Numeric-analytic form of the adomian decomposition method for two-point boundary value problems in nonlinear mechanics / S. Ghosh in Journal of engineering mechanics, Vol. 133 N°10 (Octobre 2007)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 133 N°10 (Octobre 2007) . - pp. 1124-1133 Titre : Numeric-analytic form of the adomian decomposition method for two-point boundary value problems in nonlinear mechanics Type de document : texte imprimé Auteurs : S. Ghosh, Auteur ; D. Roy, Auteur Année de publication : 2007 Article en page(s) : pp. 1124-1133 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Decomposition Numerical analysis Algorithms Differential equations Résumé : A new numeric-analytic technique is developed for two-point nonlinear boundary-value problems (BVPs) of engineering interest. The analytic part of the method is based on a conventional Adomian decomposition method (ADM). However, given a discretization of the one-dimensional domain, the present algorithm applies the ADM, repetitively over successive intervals and exploits a shooting algorithm to solve the BVPs. Apart from a very high rate of convergence as the discretization is made finer, yet another significant advantage of the method is that it provides the solution in a piecewise functional form and one can finally arrive at a continuous form of the global solution. The procedure is used to study planar, large-deflection (Elastica) problem of a cantilever beam subjected to a transverse, concentrated load, at its free end. Moreover the elastoplastic behavior of a cantilever is also studied. Comparisons with exact solutions as well as with results via a few other competing algorithms demonstrate the remarkable accuracy of the proposed method. ISSN : 0733-9399 En ligne : http://cedb.asce.org/cgi/WWWdisplay.cgi?160819 [article] Numeric-analytic form of the adomian decomposition method for two-point boundary value problems in nonlinear mechanics [texte imprimé] / S. Ghosh, Auteur ; D. Roy, Auteur . - 2007 . - pp. 1124-1133. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 133 N°10 (Octobre 2007) . - pp. 1124-1133 Mots-clés : Decomposition Numerical analysis Algorithms Differential equations Résumé : A new numeric-analytic technique is developed for two-point nonlinear boundary-value problems (BVPs) of engineering interest. The analytic part of the method is based on a conventional Adomian decomposition method (ADM). However, given a discretization of the one-dimensional domain, the present algorithm applies the ADM, repetitively over successive intervals and exploits a shooting algorithm to solve the BVPs. Apart from a very high rate of convergence as the discretization is made finer, yet another significant advantage of the method is that it provides the solution in a piecewise functional form and one can finally arrive at a continuous form of the global solution. The procedure is used to study planar, large-deflection (Elastica) problem of a cantilever beam subjected to a transverse, concentrated load, at its free end. Moreover the elastoplastic behavior of a cantilever is also studied. Comparisons with exact solutions as well as with results via a few other competing algorithms demonstrate the remarkable accuracy of the proposed method. ISSN : 0733-9399 En ligne : http://cedb.asce.org/cgi/WWWdisplay.cgi?160819

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Two-stage extended kalman filters with derivative-free local linearizations / Nilanjan Saha in Journal of engineering mechanics, Vol. 137 N° 8 (Août 2011)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 137 N° 8 (Août 2011) . - pp.537546 Titre : Two-stage extended kalman filters with derivative-free local linearizations Type de document : texte imprimé Auteurs : Nilanjan Saha, Auteur ; D. Roy, Auteur Année de publication : 2011 Article en page(s) : pp.537546 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Two-stage filter Extended Kalman filters Model uncertainty Derivative-free local linearizations Parameter estimations Résumé : This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.org/emo/resource/1/jenmdt/v137/i8/p537_s1?isAuthorized=no [article] Two-stage extended kalman filters with derivative-free local linearizations [texte imprimé] / Nilanjan Saha, Auteur ; D. Roy, Auteur . - 2011 . - pp.537546. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 137 N° 8 (Août 2011) . - pp.537546 Mots-clés : Two-stage filter Extended Kalman filters Model uncertainty Derivative-free local linearizations Parameter estimations Résumé : This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.org/emo/resource/1/jenmdt/v137/i8/p537_s1?isAuthorized=no

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Variance - reduced particle filters for structural system identification problems / S. Roy Chowdhury in Journal of engineering mechanics, Vol. 139 N° 2 (Février 2013)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.210–218. Titre : Variance - reduced particle filters for structural system identification problems Type de document : texte imprimé Auteurs : S. Roy Chowdhury, Auteur ; D. Roy, Auteur ; R. M. Vasu, Auteur Année de publication : 2013 Article en page(s) : pp.210–218. Note générale : Applied mechanics Langues : Anglais (eng) Mots-clés : Directed bootstrap filter Gain-based direction Quasi-Newton Quasi-Monte Carlo simulations Structural system identification Résumé : A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000480 [article] Variance - reduced particle filters for structural system identification problems [texte imprimé] / S. Roy Chowdhury, Auteur ; D. Roy, Auteur ; R. M. Vasu, Auteur . - 2013 . - pp.210–218. Applied mechanics Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.210–218. Mots-clés : Directed bootstrap filter Gain-based direction Quasi-Newton Quasi-Monte Carlo simulations Structural system identification Résumé : A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000480

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