Accurate Displacement Measurement Research Articles

A novel peak positioning method for nanometer displacement measurement by optical linear encoder

In the field of precision measurement, subdividing displacement within the grating period to achieve high precision and high resolution remains a significant challenge. For subdivision, traditional optical linear encoders need complex coding and complicated optical systems, which struggle to meet the demands of nanometer measurement. In this paper, based on the fundamental principles of grating displacement measurement, a high-precision peak positioning method from grating images is proposed for linear displacement measurements with nanometer resolution and submicron accuracy. By utilizing a local gradient interpolation algorithm to optimize curves, it could further improve the accuracy of displacement measurement. Experiments demonstrate that this method achieves a resolution of 2 nm and an accuracy of ± 0.1 μm in a range of 50 mm using a grating with a 20 μm period. This sets the groundwork for subdividing optical linear encoders further, the resolution and accuracy could be further improved by optimizing the subdivision method.

Non-contact measurement of structural dynamic displacement based on improved edge detection and video interpolation

In structural health monitoring (SHM), smartphones are increasingly used for non-contact dynamic displacement measurement using computer vision. To overcome limitations in capturing high-frame-rate data, a non-contact measurement method of structural dynamic displacement based on an improved edge detection algorithm and video frame interpolation is proposed. Initially, a smartphone is employed to capture the structure’s vibration video and then generates intermediary frames between adjacent frames that match the structure’s motion state by using a video frame interpolation algorithm to obtain a video with a high frame rate. Subsequently, the improved edge detection algorithm is applied to measure the displacement within the interpolated video. In order to address the problem that traditional edge detection may have false edges leading to the degradation of measurement accuracy, a feature point tracking technique is proposed based on the traditional edge detection technique, which effectively excludes the interference of false edges in ROI and improves the accuracy of displacement monitoring. Experimental validation on a cantilever beam and steel frame bridge demonstrates the method’s viability and precision, highlighting its effectiveness in improving displacement measurement accuracy compared to traditional methods.

Deformation measurement of aero-engine rotating twisted blade based on multi-vision overlapping area feature registration method

Due to the complexity of the spatial surface of the twisted blade of the aero-engine, there are occlusions and shadows between the blades, resulting in visual blind spots. This causes the loss of certain information in the deformation measurement of twisted blade. A deformation measurement method of rotating twisted blades based on multi-vision overlapping area feature registration is proposed. It aims to solve the problem of limited field of view (FOV) in the deformation measurement of twisted blade, and overcome the problems of small measurement range and difficult measurement of traditional contact sensor method in the rotating state of the blade. First, a calibration and image-matching method based on multi-vision digital image correlation method is proposed. Under the premise of ensuring the simultaneous calibration of multi-vision camera stereo calibration, the matching of image detection points on the twisted blade surface is realized. Second, a three-dimensional reconstruction method based on the feature registration of the overlapping area of the FOV is proposed. It is used to solve the problem that the traditional image stitching method is prone to mismatching and to provide complete point cloud information for the deformation field calculation. Finally, the strain of each point is solved by piecewise point-by-point fitting of the local subdomains of the discrete displacement data, which suppresses the amplification of noise and improves the accuracy of blade strain calculation. In this paper, the deformation measurement experiment is carried out for the rotating twisted blade (up to 6000 rpm). The experimental results show that the proposed method can achieve a displacement measurement accuracy of 5 μm and the strain measurement accuracy of 50 με. This method can provide an important guarantee for the accurate evaluation and safe operation of the key performance parameters of the engine.

Nonlinearity-suppressed micro-probe fiber optic interferometer for accurate long-range displacement measurements

Fiber-optic interferometry technology has advanced rapidly in recent years. However, accurate measurement of the displacement over long ranges remains a challenge. This study reveals that fiber interferometers with Fabry–Perot cavities experience non-elliptic multi-order nonlinear errors due to parasitic interference, leading to nonlinearity correction failures in the case of reflectivity mismatch. We proposes a nonlinearity-suppressed microprobe fiber interferometer to measure long-range displacement with high accuracy. The proposed microprobe interferometer structurally avoids non-elliptic nonlinearities from higher-order harmonics and ensures the effectiveness of the nonlinearity correction method. Moreover, we optimized the micro-sensing probe parameters based on an established multimedia transmission interference model to further improve the measurement accuracy of long-range displacement. Nonlinear errors are reduced from 2.3 nm to 0.92 nm in the application range 0–700 mm. The findings of this study demonstrate that the proposed nonlinearity-suppressed microprobe fiber interferometer is suitable for sub-nanometer accuracy measurements over displacements of several hundred millimeters, especially in limited-space scenarios. It has great potential for industries seeking breakthroughs in long-range displacement measurement, such as robotics, medical devices and manufacturing.

Smart DIC: User-independent, accurate and precise DIC measurement with self-adaptively selected optimal calculation parameters

Existing subset-based digital image correlation (DIC) must rely on user-selected key calculation parameters (i.e., subset size and shape function) to proceed with displacement/deformation analysis. However, the lack of clear guidelines for selecting these parameters leads to varying choices among users, thus introducing artificial uncertainty in DIC measurements. Previous theoretical analyses and experimental studies revealed that optimal calculation parameters must account for both local speckle pattern quality and deformation at each required point. That means these key parameters should vary at each calculation point, posing a significant challenge for optimal parameter selection. To tackle this challenge, a novel Smart-DIC is proposed to achieve user-independent, accurate and precise displacement field measurements. This method comprehensively considers the local speckle pattern quality and local deformation at each calculation point, and gives the explicit formulas to determine optimal calculation parameters. Based on these optimal calculation parameters, Smart-DIC outputs accurate and precise displacement measurements without the need for users’ inputs. To validate its metrological performance, numerical tests were processed using data from DIC Challenge 1.0 and real images of tensile tests of a commercial AL-based alloy. The experimental results underscore the capacity of Smart-DIC to efficiently achieve accurate and precise displacement measurements across various scenarios by automatically selecting optimal subset sizes and shape functions.

A novel quasi-static compression test set-up with micron order accuracy for small specimens

Accurate displacement measurements during compression tests on small specimens using large standard universal testing machines are adversely affected by the compliance of the apparatus. The influence of compliance becomes more acute when conducting tests on quasi-brittle materials, such as cortical bone, that exhibit low failure strains and for which accurate modulus values are required. This paper presents a custom compression test set-up (i.e., a subpress) that facilitates routine quasi-static compression tests on small specimens by eliminating the effect of testing machine compliance on the results. The displacement of the compression test set-up was recorded using a combination of Hall effect sensors and multipole magnetic strips, which offers a resolution of less than one micron. The results of quasi-static compression tests on small polymer specimens are reported where the displacements were measured using the custom compression test set-up, the integrated displacement measurement system of a universal testing machine and a visual extensometer. Additional tests on cortical bone specimens demonstrate the effectiveness of the compression test set-up. Based on the results, the compression test set-up appeared to yield more consistent and accurate measurements compared to both the integrated measurement system of a universal testing machine and a visual extensometer. Novel data regarding the incipient fracture of cortical bone were obtained. The compression test set-up allows for the routine testing of a large number of bone specimens with micron accuracy in a short time frame, thus reducing the effects of degradation on biological specimens.

Experimental assessment of a low-cost aberration-free compact double aperture four-hololens imaging system: application to the enhancement of sensitivity and accuracy of in-plane displacement measurement

In this work, an experimental analysis of hololens imaging configuration consisting of four holographic lenses has been carried out to realize Duffy’s double aperture speckle interferometer. It is demonstrated that using holographic lenses recorded for typical f-number in the four-hololens imaging system, the sensitivity of measurement is not limited due to the f-number of the lens. However, the sensitivity can be significantly enhanced by increasing the angle between the plane and spherical waves while recording the holographic lenses. In-plane displacements were measured using holographic lenses recorded at nearly equal f-number and with different beam angles between the plane and spherical waves. Experimental results show that holographic lenses recorded with a large beam angle between the plane and the spherical waves give a higher measurement sensitivity in comparison to those holographic lenses that were recorded with a lower beam angle at an equal f-number. This work shows that a four-hololens imaging system can be used advantageously as a low-cost alternative to Duffy’s double aperture interferometer to overcome the need for expensive diffraction-limited low f-number lenses for higher measurement accuracy and sensitivity.

Research on image deformation monitoring algorithm based on binocular vision

Monitoring the deformation of critical structures such as tunnel、buildings and bridges is critical to ensure the safety of infrastructures. Non-contact deformation monitoring technology based on digital imagery has emerged as a prevalent and effective monitoring method, which enables cost-effective and efficient tracking of structural deformations. This paper aims to develop an automated deformation monitoring methodology using the binocular vision. First, standard preprocessing of digital images is performed through the integration of filtering algorithms and image enhancement techniques. Furthermore, by combining the Scale Invariant Feature Transform (SIFT) feature matching algorithm, the inverse compositional gauss–newton iterative algorithm, and interpolation methodologies, the planar displacement of the monitored targets can be calculated precisely, with sub-pixel precision being achieved. Subsequently, by adopting an enhanced Semi-Global Matching (SGM) algorithm, stereo matching of binocular images were accomplished. This process yields a disparity map, from which the depth map is computed. Then, precise measurement of the vertical displacement of the monitoring target can be obtained. This enables accurate measurement of three-dimensional displacements of the monitored targets. Finally, the developed methodology undergoes a comparative assessment against traditional measurement methods and existing algorithms to validate its measurement accuracy. The results prove that the deformation measurement technique based on binocular vision proposed in this paper captures structural deformation effectively. The accuracy surpasses that of existing measurement algorithms, and its efficiency outperforms traditional measurement methods.

“Subvolume Splitting” DVC applied for accurate discontinuous deformation measurement and fracture parameter extraction

As a powerful experimental tool for quantifying internal full-field mechanical response, digital volume correlation (DVC) has been increasingly used for extracting crucial fracture parameters. Nevertheless, due to the limitations of its regularly-used shape functions in describing discontinuous deformation, routine subvolume-based DVC encounters challenges in accurately capturing displacement maps around discontinuities, thus impeding reliable and accurate extraction of fracture parameters. To address this issue, a “subvolume splitting” DVC (SS-DVC) method is proposed. SS-DVC first splits subvolumes into two subblocks along a pre-calculated fitted crack plane and then only tracks the subblock with continuous deformation, thereby circumventing the limitations associated with discontinuities. Additionally, a straightforward and effective computational strategy is devised to ensure correct displacement measurements around discontinuities. For validation, both numerical simulation and real three-point bending tests were conducted to examine the performance of SS-DVC in terms of displacement measurement accuracy and extraction of fracture parameters. The experimental results demonstrate that, in comparison to routine DVC, SS-DVC exhibits a significant reduction in measurement errors of displacement around discontinuities, thus enabling more accurate determination of material fracture mechanical properties.

Accuracy and precision of internal displacement and strain measurements in long human bones using HR-pQCT and digital volume correlation

ABSTRACT Digital volume correlation (DVC) is a technique for measuring 3D, internal displacements and strains in loaded structures. One application of DVC is the study of internal bone mechanics and the validation of subject-specific finite element (FE) models. While micro-computed tomography (µCT) is a common choice for DVC studies of small samples of bone, long human bones such as the tibia may exceed the spatial limitations of conventional µCT. High resolution peripheral quantitative CT (HR-pQCT) scanners, with their large bore and open-ended design, may be a viable option for long-bone DVC. However, HR-pQCT is afflicted by stitching artefacts, caused by the stacking of scan blocks to form the large scan volume, resulting in erroneous steps in DVC displacements and bands of increased strain error. This study proposed a modified HR-pQCT scanning protocol and stitching methodology to mitigate the effects of stitching artefacts on DVC measurements of displacement and strain. With the application of the proposed scanning/stitching methodology, displacements greater than 11.7µm (0.29 voxels) and strains greater than 1633µε could be repeatedly measured by DVC. These results show that HR-pQCT combined with DVC is suitable for measuring internal bone displacements in long human bones with sub-voxel precision and strains greater than 1633µε.

Multi-wavelength confocal displacement sensing using a highly dispersive flat-field concave grating.

A multi-wavelength confocal displacement sensor based on a flat-field concave grating (FFCG) was proposed and designed; the large dispersion and small volume of the FFCG make it an ideal candidate for replacing the complex dispersive lens group. The designed displacement sensor was calibrated by displacement meter, and the characteristics were measured. Consequently, for the proposed displacement sensor, the displacement range of 6.8mm was measured with the R-square linearity evaluation coefficient of 0.998, and the sensitivity preceded 17.1nm/mm. The resolution of the displacement sensor was characterized by 70µm, as well as a full width at half maximum (FWHM) fluctuating around 1.63nm, indicating high precision and accuracy in displacement measurement. Moreover, the stability and reliability of the sensor were verified within 20min, with no significant wavelength shifts, and gentle power fluctuations of 557.73 counts at 520nm and 563.67 counts at 545.05nm, respectively.

Global Displacement Reconstruction of Lattice Tower Using Limited Acceleration and Strain Sensors

Displacement is an important parameter for evaluating structural performance. However, the accurate measurement of global dynamic displacement remains a challenging task. To solve this problem, this paper proposes a global dynamic displacement reconstruction method for lattice tower structures, fusing limited acceleration and strain data. First, the strain-displacement mapping method for cantilever beams with variable cross-sections is presented and then extended to lattice towers. Thereafter, a modified multi-rate data fusion algorithm incorporating Kalman filtering and the proposed strain-displacement mapping methods is developed to fuse the acceleration and strain data to reconstruct the global dynamic displacement of the tower. The numerical simulation, model test and full-scale test demonstrate that the reconstructed dynamic displacements using the proposed method agree well with the reference values in both the time and frequency domains, and the parametric analysis has also been carried out, exhibiting great robustness and high reconstruction accuracy.

Full-field deformation measurement and cracks detection in speckle scene using the deep learning-aided digital image correlation method

An enhanced full-field deformation and crack measurement method for oblique optical-axis conditions was proposed. First, the thickness of the calibration plate causes an error in the homography conversion (H matrix) and the final displacement results. To solve this problem, a Perspective-n-Point (PnP) based thickness compensation method for H calibration was proposed. Second, for better measurement of the full-field deformation, the measured surface is mapped with random speckles and markers, and the complex background and covering problems create obstacles for crack skeleton detection. To overcome these interferences, a strain-guided two-phase detection method based on the deep learning model was innovatively designed. Third, the traditional crack width calculation method is susceptible to the binarization threshold and the connection to the speckles, and a crack width calculation method using the displacement of control points was suggested. During a bending test, the above methods were applied to a basalt fiber-reinforced polymer (BFRP) beam. The enhancement in the displacement measurement accuracy and the robustness of crack detection, particularly the potential of detecting hidden cracks, were verified by comparing the performance of the proposed method to that of traditional contact sensors.

Laser self-mixing interference displacement signal filtering method based on empirical mode decomposition and wavelet threshold

In laser self-mixing interferometry displacement measurement, noise interference has a significant impact on the measurement results. To improve measurement accuracy, this paper proposes a filtering method that combines empirical mode decomposition (EMD) with wavelet thresholding. First, the signal is decomposed into several intrinsic mode functions (IMFs) using EMD. Then, wavelet thresholding is applied to each IMF. Subsequently, the processed IMFs are reconstructed to achieve signal filtering. Finally, by integrating the principles of interpolation and fringe counting, the reconstructed displacement signal is recovered, realizing accurate displacement measurement. This paper presents comprehensive simulation analyses and experimental validations for the proposed method. The accuracy of the displacement recovery is quantitatively evaluated using the absolute error and standard error, comparing the recovered displacement signal with the actual displacement. The experimental results demonstrate that the laser self-mixing interferometry displacement signal filtering method based on EMD and wavelet thresholding has high accuracy.

Correction of Misalignment Errors in the Integrated GNSS and Accelerometer System for Structural Displacement Monitoring

Structural health monitoring (SHM) systems are widely deployed to monitor the dynamic behaviors of large civil infrastructures such as bridges and tall buildings. Global Navigation Satellite System- (GNSS-) based technologies are often a key component in such an SHM system considering the unique capability of GNSS in determining real-time displacements. GNSS often integrates with an accelerometer to achieve complementary advantages. However, due to the various error sources in GNSS measurements and accelerometer, accuracies of GNSS and accelerometer fusion results often cannot meet the requirements of SHM. We propose to integrate a multi-antenna GNSS and an accelerometer with an unscented multi-rate Kalman filter (UMRKF-MA) to correct the system misalignment errors between the sensors, aiming to produce a much more accurate real-time displacement measurement technology for monitoring large civil infrastructures. Extensive experiments with datasets gathered using a shaking table have indicated that the proposed method was able to improve the accuracy of real-time displacement measurements by up to about 40–65% compared to some existing approaches, and that a 1 mm level of real-time monitoring of displacements could be achieved with the method. The method has also been applied to process a dataset from a real-world long-span bridge when heavy vehicles passed through the bridge in a loading test and significantly improved results were obtained.

Quantifying dune migration patterns and influencing factors in the central Sahara Desert

Based on Landsat images and ERA5 climate data, here we analyzed geomorphic dune patterns and the spatial characteristics of dune migration in the central Sahara Desert region (SW Libya, SE Algeria), using the COSI-Corr technique. Our results revealed clear observable drift potential (DP) and resultant drift potential (RDP) gradients, these decreasing from a northerly to southerly direction. Moreover, the annual average RDP/DP in most areas was <0.3 (i.e., highly variable). The main dune types in the study area included complex transverse ridges (22.82 %), linear dunes (19.87 %), barchan and barchanoid chains (16.95 %), and star dunes (13.55 %). Of these, barchans and barchanoid chains, as well as complex transverse ridges, appeared in areas of relatively high DP, while complex longitudinal ridges and honeycomb dunes were found in those of low DP. Linear dunes had a simpler wind composition, being mainly distributed in areas with intermediate wind variability. Both the honeycomb dunes and complex longitudinal ridges had nearly always formed in complex multi-directional wind environments. Dune migration displacement in dune fields ranged widely, from 0.5 to 23.57 m (mean = 6.71 m), during the 30-year study period (1993–2022). Barchans and barchanoid chains migrated fastest, with a mean value > 10 m/yr; in contrast, complex longitudinal ridges and honeycomb dunes had the slowest migration rate, always at < 5 m/yr. Overall, the dune migration rate was mainly related to dune height and wind regime. Spatially, the dune migration trend was basically consistent with that of the resultant drift direction (RDD), mainly in a northwesterly direction (28.36 %). The accuracy testing results indicated that the COSI-Corr displacement measurement accuracy was generally higher than the dune migration direction accuracy. This study provides not only valuable reference data for regional aeolian activities, but also insight into the developmental environments and migration dynamics of differing dune types, which could be used for prospective regional aeolian geomorphology research in the Sahara Desert.

Betterment of a displacement retrieval method based on data fitting in a near-half-fringe zone.

Raising the speed and accuracy of displacement retrieval by overcoming the weakness of time-consuming parameter estimation and a complex displacement retrieval algorithm is of key importance in improving the real-time quality of optical feedback self-mixing-based displacement measurement sensor. This paper proposes a high-speed and accurate simultaneous estimation method of displacement, optical feedback factor, and linewidth enhancement factor based on data fitting near a half-fringe cooperating with the fringe-counting method. The displacement measurement accuracy of the proposed method is about 16nm. The high estimation speed ensured by the principle of the reported method constitutes the main character of the method; besides, the method can be applied to any motion, as well as a harmonic vibration.

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.

A Laser Triangulation Displacement Sensor Based on a Cylindrical Annular Reflector

The ellipticity of the spot caused by laser jitter has a significant effect on the measurement accuracy of the traditional laser triangulation method. In order to overcome the influence of laser characteristics on measurement and improve the accuracy of displacement measurement, this paper proposes a measurement model for a laser displacement sensor based on a cylindrical annular reflector. A physical prototype is designed through parameter optimization using NSGA-II, and a two-step detection algorithm is proposed for the imaging ring of the prototype. The algorithm performs contour thinning after rough positioning of the imaging annular ring, and then performs precise detection. Through physical experiments, it is verified that the repeatability error of this method can reach below 0.02%, and the accuracy is significantly improved compared to traditional laser triangulation displacement sensors. Meanwhile, the measurement results of displacement show linearity. The optical path design of this sensor is simpler than the previously proposed rotational symmetrical laser triangulation displacement sensor, which has good application prospects.

Prediction of crack opening in steel beam based on strains measured from distributed optical fiber sensor

Optical fiber sensors based on the Brillouin optical time domain analysis (BOTDA) have good accuracy of crack opening displacement (COD) measurements. In this paper, we propose a method for COD quantification based on the area under the Brillouin frequency peaks induced by a crack. The study adopted a three-dimensional (3D) finite element model (FEM) to simulate the strain distribution within a segment of an optical fiber. The simulation results revealed that an increase in COD was associated with an increase in the Brillouin frequency peak area. The peak strain increased by 93 μϵ when the COD increased from 30 μm to 110 μm. The numerical findings were proved experimentally by employing a BOTDA interrogator for distributed sensing of strains. Two cracks in a 15-m-long steel beam were detected with the smallest error of 13%. The COD was predicted from the areas under the crack-introduced strain peaks under varying loads of 97, 196, 294 and 392 N. The effect of different spatial resolutions (10, 20 and 50 cm) and intervals (1, 2.5 and 5 cm) on sensing performance was discussed. Compared to previous research, the 3D FEM not only accurately predicted the changes in distributed optical fibers with cracks but also simplified traditional theoretical analysis. For the first time, a method has been introduced to predict cracks by comparing the area under the Brillouin peaks. This approach not only enhanced linearity but also reduced errors. The proposed method can be easily implemented in engineering practice for multi-point crack sensing in civil infrastructure.