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It has been shown that the relation errors of classical FD solutions are far larger than those of reduced-order solutions obtained from the POD-based reduced-order FD extrapolating model.
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The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields.
From the grow trends of relation errors of the classical FD solutions, in the classical FD scheme with fully second-order accuracy will appear no convergence after some computing steps, while the error accumulation of the POD-based reduced-order FD extrapolating model is very slow such that it can continuously simulate the development of the fluid flow.
The constitutive relation error updating method is used for the identification of the location and the size of multi-cracks in a simply supported beam.
The updating technique used in this paper is based on recent works dealing with the constitutive relation error (CRE) method applied to acoustics.
In that framework, this paper proposes a new updating technique for acoustic simulations, which is based on the constitutive relation error (CRE) proposed by Ladevèze in structural dynamics.
Secondly, we look at the relations between the relative error (RE) and sparsity.
The relation of error rate to low detection probability is mathematically mapped to the constraint of mean squared power, as explained in [2].
Yet, a fundamental difference which may pose an important challenge to formal accumulation models is the relation between error rates and response times.
The validation process we propose is based on the mechanical concept of Constitutive Relation Error (CRE) and aims at reducing the Lack Of Knowledge (LOK) attached to both the excitation forces and the parameters of the numerical model.
Among the indirect or parametric methods available, one is based on the "mechanical" concept of constitutive relation error estimator introduced in order to quantify the quality of finite element analyses.
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