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Sensitivity and hessian matrix analysis of evolutionary PSD functions for nonstationary random seismic responses / Qimao Liu in Journal of engineering mechanics, Vol. 138 N° 6 (Juin 2012) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 138 N° 6 (Juin 2012) . - pp.716-720 Titre : Sensitivity and hessian matrix analysis of evolutionary PSD functions for nonstationary random seismic responses Type de document : texte imprimé Auteurs : Qimao Liu, Auteur Année de publication : 2012 Article en page(s) : pp.716-720 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Evolutionary  PSD  function  Sensitivity  Hessian  matrix  Nonstationary  random  seismic  response Résumé : This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000380 [article] Sensitivity and hessian matrix analysis of evolutionary PSD functions for nonstationary random seismic responses [texte imprimé] / Qimao Liu, Auteur . - 2012 . - pp.716-720. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 138 N° 6 (Juin 2012) . - pp.716-720 Mots-clés : Evolutionary  PSD  function  Sensitivity  Hessian  matrix  Nonstationary  random  seismic  response Résumé : This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000380