Axis Of Ellipse Research Articles

Mappings contracting axes of ellipse

Mappings contracting axes of ellipse

Polarization Möbius strip at the tight focus of a generalized Poincaré beam

Based on the Richards-Wolf formalism, we investigate tight focusing of a generalized Poincaré beam. Analytical expressions are derived for all components of the electric field strength vector in the focal plane. For superposition of a right-handed circularly polarized plane wave with a left-handed circularly polarized optical vortex with topological charge –1, we obtain expressions for the intensity distribution and the longitudinal component of the spin angular momentum vector at the tight focus. We demonstrate both theoretically and numerically that the initial beam has topological charge –1/2 and, in the center of the focal plane, there is a C-point (a point with circular polarization which makes a C-line along the optical axis) with the singularity index of –1/2 (star), whereas the vector of major axis of the polarization ellipse makes along a certain-radius circle around the optical axis a single-side polarization Möbius stripe of the order –3/2, which has three half-turnovers and one stitching, where two opposite major axis vectors of the polarization ellipse meet.

GENETIC ALGORITHM FOR SELECTING OPERATIONS FOR LOCALIZATION OF OBJECTS ON COMPLEX STRUCTURED IMAGES

A genetic algorithm has been developed that implements the automatic selection of operations for processing complex structured images at the stage of localization of point objects. The algorithm is distinguished by the representation of a set of operations in the form of a variable-length chromosome, combining the performance of both halftone and binary morphological transformations and filters, a developed fitness function that takes into account the recall and IoU measure together, and a set of genetic operators (crossover and special types of mutation) corresponding to the task. Dilation, erosion, opening, closing, and skeletonization were studied as morphological operations. Clipping by area, eccentricity, and dimensions of the major and minor axes of the equivalent ellipse were used as filters. The genetic algorithm was launched and experimentally tested on scanned topographic maps of the USSR from 1965−1982, as typical representatives of images with a complex structure, together with sets of morphological operations obtained manually to determine objects of the “elevation mark” type. The quality criteria were the proportion of localized pixels, the number of missed images, and the processing time. For training on multiple images, the fitness function was modified in two ways: soft (averaging calculation for all images) and hard (zeroing the value of fitness function with a decrease in recall on at least one training image). The hard calculation of the fitness function turned out to be more effective, the final set of operations consists of 10 operations with a decrease in the number of localized pixels by 2,6 times. The results show that the use of a genetic algorithm for the selection of localization operations makes it possible to reduce the total number of localized pixels with reducing the overall operating time, taking into account the recognition stage, which allows us to conclude that it is consistent for image processing.

Tidal and residual currents in the inner shelf of East China Sea detected from underway ADCP observations

Characterizing the spatial variability of net flow transport in a tide-dominated area like the East China Sea (ECS) is key to understanding the material and heat budget as well as their impacts on local ecosystem. However, the residual circulation in the ECS was much less confirmed by observations as it can only be derived from very sparse mooring data. Here for the first time we obtain the spatial patterns of tidal and residual currents in the inner ECS shelf from ADCP underway measurements conducted in 12 cruises using a spatial least squares (SLS) fitting technique. The SLS method is validated with the traditional harmonic analysis using numerical simulation results and then implemented with the observational data. The tidal current is dominated by two semidiurnal components M2 and S2 in this area, with the major axis of tidal ellipse along northwest-southeast direction. The ADCP-derived tide parameters are in good agreement with those from the mooring data and barotropic tide model. The annual spatial pattern of residual circulation is characterized by a southward coastal current and a northward shelf current, which are identified as the East China Sea Coastal Current (ECSCC) from Changjiang River runoff and the Taiwan Warm Current (TWC) originated from Taiwan Strait and Kuroshio. Their magnitudes are comparable but of one order smaller than tides. The vertical structure of TWC shows a subsurface-intensified feature in line with previous mooring observations. The north limit of TWC is approximately at 31.5°N around the submerged valley, beyond which the northward TWC becomes almost invisible. By a series of virtual cruise experiments, we show that the observation data length is the most crucial factor controlling the SLS fitting accuracy, while the role of other factors like sampling frequency is secondary. With a fixed-length dataset, the degree of polynomial function used for SLS fitting must be properly determined to minimize the under-fitting and over-fitting error, and there is also a trade-off in the fitting accuracy between tidal and residual currents depending on the fitting strategy.

Identification of failure behaviors of underground structures under dynamic loading using machine learning

Understanding the dynamic responses of hard rocks is crucial during deep mining and tunneling activities and when constructing nuclear waste repositories. However, the response of deep massive rocks with openings of different shapes and orientations to dynamic loading is not well understood. Therefore, this study investigates the dynamic responses of hard rocks of deep underground excavation activities. Split Hopkins Pressure Bar (SHPB) tests on granite with holes of different shapes (rectangle, circle, vertical ellipse (elliptical short (ES) axis parallel to the impact load direction), and horizontal ellipse (elliptical long (EL) axis parallel to the impact load direction)) were carried out. The influence of hole shape and location on the dynamic responses was analyzed to reveal the rocks' dynamic strengths and cracking characteristics. We used the ResNet18 (convolutional neural network-based) network to recognize crack types using high-speed photographs. Moreover, a prediction model for the stress-strain response of rocks with different openings was established using Deep Neural Network (DNN). The results show that the dynamic strengths of the granite with EL and ES holes are the highest and lowest, respectively. The strength-weakening coefficient decreases first and then increases with an increase of thickness-span ratio (h/L). The weakening of the granite with ES holes is the most obvious. The ResNet18 network can improve the analyzing efficiency of the cracking mechanism, and the trained model's recognition accuracy reaches 99%. Finally, the dynamic stress-strain prediction model can predict the complete stress-strain curve well, with an accuracy above 85%.

P.152 In-vivo accuracy of pedicle screws utilizing a supervisory controlled 7DOF robot with OCT guidance

Background: Pedicle screw fixation is an important technique in spine surgery. Violation of the pedicle can lead to neurovascular injury. Due to excellent pose repeatability, robotic technology may improve accuracy. Existing surgical spine robots use surgical assist architecture. This work explores the performance of a supervisory-control architecture robot (8i Robotics) for autonomous pedicle instrumentation. Methods: 3 porcine subjects underwent pedicle instrumentation utilizing the 7dof robot and were observed for 24 hours. Post-operative CT assessed screw location. Screws were graded clinically with the Gertzbein-Robbins Scale (GRS). Precision was assessed by a customized image processing pipeline. Euclidean error was calculated at screw head and screw tip. All points were normalized to a nominal screw, and confidence ellipses generated. Results: All animals were neurologically intact at 24 hours. All screws where GRS A. Mean tip and head Euclidean error where 2.47+/−1.25mm and 2.25+/-1.25mm respectively. Major and minor axes of the confidence ellipse at 99% was 2.19mm, and 1.28mm, and 2.07mm, and 0.42mm for tip and head respectively. Conclusions: 100% of screws obtained satisfactory clinical grading, with intact function in all animals post-operatively. This shows the capability of a supervisory-controlled 7DOF robot with OCT registration. Further investigation is warranted to further explore robotic capabilities, safety, and cost effectiveness.

Transverse Spin Hall Effect and Twisted Polarization Ribbons at the Sharp Focus

Transverse Spin Hall Effect and Twisted Polarization Ribbons at the Sharp Focus

A novel method for predicting coarse aggregate particle size distribution based on segment anything model and machine learning

Particle size distribution (PSD) is an important index property of granular materials. The conventional mechanical sieve analysis for PSD determination is labor-intensive, time-consuming, and inefficient. With the development of computer vision, image-based gradation prediction methods gradually emerge. However, previous studies mainly focused on images where individual aggregate particles are separated from each other without overlapping (i.e., not densely packed together), thus limiting their applicability. This study proposed a novel framework to predict the PSD of densely packed coarse aggregate particles, which is based on visual foundation model and machine learning with appropriate feature engineering. First, the segment anything model, which is one of the visual foundation models, was used for the instance segmentation of the densely packed aggregate particles. Then, the feature engineering was implemented with the segmentation result. The major quantitative indicators related to particle sizes were extracted from each mask, such as the area, the diameter of minimum enclosing circle, and the major axes of the equivalent ellipse of particle contours. Subsequently, the cumulative distribution curves of these indicators were plotted, followed by the data sampling operation on these curves to generate the feature vectors. The artificial neural network (ANN) model was then trained for gradation prediction with each of the feature vectors and the data points extracted from PSD curves used as the inputs and data labels, respectively. The model-training dataset consisted of 8160 different sets of digitally generated particle samples with known PSDs. Finally, verification test results of additional five different groups of digital particle samples and real coarse aggregate samples with known PSDs show that the root mean squared error (RMSE) of predicted aggregate sizes is 1.79 mm and 1.86 mm for digital and real aggregate particle samples, respectively. Therefore, the efficacy and feasibility of the proposed method was validated in terms of predicting the PSD of densely packed coarse aggregates from two-dimensional image information. As compared to the Mask RCNN combined with empirical formula of which the RMSE values were 5.12 mm and 5.84 mm for digital and real aggregate particle samples, respectively, the proposed framework demonstrates improved particle segmentation applicability and better PSD prediction accuracy.

Bone Density Distribution Pattern in the Lateral Wall of the Femoral Intercondylar Notch: Implications for the Direct Insertion of the Femoral ACL Attachment

Background: The ideal position of the femoral bone tunnel in the anterior cruciate ligament (ACL) is controversial. The functional importance of the ACL fiber varies depending on where it is attached to the femur. Functionally important fibers can cause high mechanical stress on the bone, and the Wolff law predicts that bone mineral density will increase at high mechanical stress sites. Purpose/Hypothesis: The purpose of this study was to use computed tomography imaging to determine the distribution pattern of bone density in the lateral intercondylar wall. It was hypothesized that the high-density area (HDA) of the lateral intercondylar wall would reflect the functional insertion of the ACL as reported in previous anatomic studies. Study Design: Descriptive epidemiology study. Methods: Data from 39 knees without ACL injuries were retrospectively collected. The HDA of the lateral intercondylar wall was defined as the region containing the top 10% of the radiodensity values. The shape of the HDA was approximated as an ellipse, and the quadrant method was used to determine the center of the ellipse. The association between the ratio of the minor axis to the major axis of the ellipse and background characteristics was investigated. Results: According to the quadrant method, the center of the HDA ellipse was 33.6% in the deep-shallow direction and 23.4% in the high-low direction. The center of the ellipse was comparable to the anatomic center of the ACL footprint, as previously reported. The ratio of the minor axis to the major axis of the ellipse was 0.58 (95% CI, 0.54-0.62). There was a significant negative correlation between the ratio of the minor axis to the major axis of the HDA ellipse and the posterior tibial slope ( r = −0.38, P = .02). Conclusion: The center of the HDA ellipse was found to be similar to the anatomic center of the ACL footprint. Considering the mechanical stress responses in bone, the HDA of the lateral intercondylar wall has the potential to represent the ACL insertion, especially functional insertion.

Short-term forecasting method for prevailing orientation of leads in the Laptev Sea ice cover during winter-spring season

Sea ice leads are potential routes of easier navigation in the Arctic seas during winter-spring season. Forecasts of the prevailing orientation of ice leads are required for the early selection of the optimal route of a ship in ice. An automated method for short-term forecasting of the prevailing orientation of leads in the Laptev Sea is developed in AARI based on the analog method. Data sources for making a forecast include predictive fields of atmospheric pressure up to 3 days in advance and historical data on surface atmospheric pressure, ice drift and sea ice leads. The data on ice leads are obtained by interpreting SuomiNPP satellite images in a visible and infrared range at 375 m spatial resolution for the cold seasons 2016–2022. The ice drift data are freely available OSI SAF data. In order to make a forecast of the prevailing orientation of leads by a predictive atmospheric pressure field, it is necessary to select from an electronic data archive a historical field of atmospheric pressure that is the most similar to the predictive field. The lead characteristics on the selected date are taken as the predictive ones. Automated selection of an analog consists in searching for an atmospheric pressure field from the electronic data archive which has minimal metrics for the forecast date together with 2 previous days. The metric is calculated as the sum of the squared differences between the change in atmospheric pressure per 1 km in the latitudinal and meridional directions between the predictive atmospheric pressure field and the potential analog field. Actual lead data for a date of the selected analog may not be available due to thick clouds. In this case, the direction of the minor axis of the strain ellipse calculated from ice drift data is taken as the prevailing orientation of leads. The success ratio of diagnostic forecasts by the method developed is 72 %. Comparison of the success ratio of the diagnostic forecasts with the results of inertial and climatic forecasts demonstrates a high effectiveness of the method for cases of abrupt change in the direction of air flows over the Laptev Sea within the first 1–2 days.

A PGC demodulation scheme based on the Lissajous ellipse fitting for homodyne interferometer without using second harmonic carrier signal

This paper proposes a phase generated carrier (PGC) demodulation scheme for sinusoidal phase modulation interferometer (SPMI) that does not require a second harmonic carrier signal. In this scheme, an in-phase interference signal component with direct current (DC) bias is obtained by low-pass filtering the original interference signal, and a quadrature interference signal component is obtained by conventional means. The Lissajous figure formed by these two quadrature interference signal components is an ellipse whose center deviates from the origin of the I-Q coordinates. By fitting this ellipse, the major and minor axes and the center coordinates can be obtained. These elliptic parameters are then used to eliminate DC bias and normalize the amplitude of the quadrature signal components. Finally, the phase demodulation of the interference signal can be realized by using arctangent algorithm or differential cross multiplication (DCM) algorithm. The results of simulation and experiment have verified the validity and accuracy of the proposed PGC demodulation scheme, and show that it is insensitive to the phase modulation depth C. Compared with conventional PGC demodulation, this scheme requires lower depth of carrier phase modulation. The vibration measurement results indicate that the average signal-to-noise and distortion Ratio (SINAD) and total harmonic distortion (THD) values of demodulation results in the frequency range of 130 Hz to 250 Hz are 34 dB and -33 dB respectively. The proposed PGC demodulation scheme shows good performance in displacement measurement using SPMI.

Polarization-controlled ultrasmall single photon emitter combining a quantum dot and an elliptical split ring metamaterial element

We propose a polarization-controlled ultrasmall single-photon emitter that combines a single photon source and an elliptical split ring (SR) type metamaterial element. Simulations using the finite difference time domain method showed that in elliptical metamaterial elements, the annular mode is suppressed and axial electric field oscillations occur preferentially, resulting in upward light emission from the photon source with controlled polarization. We fabricated prototype devices by focused ion beam lithography and PbS quantum dots. Evaluation of the optical properties of the devices revealed that the emission spectrum width was narrower and the emission lifetime was shorter than those of quantum dot ensemble, and that the polarization was controlled along the minor axis of ellipse. These suggested that the quantum dot emission and the metamaterial element resonated as expected. The combination of a single quantum dot and a single elliptical SR-type metamaterial element was shown to have the potential to operate as a polarization-controlled single-photon emitter.

Wear characteristics analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission considering assembly error theory

Wear is the main failure form of the gear transmission interface, runs through the whole life cycle of gear service, and the distributed error of the tooth surface due to the introduced assembly error will make the actual meshing state of the tooth surface different from the ideal meshing state, thus affecting the tooth surface wear trajectory and state. Therefore, considering the coupling relationship between assembly error and tooth surface contact analysis, the variation laws of the wear amount of the gear transmission interface of the variable hyperbolic circular-arc-tooth-trace cylindrical gear were studied under the consideration of assembly error in this article. Based on the tooth surface contact analysis method and Hertz contact theory, the transient linear load, the combined radius of curvature, the length axis and short axis of the contact ellipse, and the instantaneous sliding velocity were calculated. Through revising the calculation method of adhesive wear of variable hyperbolic circular-arc-tooth-trace cylindrical gears, the correlations between the tooth surface wear amount and gear parameters of variable hyperbolic circular-arc-tooth-trace cylindrical gears under different assembly errors were analyzed. The results show that the maximum wear occurs at the root of the tooth, and the wear at the indexing circle approaches zero, whether it is standard installation or non-standard installation. The vertical axial error and horizontal axial error have little effect on the wear, while the center distance error will aggravate the wear. The proposed method comprehensively considers the influence of assembly error and gear parameters on tooth surface wear, and this method can provide a theoretical reference for the design and analysis of anti-wear, wear reduction, and life extension of variable hyperbolic circular-arc-tooth-trace cylindrical gear tooth surface.

Effect of light ellipticity and polarization angle on the transient dynamics of the ground-state Hanle effect

We report theoretical investigations on the transient dynamics of the ground-state Hanle effect in the Voigt geometry, where a time-varying scanning magnetic field B (t) is applied perpendicular to the light propagation direction. Transient Hanle signals are calculated for different light polarizations using a theoretical model based on the density matrix approach. First, we study the ellipticity dependence of transient Hanle signals in two configurations in which the major axis of the light polarization ellipse () is aligned either perpendicular or parallel to the field B . For B , elliptical polarization of the light produces oscillations of frequencies 2ΩL(t) and ΩL(t) simultaneously, where ΩL(t) is the Larmor frequency of the corresponding field B (t). On the other hand, in the case of || B , only ΩL(t) oscillation is observed using elliptically polarized light. Second, we vary the tilt angle between the polarization vector of a linearly polarized light and the orientation of the field B and study its effect on the transient response of Hanle signals. Both the amplitude and the decay rate of the oscillations show a strong dependence on the light ellipticity and tilt angle of the polarization vector. In addition, the influence of the magnetic field sweep rate on the transient signals is demonstrated for given values of light ellipticity and polarization angle.

The influence of diabetes and age-related degeneration on body balance control during static standing: a study based on plantar center-of-pressure trajectories and principal component analysis

BackgroundAging and diabetes can impair the balance function of the elderly and diabetic patients and increase their fall risk. This study aimed to assess the shaking amplitude of the center-of-pressure (CoP) during static standing, to analyze the effects of aging and diabetes on the balance control.Materials and methodsThis cross-sectional observational study, compared the balance performance of 20 healthy younger adults (27.65 ± 5.60 years), 16 healthy older adults (58.88 ± 3.54 years) and 15 diabetic patients (58.33 ± 5.33 years) in four static standing conditions on a force plate: horizontal, anteroposterior (AP), left and right slope planes (5° angles on AP, left and right directions, respectively). The trajectory coordinates of the CoP over time were recorded and analyzed by principal components analysis to obtain the 95% confidence ellipse and its parameters: angle, major and minor axes lengths, and area. The balance indicators were compared among the three groups using one-way analysis of variance (ANOVA), Brown–Forsythe test or Kruskal–Wallis H test, depending on the normality and homogeneity of variance assumptions.ResultsThe diabetic group had a significantly larger confidence ellipse area than the healthy younger adults on the horizontal plane (P = 0.032) and than the healthy older adults on the horizontal (P = 0.036), AP slope (P = 0.023), and right ML slope (P = 0.037) planes. There were no significant differences in the major axis length of the confidence ellipse among the three groups. The diabetic group had a significantly longer minor axis length than the healthy younger adults on the AP slope (P = 0.039), left ML slope (P = 0.045) and right ML slope (P = 0.016) planes and than the healthy older adults on the AP slope (P = 0.007), left ML slope (P = 0.035) and right ML slope (P = 0.012) planes.ConclusionsThe balance control of diabetic patients is decreased compared with healthy younger and older people, and the body swing amplitude increases mainly in the direction of minor axis of confidence ellipse during static standing, while the swing amplitude in the direction of the major axis has no significant change. Evaluating the balance function of diabetic patients can help clinicians identify people with fall risk early and intervene early, thereby reducing the occurrence of fall events in this population.

Research on desktop object grasping based on ellipse fitting

The grasping operation task in service scenes faces several problems including too many kinds of objects and a large amount of training data. This paper focuses on the grasping strategy and pose detection in desktop object grasping tasks. A grasping strategy is given based on the combination of desktop normal vector detection, object category detection, and grasping pose detection. The grasping pose is calculated by ellipse fitting on the depth map. An optimal function is designed to evaluate the possibility of the object sliding along the ellipse axis and the stability of the grasping height. The most reliable grasping pose is selected. Finally, experiments were carried out with a six-degree-of-freedom manipulator, and the proposed grasping method achieved effective grasping of desktop objects without prior knowledge of the object.

On the flow past ellipses in a Hele-Shaw cell

In this work we investigate the effect of vertical confinement and inertia on the flow past thin ellipses in a Hele-Shaw cell (with centre line velocity $U_c$ and height 2 $h$ ) with different aspect ratios for symmetrical flows and at an angle of attack, using asymptotic methods and numerical simulations. A Stokes region is identified at the ellipse vertices which results in flow different to flow past bluff bodies. Comparison with asymptotic analysis indicates close agreement over the ‘flat’ portion of the ellipse, for $\delta =(b/a)=0.05$ , where $a$ and $b$ are the semi-major and -minor ellipse axes, respectively. Two flow conditions are investigated for ellipses at an angle of attack of 10 $^\circ$ for a fixed $\delta =0.05$ . Firstly, for $\varLambda =(U_ca/\nu )(h/a)^2 \ll 1$ , the effect of increasing the vertical confinement of the Hele-Shaw cell results in the rear stagnation point (RSP) moving from close to the potential-flow prediction when $\epsilon =h/a$ is very small to the two-dimensional Stokes-flow prediction when $\epsilon$ is large. Secondly, for a fixed $\epsilon \ll 1$ , when inertia is increased past $\varLambda ={O}(\epsilon )$ the RSP moves towards the trailing edge and is located there for $\varLambda ={O}(1)$ . Under these conditions an attached exponentially decaying shear layer or ‘viscous tail’ is formed. A modified Bernoulli equation of the depth-averaged flow, together with the Kutta–Joukowski theorem is used to predict the drag and lift coefficients on the ellipse, which include a linear and a nonlinear contribution, corresponding to a Hele-Shaw and circulation component, respectively. Close agreement is found up to $\varLambda ={O}(1)$ .

The star in RNO 54: A possible post-FUor with a short faint jet

Aims. The aim of the present study is to analyze the spectra of an unusual pre-main sequence star in the cometary nebula RNO 54, which is suspected by several researchers to be a FUori-like object. Methods. We performed long-slit spectroscopy of the star using the 6m telescope with the SCORPIO-2 multi-mode focal reducer. Results. We discover a short (~4″ or ~6000 AU) and faint emission shock-excited jet from this star, probably oriented toward the long axis of the nebular ellipse. The spectral type of the star is estimated as G0-2 II; we confirm the split of the Li I absorption line, which is a typical sign indicating a FUori-like spectrum. Our analysis of the available data reveals an almost null photometric variability over at least the last 20 years. The lower limit of the bolometric luminosity of the star is estimated as 300 L⊙. Our study supports the classification of RNO 54 as a FUor-like star in the long post-outburst stage.

Numerical study of the influence of blade inlet design parameters on the internal flow characteristics and energy performance of a Francis turbine

One of the challenges of hydraulic turbine design is the creation of a conveyor with high hydraulic performance in accordance with the parameters of the hydraulic energy. The blade inlet parameters, such as blade beta angle, lean angle, and ellipse axis ratio, have an effect on the performance and cavitation characteristics of the runner, among the numerous geometric elements that regulate turbine performance. All of these parameters must be optimized to ensure that the runner inlet is matched to the guide vane under design conditions and a wider range of off-design conditions. For hydraulic designers, computational fluid dynamics based performance prediction methods can provide rapid turbine performance predictions and expedite runner development. Finding a collection of accessible parameters, meanwhile, strongly depends on the designer’s previous design work, which is frequently time-consuming. In this article, the internal flow characteristics and energy performance of a Francis turbine with moderate specific-speed, as well as the blade leading edge geometrical parameters that influence them, are investigated in depth. The Francis turbine is designed in accordance with the rated head H (m), rated flow rate Q (m), and rated speed n (rpm) within the constraints of the fixed meridional projection, including the leading-edge and trailing-edge positions. The energy performance, internal flow characteristics, velocity profile, flow angles, pressure distribution, blade loading, and cavitation characteristics are computed, analyzed, and compared. The main findings can serve as a guide for the development of Francis turbines with moderate specific-speed.

Crack detection in ultrahigh-performance concrete using robust principal component analysis and characteristic evaluation in the frequency domain

Studying the crack propagation of ultrahigh-performance concrete (UHPC) helps us understand its mechanical mechanism and assess its structural performance. A novel method for crack separation and its characteristic evaluation was developed in this work. The proposed method introduces robust principal component analysis (RPCA) to decompose a data matrix from video streams stacked into a low-rank matrix and a sparse matrix, in which the sparse matrix represents the crack information. Compared with the cracks in a binary image, the obtained sparse matrix preserves rich crack information that can be used to quantify crack characteristics. The statistical characteristics of the crack area, the major and minor axes of the equivalent ellipse for crack regions, and the power spectral density are investigated and compared continuously. The proposed method is demonstrated by the crack development of UHPC under tensile loading. The analysis results indicate that RPCA can accurately separate cracks from the background. In the frequency domain by performing the Fourier transform of the sparse matrix, cracks are concentrated at small wavenumbers and the magnitude of small wavenumbers increases with an increase in the crack width. The relationship between the crack propagation and the stress–strain is also discussed. This work provides insight into the crack propagation of UHPC and an accumulated crack database for predicting the damage evolution of UHPC.