S., Maier, G., Nappi, A., “Inverse problems in structural elastoplasticity: A Kalman filter approach”, in Plasticity Today: Modelling, Methods and Applications, Eds. A. Sawczuck, G. Bianchi, Elsevier A.S.P., Amsterdam, 1984.Google Scholar
  25. 25.
    Cividini, A., Maier, G., Nappi, A., “Parameter estimation of a static geotechnical model using a Bayes’ approach”, Int. J. Rock Mech. Mining Sci., 20, 1983, 215–226.CrossRefGoogle Scholar
  26. 26.
    Maier, G., Giannessi, F., Nappi, A., “Indirect identification of yield limits by mathematical programming”, Eng. Struct., 4, 1982, 86–89.CrossRefGoogle Scholar
  27. 27.
    Maier, G., “Inverse problem in engineering plasticity: a quadratic programming approach”, Atti Acc. Naz. dei Lincei, Cl, Sc. Apr. 1982.Google Scholar
  28. 28.
    Nappi, A., “System identification for yield limits and hardening moduli in discrete elastic-plastic structures by nonlinear programming”, Math. Modelling, 6, 1982, 441–448.CrossRefMATHGoogle Scholar
  29. 29.
    Nappi, A., “Identificazione indiretta dei limiti elastici e dei coefficienti di incrudimento in strutture elastoplastiche discrete”, Atti IX Convegno AIAS, Trieste, 1981.Google Scholar
  30. 30.
    Maier, G., “Mathematical programming methods in structural analysis”, in Variational methods in engineering, Eds. H. Tottenham, C. Brebbia, Southampton Univ., Press 1973.Google Scholar
  31. 31.
    Kunzi, F, Krelle, R., Nonlinear programming, Blaisdell Publ., 1967.Google Scholar
  32. 32.
    Maier, G., “A quadratic programming appoach for certain classes of non linear structural problems”, Meccanica, 2, 3, 1968, 121–130CrossRefGoogle Scholar
  33. 33.
    Lewis, T.O., Odell, P.L., Estimation in linear models, Prentice-Hall, Englewood Cliff, 1971.Google Scholar
  34. 34.
    Anderson, B.D.O., Moore, J.B., Optimal Filtering, Prentice-Hall, New York, 1979.MATHGoogle Scholar
  35. 35.
    Kalman, R.E.A., “A new approach to linear filtering and prediction problems”, Trans. ASME. J. Basic Engng., 82, 1960, 35–45.CrossRefGoogle Scholar
  36. 36.
    Kalman, R.E., Bucy, R.S., “New results in linear filtering and prediction theory”, Trans. ASME. J. Basic Engng. 83D 1961, 95–108.CrossRefMathSciNetGoogle Scholar
  37. 37.
    Gelb, A., (Ed.), Applied optimal estimation, MIT Press, Cambridge, Mass., 1974.Google Scholar

Copyright information

© Springer-Verlag Wien 1988

Authors and Affiliations

  • A. Nappi
    • 1
  1. 1.Politecnico di MilanoMilanItaly

Personalised recommendations