Modified constitutive relation error for field identification: Theoretical and experimental assessments on fiber orientation identification in a composite material

Abstract

This study addresses the application of the modified Constitutive Relation Error to field identification problems in the framework of elastostatics. We show how relevant is the addition of a gradient-penalizing regularization term (in norm 1 or 2 ), and emphasize the role played by unreliable boundary conditions. This leads to the proposition of a method using two parameters, for which automatic determination is addressed. All theoretical assessments are illustrated on experimental data. The test-problem consists in the identification of the heterogeneous fiber-orientation in a woven fabric composite from a unique quasi-static tensile test with digital image correlation.

Fully automated model updating framework for damage detection based on the modified constitutive relation error

“…Without any additional a priori information, one can choose to calibrate α to ensure a correct a priori balance between measurement error and modeling error. This approach, which is close to the L-curve principle in terms of formulation, has been proposed in recent works [35,42] and provided relevant model updating results.…”

“…The relevance and robustness of the mCRE for model updating has been emphasized in many applications. Among other works, the mCRE was shown to be robust to highly noisy and corrupted measurements [31] and able to perform local defect detection [25,32,33], or full-field material identification from dense measurements [34,35]. It has recently been successfully applied to Earthquake Engineering problems, with an implementation in an industrial FE software [36,37].…”

“…Historically, in addition to the specific continuation scheme proposed in [34], several approaches related to regularization techniques were employed to define an optimal value of α. The influence of α was particularly investigated in [24,35,51,52], with empirical conclusions that an equivalent confidence between the CRE and data-to-model distance terms provided relevant model updating results. In other words, one should tend to calibrate α such that the two terms are of the same order of magnitude upon convergence.…”

“…Following the developments of [35], one could also imagine adding an explicit Tikhonov regularization term to the mCRE so as to favor some a priori knowledge on the parameter estimates that are sought. In particular, when it comes to detect localized damage, sparse regularization would allow to focus the model updating process to a reduced amount of parameters.…”

Merging experimental design and structural identification around the concept of modified Constitutive Relation Error in low-frequency dynamics for enhanced structural monitoring

“…The relevance and robustness of the mCRE for model updating have been emphasized in many applications. Among other works, let us mention local defect detection [46,54,55], full-field material identification from dense measurements [56,57], and model updating from low signal-to-noise ratio random measurements in dynamics [47]. As one can explicitly establish a link between mCRE, deterministic and stochastic functionals, it is also worth mentioning the comparative study between mCRE, Tikhonov-based, and Bayesian damage detection using optical fiber strain measurements performed in [39].…”