Deformation Measurement Research Articles

3D deformation and strain fields in drying kaolinite obtained from tracking internal bubbles using X-ray CT and ANN

AbstractDrying fine-grained sediments experience shrinkage and desiccation cracking that may dramatically alter their mechanical and hydraulic properties. This study adopts X-ray computed tomography (CT) to monitor the three-dimensional (3D) internal deformation and strain fields, and their relationships with desiccation crack formation, for drying kaolinite samples contained in plastic containers. Two kaolinite samples, one dried at room temperature and the other oven-dried at 60 °C, were CT scanned at several intervals during the drying process. From sequential CT scans for the same sample, entrained gas bubbles were extracted and used as tracking markers for deformation and strain field measurements. Since the bubble morphology continuously changed during the drying process, an artificial neural network (ANN) model was developed to link bubbles in sequential scans for the same sample. The tracking algorithm was trained with manually linked bubbles and optimised by comparing different combinations of bubble information, e.g. bubble location, size and shape. The drying samples experienced primarily vertical displacement before the air-entry value, while horizontal displacement occurred during vertical crack formation. Internal vertical and horizontal strains were generally uniform, indicating a limited impact of non-uniform sample drying and substrate constraint.

Determination of geo-stress in deep strata incorporating borehole diametral deformation measurement and overcoring

In deep energy engineering such as coal mining, oil & gas extraction, underground hydropower projects and deep buried water tunnels, rock failure and large deformation hazards often occur due to the complicated geological conditions and high geo-stress. Knowledge of the geo-stress state is an essential content in deep rock engineering. The complex environment of high temperature and high hydraulic pressure in deep rock mass makes geo-stress measurement more difficult than shallow strata. In this study, a novel method for geo-stress measurement based on the cross-sectional borehole diametral deformation is proposed. A borehole diametral deformation gage (BDD gage) is developed based on the measurement method. The scheme design of multi-contacts and micro-optical imaging avoid the influence of the high temperature and high hydraulic pressure environment. The results of the calibration experiment show that the measurement accuracy of BDD gage reaches 3 μm. Incorporating with the wireline coring tool for rapid overcoring, geo-stress measurement in deep vertical borehole via stress relief is realized. Field test procedure is summarized and application is carried out in a deep borehole of limestone stratum in Guizhou Province, China. Measurement process is verified to be rapid and simple. Measurement results including magnitude and direction of principal stresses are consistent with the results from hydraulic fracturing method. Special discussions were conducted on the measurement error of BDD gage and the improvement design of wireline coring tools. This article provides new ideas for geo-stress measurement in deep borehole.

High-precision dynamic measurement of roll angle based on digital holography

Among the six degrees of freedom for a moving body, measuring roll angle is the most difficult. In this study, a noncontact, no-imaging dynamic roll angle measurement system based on holography is proposed. Two beams of light are used to irradiate the measured object symmetrically, then two reflected light and the reference light interfere with each other to produce a hologram. By extracting the phase information of the two reflected light from two illumination beams using single hologram, this method achieves dynamic measurement of in-plane deformation, and then the roll angle is obtained through subsequent data processing. The effectiveness of the proposed method in-plane roll angle measurement is validated based on theoretical and experimental results. Experimental results show that the proposed method measures roll angle with high accuracy at both fixed and varied distances.

In Situ Dilatometry Measurements of Deformation of Microporous Carbon Induced by Temperature and Carbon Dioxide Adsorption under High Pressures

Adsorption-based carbon dioxide capture, utilization, and storage technologies aim to mitigate the accumulation of anthropogenic greenhouse gases that cause climate change. It is assumed that porous carbons as adsorbents are able to demonstrate the effectiveness of these technologies over a wide range of temperatures and pressures. The present study aimed to investigate the temperature-induced changes in the dimensions of the microporous carbon adsorbent Sorbonorit 4, as well as the carbon dioxide adsorption, by using in situ dilatometry. The nonmonotonic changes in the dimensions of Sorbonorit 4 under vacuum were found with increasing temperature from 213 to 573 K. At T > 300 K, the thermal linear expansion coefficient of Sorbonorit 4 exceeded that of a graphite crystal, reaching 5 × 10−5 K at 573 K. The CO2 adsorption onto Sorbonorit 4 gave rise to its contraction at low temperatures and pressures or to its expansion at high temperatures over the entire pressure range. An inversion of the temperature dependence of the adsorption-induced deformation (AID) of Sorbonorit-4 was observed. The AID of Sorbonorit-4 and differential isosteric heat of CO2 adsorption plotted as a function of carbon dioxide uptake varied within the same intervals of adsorption values, reflecting the changes in the state of adsorbed molecules caused by contributions from adsorbate–adsorbent and adsorbate–adsorbate interactions. A simple model of nanoporous carbon adsorbents as randomly oriented nanocrystallites interconnected by a disordered carbon phase is proposed to represent the adsorption- and temperature-induced deformation of nanocrystallites with the macroscopic deformation of the adsorbent granules.

Digital Image Correlation with a Prism Camera and Its Application in Complex Deformation Measurement.

Given the low accuracy of the traditional digital image correlation (DIC) method in complex deformation measurement, a color DIC method is proposed using a prism camera. Compared to the Bayer camera, the Prism camera can capture color images with three channels of real information. In this paper, a prism camera is used to collect color images. Relying on the rich information of three channels, the classic gray image matching algorithm is improved based on the color speckle image. Considering the change of light intensity of three channels before and after deformation, the matching algorithm merging subsets on three channels of a color image is deduced, including integer-pixel matching, sub-pixel matching, and initial value estimation of light intensity. The advantage of this method in measuring nonlinear deformation is verified by numerical simulation. Finally, it is applied to the cylinder compression experiment. This method can also be combined with stereo vision to measure complex shapes by projecting color speckle patterns.

Deformation Monitoring and Analysis of Reservoir Dams Based on SBAS-InSAR Technology—Banqiao Reservoir

Most dams in China have been operating for a long time and are products of the economic and technical limitations at the time of construction. Due to decades of aging engineering and ancillary problems, these reservoirs pose great threats to the safety of local people and the development of the surrounding economy. In this study, the surface deformation information for the Banqiao Reservoir is monitored with the small baseline subset–synthetic aperture radar interferometry (SBAS-InSAR) method using 80 Sentinel-1A images acquired from 3 January 2020 to 20 August 2022. Additionally, ground measurements from the BeiDou ground-based deformation monitoring stations were collected to validate the InSAR results. Based on the InSAR results, the spatiotemporal deformation features of the dam were analyzed in detail. The results show that the deformation in most areas, including the dam in the study area, is relatively stable, and the regional deformation velocity of the Banqiao Reservoir dam and other hydraulic engineering facilities varies between −1 mm/y and −4 mm/y. The Ru River area has a relatively obvious subsidence trend, and the maximum subsidence velocity reaches 30 mm/y. The InSAR monitoring results are consistent with the change trend in the BeiDou ground-based deformation measurement results. The monitoring results for the reservoir dam area provide a reference for local sustainable development and geological disaster prevention.

Automated segmentation and prediction of intervertebral disc morphology and uniaxial deformations from MRI

ObjectiveThe measurement of in vivo intervertebral disc (IVD) mechanics may be used to understand the etiology of IVD degeneration and low back pain (LBP). To this end, our lab has developed methods to measure IVD morphology and uniaxial compressive deformation (% change in IVD height) resulting from dynamic activity, in vivo, using magnetic resonance images (MRI). However, due to the time-intensive nature of manual image segmentation, we sought to validate an image segmentation algorithm that could accurately and reliably reproduce models of in vivo tissue mechanics. DesignTherefore, we developed and evaluated two commonly employed deep learning architectures (2D and 3D U-Net) for the segmentation of IVDs from MRI. The performance of these models was evaluated for morphological accuracy by comparing predicted IVD segmentations (Dice similarity coefficient, mDSC; average surface distance, ASD) to manual (ground truth) measures. Likewise, functional reliability and precision were assessed by evaluating the intraclass correlation coefficient (ICC) and standard error of measurement (SEm) of predicted and manually derived deformation measures. ResultsPeak model performance was obtained using the 3D U-net architecture, yielding a maximum mDSC ​= ​0.9824 and component-wise ASDx ​= ​0.0683 ​mm; ASDy ​= ​0.0335 ​mm; ASDz ​= ​0.0329 ​mm. Functional model performance demonstrated excellent reliability ICC ​= ​0.926 and precision SEm ​= ​0.42%. ConclusionsThis study demonstrated that a deep learning framework can precisely and reliably automate measures of IVD function, drastically improving the throughput of these time-intensive methods.

Centrifuge modeling of the run-out behavior of fly ash deposits subjected to a loss of confinement

Numerous industries are concerned by the humanitarian, environmental, and economic consequences of debris flows, landslides, and material run-outs. However, the run-out behavior following a loss of confinement, e.g., dam failure, is not well understood. The material’s complex constitutive behavior means multiple mechanisms contribute to the deformation, e.g., slope instability, seepage forces, erosion, or static liquefaction. In this study, centrifuge models of fly ash deposits, with varying initial deposit density and water table height, were subjected to a rapid loss of lateral confinement. Deformation, pore pressure, and water content measurements were used to investigate and separate the mechanisms governing the run-out. Static liquefaction was observed in deposits initially looser than the critical state and led to a rapid material outflow. Slope instability was the initial failure mechanism for denser deposits or those with reduced water tables, with transient stability due to dilation-induced negative excess pore pressures followed by progressive failures caused by seepage pressures from drainage and pore pressure dissipation. Cone penetration tests, performed before the loss of confinement at different penetration rates, were used to characterize the material run-out and volume change tendencies and demonstrate a practical tool for assessing the run-out risk of deposits in the field.

Sustainability of Multiwall Carbon Nanotube Fibers and Their Cellulose Composite

Nowadays, the research community envisions smart materials composed of biodegradable, biocompatible, and sustainable natural polymers, such as cellulose. Most applications of cellulose electroactive materials are developed for energy storage and sensors, while only a few are reported for linear actuators. Therefore, we introduce here cellulose-multiwall carbon nanotube composite (Cell-CNT) fibers compared with pristine multiwall carbon nanotube (CNT) fibers made by dielectrophoresis (DEP) in their linear actuation in an organic electrolyte. Electrochemical measurements (cyclic voltammetry, square wave potential steps, and chronopotentiometry) were performed with electromechanical deformation (EMD) measurements. The linear actuation of Cell-CNT outperformed the main actuation at discharging, having 7.9 kPa stress and 0.062% strain, making this composite more sustainable in smart materials, textiles, or robotics. The CNT fiber depends on scan rates switching from mixed actuation to main expansion at negative charging. The CNT fiber-specific capacitance was much enhanced with 278 F g−1, and had a capacity retention of 96% after 5000 cycles, making this fiber more sustainable in energy storage than the Cell-CNT fiber. The fiber samples were characterized by scanning electron microscopy (SEM), BET (Braunauer-Emmett-Teller) measurement, energy dispersive X-ray (EDX) spectroscopy, FTIR, and Raman spectroscopy.

Evaluation of Strain in 3C-SiC/Si Epiwafers from X-Ray Diffraction Measurements

X-Ray diffraction measurements of lattice parameter were performed for (111) and (100) oriented 3C-SiC/Si epiwafers. Strain of 3C-SiC epilayer and Si substrate were estimated and the result was compared with routine wafer deformation measurements. An unexpected discrepancy was observed between XRD and curvature measurements for (100) oriented samples.

Monitoring of the Vertical Settlement In Heavy Structures By Precise Levelling

Monitoring and analysing of the vertical deformations or the settlements of the structures is one of the main research fields in geodetic applications, which is considered a precise periodic measurement, made at different epochs to investigate these deformations on heavy structures.In this research, the deformation measurements were carried out on one of Baghdad University buildings,” Building of Computers Department” of dimensions (70.0 * 81.3 m.). Due to some cracks observed in their walls, it was necessary to monitor the vertical displacement of this building at some particular monitoring points by constructing a vertical network and measured in different epochs. The first epoch (zero epoch) was carried out in April 2006, the second in July 2006, the third in October 2006 and the last one in October 2012.These four epochs include precise levelling measurements were adjusted by Least Squares Adjustment with the aim of investigating the settlement of this building. The two approaches “the Global Congruency test” and “the simple test” are carried out to detect if there any deformation. These two approaches were employed in the analysis and found the difference in elevations between two epochs most be ensured and found that if the monitoring points (P1 to P4) stayed really stable, when compared with the time interval or not?Then according to the analysis procedure to determine the localization of settlement at specific points in the case may change in elevation must be applied. The results showed in two different statistical techniques a significant settlement in four selected corner points on building (P1, P2, P3 and P4). The statistics are based on the probability 95% test and the congruency test with Fisher distribution table

Nanoscale Porosity in Microellipsoids Cloaks Interparticle Capillary Attraction at Fluid Interfaces.

Anisotropic particles pinned at fluid interfaces tend toward disordered multiparticle configurations due to large, orientationally dependent, capillary forces, which is a significant barrier to exploiting these particles to create functional self-assembled materials. Therefore, current interfacial assembly methods typically focus on isotropic spheres, which have minimal capillary attraction and no dependence on orientation in the plane of the interface. In order to create long-range ordered structures with complex configurations via interfacially trapped anisotropic particles, control over the interparticle interaction energy via external fields and/or particle engineering is necessary. Here, we synthesize colloidal ellipsoids with nanoscale porosity and show that their interparticle capillary attraction at a water-air interface is reduced by an order of magnitude compared to their smooth counterparts. This is accomplished by comparing the behavior of smooth, rough, and porous ellipsoids at a water-air interface. By monitoring the dynamics of two particles approaching one another, we show that the porous particles exhibit a much shorter-range capillary interaction potential, with scaling intriguingly different than theory describing the behavior of smooth ellipsoids. Further, interferometry measurements of the fluid deformation surrounding a single particle shows that the interface around porous ellipsoids does not possess the characteristic quadrupolar symmetry of smooth ellipsoids, and quantitatively confirms the decrease in capillary interaction energy. By engineering nanostructured surface features in this fashion, the interfacial capillary interactions between particles may be controlled, informing an approach for the self-assembly of complex two-dimensional microstructures composed of anisotropic particles.

A joint InSAR-GNSS workflow for correction and selection of interferograms to estimate high-resolution interseismic deformations

Knowledge of the spatial distribution of interseismic deformations is essential to better understand earthquake cycles. The existing methods for improving the reliability of the obtained deformations often rely on visual inspection and prior model corrections that are time-consuming, labor-intensive, and do not consider the spatial distribution of interseismic deformations. Interferometric Synthetic Aperture Radar (InSAR) data provides wide-scale coverage for interseismic deformation monitoring over a wide area. However, the interseismic signal featured as millimeter-scale and long-wave deformations is often contaminated with noise. In the present study, a new workflow to correct the interferometric phase and quantitatively select interferograms is proposed to improve the accuracy of interseismic deformation measurements. Initially, the Generic Atmospheric Correction Online Service (GACOS), Intermittent Code for Atmospheric Noise Depression through Iterative Stacking (I-CANDIS), and plate model are combined to correct the atmospheric screen and long-wave ramp phase. Subsequently, the Pearson’s Correlation Coefficient (PCC) between the interferometric phase and the Global Navigation Satellite System (GNSS) constrained interseismic model as well as the STandard Deviation (STD) of the interferometric phase are introduced as criteria to optimize the selection of interferograms. Finally, the intermittent stacking method is used to generate an average velocity map. A comprehensive test using Sentinel-1 images covering the Haiyuan Fault Zone validate the effectiveness of our workflow in measuring interseismic deformations. This demonstrates that the proposed joint InSAR-GNSS workflow can be extended to study the subtle interseismic deformations of major fault systems in Tibet and worldwide.

Strategies for improving the communication of satellite-derived InSAR data for geohazards through the analysis of Twitter and online data portals

Abstract. Satellite-based earth observation sensors are increasingly able to monitor geophysical signals related to natural hazards, and many groups are working on rapid data acquisition, processing, and dissemination to data users with a wide range of expertise and goals. A particular challenge in the meaningful dissemination of Interferometric Synthetic Aperture Radar (InSAR) data to non-expert users is its unique differential data structure and sometimes low signal-to-noise ratio. In this study, we evaluate the online dissemination of ground deformation measurements from InSAR through Twitter, alongside the provision of open-access InSAR data from the Centre for Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET) Looking Into Continents from Space with Synthetic Aperture Radar (LiCSAR) processing system. Our aim is to evaluate (1) who interacts with disseminated InSAR data, (2) how the data are used, and (3) to discuss strategies for meaningful communication and dissemination of open InSAR data. We found that the InSAR Twitter community was primarily composed of non-scientists (62 %), although this grouping included earth observation experts in applications such as commercial industries. Twitter activity was primarily associated with natural hazard response, specifically following earthquakes and volcanic activity, where users disseminated InSAR measurements of ground deformation, often using wrapped and unwrapped interferograms. For earthquake events, Sentinel-1 data were acquired, processed, and tweeted within 4.7±2.8 d (the shortest was 1 d). Open-access Sentinel-1 data dominated the InSAR tweets and were applied to volcanic and earthquake events in the most engaged-with (retweeted) content. Open-access InSAR data provided by LiCSAR were widely accessed, including automatically processed and tweeted interferograms and interactive event pages revealing ground deformation following earthquake events. The further work required to integrate dissemination of InSAR data into longer-term disaster risk-reduction strategies is highly specific, to both hazard type and international community of practice, as well as to local political setting and civil protection mandates. Notably, communication of uncertainties and processing methodologies are still lacking. We conclude by outlining the future direction of COMET LiCSAR products to maximize their useability.

Eulerian fast motion identification algorithm for deformation measurement of cable-stayed bridge

Eulerian fast motion identification algorithm for deformation measurement of cable-stayed bridge

In situ measurement of full-field deformation for arc-based directed energy deposition via digital image correlation technology

Deformation measurement and control is a critical challenge in metal additive manufacturing. The metal deposition and solidification occur under the condition of high temperature gradient and large restriction accompany with complex metallurgical phenomena and stress evolutions. High stresses may result in deformation over yield strength of material, or even crack and fracture over the ultimate strength. Thus, it is necessary to monitor the deformation during additive manufacturing process. This paper focus on an in situ measurement of full-field deformation for arc-based directed energy deposition process via digital image correlation (DIC) technology. The measurement qualities were evaluated from the following aspects including system error, speckle pattern, influence of arc light and comparison in 2D-DIC and 3D-DIC. Results indicated that the relative system error of the measured deformation is no more than 0.12 % within a total deformation of 12 mm. Both the artificial speckle and natural speckle can meet the requirement of 2D-DIC system. The image qualities for artificial speckle is higher than that of natural speckle. For 3D-DIC, however, artificial speckle must be applied. The moving arc light will weaken the image qualities, which must be shielded in order to prevent the interference of intense light and the damage of speckle. An L-type shield was proposed and proved to be practical. Finally, DIC measuring was applied in both single-wall and cylindrical AM parts, comparing with numerical simulation. Results indicated that the evolution of the measured deformations showed good agreement with that of numerical simulation. Deformation evolution mechanism was revealed through numerical simulation and the evolution process was divided into three stages. For the cylindrical part, the final outer contour measured by DIC was consistent with that of 3D laser scanning and numerical simulation. As a conclusion, DIC technology was proved to be a feasible approach for in situ monitoring of full-field deformation of arc-based directed energy deposition process.

Непружність та демпфуюча здатність магнію і сплавів Mg—Al в умовах циклічного високоамплітудного навантаження

For Mg—Al alloys with magnesium content from 0 to 9%, measurements of anelastic deformation, damping capacity, and twinning start stresses were carried out. The method of cyclic loading under tension for a wide range of oscillations amplitudes with precision fixation of displacement was used. A method for determination of the start twinning deformation point σ0,002tw under conditions of cyclic loading is proposed, This stress characterizes the beginning of the inverse twinning stage, when the anelastic strain is 2∙10-5. Characteristics of σ0,002tw for technical magnesium and its alloys with aluminum in a wide range of plastic deformation are determined. An insignificant linear increase of σ0,002tw with increasing deformation was established for all Mg—Al alloys. The start twinning deformation point increases with increasing aluminum concentration. For low-alloy alloys with a solid-solution strengthening mechanism, the stress at the beginning of twinning increases insignificantly. For highly alloyed alloys, a significant increase of σ0,002tw stress is observed. It is established that repeated loading within the hysteresis loop to stresses. which is less than the maximum and is not accompanied by additional plastic deformation. If the level of applied stresses during repeated loading reaches the maximum value, the amount of plastic deformation after unloading increases. The addition in εpl gradually decreases with the rise of cycles number. The dependences of inelastic deformation and dissipated energy on the previous deformation degree for all investigated magnesium alloys demonstrate an extreme character. The growth of these characteristics is observed only in the initial part of the load to the residual deformation of 1—2%. With a further increase in deformation, the tendency to anelasticity and the damping capacity decrease. For the dependences dissipatson energy vs amplitude of loob stress, the maximum of dissipation energy is observed under the condition when the stress reaches a critical value, which corresponds to the beginning of prismatic or pyramidal sliding. Keywords: Mg—Al alloys, quasi-static cyclic loading, hysteresis loops, dissipation energy, damping capacity, elasticity, anelasticity, twinning start point.

High-speed Digital Image Correlation (DIC) for measuring deformation and vibration of fast rotating fan blades

Due to ecological requirements, the bypass-ratio of future civil turbofan engines will be increased. This leads to ultra-high bypass ratio (UHBR) engines, which bring in new challenges concerning the blade material, structural integration, and aeroelastic behaviour of the fan. The ambition of the project Composite fan Aerodynamic, Aeroelastic, and Aeroacoustic Validation Rig (CA3ViAR) is to design and test an open-test-case fan that experiences instability mechanisms, which are representative for UHBR fans of civil aircrafts. The optical measurement technique Digital Image Correlation (DIC) allows for the spatial measurement of deformations. The aim is to apply this technique to measure rotor blade deformation under loading and its vibration due to aeroelastic phenomena to get a better understanding of the structural and aeroelastic behaviour of the composite fan. However, the high rotational speeds, blade vibration frequencies, and expected amplitudes pose challenges for the measurement setup. In this work, a high-speed DIC system is prepared and tested to measure deformation and vibration of a fast rotating blade. Additionally, the requirements for the DIC setup are defined and presented. The expected blade tip speeds in the CA3ViAR project are up to 295 m/s and the blade frequencies of interest up to 650 Hz. Therefore, particular emphasis must be given to the setup in order to eliminate motion blur due to the rotation and to achieve the required frequency. This leads to a setup with synchronised high-speed cameras and a laser to measure frequency vibrations up to 1 kHz with an exposure time below 210 ns. Test measurements are conducted on a stationary beam and an axial blower with a max. blade tip speed of 50 m/s. A data analysis method is developed and described to eliminate the rigid body rotation, analyse the deformation of each blade compared to a reference condition, and analyse the spatial vibration in the frequency domain for a high number of data points per time step. The results of the structural beam are in agreement with the reference measurements and numerical simulations. By analysing the spatial vibration modes of the axial blower, the 1F-flap mode is identified at 38 Hz. In conclusion, this DIC setup shows promising results for future deformation and vibration measurements on a scaled UHBR fan.

Constraints on the Nuclear Symmetry Energy from Experiments, Theory and Observations

Nuclear mass measurements and neutron matter theory tightly constrain the nuclear symmetry energy parameters J, L, Ksym and Qsym . Corroboration of these constraints on J and L can be found from measurements of the neutron skin thicknesses and dipole polarizabilities of neutron-rich nuclei. The experimental constraints on these parameters are compared with those obtained from consideration of astrophysical measurements of the neutron star radius, which we show is highly correlated with L. Attention is aimed at the recent PREX and CREX neutron skin measurements from Jefferson Lab, NICER neutron star radius measurements, and a new interpretation of the GW170817 tidal deformability measurement. We find joint satisfaction of PREX and CREX gives J = 32.2 ± 1.7 MeV and L = 52.9 ± 13.2 MeV, in excellent agreement with neutron matter predictions of J = 32.0±1.1 MeV and L = 51.9±7.9 MeV.

A Dual-Beam Differential Method Based on Feedback Interferometry for Noncontact Measurement of Linear and Angular Displacement

A dual-beam differential method for noncontact measurement of linear and angular displacement is reported in this paper. Compared to other optical sensors, the system based on the frequency-modulated feedback interferometry has higher sensitivity for non-cooperative targets and a wider range with respect to the angle measurement. Performance of the proposed method is evaluated via testing a prototype system. The experimental results show that the prototype has a stability of 35 nm and 0.15“ over 1 hour with a resolution of 1 nm and 0.02” respectively. The linearity is 5.58×10^-6 in the range of 100 mm and 1.34×10^-4 in the range of 360°. The experiments for PZT deformation measurement and rotary motor monitor indicate that the proposed method possesses considerable potential for high-precision metrological applications, such as lathe calibration and motor control.