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Parameter identification with sensitivity assessment and error computation
Author(s) -
Johansson H.,
Runesson K.,
Larsson F.
Publication year - 2007
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.200790026
Subject(s) - sensitivity (control systems) , discretization , computation , identification (biology) , mathematics , salient , mathematical optimization , transient (computer programming) , field (mathematics) , state space , calibration , computer science , algorithm , mathematical analysis , statistics , botany , electronic engineering , artificial intelligence , pure mathematics , engineering , biology , operating system
Abstract In this paper a particular framework for the parameter identification (calibration) of constitutive models is discussed. The framework involves the formulation of an optimization problem as the stationarity condition for a Lagrangian, whose arguments include an additional costate field in order to incorporate the state equation. This formulation has two distinct advantages: (1) The sensitivity of parameters with respect to uncertainties in the observed data can be assessed efficiently using a dual method, which compares favorably with the more conventional primal method, and (2) The errors arising from the FE discretization can be computed using the same dual method, which is an additional bonus. In fact, both the sensitivity and the discretization error can be estimated in an arbitrarily chosen “goal quantity” (or quantity of interest). Two numerical problems, one in terms of stationary groundwater flow (elliptic, in space) and another in terms of transient moisture diffusion in wood (parabolic, in space‐time) illustrate the salient features of the proposed algorithm(s). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)