Research on a New Power Window Weighted Digital Image Correlation for Accurate Measurement

Abstract

Background

Digital Image Correlation (DIC) is a widely employed full-field measurement technique in the realm of experimental mechanics. Nevertheless, mitigating measurement errors, particularly in fields with large strain gradients, remains a challenge.

Objective

The Gaussian window is employed to weight the correlation criterion in order to enhance measurement accuracy, and this method is called Gaussian window weighted DIC (GW-DIC). However, the optimization of the weighted correlation criterion does not guarantee that the displacement vector iterates to its optimal solution as the Gaussian window parameter changes during the iteration.

Methods

A new power window and the power window weighted DIC (PW-DIC) are proposed. The parameters of this power window keep constant during the iteration, and can be selected by given self-adaptive strategy for accuracy or preset according to the presumed deformation of the region of interest (ROI) for efficiency.

Results

The calculation example of synthetic images with imposed homogeneous deformation indicates that, the proposed power window is more effective than the Gaussian window when weighting the correlation criterion. For multi-directional deformation fields, both the displacement and strain accuracy of PW-DIC with self-adaptive parameters are at least 18% superior to those of conventional DIC. The tensile experimental dataset indicates that PW-DIC is more accurate and stable than GW-DIC.

Conclusions

PW-DIC with self-adaptive parameters is better suited for strain measurement in fields with large strain gradients. The weighted correlation criterion with preset parameters can potentially serve as a substitute for conventional correlation criterion.

Appendix. Establishment of the self-adaptive Selection Strategy for Parameters

As the displacement system error increases, it indicates a greater strain gradient within the subset, thereby necessitating a smaller power window parameter. Hence, there is an inverse relationship between the displacement system error and the parameter. In order to reduce the computational burden, a straightforward piecewise function is assumed to describe the relationship between the displacement system error and the power window parameter, as shown in Fig. 17, taking D₁ as an example. The range of the power window parameter is [2, 20]. Then the displacement systematic errors corresponding to the limits of parameters need to be determined, as denoted by e₁ and e₂ in Fig. 17.

The typical displacement error of the DIC method is 0.01 pixels, as stated in reference [26]. Based on this magnitude of displacement systematic error, several sets of candidate values of e₁ and e₂ are designed. The final values of e₁ and e₂ are determined according to the displacement results on Sample14 and rotated Sample14 image sets, chosen because exact errors can be obtained from them. The RMSE of results for different image sets and various subset sizes is used to assess each candidate set of e₁ and e₂. The error comparison of different candidate sets of e₁ and e₂ are shown in Table 6. It is seen that, RMSE is the smallest when e₁ = 0.01 and e₂ = 0.005. Then the piecewise function takes the form of equation (15).

Table 6 The error comparison of different candidate sets of e₁ and e₂

Fig. 17

The assumed relationship between D₁ and |ErrU|