Sensitivity of the virtual fields method to noisy data

Abstract

This paper deals with the application of the virtual fields method (VFM) to the identification of constants governing anisotropic constitutive equations. After a short recalling of the main features of the VFM, its sensitivity to noisy data is addressed. The study focuses on the random component of the noise which always adds to the actual fields in experimental full-field measurements. The uncertainty of the identified constants due to this random component is derived analytically. The obtained closedform expression is set as a criterion for grading virtual fields. The least sensitivity to noise leads to the best identification. The grading procedure is implemented directly in the VFM algorithm, providing systematically the virtual field which minimizes the sensitivity to random noises. Examples are provided for validating the approach with numerically simulated noisy data. Finally, the grading procedure is applied for adjusting the geometry which leads to an optimal use of the three-point bending test for identifying the elastic constants of a composite material. It shows that the criterion ''sensitivity to noise'' characterizes quantitatively the identifiability of one or several parameters. Future applications appear quite promising within the design of novel test methods for composites using the VFM.

Exploration of Saint-Venant’s Principle in Inertial High Strain Rate Testing of Materials

“…The virtual fields can be defined manually as described in [22]. However, this paper will make use of the special optimised virtual fields proposed in [41,42]. This is an automated procedure to define virtual fields minimizing the effect of noise on the identified parameters.…”

“…The bilinear elements ensure displacement continuity between elements, as needed for the principle of virtual work. More details can be found in [13,42].…”

“…As such, these parameters provide an indication of the quality of the identification. High values of these ratios indicate poor signal to noise ratios for the identification [42].…”

Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

“…Different techniques can be adopted, e.g. in recent applications of the VFM a procedure to automatically generate optimized virtual fields by a minimization of the sensitivity to noise was developed in Avril et al [56] and adapted to elasto-plasticity in Pierron et al [37]. In the present application noise is less of an issues than for elasticity, therefore the virtual fields have been manually defined, however other possibilities could be explored in the future.…”

A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

“…The key feature in any application of the VFM is the selection of the virtual fields. Several techniques based on different choices of virtual fields have been presented [9][10][11][12]. The common point of these techniques is the selection of the virtual fields as polynomials of spatial variables (either on the whole domain or in a piecewise form), and the material properties are considered as having single values (homogeneous) within the domain.…”