A digital image correlation-aided sampling moiré method for high-accurate in-plane displacement measurements
Introduction
Displacement monitoring is a key issue for structural health and infrastructure safety. For instance, the dynamic response can help to assess the structural health condition [1], while displacement can help to estimate the secure state of infrastructure [2]. To obtain accurate displacement data, non-contact measurement methods based on Global Navigation Satellite System (GNSS) [3], [4], Synthetic Aperture Radar (SAR) [5] and Laser Displacement Sensor (LDS) [6] are widely used. Both GNSS and LDS are real-time displacement sensors, giving mm-level and sub-millimeter displacement accuracy respectively. However, they are only suitable for point-by-point measurements. Moreover, they are less cost effective. SAR is often used for large areas and gives cm-level displacement while it is not real-time and complex to use.
On the other hand, vision-based measurement methods are real-time, low in cost and can be used for both static and dynamic displacement monitoring [7]. As a representative vision-based method, DIC is an inexpensive and easy-to-use technique for accurate displacement measurements by searching the reference subset in the deformed image, which has been widely used for displacement monitoring [8], [9], [10], [11]. The main procedure of DIC is the integer-pixel searching and sub-pixel registration. In the first step, the integer-pixel accuracy displacement is obtained by image correlation coefficient, and then the sub-pixel displacement can be deduced by iteration method such as Newton-Raphson method, Gauss-Newton method, and Levenberg-Marquardt [11]. However, the DIC require much computation cost and may lose accuracy near boundaries [12].
As another representative vision-based method, the sampling moiré method (SMM) proposed by Ri [12], has achieved significant progress in displacement and strain measurements in recent years [13], [14], [15], [16], [17], [18], [19], [20]. SMM is conducted by applying the sampling and interpolating the intensity of grating. The multiple phase-shift moiré fringes are then formed. High accuracy displacement measurements are realized by calculating the phase difference of moiré fringe. The accuracy of this method can achieve up to 1/1000 of the pitch (1/100 of the pixel) without complex computation [13], [21], [22], [23]. The measurement range widely distributes from nanometer to meter level by changing the layout and setting the pitch of grating [24], [25]. Moreover, SMM requires fewer pixels than other vision-based measurement methods to obtain in-plane displacements, with advantages of high accuracy, high speed and low cost.
For in-plane displacement measurement by SMM, the phase difference is calculated by picking-out the intensity of the grating. However, it is difficult to determine the phase difference when the displacement exceeds half of the pitch [17]. That is to say, it is difficult to determine the phase difference of exceeding the value π. As the phase distribution of moiré fringe is a periodic sawtooth function which is wrapped by (-ππ), computing the phase difference using the traditional method may cause an error that is integer multiple of 2π. Therefore, many applications only focus on small displacement corresponding to the pitch of grating when using SMM. The relatively large displacements of engineering structures such as tall buildings, bridges and slopes cannot be measured by the traditional SMM, which are usually greater than half of the grating pitch.
To adapt the SMM technique to large displacement situations, the integer-pixel DIC is used to estimate the phase shift value. The integer-pixel DIC can estimate the phase difference when the displacement exceeds half of one pitch. With the help of the integer-pixel DIC, the displacement measurement range of SMM is enlarged remarkably. On this basis, the interval between the camera shots can be prolonged without precision loss, which is essential for long-term displacement monitoring.
In this paper, we proposed a digital image correlation-aided sampling moiré method, i.e. an improved SMM, for high-accuracy in-plane displacement measurements. The basic principles of the improved SMM are illustrated in Section 2 for better understanding. A simulation is then conducted to analyse the relationship between the measurement accuracy and the environmental noise level. Thereafter, the technique for determining the optimal sampling pitch in the improved SMM is given in Section 3. Finally, field experiments that measure in-plane displacement at different measurement distances are conducted in 4 Short-range experiment, 4.2 Image processing with the improved SMM, 5 Long-range experiment to validate the efficiency of the improved SMM.
Section snippets
Digital image correlation-aided sampling moiré method
The principle of the proposed digital image correlation-aided sampling moiré method is introduced in detail in this section. With the aiding of the integer-pixel DIC to determine the phase shift value, the SMM can be used to accurately measure displacements, whether the displacement is greater than a half of grating pitch or not. The improved SMM overcomes previous limitation of SMM where the displacement needs to be lower than half of the grating pitch.
Simulation analysis of the improved SMM measurement accuracy
The displacement measurement accuracy is determined by many factors such as the grating pitch, the sampling pitch, the interpolation method applied, the form of the grating pattern and the noise level. The form of the grating pattern is usually rectangular for the purpose of convenience, and the 1st-order interpolation has proven to be efficient [21]. Therefore, the improved SMM measurement accuracy analyses focuses on factors including the noise level, the grating pitch, and the sampling pitch.
Short-range experiment
Laboratory experiments were conducted to assess the short-range displacement measurement accuracy of the improved SMM. The distance between the camera and the grating pattern is 7.0 m. The grating pattern is fixed on a three coordinate measuring machine (TCMM), and is accurately moved along the × and y-axes 14 times with distances of ± 0.05, ± 0.15, ± 0.25, ± 0.35, ± 0.45, ± 0.5, and ± 1.5 mm respectively by adjusting the final-motion screw of the TCMM.
Long-range experiment
The long-range displacement measurement experiments were conducted to validate the efficiency of the improved SMM in the field where ground vibration and light fluctuation cannot be isolated. The camera was placed at 60 m, 80 m, 100 m and 120 m away from the grating, respectively where the displacement of grating was controlled by gauge blocks.
Conclusions
In this paper, a novel displacement measurement method called the improved SMM is developed, which is based on SMM and improved by the integer-pixel DIC. This method can be applied to measure large displacements whose magnitude is greater than a half of one grating pitch. Experiments are then conducted in the laboratory. Contributions in this study are summarized as follows.
The computer simulations were applied to reveal the relationship between measurement accuracies and grating pitch,
CRediT authorship contribution statement
Chang-Fu Chen: Supervision, Methodology. Feng-Shan Mao: Software, Validation. Jia-Yong Yu: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study was supported by the National Key Research and Development Program of China (Grand no. 2016YFC0800207) and Changsha Science and Technology Project (Grand no. kq1907110). The authors would like to thank the anonymous reviewers for their helpful remarks.
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