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Towards Criteria Characterizing the Metrological Performance of Full-field Measurement Techniques

Application to the Comparison Between Local and Global Versions of DIC

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Abstract

Users of full-field measurement methods like Digital Image Correlation (DIC) often aim to perform measurements with the best trade-off between spatial resolution, bias and measurement resolution. Whenever two full-field methods are compared, it is essential that these criteria are taken into consideration. Recently a metrological efficiency indicator for full-field measurements has been proposed and discussed. This indicator combines measurement resolution and spatial resolution. It has been shown to be invariant to the subset size in the case of Local DIC. The goal of this article is to discuss a method, which determines both the spatial and the measurement resolutions for a given bias for two different DIC methods, in order to obtain the metrological efficiency indicator for each of these methods. The benefit of this indicator is that it does not depend on setting parameters such as the subset size, which are chosen by the user. As such, it can be considered as intrinsic to each technique, thus enabling fair comparison. Local DIC and triangular finite element based Global DIC will be the subject of this investigation. With this setting, their respective subset and triangular element sizes will be related to the spatial resolution of both methods for a given acceptable bias. By using the metrological efficiency indicator, the performance of the two methods will be compared and discussed to a new level of detail. Generally speaking, the indicator shows that the metrological performance of both methods is similar, confirming their popularity. However, it will be shown that, depending on the choice of what an acceptable bias is, one of the method may be preferred to another. The results show that for the specific DIC versions used in the study, for cases for which a significant bias is acceptable, Local DIC outperforms Global DIC, while the opposite is true in the case for which the bias requirements are more stringent. Finally, the quadratic versions of both DIC versions are shown to significantly outperform their respective linear versions.

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Acknowledgements

The authors are grateful to the French National Research Agency (ANR) for their financial support (ICAReS project, N∘ANR-18-CE08-0028-01).

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Authors and Affiliations

  1. CNRS, SIGMA Clermont, Institut Pascal, Université Clermont Auvergne, F-63000, Clermont-Ferrand, France

    B. Blaysat & M. Grédiac

  2. LMT (ENS Paris-Saclay/CNRS/Université Paris-Saclay), 94235, Cachan, France

    J. Neggers

  3. Laboratoire Lorrain de Recherche en Informatique et ses Applications, UMR CNRS 7503, Université de Lorraine, CNRS, INRIA, Campus Scientifique, BP 239, 54506, Vandoeuvre-lès-Nancy Cedex, France

    F. Sur

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Appendix: Appendix: Vocabulary and definitions

Appendix: Appendix: Vocabulary and definitions

Three metrological parameters are discussed in this paper, namely the measurement resolution, the bias and the spatial resolution. Their definition, already given in [17, 69] , are recalled below for the sake of complitness:

  • Measurement resolution: in Ref. [70], the measurement resolution is defined by the smallest change in a quantity being measured that causes a perceptible change in the corresponding indication. More precisely, it is proposed in [71] to define it as the change in quantity being measured that causes a change in the corresponding indication greater than one standard deviation of the measurement noise, which enables us to quantify the measurement resolution. This definition is quite arbitrary, any other (reasonable) multiple of the standard deviation being also potentially acceptable, but the idea is that the resolution quantifies the smallest change not likely to be caused by measurement noise [71].

  • Spatial resolution: the spatial resolution denoted by ℓλ is defined here by the lowest period of a sinusoidal deformation that the technique is able to reproduce before losing a certain percentage λ of amplitude, this quantity being chosen a priori [25]. The advantage of this definition is that it is not based on an arbitrary value for the subset size in Local DIC or for the elements size in Global DIC. This makes it possible to compare the spatial resolution between these two techniques.

  • Bias: a systematic error generally occurs when a given technique returns actual details in displacement and strain maps. It is due to the fact that the amplitude of such apparent details is generally lower than the amplitude of the actual detail. This apparent “damping” is a bias, which can be quantified by considering a sinusoidal reference displacement field, and measuring the relative loss of amplitude exhibited by the displacement field returned by the technique under study, as suggested in Refs. [25, 44, 72, 73]. Of course, the loss of amplitude depends on the frequency f of the sine function. This loss of amplitude is denoted here by l(f). In this context, the spatial resolution defined above is defined for a given bias λ, the relation between ℓλ and λ being that ℓλ is the smallest value such that l(1/ℓλ) = λ. We call here λ the bias of the method. This is a slight abuse of language since fixing λ does not mean that the damping of any displacement or strain field is actually equal to this λ value. Note finally that for DIC, the effect quantified here by λ is often referred to as the “matching bias”, because it occurs when there is a mismatch between the matching function used to describe the displacement within subsets on the one hand, and the degree of the actual displacement if the latter is described by a polynomial on the other hand.

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Blaysat, B., Neggers, J., Grédiac, M. et al. Towards Criteria Characterizing the Metrological Performance of Full-field Measurement Techniques. Exp Mech 60, 393–407 (2020). https://doi.org/10.1007/s11340-019-00566-4

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