Development and application of computational intelligence approaches for the identification of complex nonlinear systems

Nonlinear Dynamics

Volumn 79, Issue 2, 2015, Pages 765-786

  Bolourchi, Ali ^a   Masri, Sami F ^a   Aldraihem, Osama J ^b  

^a University of Southern California   (United States)

^b KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Differential equation; Genetic programming; Nonlinear dynamical systems; Nonlinear optimization; System identification

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; GENETIC ALGORITHMS; GENETIC PROGRAMMING; IDENTIFICATION (CONTROL SYSTEMS); INTELLIGENT COMPUTING; MATHEMATICAL OPERATORS; NONLINEAR DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; NONLINEAR PROGRAMMING;

COMPLEX NONLINEAR SYSTEM; COMPUTER ALGEBRA TECHNIQUES; DEVELOPMENT AND APPLICATIONS; EVOLUTIONARY OPTIMIZATION METHOD; GOVERNING DIFFERENTIAL EQUATIONS; NON-LINEAR OPTIMIZATION; NON-PARAMETRIC TECHNIQUES; STOCHASTIC OPTIMIZATION METHODS;

COMPUTER SYSTEMS PROGRAMMING;

EID: 84925461375     PISSN: 0924090X     EISSN: 1573269X     Source Type: Journal    
DOI: 10.1007/s11071-014-1702-9     Document Type: Article

References (65)

1. Ibanez, P.: Identification of dynamic parameters of linear and non-linear structural models from experimental data. Nucl. Eng. Des. 25(1), 30–41 (1973)
2. Masri, S.F., Caughey, T.K.: A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46(2), 433–447 (1979)
3. Masri, S.F., Sassi, H., Caughey, T.K.: Nonparametric identification of nearly arbitrary nonlinear systems. J. Appl. Mech. 49(3), 619–628 (1982)
4. Marsi, S.F., Bekey, G.A., Sassi, H., Caughey, T.K.: Non-parametric identification of a class of non-linear multidegree dynamic systems. Earthq. Eng. Struct. Dyn. 10(1), 1–30 (1982)
5. Yun, H.B., Tasbighoo, F., Masri, S.F., Caffrey, J.P., Wolfe, R.W., Makris, N., Black, C.: Comparison of modeling approaches for full-scale nonlinear viscous dampers. J. Vib. Control 14(1–2), 51–76 (2008)
6. Yun, H.B., Masri, S.F., Wolfe, R.W., Benzoni, G.: Data-driven methodologies for change detection in large-scale nonlinear dampers with noisy measurements. J. Sound Vib. 322(1–2), 336–357 (2009)
7. Kim, C.H., Mijar, A.R., Arora, J.S.: Development of simplified models for design and optimization of automotive structures for crashworthiness. Struct. Multidiscip. Optim. 22(4), 307–321 (2001)
8. Allen, M.S., Sumali, H., Epp, D.S.: Piecewise-linear restoring force surfaces for semi-nonparametric identification of nonlinear systems. Nonlinear Dyn. 54(1–2), 123–135 (2008)
9. Crawley, E.F., Aubert, A.C.: Identification of nonlinear structural elements by force-state mapping. AIAA j. 24(1), 155–162 (1986)
10. Benedettini, F., Capecchi, D., Vestroni, F.: Identification of hysteretic oscillators under earthquake loading by nonparametric models. J. Eng. Mech. 121(5), 606–612 (1995)
11. Shin, K., Hammond, J.K.: Pseudo force-state mapping method: incorporation of the embedding and force-state mapping methods. J. Sound Vib. 211(5), 918–922 (1998)
12. Haroon, M., Douglas, E.A., Luk, Y.W., Ferri, A.A.: A time and frequency domain approach for identifying nonlinear mechanical system models in the absence of an input measurement. J. Sound Vib. 283(3–5), 1137–1155 (2005)
13. Ajjan Al-Hadid, M., Wright, J.R.: 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 (1989)
14. Box, G.: Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco (1970)
15. Leontaritis, I.J., Billings, S.A.: Input-output parametric models for non-linear systems. part i: deterministic non-linear systems. Int. J. Control 41(2), 303–328 (1985)
16. Leontaritis, I.J., Billings, S.A.: Input-output parametric models for non-linear systems. Part ii: stochastic non-linear systems. Int. J. Control 41(2), 329–344 (1985)
17. Haitao, L., Mita, A.: Damage indicator defined as the distance between arma models for structural health monitoring. Struct. Control Health Monit. 15(7), 992–1005 (2008)
18. Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.-C.: Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20(3), 505–592 (2006)
19. Saito, T., Beck, J.L.: Bayesian model selection for arx models and its application to structural health monitoring. Earthq. Eng. Struct. Dyn. 39(15), 1737–1759 (2010)
20. Masri, S.F., Chassiakos, A.G., Caughey, T.K.: Structure-unknown non-linear dynamic systems: identification through neural networks. Smart Mater. Struct. 1(1), 45–56 (1992)
21. Masri, S.F., Chassiakos, A.G., Caughey, T.K.: Identification of nonlinear dynamic systems using neural networks. Trans. ASME J. Appl. Mech. 60(1), 123–133 (1993)
22. Worden, K., Tomlinson, G.R.: Modeling and classification of non-linear systems using neural networks-i. simulation. Mech. Syst. Signal Process. 8(3), 319–356 (1994)
23. Worden, K., Tomlinson, G.R., Lim, W., Sauer, G.: Modeling and classification of non-linear systems using neural networks. ii. a preliminary experiment. Mech. Syst. Signal Process. 8(4), 395–419 (1994)
24. Chassiakos, A.G., Masri, S.F.: Modelling unknown structural systems through the use of neural networks. Earthq. Eng. Struct. Dyn. 25(2), 117–128 (1996)
25. Smyth, A.W., Masri, S.F., Chassiakos, A.G., Caughey, T.K.: On-line parametric identification of mdof nonlinear hysteretic systems. J. Eng. Mech. 125(2), 133–142 (1999)
26. Masri, S.F., Smyth, A.W., Chassiakos, A.G., Caughey, T.K., Hunter, N.F.: Application of neural networks for detection of changes in nonlinear systems. J. Eng. Mech. 126(7), 666–676 (2000)
27. Pei, J.S., Smyth, A.W.: New approach to designing multilayer feedforward neural network architecture for modeling nonlinear restoring forces. i: formulation. J. Eng. Mech. 132(12), 1290–1300 (2006)
28. Pei, J.S., Smyth, A.W.: New approach to designing multilayer feedforward neural network architecture for modeling nonlinear restoring forces ii: applications. J. Eng. Mech. 132(12), 1301–1312 (2006)
29. Darwin, C.: The Origin of Species by Means of Natural Selection or the Preservation of Favored Races in the Struggle for Life. Murray, London (1859)
30. Koza, J.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)
31. Tackett, W.A.: Genetic Programming for Feature Discovery and Image Discrimination. San Mateo, CA (1993)
32. Gruau, F.: Automatic definition of modular neural networks. Adapt. Behav. 3(2), 151–183 (1994)
33. Spector, L., Alpern, A.: Induction and Recapitulation of Deep Musical Structure. Montreal, Quebec (1995)
34. Handley, S.: Predicting Whether or Not a Nucleic Acid Sequence is an e. coli Promoter Region using Genetic Programming. Herndon, VA (1995)
35. Wong, M.L., Leung, K.S., Cheng, J.C.Y.: Discovering knowledge from noisy databases using genetic programming. J. Am. Soc. Inf. Sci. 51(9), 870–881 (2000)
36. Howard, D., Roberts,S.C.: The Prediction of Journey Times on Motorways using Genetic Programming, pp. 210–21. Berlin, Germany (2002)
37. Becker, Y., Fei, P., Lester, A.: Stock selection: an innovative application of genetic programming methodology. In: Riolo, R., Soule, T., Worzel, B. (eds.) Genetic Programming Theory and Practice IV, Genetic and Evolutionary Computation, pp. 315–334. Springer, US (2007)
38. Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324(5923), 81–85 (2009)
39. Hornby, G.S., Lohn, J.D., Linden, D.S.: Computer-automated evolution of an x-band antenna for nasa’s space technology 5 mission. Evolut. Comput. 19(1), 1–23 (2011)
40. Silva, S., Anunciação, O., Lotz, M.: A comparison of machine learning methods for the prediction of breast cancer. In: Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics, pp. 159–170. Springer, Berlin (2011)
41. Dracopoulos, D., Effraimidis, D.: Genetic programming for generalised helicopter hovering control. In: Genetic Programming, volume 7244 of Lecture Notes in Computer Science, pp. 25–36. Springer, Berlin (2012)
42. Fisher, R.A.: The Genetical Theory of Natural Selection. Diver, NY (1958)
43. Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence Through Simulated Evolution. Wiley, New York (1966)
44. Schwefel, H.P.: Kybernetische evolution als strategie der experimentellen forschung in der stromungstechnik (1973)
45. Rechenberg, I.: Evolutionsstrategie: Optimierung technischer systeme nach prinzipien der biologischen evolution. Frommann-Holzboog (1973)
46. Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)
47. Thierens, D., Goldberg, D.: Convergence Models of Genetic Algorithm Selection Schemes, pp. 119–29. Berlin, Germany (1994)
48. Fleming, P.J., Purshouse, R.C.: Evolutionary algorithms in control systems engineering: a survey. Control Eng. Pract. 10(11), 1223–1241 (2002)
49. Baker, J.E.: Reducing Bias and Inefficiency in the Selection Algorithm, pp. 14–21. Hillsdale, NJ (1987)
50. Goldberg, D.E., Deb, K.: A Comparative Analysis of Selection Schemes used in Genetic Algorithms, pp. 69–93. Foundations of genetic algorithms (1991)
51. Langdon, W.B., Poli, R.: Genetic programming bloat with dynamic fitness. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) The First European Workshop on Genetic Programming, volume 1391 of LNCS, pp. 96112. Springer, Paris (1998)
52. Banzhaf, W., Langdon, W.B.: Some considerations on the reason for bloat. Genet. Program. Evolvable Mach. 3(1), 81–91 (2002)
53. Silva, S., Costa, E.: Dynamic Limits for Bloat Control: Variations on Size and Depth. pp. 666–77. Berlin, Germany (2004)
54. Luke, S., Panait, L.: Lexicographic parsimony pressure. In: Langdon, W.B., et al. (eds.) GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 829–836. Morgan Kaufmann Publishers, New York (2002)
55. Gagne, C., Schoenauer, M., Parizeau, M., Tomassini, M.: Genetic Programming, Validation Sets, and Parsimony Pressure, pp. 109–20. Berlin, Germany (2006)
56. Masri, S.F., Caffrey, J.P., Caughey, T.K., Smyth, A.W., Chassiakos, A.G.: Identification of the state equation in complex non-linear systems. Int. J. Non-Linear Mech. 39(7), 1111–1127 (2004)
57. Baker, G.A., Graves-Morris, P.: Pade Approximations, 2nd edn. Cambridge University Press, Cambridge (1996)
58. Emmel, L., Kaber, S.M., Maday, Y.: Pade-jacobi filtering for spectral approximations of discontinuous solutions. Numer. Algorithms 33(1–4), 251–264 (2003)
59. Kaber, S.M., Maday, Y.: Analysis of some pade-chebyshev approximants. SIAM J. Numer. Anal. 43(1), 437–454 (2005)
60. Hesthaven, J.S., Kaber, S.M., Lurati, L.: Pade-legendre interpolants for gibbs reconstruction. J. Sci. Comput. 28(2–3), 337–359 (2006)
61. Foster, J., Richards, F.B.: The gibbs phenomenon for piecewise-linear approximation. Am. Math. Mon. 98(1), 47–49 (1991)
62. Driscoll, T.A., Fornberg, B.: A pade-based algorithm for overcoming the gibbs phenomenon. Numer. Algorithms 26(1), 77–92 (2001)
63. Shizgal, B.D., Jung, J.H.: Towards the resolution of the gibbs phenomena. J. Comput. Appl. Math. 161(1), 41–65 (2003)
64. Chantrasmi, T., Doostan, A., Iaccarino, G.: Pade-legendre approximants for uncertainty analysis with discontinuous response surfaces. J. Comput. Phys. 228(19), 7159–7180 (2009)
65. Lew, T.L., Spencer, A.B., Scarpa, F., Worden, K., Rutherford, A., Hemez, F.: Identification of response surface models using genetic programming. Mech. Syst. Signal Process. 20(8), 1819–1831 (2006)