Displacement Measurement Error Research Articles

A Novel Demodulation Algorithm for Micro-Displacement Measurement Based on FMCW Sinusoidal Modulation

Frequency-modulated continuous wave (FMCW) interferometry, an emerging laser interferometry technology, can be applied in the field of fibre-optic sensing to achieve high-precision micro-displacement measurements. To address nonlinearity issues in laser frequency modulation and localisation deviations of feature points in traditional algorithms, this paper proposes a demodulation algorithm suitable for sinusoidal frequency modulation schemes, incorporating the principle of orthogonal phase-locked amplification. The algorithm includes signal preprocessing, phase-locked amplification, error correction, and phase calculation. Experimental results show that the system achieves a measurement error standard deviation of 3.23 nanometres for static targets. The displacement measurement error at 100 μm is 0.057% F.S., and the linearity between the measured values and the actual displacement values is 0.99997. Compared with conventional methods, the approach introduced in this paper eliminates the need for separate nonlinear corrections of the current-to-optical frequency relationship and minimises the issue of feature point localization deviations, showing significant potential for practical applications.

Drifted Uncertainty Evaluation of a Compact Machine Tool Spindle Error Measurement System

The accurate measurement of spindle errors, especially quasi-static errors, is one of the key issues for the analysis and compensation of machine tool thermal errors in machining accuracy. To quantitatively analyze the influence of the measurement system’s own drift on the measurement results, a drifted uncertainty evaluation method of the precision instrument considering the time drift coefficient is proposed. This study also produced a high-precision compact spindle error measurement device (with a displacement measurement error of less than ±1.33 μm and an angular measurement error of less than ±1.42 arcsecs) as the research object to verify the proposed drift uncertainty evaluation method. A method for evaluating the drift uncertainty of the measurement system is proposed to quantitatively evaluate the system error and drift uncertainty of the measurement device. Experiments show that the drift uncertainty evaluation method proposed in this paper is more suitable for evaluating the uncertainty changes in measurement instruments during long-term measurements compared to traditional methods.

Research on Full-Field Dynamic Deflection Measurement of Beams Based on Dense Feature Matching and Mismatch Removal Method

To solve the problems of measurement errors led by mismatches of dense feature matching in machine vision structural deflection measurement, this paper proposes a dense feature extraction, matching, and dual-step mismatch-removal-based full-field structural dynamic deflection measurement method. First, the of dense feature detection and matching theory is introduced to extract the SIFT feature points on a structural surface in an image sequence and matched by FLANN to trace the structure movement, and the mechanisms and causes of mismatches are analyzed. Then, a dual-step mismatch removal method combining RANSAC and Structural Displacement Continuity Restriction (SDCR) is introduced to achieve full-field dynamic beam deflection measurement. The proposed method is validated through indoor cantilever beam experiments, and results show that the method can effectively eliminate a large number of SIFT feature mismatches (accounting for approximately 55% of the total matched feature points). The full-field dynamic displacement field of the beam can be measured with the correctly matched dense feature points by converting dense feature point displacements into continuous and uniform spatiotemporal deflections of the structure. A comparison with the GOM Correlate Professional DIC measurement system was conducted, and the maximum measurement error of the cantilever beam dynamic displacement of the proposed method is between 0.024 and 0.053 mm, the root mean squared error of displacement is approximately 0.01 mm, and the correlation coefficient between two deflection–time curves reaches 0.9964. The proposed algorithm is proven to be effective in full-field displacement measurement and has great potential in future structural health monitoring of bridges.

Accurate monitoring of coal pillar deformation based on distributed optical fiber

In many structural deformation monitoring applications, determination of the response length of embedded optical fibers is difficult due to the use of strain integration method, which increases the measurement errors. For systematic investigation of the deformation law of coal pillars under mining action, distributed fiber optic technology was used herein to analyze its response length. This study discusses how non-uniform strain distribution can increase the accuracy error of fiber optic displacement measurement, and verifies the effectiveness of theoretical analysis by using coupled FEM–DEM numerical simulation method. Furthermore, the relationship between the Brillouin gain spectrum characteristics of different sampling points and the non-uniformity of strain distribution was explained. To reduce accuracy errors, a new method was proposed herein for determining the response length of optical fibers. The feasibility of this method was verified through indoor experiments. Next, this method was applied to the deformation monitoring of coal pillars in a section of Huojitu Well. By using the proposed method, the deformation of coal pillars can be accurately monitored.

Displacement measurement error of grating interferometer based on vector diffraction theory

Displacement measurement error of grating interferometer based on vector diffraction theory

Error Correction Method of Platform Displacement for Large Load Static Test

The test platform is an indispensable supporting bearing structure in static tests, which is mainly used to fix test products, simulate the real loading boundary, and provide better operation space for measurement. With the large-scale and complicated spacecraft structure, the static test platform tends to be large-scale, and the displacement measurement error of the static test platform under large load conditions cannot be ignored. The conventional error correction method only uses the displacement value of the monitoring point at the corresponding position of the platform to compensate, ignoring the comprehensive influence of the six degrees of freedom displacement for the test platform on the displacement measurement of the specimen. When it is used for the error correction of the static test of large spacecraft structures, there is a large measurement error affected by the structural size. In view of this, according to the static test requirements of a large spacecraft, a large bearing static test platform with a lateral load of 22 T and a longitudinal load of 52 T is designed, and a displacement measurement error correction method based on six degrees of freedom is proposed. Through the static test of a large spacecraft structure, the method can effectively reduce the displacement measurement error caused by the displacement of the test platform, and the error correction rate can reach 20%.

A Feasibility Study on Extension of Measurement Distance in Vision Sensor Using Super-Resolution for Dynamic Response Measurement.

The current civil infrastructure conditions can be assessed through the measurement of displacement using conventional contact-type sensors. To address the disadvantages of traditional sensors, vision-based sensor measurement systems have been derived in numerous studies and proven as an alternative to traditional sensors. Despite the benefits of the vision sensor, it is well known that the accuracy of the vision-based displacement measurement is largely dependent on the camera extrinsic or intrinsic parameters. In this study, the feasibility study of a deep learning-based single image super-resolution (SISR) technique in a vision-based sensor system is conducted to alleviate the low spatial resolution of image frames at long measurement distance ranges. Additionally, its robustness is evaluated using shaking table tests. As a result, it is confirmed that the SISR can reconstruct definite images of natural targets resulting in an extension of the measurement distance range. Additionally, it is determined that the SISR mitigates displacement measurement error in the vision sensor-based measurement system. Based on this fundamental study of SISR in the feature point-based measurement system, further analysis such as modal analysis, damage detection, and so forth should be continued in order to explore the functionality of SR images by applying low-resolution displacement measurement footage.

Polarized light vision pose measurement method by fusing the constraints provided between control points for hand-eye calibration

The accuracy of hand-eye calibration is determined by the pose measurement accuracy of the calibration target. In the hand-eye calibration of industrial robots, the pose measurement can be performed based on the polarization information to filter out high-brightness areas of the image, optimize image processing, and increase effective control points. However, it is hard to decide on an adequate polarization angle. An inadequate polarization angle will affect the image contrast and ultimately affect the extraction accuracy of the 2D projections of the control points. In addition, the existing non-iterative pose measurement methods only consider the constraints provided by the single control points. The constraints provided between the control points are not in consideration. This results in reduced pose measurement accuracy in noisy environments. Aiming at the above problems, a polarized light vision pose measurement method by fusing the constraints provided between control points for hand-eye calibration is proposed: the adequate polarization angle was determined based on the cross-ratio invariance, and the target image collected under the adequate polarization angle was used for subsequent pose measurement to reduce the high-brightness areas on the premise of ensuring the image contrast. We introduced the plane created by two control points and the optical center to represent the constraints provided between these two control points. In this way, the constraints provided by any two control points can be fused with the constraints provided by the single control points to solve the pose non-iteratively. Compared to other current methods, there are more significant increases in our method's pose measurement accuracy and stability. The experimental results show that the angle measurement error is less than 0.052° over the measuring range of -60°-+60°, and the displacement measurement error is less than 0.01 mm over the measuring range of 0-20 mm.

Accumulated Error Reduction of Linear Motor Mover Position Measurement Based on SKLM

Cumulative measurement error is the most critical factor affecting the accuracy of long-stroke displacement measurement. Based on the one-dimensional image gradient method and Smooth Kalman filter algorithm (SKLM), this paper proposes a long-stroke linear motor displacement cumulative error reduction and high precision measurement methods. First, according to the motion characteristics of the linear motor and the principle of image measurement, a one-dimensional speckle target image is generated, and the one-dimensional Barron gradient algorithm is used to calculate the displacement of adjacent frames quickly. Second, according to the rea-sons for the accumulated error of long-stroke displacement measurement, the smooth Kalman algorithm for optimized autoregressive data processing is introduced to optimally estimate the measured displacement of adjacent frames to realize the reduction of accumulated error. To improve the robustness of the measurement system, a wavelet soft threshold image filter is introduced to per-form noise reduction and restoration processing on the collected signal, and further realize the high-precision dis-placement measurement of the long-stroke linear motor. Simulations and experiments show that the method in this paper not only improves the measurement accuracy of adjacent frames, but also reduces the cumulative error of long-stroke displacement measurement. And under different working conditions, compared with other methods, it has higher accuracy and anti-interference.

A high-sensitivity rotatable 3D displacement sensor

Aiming at the problems of low sensitivity and low accuracy caused by the displacement transfer mechanism of three displacement sensors used simultaneously in the 3D displacement monitoring of seismic isolation bearings, the paper has proposed a high-sensitivity rotatable 3D displacement sensor. The sensor adds through holes on the surface of the equal-strength cantilever beam to form a cross beam, which increases the bending strain on the beam surface to improve the sensitivity. By adding a gyroscope and a mechanical rotation structure, a single sensor can measure the 3D displacement at the same time, reducing the adverse effects displacement transmission mechanism on the accuracy of the measurement. ANSYS software was used to simulate and optimize the parameters of the size of through-hole of the sensor beam to determine the appropriate size and location of the through-hole. Finally, the sensor was developed and its static characteristics and displacement measurement performance in static and dynamic 3D space were tested based on the simulation results. The test results have shown that the sensor has a sensitivity of 16.29 mV/mm and an accuracy of 0.9% in the range of 0–160 mm. Its static and dynamic 3D spatial displacement measurement errors are less than 2 mm, which can meet the accuracy requirements of 3D displacement measurement and sensitivity for structural health monitoring of seismic isolation bearings.

Real-time profile measurement method for a large-scale satellite antenna.

To improve the detection capability of satellite-based synthetic aperture radar, a large antenna array with a length scale of 100 meters is urgently needed. However, the structural deformation of the large antenna leads to phase errors, which will significantly reduce the antenna gain; hence, real-time and high-precision profile measurements of the antenna are essential for active compensation of the phase and thus improving the antenna gain. Nevertheless, the conditions of antenna in-orbit measurements are rather severe because of limited installation locations of measurement instruments, large areas, and long distance to be measured, and unstable measurement environments. To deal with the issues, we propose a three-dimensional displacement measurement method for the antenna plate based on laser distance measuring and digital image correlation (DIC). The proposed method uses the DIC method to retrieve the in-plane displacement information in combination with a laser range finder to provide depth information. A Scheimpflug camera is used to overcome the limitation of the depth of field of traditional cameras and enable clear imaging of the full field. Moreover, a vibration compensation scheme is proposed to eliminate the measurement error of the target displacement caused by the random vibration (within 0.01°) of the camera support rod. The results of the experiment in a laboratory setting show that the proposed method can effectively eliminate the measurement error caused by camera vibration (50mm) and reduce the displacement measurement error to within 1mm with a measurement range of 60m, which can meet the measurement requirements of next-generation large satellite antennas.

A Mitigation Method for Optical-Turbulence-Induced Errors and Optimal Target Design in Vision-Based Displacement Measurement.

Computer vision-based displacement measurement techniques are increasingly used for structural health monitoring. However, the vision sensors employed are easily affected by optical turbulence when capturing images of the structure, resulting in displacement measurement errors that significantly reduce the accuracy required in engineering applications. Hence, this paper develops a multi-measurement point method to address this problem by mitigating optical-turbulence errors with spatial randomness. Then, the effectiveness of the proposed method in mitigating optical-turbulence errors is verified by static target experiments, in which the RMSE correction rate can reach up to 82%. Meanwhile, the effects of target size and the number of measurement points on the proposed method are evaluated, and the optimal target design criteria are proposed to improve our method's performance in mitigating optical-turbulence errors under different measurement conditions. Additionally, extensive dynamic target experiments reveal that the proposed method achieves an RMSE correction rate of 69% after mitigating the optical-turbulence error. The experimental results demonstrate that the proposed method improves the visual displacement measurement accuracy and retains the detailed information of the displacement measurement results.

Compact chromatic confocal sensor for displacement and thickness measurements

Chromatic confocal sensors are widely used in various precision measurement fields because of their high measurement accuracy, fast response speed, and good stability. Unlike traditional fiber-coupled structures, we propose an integrated compact chromatic confocal sensing system that can overcome the device-integrating constraints met in industrial environments. Aiming at the distortion of the peak waveform caused by the inconsistent spectral response of the system and to accurately extract the peak wavelength, a spectral characteristic compensation algorithm and a peak wavelength extraction method based on Gaussian curve fitting are proposed. Based on these methods, a segmented curve calibration algorithm is applied to achieve accurate mapping between peak wavelength and position. For the thickness measurement of transparent objects, a simple thickness measurement model and its calibration procedure are proposed, which do not need to obtain previous parameters, such as incident angle or refractive index. Finally, the performance of the proposed sensing system is tested by displacement measurement and thickness measurement experiments. The experimental results show that the root mean square error (RMSE) of displacement measurement is less than 0.1 μm, and the RMSE of thickness measurement is less than 1 μm, which verifies the effectiveness and feasibility of the proposed sensing system.

Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements, and among such technology are laser and vision-based displacement measuring modules (LVDMMs). The displacement transformation coefficient (DTC) of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process, and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view (FFOV). To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands, a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV. First, an image coordinate system, a pixel measurement coordinate system, and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM. In addition, marker spots in the FFOV are selected, and the DTCs at the marker spots are obtained from calibration experiments. Also, a fitting method based on locally weighted scatterplot smoothing (LOWESS) is selected, and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots. Finally, the calibrated distribution functions of the DTCs are applied to the LVDMM, and experiments conducted to verify the displacement measurement accuracies are reported. The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than ±15 µm and ±19 µm, respectively, and that for oblique displacement is better than ±24 µm. Compared with the traditional calibration method, the displacement measurement error in the FFOV is now 90% smaller. This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV, and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.

A Dual Transformer Super-Resolution Network for Improving the Definition of Vibration Image

Visual measurement methods are gaining more and more attention in the field of structural body health monitoring due to the advantages of long-range, noncontact, and multipoint monitoring. However, the imaging system is usually affected by many factors, such as distortion, blurring, and noise, which lead to displacement measurement errors after the degradation of the acquired image quality. Therefore, in this article, we propose a structural body image super-resolution network based on a dual transformer architecture to improve the clarity of the collected structural body vibration displacement image to better capture the vibration displacement information of the target. Meanwhile, we design a dual transformer block based on an encoder–decoder architecture for the characteristics of vision-based structural body vibration displacement measurement tasks to better extract structural body image details and edge feature information. In this module, we introduce two different transformers. In addition, modules based on the encoder–decoder architecture focus more on the input and output image information and often ignore the feature information in different layers. Therefore, we introduce an attention mechanism in the network and interact with the feature information in different layers of the encoder–decoder architecture to obtain a better structural body image super-resolution effect. After comparison tests with the rest of the latest and most classical networks as well as the current optimal networks, it is shown that our network obtains excellent image reconstruction results under different structural body vibration image datasets (SETs), which also provides a strong guarantee for the task of accurate vision-based structural body vibration displacement measurement.

Structural monitoring method for RC column with distributed self-sensing BFRP bars

Reinforced concrete (RC) columns may be damaged under earthquakes or wind loads, which will severely affect their bearing capacity. Current damage evaluation methods are mainly based on displacement measurement, which makes evaluating local structural damage difficult. Therefore, this study proposes an RC column structural monitoring and evaluation method based on a distributed self-sensing basalt fiber reinforced polymer (BFRP) bar with optical fiber sensors inside. First, the self-sensing BFRP bar is introduced, including the sensing principle, inner structure, and basic sensing performance. It is found that the strain sensing coefficient of the proposed self-sensing BFRP bar presents only 2.2 % difference from that of the bare optical fiber sensor, meaning the BFRP package take no negative effect on the strain sensitivity. Second, the analytical methods of curvature and displacement are established based on the strain distribution measurement, in which the influence of bond-slip on parameter calculations is mainly considered. Finally, the proposed method was well verified by the loading tests of one RC column with self-sensing BFRP bars. Among the results, the absolute displacement measurement error increase with the development of structure damage, which can be even up to several mm after the steel yielding. However, the relative displacement measurement error can be still controlled within 20 % until the structure failure of the RC column. Considering the additional long-term performance of the proposed self-sensing BFRP bar, the proposed method is expected to implement long-term monitoring of RC columns.

Measurement and Region Identification in Deep Displacement of Slopes Based on Rod-Fiber Coupling Structure.

For measuring and region-identifying the deep displacement of slopes, a rod-fiber coupling structure based on optical time-domain reflection technology was designed. Accuracy of measurement and region identification in the deep displacement of slopes were studied by calibration experiment and model experiment. A rod-fiber coupling structure was able to calculate the variation and accurately identify the region of deep displacement of a slope compared with the measured downslide displacement of the slope model. The maximum measurement error of the deep displacement of the slope was 10.1%, the identification error of the displacement region was less than 4.4%, and the accuracy of the displacement-region identification of the rod-fiber coupling structure was 3.1 cm. Thus, the rod-fiber coupling structure based on optical time-domain reflection technology can be used for measuring and for region identification in the deep displacement of the slopes, and can provide a new method for the identification of the sliding surfaces of slopes.

A simple and precise calibration method for binocular vision

Binocular vision is an important part of machine vision measurement. Calibration accuracy is crucial for binocular vision. As for the determination of the structure parameters of the two cameras, the existing approaches usually obtain the initial values and optimize them according to the image-space errors, object-space errors or a combination of these. In the optimization process, constructing the objective function only through the image-space errors or object-space errors is not enough. Moreover, the image-space and object-space errors can form a variety of combinations to construct the objective function. Therefore, it is hard to choose the error criterion. An inadequate error criterion may lead to over-optimized or local minima (ambiguity solution). To solve this problem, this paper proposes a simple and precise calibration method for binocular vision based on the points distance constraints and image-space errors. The process of determining the structure parameters was divided into noniterative and iterative parts. We calculated the structure parameters of the two cameras according to the distance constraints of every two feature points noniteratively. The results obtained in this step were set as the initial value and refined through minimizing the reprojection errors using the Levenberg–Marquardt method. Because the results obtained in the noniterative step are accurate enough, only one iteration is needed. In this way, we finish the calibration avoiding the need to choose the error criterion. Furthermore, our method reduces the number of iterations to improve the calibration efficiency on the premise of guaranteeing the calibration accuracy. The experimental results show the superiority of this calibration method compared with other calibration methods. Using the calibration results of our method, in the measurement range of −45°∼ 45°, the rotation angle measurement error was less than ±0.032°. In the measurement range of 0 ∼ 39 mm, the displacement measurement error was less than ±0.047 mm. As for the length measurement of a 300 × 225 mm target, the length measurement error was less than ±0.039 mm.

Deep lateral displacement sensing experiment for rod–fiber coupling structure based on macrobending loss

Deep lateral displacement is an important index for evaluating the safety of geological bodies. The short range and low resolution of sensor monitoring often lead to large errors and inaccurate positioning in monitoring deep lateral displacement of geological bodies. Based on the principle of macrobending loss of a single-mode fiber, a rod–fiber coupling structure is designed in this study using a single-mode fiber and a highly elastic rubber rod to measure a large lateral displacement of a geological body. By analyzing the dispersion degree of the macrobending loss caused by loading displacement, the effects of pitch, diameter, and loading position on the measuring sensitivity and axial resolution of the rod–fiber coupling structure are investigated. Through a comparative experiment, the stability and measurement accuracy of the rod–fiber coupling structure are studied. The experimental results show that the lateral displacement of the rod–fiber coupling structure corresponds to the macrobending loss of the single-mode fiber; the relative measurement error of lateral displacement is within 10% for different lateral deformations. The proposed rod–fiber coupling structure provides powerful support for efficient, high-resolution monitoring of large lateral displacements of geological bodies.

Гомодинный квадратурный интерферометр перемещений. Эксперимент

In the previous work, the results of mathematical modeling of the optical scheme of a single-pass homodyne interferometer of displacements with the quadrature principle of phase registration are presented. The interferometer is built according to the Michelson scheme, and polarizing optical elements are used to obtain quadrature signals. The interferometer is supposed to be used as part of a new national standard of the kilogram based on watt balance method for precision measurements of the displacement and speed of the coil in the vertical direction. In this paper, experimental studies of the operation of a model of a homodyne quadrature displacement interferometer are presented. In this work, instead of a polarization beam splitter, a conventional (non-polarization) beam splitter and two polarizers are used in the optical scheme of a homodyne interferometer in the registration units. This added additional degrees of freedom when aligning optical channels for recording interference channels and made it possible to achieve the required signal shift by 90° with an accuracy of 0.1°. As a result, a displacement measurement error of 02. nm was experimentally achieved. Generalized expressions are obtained for quadrature signals for arbitrary azimuths of polarizers in three channels of recording interference signals. An assessment of the accuracy of displacement measurements using a quadrature homodyne interferometer was carried out and it was obtained that the expanded uncertainty of such measurements does not exceed 0.3 nm.