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Set‐valued processes induced by parameterised stochastic differential equations with an application to Tuned Mass Dampers
Author(s) -
Schmelzer Bernhard,
Oberguggenberger Michael,
Adam Christoph
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110342
Subject(s) - stochastic differential equation , tuned mass damper , set (abstract data type) , damper , ordinary differential equation , representation (politics) , stochastic partial differential equation , differential (mechanical device) , stochastic process , differential equation , mathematics , continuous time stochastic process , mathematical optimization , control theory (sociology) , computer science , mathematical analysis , engineering , control engineering , control (management) , statistics , aerospace engineering , politics , artificial intelligence , law , political science , programming language
In this paper ordinary stochastic differential equations whose coefficients depend on uncertain parameters are considered. An approach is presented how to combine both types of uncertainty (stochastic excitation and parameter uncertainty) leading to set‐valued stochastic processes. The latter serve as a robust representation of solutions of the underlying stochastic differential equations. The mathematical concept is applied to a problem from earthquake engineering, where it is shown how the efficiency of Tuned Mass Dampers can be realistically assessed in the presence of uncertainty. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)