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Wishart random matrices in probabilistic structural mechanics / Sondipon Adhikari in Journal of engineering mechanics, Vol. 134 n°12 (Décembre 2008) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 134 n°12 (Décembre 2008) . - pp.1029–1044 Titre : Wishart random matrices in probabilistic structural mechanics Type de document : texte imprimé Auteurs : Sondipon Adhikari, Auteur Année de publication : 2009 Article en page(s) : pp.1029–1044 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Matrix  methods  Parameters  Estimation  Vibration  Structural  response Résumé : Uncertainties need to be taken into account for credible predictions of the dynamic response of complex structural systems in the high and medium frequency ranges of vibration. Such uncertainties should include uncertainties in the system parameters and those arising due to the modeling of a complex system. For most practical systems, the detailed and complete information regarding these two types of uncertainties is not available. In this paper, the Wishart random matrix model is proposed to quantify the total uncertainty in the mass, stiffness, and damping matrices when such detailed information regarding uncertainty is unavailable. Using two approaches, namely, (a) the maximum entropy approach; and (b) a matrix factorization approach, it is shown that the Wishart random matrix model is the simplest possible random matrix model for uncertainty quantification in discrete linear dynamical systems. Four possible approaches for identifying the parameters of the Wishart distribution are proposed and compared. It is shown that out of the four parameter choices, the best approach is when the mean of the inverse of the random matrices is same as the inverse of the mean of the corresponding matrix. A simple simulation algorithm is developed to implement the Wishart random matrix model in conjunction with the conventional finite-element method. The method is applied vibration of a cantilever plate with two different types of uncertainties across the frequency range. Statistics of dynamic responses obtained using the suggested Wishart random matrix model agree well with the results obtained from the direct Monte Carlo simulation. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282008%29134%3A12%281 [...] [article] Wishart random matrices in probabilistic structural mechanics [texte imprimé] / Sondipon Adhikari, Auteur . - 2009 . - pp.1029–1044. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 134 n°12 (Décembre 2008) . - pp.1029–1044 Mots-clés : Matrix  methods  Parameters  Estimation  Vibration  Structural  response Résumé : Uncertainties need to be taken into account for credible predictions of the dynamic response of complex structural systems in the high and medium frequency ranges of vibration. Such uncertainties should include uncertainties in the system parameters and those arising due to the modeling of a complex system. For most practical systems, the detailed and complete information regarding these two types of uncertainties is not available. In this paper, the Wishart random matrix model is proposed to quantify the total uncertainty in the mass, stiffness, and damping matrices when such detailed information regarding uncertainty is unavailable. Using two approaches, namely, (a) the maximum entropy approach; and (b) a matrix factorization approach, it is shown that the Wishart random matrix model is the simplest possible random matrix model for uncertainty quantification in discrete linear dynamical systems. Four possible approaches for identifying the parameters of the Wishart distribution are proposed and compared. It is shown that out of the four parameter choices, the best approach is when the mean of the inverse of the random matrices is same as the inverse of the mean of the corresponding matrix. A simple simulation algorithm is developed to implement the Wishart random matrix model in conjunction with the conventional finite-element method. The method is applied vibration of a cantilever plate with two different types of uncertainties across the frequency range. Statistics of dynamic responses obtained using the suggested Wishart random matrix model agree well with the results obtained from the direct Monte Carlo simulation. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282008%29134%3A12%281 [...]