3D Displacement Research Articles

GNSS-Over-Fiber Sensing System for High Precision 3D Nodal Displacement and Vibration Detection

Aiming at realizing comprehensive structural health monitoring, a GNSS (Global Navigation Satellite System) over fiber sensing approach is presented and experimentally demonstrated to achieve 3D nodal displacement and vibration detection simultaneously. GNSS signals from multi-antennas are transferred to a receiver based on an optical fiber link, also used as distributed sensing fiber. Broadband linear frequency-modulated (LFM) probe light with high linearity is generated based on electro-optic modulation to probe distributed vibrations and monitor the transmission time delay along the whole fiber with high precision. The spectral components generated by vibrations are detected using the cross-correlation method to achieve distributed vibration sensing. In addition, with the assistance of high-precision hardware-delay measurement, the variation of transmission time delay can be obtained, improving the precision of 3D displacement measurement in the GNSS-over-fiber architecture. In the proof-of-concept experiment, a 3D baseline can be obtained with the precision of 2.8, 3.6, and 2.0 mm, while vibrations with frequencies of 40 kHz, 80 kHz, and 100 kHz along 250 m fiber are successfully detected with a spatial resolution of 1 m.

InSARTrac Field Tests—Combining Computer Vision and Terrestrial InSAR for 3D Displacement Monitoring

InSARTrac is an innovative method for 3D displacement monitoring that combines terrestrial interferometric synthetic aperture radar (InSAR) and computer vision-based feature tracking. The 3D measurements obtained are considered far superior to 1D or 2D data and facilitate evaluations concerning the mechanisms controlling kinematics. This study presents the results of InSARTrac measurements at the Mölltal Glacier in Carinthia, Austria. The duration of glacier monitoring was four weeks and involved two instrument setup positions to obtain comparative measurements of supraglacial rock debris from different angles without utilizing retroreflectors. The mean displacement rate of the resultant vector is 22 mm/day and includes ~11 mm/day in the downgradient ice surface direction and 6 to 18 mm/day vertically downward. Additionally, the entire glacier surface was measured three times using a LIDAR-equipped UAV, revealing mean vertical displacements of 16 mm/day. The measurements indicate an InSARTrac accuracy of 4.2 ppm, which is 27% lower than in the initial controlled tests utilizing retroreflectors. The field test demonstrates the capability of InSARTrac to provide meaningful 3D displacement measurements of supraglacial rock debris. The material monitored has texture and reflectivity similar to certain classes of landslides, rock glaciers, and other alpine processes, indicating that InSARTrac has promising applications for monitoring a variety of geologic phenomena.

Erratum: “A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers” [AIP Adv. 8, 025315 (2018)

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Modeling of Sand Triaxial Specimens under Compression: Introducing an Elasto-Plastic Finite Element Model to Capture the Impact of Specimens’ Heterogeneity

This paper follows up on a series of reference papers that inspired MDPI’s Topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, where global and local deformation effects on sand specimens are fully described from high-resolution boundary displacement fields, as supported by a comprehensive experimental database (which includes varying degrees of specimen’s heterogeneity) that is available to the scientific community for further study. This paper presents an elasto-plastic comparative analysis of different finite element models reproducing different sand specimen heterogeneity configurations as follows: loose, dense, and half-dense half-loose specimens. The experimental conditions for these specimens’ heterogeneity configurations were simulated with an axisymmetric finite element model. To characterize the stress-strain response obtained from the experiments, an elasto-plastic constitutive model with strain-hardening and softening laws was adopted to reproduce the sand specimens’ mechanistic response. An expert-based calibration of the numerical models accounted for both global and local effects by making use of global observations captured by the triaxial point sensors (i.e., axial force and displacement) and by local observations captured by 3D digital image correlation analysis (i.e., 3D boundary displacement fields). Results show that predictions of the proposed numerical models are in good agreement with the experimental observations, both global and local responses. The combined use of global and local observations to calibrate sand triaxial specimens sets the basis for a more comprehensive parameterization process. For the first model set, three experiments were assumed with homogeneous materials. While both dense and loose models showed good agreement with the experiments, the displacement field prediction of the half-dense half-loose layered model identified limitations in reproducing heterogeneous configurations. Afterward, the second set compared and analyzed the half-dense half-loose layered models by implementing a heterogeneous model, showing significantly better model predictions (i.e., after the implementation of the heterogeneous model, which accounts for a transition zone between the upper and lower segments).

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.

High-speed measurement of two-dimensional displacement of myocardium using element RF data of ultrasonic probe

Improving the accuracy of heart wall motion measurement is essential to realise better cardiac function evaluation. This paper proposed a two-dimensional (2D) displacement estimation method with a high temporal resolution using the 2D complex cross-correlation of element RF signals of an ultrasonic probe between frames returned from the target scatterers. The application of the proposed method to the phantom displacement confirmed its principle. The estimated 2D displacement of the phantom was consistent with the set displacement. Subsequently, the method was applied to two healthy subjects to measure the 2D displacement of the interventricular septum during one cardiac cycle. Consequently, during systole and diastole, the movement of the myocardium was measured, and the results were validated.

Analytical solutions of peristatics and peridynamics for 3D isotropic materials

In a recent paper, Mikata (2019) has established two explicit analytical governing equations of peridynamics for 3D isotropic and orthotropic materials. In the present paper, general analytical solutions of peristatics and peridynamics for 3D isotropic peridynamic materials are obtained in infinite media for an arbitrary body force density, and arbitrary initial conditions in the case of peridynamics. In addition, peristatic and peridynamic Green's functions corresponding to a point load are also obtained. Classical limit of the peristatic and peridynamic Green's functions in the limit of the generalized material horizon δ going to 0 (δ→0) is analytically discussed in detail for one of the most commonly used nonlocality functions with a finite material horizon with a sharp cut-off. It is analytically and explicitly shown that the peristatic and peridynamic Green's functions converge to the elastostatic and elastodynamic Green's functions, respectively, as the generalized material horizon δ goes to 0 (δ→0). Numerical results are obtained and discussed for the peristatic Green's function and a 3D peristatic displacement field under a 1D-like loading. The governing equation investigated in the present paper is the first explicit analytical governing equation of peridynamics for 3D isotropic materials, which is comparable to Navier-Cauchy's equation. Thus, this equation opens up various ways to investigate peridynamics in 3D isotropic materials in an exact analytical fashion, which was not possible before.

Remote 3D Displacement Sensing for Large Structures with Stereo Digital Image Correlation

The work performance of stereo digital image correlation (stereo-DIC) technologies, especially the operating accuracy and reliability in field applications, is not fully understood. In this study, the key technologies of the field remote 3D displacement sensing of civil structures based on stereo-DIC have been proposed. An image correlation algorithm is incorporated in improving the matching accuracy of control points. An adaptive stereo-DIC extrinsic parameter calibration method is developed by fusing epipolar-geometry-based and homography-based methods. Furthermore, a reliable reference frame that does not require artificial markers is established based on Euclidean transformation, which facilitates in-plane and out-of-plane displacement monitoring for civil structures. Moreover, a camera motion correction is introduced by considering background points according to the camera motion model. With an experiment, the feasibility and accuracy of the proposed system are validated. Moreover, the system is applied to sense the dynamic operating displacement of a 2 MW wind turbine’s blades. The results show the potential capability of the proposed stereo-DIC system in remote capturing the full-field 3D dynamic responses and health status of large-scale structures.

Evaluation of Parent Well Depletion Effects on Fracture Geometry Based on Low-Frequency Distributed Acoustic Sensing in Hydraulic Fracture Test Site-2

Summary Low-frequency distributed acoustic sensing (LF-DAS) has recently received much attention for its ability to monitor fracture propagation at offset wells. Hydraulic Fracture Test Site-2 (HFTS-2), a Department of Energy–sponsored field-based research experiment, has acquired LF-DAS data sets during the stimulation of many horizontal wells in the Wolfcamp Formation of the Permian Basin. Over 100 stimulated stages with different completion designs in four horizontal wells were monitored by two horizontal offset wells and one vertical pilot hole with permanent fibers. The parent well depletion affected all four horizontal wells in almost half of their lateral section. Several studies have been performed on the acquired comprehensive data set. In this study, we apply our novel Green’s function-based inversion algorithm to calculate the fracture width of each stage and investigate the impact of parent well depletion on fracture geometry. The Green’s function-based inversion algorithm has been successfully applied to a few stages of field case studies. The Green’s function matrix was built based on linear elasticity theory (3D displacement discontinuity method) to relate the fracture openings with strain responses measured along the length of the fiber. This novel algorithm only relies on measured strain to solve fracture geometry at the monitoring well. Therefore, it is independent of the physics of the fracture propagation process and can be used to validate hydraulic fracture modeling results. Using our inversion algorithm, we can efficiently and quantitatively interpret LF-DAS data to provide information on fracture geometry and completion efficiency. We analyze more than 100 stages of the LF-DAS measurements obtained at the fiber wells B3H and B4H during B1H, B2H, and B4H stimulations. We apply our inversion algorithm for four data sets covering the stimulation of the abovementioned three wells. The fracture growth at stages in the parent well’s depleted zone is biased more toward upper formation and in the easterly direction. The fracture width at the stages in the parent well’s depletion zone is reduced compared to fracture widths at stages in the nondepleted zone irrespective of the monitoring well location relative to the treatment wells. This difference in fracture widths will affect the proppant distribution to a great extent, thereby affecting the effectiveness of the stimulation. We also illustrate the application of the inversion algorithm for stages that have both conventional fracture hits with “heart-shaped” signals as well as fracture reopening signals. Our inversion algorithm gives a reasonable estimate of the fracture width that aligns with the qualitative analysis of microseismic data sets and statistic summary of fracture hit numbers of HFTS-2. We believe that this quantitative study provides us with insights into the fracture geometry due to parent well depletion effects.

Evaluation of Tunnel Elastic and Elasto-Plastic Deformations with Approximations Obtained from 3D-FEM Simulations

Nowadays, there are computer tools designed to simulate engineering problems. Numerical simulations in three dimensions (3D) are the closest to reality, but they require a significant amount of time and experience. In this paper, the aim is to present formulae and graphs obtained from numerical simulations using the finite element method (FEM). Their application decreases the time required to obtain deformations in the periphery of different tunnel sections and further serves to evaluate them for different excavation lengths in the face of unexpected geotechnical changes during drilling. Using the RS2 and RS3 software, 3D analyses were carried out according to the Mohr-Coulomb (MC) model, considering elastic and elasto-plastic perfect behaviors as well as isotropic and anisotropic conditions. The graphs presented herein allow obtaining displacements from an axisymmetric model to infer the 3D displacements horseshoe tunnels, and the polynomial expressions aid in determining the displacements of an established excavation length. Finally, comparisons between the displacements reported by other authors and those obtained with the polynomial expressions are presented as a means of validation for this research.

Three-dimensional coseismic displacements and slip distribution of the 2021 Mw 7.4 maduo earthquake: Synergy of SAR, InSAR and optical images

On 21 May 2021, an earthquake of moment magnitude (Mw) 7.4 occurred near Maduo county in Qinghai Province China. This is the first major earthquake that occurred in the interior of the Bayan Har block in the Tibetan Plateau over the past 70 decades. Focusing on this event, we conducted a study on three-dimensional (3D) coseismic displacement reconstruction and its tectonic implication. We acquired both Synthetic Aperture Radar (SAR) and optical imaging satellite imagery, including SAR images from Sentinel-1 and Advanced Land Observation Satellite-2 (ALOS-2) as well as the multi-spectrum images from the Sentinel-2 (S2) satellite. We applied the Interferometric SAR (InSAR) and pixel-offset tracking (POT) techniques to coseismic SAR data pairs and reconstructed two dimensional displacements. With the constructed displacement fields in multiple viewing directions, we resolved the 3D coseismic displacements (north-south, east-west, and up components) by integrating the regional strain model with variance components estimation (SM-VCE). We recommend using the standard deviation value at each grid cell, which can be calculated in the resampling, as the initial weight. Based on the resolved 3D coseismic displacements, we further estimated the dip angles for the two segments (F4 and F5) in the east of the rupture zone. The associated moment magnitude is about Mw7.4, which corresponds to the released energy of ∼ 1.74×1020 Nm.

Simultaneous acquisition of vibration and diffusion by multifrequency diffusion tensor imaging-magnetic resonance elastography (mDTI-MRE)

Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI) are MRI techniques that provide complementary diagnostic information and utilize motion-sensitive magnetic field gradients. In MRE, tissue vibrations are encoded into the MRI signal phase, while in DTI the diffusive motion of water molecules is assessed by means of the MRI signal magnitude. Careful consideration of the motion-encoding gradient timing conditions and the mechanical frequencies allows the simultaneous acquisition of vibration and diffusion data without observable mutual interferences. We propose a multifrequency Diffusion Tensor Imaging-Magnetic Resonance Elastography (mDTI-MRE) protocol that measures the diffusive behavior along 24 directions and the full 3D displacement field at two mechanical frequencies. Using this method, mDTI-MRE provides information about the mechanical wave field and about a preferred direction, which may facilitate the accurate mechanical characterization of anisotropic biological tissues, such as brain white matter and skeletal muscle.

Optimization of Mirror Positioning for Single‐Camera 3D Displacement Measurements

AbstractCamera‐based 3D displacement measurements are only possible when two different viewing angles of the respective measurement point are available. We earlier introduced a simplified 3D reconstruction algorithm for camera‐mirror measurements where the mirror reflects the second view onto the camera sensor to eliminate the need for a second (costly) high speed camera. In this study, we concentrate on formulating guidelines on how to position the mirror with respect to the camera and the measured structure, the goal being to minimize errors arising in the 3D reconstruction procedure. The focus lies on the angle between the optical axes of both camera views. We hereby also take into account limitations in the experimental setup that the special camera‐mirror‐setup brings with it. This study is conducted in terms of simulations using the animation software BLENDER as well as real experiments on a simple vibrating structure.

Mitotic outcomes and errors in fibrous environments

During mitosis, cells round up and utilize the interphase adhesion sites within the fibrous extracellular matrix (ECM) as guidance cues to orient the mitotic spindles. Here, using suspended ECM-mimicking nanofiber networks, we explore mitotic outcomes and error distribution for various interphase cell shapes. Elongated cells attached to single fibers through two focal adhesion clusters (FACs) at their extremities result in perfect spherical mitotic cell bodies that undergo significant 3-dimensional (3D) displacement while being held by retraction fibers (RFs). Increasing the number of parallel fibers increases FACs and retraction fiber-driven stability, leading to reduced 3D cell body movement, metaphase plate rotations, increased interkinetochore distances, and significantly faster division times. Interestingly, interphase kite shapes on a crosshatch pattern of four fibers undergo mitosis resembling single-fiber outcomes due to rounded bodies being primarily held in position by RFs from two perpendicular suspended fibers. We develop a cortex-astral microtubule analytical model to capture the retraction fiber dependence of the metaphase plate rotations. We observe that reduced orientational stability, on single fibers, results in increased monopolar mitotic defects, while multipolar defects become dominant as the number of adhered fibers increases. We use a stochastic Monte Carlo simulation of centrosome, chromosome, and membrane interactions to explain the relationship between the observed propensity of monopolar and multipolar defects and the geometry of RFs. Overall, we establish that while bipolar mitosis is robust in fibrous environments, the nature of division errors in fibrous microenvironments is governed by interphase cell shapes and adhesion geometries.

Estimating 3D displacement vectors from line-of-sight observations with application to MIMO-SAR

Abstract Displacements in typical monitoring applications occur in 3D but having sensors capable of measuring such 3D deformations with areal coverage is rare. One way could be to combine three or more line-of-sight measurements carried out from different locations at the same time and derive 3D displacement vectors. Automotive Multiple-Input-Multiple-Output Synthetic Aperture Radar (MIMO-SAR) systems are of interest for such monitoring applications as they can acquire line-of-sight displacement measurements with areal coverage and are associated with low cost and high flexibility. In this paper, we present a set of algorithms deriving 3D displacement vectors from line-of-sight displacement measurements while applying spatial and temporal least squares adjustments. We evaluated the algorithms on simulated data and tested them on experimentally acquired MIMO-SAR acquisitions. The results showed that especially spatial parametric and non-parametric least squares adjustments worked very well for typical displacements occurring in geomonitoring and structural monitoring (e.g. tilting, bending, oscillating, etc.). The simulations were confirmed by an experiment, where a corner cube was moved step-wise. The results show that acquisitions of off-the-shelf automotive-grade MIMO-SAR systems can be combined to derive 3D displacement vectors with high accuracy.

Experimental research on a novel soil displacement monitoring system based on measurement unit cells (MUCs)

Advanced measurement technology is of great significance to the prevention of geological disasters and engineering construction and simultaneously promotes geotechnical engineering development. This paper reports a novel soil displacement monitoring system based on multiple measurement unit cells. A modularized structure and corresponding positioning algorithm were proposed to monitor the 3D displacement of soil. The monitoring software was developed to dynamically display deformation. Then, a calibration experiment was performed to verify the feasibility of the measurement unit cell. Furthermore, a model experiment adopting X-ray visualization was performed to validate the reliability of the soil displacement monitoring system. It is determined that the proposed soil displacement monitoring system has a mm-level accuracy and satisfies geotechnical engineering requirements.

Three-dimensional micro displacement sensor based on fiber SPR mechanisms.

Three fiber micro displacement sensors can be combined to realize three-dimensional (3D) displacement sensing, but the system is complex. In this paper, a 3D displacement sensor based on fiber SPR was proposed, which was composed of displacement fiber and sensing fiber. By cascading the eccentric dual-core fiber and graded multimode fiber, the displacement fiber was realized. The V-groove was processed in the vertical and horizontal directions of the graded multimode fiber, and the inclined SPR sensing areas were fabricated to realize the sensing fiber. A straight beam from the middle core of the displacement fiber contacted the vertical V-groove inclined plane of the sensing fiber to realize the Y axis (up and down) direction micro displacement, contacted the horizontal V-groove inclined plane of the sensing fiber to realize the Z axis (front and back) direction micro displacement sensing. An oblique beam from the eccentric core of the displacement fiber cooperated with the sensing fiber to realize the micro displacement sensing in the X-axis (left and right) direction. The testing results indicate that the fiber SPR 3D micro displacement sensor can sense micro displacement in the X axis, Y axis and Z axis, and the wavelength sensitivity is 0.148 nm/µm, -3.724 nm/µm and 3.543 nm/µm, respectively. The light intensity sensitivity is -0.0014a.u./µm, -0.0458a.u./µm and -0.0494a.u./µm, respectively. When adjusting the parameters of eccentric dual-core fiber, the larger the core distance is, the greater the displacement sensitivity in the X-axis direction of the sensor is, and the smaller the detection range is. The proposed sensor can realize 3D micro displacement sensing by itself, which is expected to be used in the field of 3D micro displacement measurement and 3D space precision positioning.

Panoramic Digital Image Correlation for 360-Deg Full-Field Displacement Measurement

In full-field 3D displacement measurement, stereo digital image correlation (Stereo-DIC) has strong capabilities. However, as a result of difficulties with stereo camera calibration and surface merging, 360-deg panoramic displacement measurements remain a challenge. This paper proposes a panoramic displacement field measurement method in order to accurately measure the shape and panoramic displacement field of complex shaped objects with natural textures. The proposed method is based on the robust subset-based DIC algorithm and the well-known Zhang’s calibration method to reconstruct the 3D shape and estimate the full-field displacements of a complex surface from multi-view stereo camera pairs. The method is used in the determination of the scale factor of the 3D reconstructed surface and the stitching of multiple 3D reconstructed surfaces with the aid of the laser point cloud data of the object under test. Based on a discussion of the challenges faced by panoramic DIC, this paper details the proposed solution and describes the specific algorithms implemented. The paper tests the performance of the proposed method using an experimental system with a 360-deg six camera setup. The system was evaluated by measuring the rigid body motion of a cylindrical log sample with known 3D point cloud data. The results confirm that the proposed method is able to accurately measure the panoramic shape and full-field displacement of objects with complex morphologies.

Compactive deformation of incoming calcareous pelagic sediments, northern Hikurangi subduction margin, New Zealand: Implications for subduction processes

Calcareous rocks are commonly found in subduction zones, but few studies have investigated the consolidation and compactive deformation of these rocks prior to subduction, and their potential effects on subduction and accretionary processes are thus poorly understood. Using drilling data obtained during International Ocean Discovery Program (IODP) Expeditions 372 and 375 combined with 2D and 3D seismic reflection data, the structure, growth history, and slip rates of normal faults identified in the incoming pelagic sedimentary sequences of the Hikurangi Margin were investigated. A seismic coherence depth slice and vertical profiles show that these faults exhibit polygonal structure that has rarely been documented at subduction margins. The polygonal faults are closely spaced and layer-bound within sequences dominated by pelagic carbonate and calcareous mudstone of Paleocene-Pliocene age. Kinematic modeling and 2D displacement analysis reveal that fault throws decrease toward the upper and lower tipline. In detail, two groups of throw profiles are defined by locations of displacement maxima, possibly reflecting lateral variations in physical properties. The polygonal fault system (PFS) likely formed by syneresis processes that involve diagenetically induced shear failure and volumetric contraction of the pelagic unit associated with fluid escape. Fault growth sequences reveal multiple, weakly correlated intervals of contemporaneous seafloor deformation and sedimentation and allow estimates of fault slip rates. We find evidence for a significant increase in typical slip rates from 0.5-3 m/Ma during pelagic sedimentation to >20 m/Ma following the onset of terrigenous sedimentation. These observations suggest that rapid loading of the pelagic sediments by the trench-wedge facies was associated with renewed and faster growth of the PFS. The PFS will eventually be transported into the base of the accretionary wedge, enhancing geometric roughness and heterogeneity of materials along the megathrust, and providing inherited zones of weakness. Selective fault reactivation may facilitate deformation and episodic vertical fluid migration in the lower wedge associated with microearthquakes, tremor, and slow slip events.

Structural displacement monitoring using ground-based synthetic aperture radar

This study develops a ground-based synthetic aperture radar (GBSAR) imaging system and interferometric processing framework for structural health monitoring (SHM). Radar remote sensing for displacement monitoring plays a vital role in SHM. Radar sensors and, more specifically, GBSAR systems have gained more attention in recent studies due to their capability to overcome the limitations of other contact or non-contact SHM sensors. This paper proposes a three-dimensional SAR imaging system and advanced signal processing scheme to extract continuous (fast) displacement components, such as structural vibrations, and discontinuous (slow) displacements, such as subsidence or uplift, using SAR time-series datasets. Using controlled experiments, this study shows that the developed GBSAR can monitor sub-millimeter displacements with high spatial resolution and 0.02 mm precision in the LOS direction. Moreover, several simulations are carried out to evaluate the proposed displacement monitoring algorithms. Accordingly, the proposed continuous monitoring framework can measure fast LOS displacements with better than 0.03 mm precision by reducing the effects of radar movement, clutters, and disturbances. Also, evaluations on a simulated monitoring scene at 20 m from the GBSAR’s LOS show that the proposed discontinuous displacement monitoring algorithm can estimate 3D displacement vectors with sub-millimeter precision. The results show that the developed GBSAR can be used for repeat-pass LOS displacement monitoring and the proposed algorithms demonstrate high potential for measuring continuous sub-second LOS displacements and long-term 3D displacement vectors.