Displacement Estimation Research Articles

Investigation of the Effect of Integrated Offset, GPS, and InSAR Data in the Stochastic Source Modeling of the 2002 Denali Earthquake

This study investigates the effect of geological field measurement (offset), global positioning system (GPS), and interferometric synthetic aperture radar (InSAR) data on the estimation of the co-seismic earthquake displacements of the 2002 Denali earthquake. The analysis is conducted using stochastic source modeling. Uncertainties associated with each dataset limit their effectiveness in source model selection and raise questions about the adequate number of datasets and their type for reliable source estimation. To address these questions, stochastic source models with heterogeneous earthquake slip distributions are synthesized using the von Kármán wavenumber spectrum and statistical scaling relationships. The surface displacements of the generated stochastic sources are obtained using the Okada method. The surface displacements are compared with the available datasets (i.e., offset, GPS, and InSAR) individually and in an integrated form. The results indicate that the performance of stochastic source generation can be significantly improved in the case of using GPS data and in the integrated case. Overall, based on the case study of the 2002 Denali earthquake, the combined use of all available datasets increases the robustness of the stochastic source modeling method in characterizing surface displacement. However, GPS data contribute more than InSAR and offset data in producing reliable source models.

Robust Multimodal Image Matching Based on Radiation Invariant Phase Correlation

Abstract. Due to the influence of nonlinear radiation distortion and geometric deformation, achieving multimodal image matching remains a challenging task. To address these issues, this paper proposes a method called radiation invariant phase correlation (RIPC) to simultaneously estimate the rotation, scale, and displacement changes of multimodal image pairs. Firstly, based on the local structure characteristics of the image itself, we harness the nonlinear invariance of kernel canonical correlation analysis to devise the multimodal local self-correlation (MLSC) descriptor. This descriptor is resilient to nonlinear radiative differences, as well as local rotation and scale variations. Subsequently, we incorporate the log-polar coordinate transformation to capture the overall rotation and scale changes in the image, enabling independent representation of these factors on the Cartesian coordinate system. Finally, drawing upon the continuity of displacement estimation, as well as rotation and scale estimation, we construct a five-dimensional descriptor tailored for phase correlation. Extensive experiments conducted on five open-source datasets demonstrate that our proposed method surpasses state-of-the-art (SOTA) techniques in matching performance. Furthermore, our RIPC method achieves matching accuracy within 2-pixel threshold, which underscores its effectiveness in multimodal remote sensing image matching.

Coordinate-Independent 3-D Ultrasound Principal Stretch and Direction Imaging.

In clinical ultrasound, current 2-D strain imaging faces challenges in quantifying three orthogonal normal strain components. This requires separate image acquisitions based on the pixel-dependent cardiac coordinate system, leading to additional computations and estimation discrepancies due to probe orientation. Most systems lack shear strain information, as displaying all components is challenging to interpret. This paper presents a 3-D high-spatial-resolution, coordinate-independent strain imaging approach based on principal stretch and axis estimation. All strain components are transformed into three principal stretches along three normal principal axes, enabling direct visualization of the primary deformation. We devised an efficient 3-D speckle tracking method with tilt filtering, incorporating randomized searching in a two-pass tracking framework and rotating the phase of the 3-D correlation function for robust filtering. The proposed speckle tracking approach significantly improves estimates of displacement gradients related to the axial displacement component. Non-axial displacement gradient estimates are enhanced using a correlation-weighted least-squares method constrained by tissue incompressibility. Simulated and in vivo canine cardiac datasets were evaluated to estimate Lagrangian strains from end-diastole to end-systole. The proposed speckle tracking method improves displacement estimation by a factor of 4.3 to 10.5 over conventional 1-pass processing. Maximum principal axis/direction imaging enables better detection of local disease regions than conventional strain imaging. Coordinate-independent tracking can identify myocardial abnormalities with high accuracy. This study offers enhanced accuracy and robustness in strain imaging compared to current methods.

Population displacement after earthquakes: benchmarking predictions based on housing damage

In the aftermath of an earthquake, the number of residents whose housing was destroyed is often used to approximate the number of people displaced (i.e., rendered homeless) after the event. While this metric can provide rapid situational awareness regarding potential long-term housing needs, more recent research highlights the importance of additional factors beyond housing damage within the scope of household displacement and return (e.g., utility disruption, tenure, place attachment). This study benchmarks population displacement estimates using this simplified conventional approach (i.e., only considering housing destruction) through three scenario models for recent earthquakes in Haiti, Japan, and Nepal. These model predictions are compared with officially reported values and alternate mobile location data-based estimates from the literature. The results highlight the promise of scenario models to realistically estimate population displacement and potential long-term housing needs after earthquakes, but also highlight a large range of uncertainty in the predicted values. Furthermore, purely basing displacement estimates on housing damage offers no view on how the displaced population counts vary with time as compared to more comprehensive models that include other factors influencing population return or alternative approaches, such as using mobile location data.

Constant-ductility inelastic displacement ratio spectra for design of superstructures in seismically isolated buildings

Constant-ductility inelastic displacement ratio (Cμ) spectra can be utilized for the estimation of peak inelastic structural displacements in the seismic design procedure. Currently, suitable analytical estimates of Cμ are lacking for base-isolated buildings with inelastic behavior of superstructures in a beyond design basis earthquake. This paper attempts to fill this research gap and hence conducts parametric studies on the Cμ spectra of base-isolated inelastic superstructures with lead-rubber bearings (LRBs). For that purpose, the inelastic model and equations of motion, boundary conditions of the analytical formulation of Cμ, and controlling parameters for the two-degree-of-freedom (2DF) superstructure-isolator system with LRBs are presented first. Subsequently, by analyzing the parameterized 2DF systems using an ensemble of strong earthquake records representative of a site with stiff soil conditions, the influence of controlling parameters, namely, displacement ductility ratios, superstructure periods, post-yielding stiffness ratios of superstructures, mass ratios, isolation periods and normalized isolator strength, on the mean and dispersion of Cμ are discussed, and the boundary conditions of Cμ are validated based on the calculated data. Comparisons of how the controlling parameters influence the Cμ and earlier investigated CR (i.e. constant-strength inelastic displacement ratio) spectra are also presented. Lastly, a predicting equation with reasonable accuracy is proposed for the mean Cμ using the nonlinear multivariable regression analysis method. The outcome of this study allows the application of displacement-based design via inelastic displacement ratio for new base-isolated structures under beyond design basis earthquakes.

Evaluation of Static Displacement Based on Ambient Vibration for Bridge Safety Management.

The evaluation of bridge safety is closely related to structural stiffness, with dynamic characteristics and displacement being key indicators. Displacement is a significant factor as it is a physical phenomenon that bridge users can directly perceive. However, accurately measuring displacement generally necessitates the installation of displacement meters within the bridge substructure and conducting load tests that require traffic closure, which can be cumbersome. This paper proposes a novel method that uses wireless accelerometers to measure ambient vibration data from bridges, extracts mode shapes and natural frequencies through the time domain decomposition (TDD) technique, and estimates static displacement under specific loads using the flexibility matrix. A field test on a 442.0 m cable-stayed bridge was conducted to verify the proposed method. The estimated displacement was compared with the actual displacement measured by a laser displacement sensor, resulting in an error rate of 3.58%. Additionally, an analysis of the accuracy of displacement estimation based on the number of measurement points indicated that securing at least seven measurement points keeps the error rate within 5%. This study could be effective for evaluating the safety of bridges in environments where load testing is difficult or for bridges that require periodic dynamic characteristics and displacement analysis due to repetitive vibrations, and it is expected to be applicable to various types of bridge structures.

Two-dimensional thermal and dynamical strain in landfast sea ice from InSAR: results from a new analytical inverse method and field observations

Abstract Observing continuous strain in sea ice at geophysical scales of tens of meters to kilometers requires displacement measurements made with millimeter-scale precision. Satellite-based interferometric synthetic aperture radar (InSAR) provides such precise measurements of relative surface displacement over broad spatial areas at regular intervals and, unlike point displacement measurements, it allows confident delineation of continuously deforming regions. However, InSAR only captures the 1-D component of surface displacement parallel to a radar's lines-of-sight. Additional analysis is required to translate between these 1-D observations and the horizontal or vertical displacements they arose from. Previous studies utilize an iterative inverse model to constrain estimates of horizontal surface displacement from InSAR. Here we build upon that work outlining a new analytical inverse modeling method for quantifying displacement and strain over continuous regions of sea ice and provide comparison between model results and independent displacement observations. We demonstrate the inverse method over both landfast and drifting ice along the Alaskan coastline. These intercomparisons highlight environments in which displacements inverted from interferograms may be used as an independent estimator of surface strain, as well as the potential for the outlined inverse methods to be used in conjunction with other observing methods.

Sub‐Pixel Displacement Estimation With Deep Learning: Application to Optical Satellite Images Containing Sharp Displacements

AbstractOptical image correlation is a powerful method for remotely constraining ground movement from optical satellite imagery related to natural disasters (e.g., earthquakes, volcanoes, landslides). This approach enables the characterization, and identification of the causal factors and mechanisms underlying such processes. By employing sub‐pixel correlation algorithms, one can obtain highly accurate (m‐to‐cm level) displacement fields at high spatial resolution (dm‐to‐cm) by comparing satellite images acquired before and after a period of movement. However, this method generally assumes a homogeneous translation of all pixels within a given correlation window, which will lead to biased estimates of ground displacement if the real case is not well represented by such a simplification, especially when resolving ground displacements next to sharp gradients in displacement, such as those found in the near‐field of earthquake surface ruptures. In this paper, we present an innovative deep learning method estimating sub‐pixel displacement maps from optical satellite images for the retrieval of ground displacement. From the generation of a realistic simulated database, comprising Landsat‐8 satellite image pairs containing simulated sub‐pixel shifts and sharp discontinuities, we develop a Convolutional Neural Network able to retrieve sub‐pixel displacements. The comparison to state‐of‐the‐art correlation methods shows that our pipeline significantly reduces by 32% the estimation bias around fault ruptures, leading to more accurate characterization of the near‐field strain in surface rupturing earthquakes. Application of our model to the 2019 Ridgecrest earthquake demonstrates the ability of our model to accurately and quickly resolve ground displacement using real satellite images. Code is made available at https://gricad‐gitlab.univ‐grenoble‐alpes.fr/montagtr/cnn4l‐discontinuities.

Improved GPS tropospheric path delay estimation using variable random walk process noise

Accurate positioning using the Global Positioning System relies on accurate modeling of tropospheric delay. Estimated tropospheric delay must vary sufficiently to capture true variations; otherwise, systematic errors propagate into estimated positions, particularly the vertical. However, if the allowed delay variation is too large, the propagation of data noise into all parameters is amplified, reducing precision. Here we investigate the optimal choice of tropospheric constraints applied in the GipsyX software, which are specified by values of random walk process noise. We use the variability of 5-min estimated positions as a proxy for tropospheric error. Given that weighted mean 5-min positions closely replicate 24-h solutions, our ultimate goal is to improve 24-h positions and other daily products, such as precise orbit parameters. The commonly adopted default constraint for the zenith wet delay (ZWD) is 3 mm/√(hr) for 5-min data intervals. Using this constraint, we observe spurious wave-like patterns of 5-min vertical displacement estimates with amplitudes ~ 100 mm coincident with Winter Storm Ezekiel of November 27, 2019, across the central/eastern USA. Loosening the constraint suppresses the spurious waves and reduces 5-min vertical displacement variability while improving water vapor estimates. Further improvement can be achieved when optimizing constraints regionally, or for each station. Globally, results are typically optimized in the range of 6–12 mm/√(hr). Generally, we at least recommend loosening the constraint from the current default of 3 mm/√(hr) to 6 mm/√(hr) for ZWD every 300 s. Constraint values must be scaled by √(x/300) for alternative data intervals of x seconds.

Ecological study measuring the association between conflict, environmental factors, and annual global cutaneous and mucocutaneous leishmaniasis incidence (2005-2022).

Cutaneous and mucocutaneous leishmaniasis (CL/ML) cause significant morbidity globally and are vulnerable to changes from environmental events and conflict. In this ecological study, we aim to measure the associations between annual CL/ML cases, conflict intensity, and environmental factors between 2005 and 2022 globally. We pulled annual case data from the WHO for 52 nations that had conflict intensity scores (ranging from 1-10) from the Bertelsmann Transformation Index. Using Earth observation tools, we gathered temperature, precipitation, vegetation, and humidity data, in addition to data on annual estimates of population, internal displacement, and GDP. We fit a negative binomial generalized additive model with a random nation-level intercept. Conflict was positively associated with increased CL/ML across the studied nations (IRR: 1.09, 95% CI: 1.01-1.16, p = 0.02). Given this, intense conflict (a score of ten) was associated with over double the risk of CL/ML compared to the lowest conflict levels (score of one). We also identified a curvilinear relationship between mean temperature and cases, as well as between vegetation level and cases. Each had small pockets of significant increased and decreased risk, respectively. Larger mean humidity ranges were negatively associated with cases. Importantly, the relationship between conflict intensity and cases was mediated by displacement. Conflict is significantly associated with increased CL/ML cases. This is especially true at higher conflict levels, marking when conflict turns violent. The destruction of critical infrastructure (e.g., that related to healthcare, water, and sanitation) often seen during conflict could drive this association. Such environments can be hospitable to sandflies and can heighten individuals' vulnerability through increased malnutrition, poverty, and displacement. Understanding this relationship is crucial for public health preparedness and response, especially as conflicts become increasingly violent and protracted.

AI-assisted analytical model of seismic displacement estimation for frictional isolated bridge portfolios under pulse-like ground motions

Accurate bearing displacement assessment is crucial for frictional isolated bridges under pulse-like ground motions. In order to cope with the efficiency requirement brought by large-scale bridge portfolio estimation, the artificial intelligence (AI) method, a powerful tool to address multi-parameter issues, is widely adopted in seismic performance analysis for bridge networks. However, the traditional machine learning (TML) method pursues the overall prediction performance, the prediction effect in sensitive intervals caused by pulse-effect can not be assured. To face this challenge, this study proposed an AI-assisted analytical (AIA) method, which owns the characteristics of high efficiency, high accuracy and clear physical meaning. In the first step of the AIA method, the relationship between primary factor (pulse period) and output (seismic displacement) is established through an analytical model; in the second step, the undetermined parameters of the analytical model are estimated with the assistance of the AI method. The results indicate that the AIA model only requires 0.1 times data for model training and achieves overall predictive performance similar to TML methods. Moreover, the predictive effect of the AIA model in the sensitive range is greatly improved compared to the TML method. Finally, based on AIA method, an effective seismic fragility prediction method is proposed for frictional isolated bridge networks. The fragility curves illustrated by AIA method and FE analysis are in good agreement, which exhibited the satisfactory efficiency of the proposed AIA method.

A unified feature-motion consistency framework for robust image matching

Establishing reliable feature matches between a pair of images in various scenarios is a long-standing open problem in photogrammetry. Attention-based detector-free matching with coarse-to-fine architecture has been a typical pipeline to build matches, but the cross-attention module with global receptive field may compromise the structural local consistency by introducing irrelevant regions (outliers). Motion field can maintain structural local consistency under the assumption that matches for adjacent features should be spatially proximate. However, motion field can only estimate local displacements between consecutive images and struggle with long-range displacements estimation in large-scale variation scenarios without spatial correlation priors. Moreover, large-scale variations may also disrupt the geometric consistency with the application of mutual nearest neighbor criterion in patch-level matching, making it difficult to recover accurate matches. In this paper, we propose a unified feature-motion consistency framework for robust image matching (MOMA), to maintain structural consistency at both global and local granularity in scale-discrepancy scenarios. MOMA devises a motion consistency-guided dependency range strategy (MDR) in cross attention, aggregating highly relevant regions within the motion consensus-restricted neighborhood to favor true matchable regions. Meanwhile, a unified framework with hierarchical attention structure is established to couple local motion field with global feature correspondence. The motion field provides local consistency constraints in feature aggregation, while feature correspondence provides spatial context prior to improve motion field estimation. To alleviate geometric inconsistency caused by hard nearest neighbor criterion, we propose an adaptive neighbor search (soft) strategy to address scale discrepancy. Extensive experiments on three datasets demonstrate that our method outperforms solid baselines, with AUC improvements of 4.73/4.02/3.34 in two-view pose estimation task at thresholds of 5°/10°/20° on Megadepth test, and 5.94% increase of accuracy at threshold of 1px in homography task on HPatches datasets. Furthermore, in the downstream tasks such as 3D mapping, the 3D models reconstructed using our method on the self-collected SYSU UAV datasets exhibit significant improvement in structural completeness and detail richness, manifesting its high applicability in wide downstream tasks. The code is publicly available at https://github.com/BunnyanChou/MOMA.

A compositional analysis of time spent in physical activity, sedentary behaviour and sleep with quality of life in Canadian older adults aged 65 years and above: Findings from the Canadian Longitudinal Study on Aging.

Associations between daily time spent in physical activity (PA), sedentary behaviour (SB) and sleep (collectively referred to as 'movement behaviour') and quality of life (QOL) are typically studied without considering they are compositional, co-dependant variables. Study objectives were to use compositional data analysis to: 1) examine the relationship between movement behaviour composition and QOL, 2) estimate the degree to which changing time spent in any movement behaviour within the movement behaviour composition is associated with QOL. 7,918 older Canadian adults ≥ 65 years of age from the Canadian Longitudinal Study on Aging were studied using a quasi-longitudinal study design. Daily time spent in PA and SB were derived from self-reported Physical Activity Scale for the Elderly responses. Nighttime sleep was self-reported separately. QOL was assessed through the Satisfaction with Life Scale. Movement behaviour composition was significantly associated with QOL. Relative time spent in SB was negatively associated with QOL [HR = 0.89 (95% CI: 0.86, 0.93)]. Relative time spent in sleep was positively associated with QOL [HR = 1.10 (95% CI: 1.05, 1.16)]. Time displacement estimates revealed that greatest change in QOL occurred when time spent in PA was decreased and replaced with SB [HR = 0.96 (95% CI: 0.92, 0.99) for 45 min/day displacement]. Using compositional data analysis is advantageous because it shows how reduction in SB and increase in PA and sleep can lead to improvements in QOL for older Canadian adults.

Investigation of the tissue displacement through textile pressure on soft avatar in Browzwear’s VStitcher software

Nowadays, soft avatars are used in various fields to simulate the behavior of human soft tissues in different applications. Likewise, they are also utilized in the garment industry in order to achieve a realistic testing of the fit and functionality of tight-fitting clothing. Therefore it is important that avatars in CAD programs for clothing conform to the mechanical properties of human soft tissue. The accuracy of the avatars' properties in simulating the change in shape of human tissue is crucial here, which is caused by the contact pressure that compressive or tight-fitting garments exert onto the body. In this study, Browzwear’s VStitcher soft avatar Sofia was investigated and different body shapes resulting from being influenced by a legging with different levels of negative ease values were compared with non-affected natural avatar body shape. The examination of the soft avatar simulation shows that although a fast estimation of the tissue displacement can be predicted, there are some shape changes limitations compared to the natural behavior of human soft tissue.

Seismic response prediction for buildings with sliding live loads using neural networks

The seismic response of primary structures (PS) can be significantly influenced by live loads, particularly when these loads consist of stacked bodies that are capable of sliding during seismic events. Conventional design methods often fail to account for the energy dissipation resulting from such sliding, leading to overly conservative structural estimates. This study examines the effects of sliding live loads on the seismic response of a PS, where two rigid bodies, referred to as secondary bodies (SBs), are stacked as live loads on a PS. The interaction between the lower SB and the PS, as well as between the SBs, is modelled using Coulomb's friction model. The governing equations are solved using the fourth-order Runge-Kutta method. Seismic Zones III and V from IS 1893:2016 are considered as hazard levels. A parametric investigation explores the impact of varying dynamic parameters of both the PS and SBs on the seismic response. The results demonstrate significant energy dissipation within the stack due to sliding, which, if not considered, results in conservative displacement estimates. The study also evaluates how friction coefficients, mass ratios, and excitation levels affect the stack's energy dissipation capacity. A novel method to compute the modified primary structural period (Tnew) for design purposes is proposed, and an artificial neural network (ANN) model is developed, achieving a high prediction accuracy (R2 = 99 %). Sensitivity analysis is performed to assess the influence of input parameters on the output. This research highlights the need to include sliding loads in seismic design.

Monocular vision-based structural out-of-plane motion estimation using a deep learning method

Computer vision-based displacement estimation methods can estimate structural motion from videos, but face challenges in estimating out-of-plane motion. Conventional vision-based methods employ either multi-view camera systems or structural model-aided monocular vision methods to estimate structural out-of-plane motion. Nonetheless, the utilization of multi-view camera systems leads to additional costs and stringent requirements for overlapping views, while structural model-aided methods require comprehensive structural information. To achieve convenient and accurate out-of-plane structural displacement measurement, this study presented a monocular vision-based measurement method using a deep learning technique. Firstly, a deep learning model was employed to estimate the global depth matrix of images. The relative depth of the region of interest (ROI) was then estimated through pyramid-accelerated tracking and relative depth matrix weighting. To convert the relative depth into actual out-of-plane motion, the scale factor was calculated through least squares fit. The performance of the proposed method was validated through static and dynamic tests. The results indicated that the proposed approach yielded reasonable out-of-plane motion estimations, with correlation coefficients with displacement sensor measurements over 0.93. The proposed method therefore offered a cost-effective and convenient alternative for structural out-of-plane motion estimation.

Investigation of the impact of local properties of 3D data on the accuracy of block matching-based speckle tracking echocardiography

Abstract Introduction: Due to its simplicity, block-matching is a popular motion-tracking method used in speckle-tracking echocardiography. Improvement of its robustness and accuracy is thus of prime interest. Although it seems plausible that the quality of block matching-based tracking depends on the local properties of image data, and thus, it should be possible to assess in advance how well certain portions of the image data are suited for displacement estimation, the potential relationship has not been studied extensively. Material and methods: This study aimed to search for a relationship between selected features of echocardiographic data and the quality of local displacement estimation. The study used a 3D synthetic B-mode imaging sequence data with known ground truth. Frame-to-frame displacements were estimated for 9856 points in five different frame pairs with mean inter-frame displacements of 0.15, 0.87, 2, 3.02, and 3.84 mm. In each case, tracking errors were evaluated against thirteen grayscale image features, the displacement’s magnitudes, and the normalized cross-correlation (NCX) values. Additionally, a multi-variable regression model was applied to test the combined ability of the proposed features to predict tracking quality. Results: Median tracking error magnitudes were 0.06, 0.13, 0.28, 0.74, and 1.5 mm for each image pair. Weak correlation between errors and individual data features was found only in the case of 3 features: NCX (Pearson’s correlation coefficients in the range of −0.366 to −0.223), number of speckles within the kernel (−0.283, −0.282, and −0.214 for three lowest deformations) and mean of the 3D gradient (−0.252, −0.237 and −0.25). The regression model, however, provided significant prediction improvement with R2 exceeding 0.5. Conclusions: In conclusion, only a weak relationship between the individual investigated kernel features and tracking accuracy has been established, but their combined strength can be assessed as at least moderate.

Gravity dam displacement monitoring using in situ strain and deep learning

AbstractRecent studies in dam displacement monitoring primarily focus on single‐response monitoring or model updating using advanced techniques. Few studies involve the combination analysis of displacement with other synchronized responses utilizing their monitoring characteristics. In situ strain data provide a strength‐safety perspective for dam displacement monitoring. The challenge lies in that estimating displacement directly using limited discrete strain data may be misleading. This paper analyzes the relationship between displacement and global, and multipoint local strains from the perspective of the differences in load effects of gravity dams, and indicates that introducing appropriate state factors improves the estimation. A displacement estimation model driven by strain data and state factors is developed using stacked convolutional neural network, and the variable relationships within the model are interpretated via accumulated local effects. Incorporating specific strength criteria, a novel displacement monitoring indicator based on the tensile safety of the dam heel is proposed. A case study of a gravity dam showcases the effectiveness of the proposed approach in comparison with the solely strain‐based model and the traditional hydrostatic‐seasonal‐time factors‐based model.

Stress-deformation analysis of the cracked elastic body

A new analytical plane Elastic Fracture Mechanics (LEFM) model of the effective elastic moduli exhibited by an isotropic elastic cracked solid in tensile and compressive stress fields is presented. The effective Young’s modulus and Poisson’s ratio E¯,v¯, respectively, relate the stresses applied to the cracked solid with its macroscopic deformation. In the case of a compressive stress field the effective elastic moduli depend solely on properly oriented cracks that are either open or closed. This model is then used for the stress and displacement estimations around a circular axisymmetric hole under internal pressure and external hydrostatic stress. The creation of the hole alters the stresses in its neighborhood, and induces a deterioration of the elastic moduli. In this manner, the effective elastic moduli depend on the radial distance from the hole’s boundary. The validation of the algorithm was done against Kirsch’s analytical solution of the axisymmetric hole problem for nearly zero density of cracks as well as for large values of the friction angle. The model predicts a lower tangential stress concentration at the wall of the hole compared to that predicted by the constant linear elasticity solution and a maximum stress concentration that is not necessarily located at the wall of the hole. This apparent enhancement of rock strength adjacent to the wall is more pronounced for larger concentrations of open cracks.

Study on the tribocharging properties of MgCO3 particles based on LFN-en-A model

Abstract As an efficient and environment-friendly method, electrostatic separation has gradually replaced flotation methods in the separation of magnesite in recent years. In the process of triboelectrostatic separation, the mineral particles are tribocharged driven by the air flow, then the trajectory is shifted under the action of the electric field, so as to realize the separation. The useful mineral in magnesite is MgCO3, but the theoretical research related to the charge characteristics of MgCO3 is not sufficient. Particle image velocimetry (PIV), as an indirect measurement technique, is able to obtain the velocity field of the fluids from images. However, the particles moving in the air have the issues such as excessive speed and small particle size, which make the traditional PIV has low accuracy in estimating the motion of particles. In this paper, a high-speed camera is used to capture the motion trajectory of tribocharged MgCO3 particles in a parallel electric field. A new optical flow method LFN-en-A network based on LiteFlowNet-en network is proposed to compute the particle motion trajectory by combining the deep learning method with the traditional PIV, which realizes the displacement estimation of particles moving in the air. It ultimately realizes the calculation of the charge-to-mass ratio on single particles. Analyzing the accuracy of the LFN-en-A network’s estimation in the experiments, the estimation of LiteFlowNet-en was compared. Changing the shooting frame rate analyzes the optimal one required by the LFN-en-A network. Combining the estimation results of LFN-en-A to calculate the particle charge-to-mass ratio (Q/m), the Q/m of MgCO3 particle was analyzed by changing the experimental conditions in the process of particles’ tribocharging, which provided a new method for particle-to-charge ratio measurement.