motion effect in the images, which causes high error in estimation of displacement with DIC method. There is even one condition (exposure time 4000 ms, gain 0 dB and initial displacement applied to beam 13.2 mm) in which DIC method was not applicable and deceleration occurs due to high motion effect in the images. However, there are some irregularities that show other conditions like the brightness of the images or saturation in them can be important as well. For instance, for the test with exposure time of 1000 ms, gain of 0 dB and initial displacement applied to beam equal to 5.1 mm, the errors are expected to be lower than the same condition and initial displacement equal to 7.8 or 12.8. But as it can be seen in Fig. 3.6, even though peak spectrum error is increasing, NRMSE is declining. This can be due to change of the gain and therefore brightness of the images in different tests. 3.4 Deconvolution Analysis One method to estimate the displacement and motion effect in acquired images is to perform a deconvolution analysis [8]. Zappa et al. [9] used deconvolution method to determine the motion effect (w) and the net displacement (a) of an object in dynamic conditions. They proved that using this net displacement can be useful to track the motion of a rigid object in motion. In this section the beam is assumed as a rigid object and this method is used to estimate the motion of the beam. It is clear that the motion of the beam at different points of its length is different. Therefore, to calculate the vertical motion of the beam at each point, the length of the beam was divided to portions with 16 pixels width. The motion of each portion was considered equal to the displacement of its center. After estimating the displacement in each image, NRMSE for this method can be calculated as explained before in formula (3.2). Figure 3.7 shows the product of the exposure time and initial displacement of the point in front of the laser sensor, i.e. the stripe length, (left) and comparison of NRMSE for DIC and deconvolution method (right) for different conditions. For the tests in which the stripe length is high, the images are blurred, hence NRMSE of normal DIC is higher. Therefore, using deconvolution method can be useful to increase the accuracy of the estimated displacement, even if it does not allow estimating the strain field, while DIC also allows estimating it. 3.5 Deconvolution Analysis to Improve DIC Uncertainty It was proven in the previous chapters that DIC analysis is accurate for tests in which images are not blurred too much. However, when the shutter time is increased or the speed of the beam is higher, the motion effect reduces the accuracy of the results. Even in some cases, the blurring of the images is so high, that after applying sigma limit on the data, displacements of some points are removed because of low accuracy. Deconvolution method, explained in the previous chapter, has higher accuracy with respect to DIC, but it is useful for rigid objects, as it cannot calculate the strain on the surface of the objects. Thus, to improve the accuracy of DIC for a deformable object the deconvolution analysis to generate new reference images 0 0.05 0.1 0.15 0.2 0.25 0.3 NRMSE Test condition Ex [µs]: G [dB]: In. di. 3000 0 2.8 3000 0 5 3000 0 9.3 4000 0 13.2 4000 0 8.9 2000 0 14.4 2000 3 6.2 5000 0 7.1 1000 0 5.1 1000 6 7.8 1000 9 12.8 Decor. 0 2 4 6 8 10 12 14 16 Peak Spectrum Error [%] Test condition Ex [µs]: G [dB]: In. di. 3000 0 2.8 3000 0 5 3000 0 9.3 4000 0 13.2 4000 0 8.9 2000 0 14.4 2000 3 6.2 5000 0 7.1 1000 0 5.1 1000 6 7.8 1000 9 12.8 Decor. Fig. 3.6 NRMSE (left) and peak spectrum error (right) of DIC for different conditions (Ex ¼Exposure time [ms], G¼Sensor gain [dB], In. di. ¼Initial displacement applied to the beam [mm], Decor. ¼Decorrelation) 3 Uncertainty of Digital Image Correlation with Vibrating Deformable Targets 25
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