Parameter identification with sensitivity assessment and error computation. (English) Zbl 1158.93323
Summary: 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).
MSC:
| 93B30 | System identification |
| 93B35 | Sensitivity (robustness) |
| 65L09 | Numerical solution of inverse problems involving ordinary differential equations |
| 90C31 | Sensitivity, stability, parametric optimization |
| 49N15 | Duality theory (optimization) |
Keywords:
parameter identification; calibration; error estimation; sensitivity assessment; adjoint formulation; dual problemReferences:
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