Geometric Similarity Research Articles

Evaluation of derivative in damping in the Newtonian limit for non-planar wedge

The current work derives the analytical expression for damping derivative of a non planar wedge when γ tends to one and Mach number tends to infinity. Ghosh’s developed strip theory is utilized to derive the expression of damping derivative. With regard to a variety of geometrical and flow characteristics, the current theory can forecast the damping derivatives of a non planar wedge. Prior to performing exhaustive calculations and trial research, it is vital to know about these damping derivatives in order to freeze and arrive at the geometrical and kinematic similarity parameters. The ongoing technique, which is exceptionally useful during the plan stage, predicts the damping subordinates in pitch for a flat wedge effortlessly. In the Newtonian limit, the equations derived for stability derivatives become precise. The pivot position is found to influence the damping derivative directly.Additionally, it has been noted that at high angles of attack, the centre of pressure shifts significantly from the leading edge to the trailing edge. Consequently, according to the viewpoint of stability, this behavior may be utilized to stabilize the aeronautical vehicle. Therefore, in this case, the expression for the damping derivative is non-linear, the findings have been affected accordingly. However, the behaviour is linear up to a fifteen degree angle of attack before the pattern becomes non-linear.

Visual localization with a monocular camera for unmanned aerial vehicle based on landmark detection and tracking using YOLOv5 and DeepSORT

Absolute visual localization is of significant importance for unmanned aerial vehicles when the satellite-based localization system is not available. With the rapid evolution in the field of deep learning, the real-time visual detection and tracking of landmarks by an unmanned aerial vehicle could be implemented onboard. This study demonstrates a landmark-based visual localization framework for unmanned aerial vehicles flying at low altitudes. YOLOv5 and DeepSORT are used for multi-object detection and tracking, respectively. The unmanned aerial vehicle localization is achieved according to the geometric similarity between the geotagged transmission towers and the annotated images captured by a monocular camera. The validation is accomplished both in the Rflysim-based simulation and the quadrotor-based real flight. The localization precision is about 10 m, and the location update frequency reaches 5 Hz with a commercially available entry-level edge artificial intelligence platform. The proposed visual localization strategy needs no satellite image as a reference map, which saves a significant amount of the GPU memory and makes possible the end-to-end implementation on small unmanned aerial vehicles.

Shape correspondence for cel animation based on a shape association graph and spectral matching

We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes. We formulate the correspondence problem as an adapted quadratic assignment problem, which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence. To simultaneously represent the geometric and topological similarities between regions, we propose a shape association graph (SAG), whose node attributes indicate the geometric distance between regions, and whose edge attributes indicate the topological distance between combined region pairs. We convert topological distance to geometric distance between geometric objects with topological features of the pairs, and introduce Kendall shape space to calculate the intrinsic geometric distance. By utilizing the spectral properties of the affinity matrix induced by the SAG, our approach can efficiently extract globally optimal region correspondences, even if shapes have inconsistent topology and severe deformation. It is also robust to shapes undergoing similarity transformations, and compatible with parallel computing techniques.

A multi-scale coupled productivity prediction model for conflagration compression fracturing of shale

A multi-fracture pressure flow regime coupled productivity prediction model considering shale gas adsorption and desorption, mass transfer and diffusion and cross-scale zoning was established based on cross-scale seepage characterization in unmodified area, interstitial matrix area, main fracture area, branched micro-fracture area and broken damage area formed from by conflagration compression fracturing. Then, geometric similarity, hydropower similarity and coupled iteration were used to build the model and complete the calculation. Finally, the effects of regional cross-scale seepage, number of fractures, production pressure difference, and fracture zone scale on gas well productivity were analyzed. The following results were obtained. First, the seepage flow of shale gas in different fractured areas is a continuous changing process. Among them, the unaffected area is dominated by transition flow and slip flow while continuous flow exists in the microfracture area-wellbore broken area and artificial fracture area. Second, the productivity of gas wells increases with the increase of fracture length and number, but the productivity increase tends to be stable after the fracture length exceeds 2 m. It is worth to mention that the increase of the number of fractures is more conducive to improving the productivity of shale gas under this condition. Third, when the number of high energy gas fractures is 6, its mining capacity is equivalent to that of hydraulic fracturing fractures with a half-fracture length of about 100 m. Fourth, when the production pressure difference exceeds 22 MPa, the free gas production capacity shows a decreasing trend. Therefore, the preferred production pressure difference is about 22 MPa. Fifth, the greater the number of artificial fractures, the greater the contribution of the increase in the diffusion coefficient to productivity, and the existence of wellbore fracture zone is also conducive to the stimulation of gas wells.

The relative contributions of multiarticular snake muscles to movement in different planes.

Muscles spanning multiple joints play important functional roles in a wide range of systems across tetrapods; however, their fundamental mechanics are poorly understood, particularly the consequences of anatomical position on mechanical advantage. Snakes provide an excellent study system for advancing this topic. They rely on the axial muscles for many activities, including striking, constriction, defensive displays, and locomotion. Moreover, those muscles span from one or a few vertebrae to over 30, and anatomy varies among muscles and among species. We characterized the anatomy of major epaxial muscles in a size series of corn snakes (Pantherophis guttatus) using diceCT scans, and then took several approaches to calculating contributions of each muscle to force and motion generated during body bending, starting from a highly simplistic model and moving to increasingly complex and realistic models. Only the most realistic model yielded equations that included the consequence of muscle span on torque-displacement trade-offs, as well as resolving ambiguities that arose from simpler models. We also tested whether muscle cross-sectional areas or lever arms (total magnitude or pitch/yaw/roll components) were related to snake mass, longitudinal body region (anterior, middle, posterior), and/or muscle group (semispinalis-spinalis, multifidus, longissimus dorsi, iliocostalis, and levator costae). Muscle cross-sectional areas generally scaled with positive allometry, and most lever arms did not depart significantly from geometric similarity (isometry). The levator costae had lower cross-sectional area than the four epaxial muscles, which did not differ significantly from each other in cross-sectional area. Lever arm total magnitudes and components differed among muscles. We found some evidence for regional variation, indicating that functional regionalization merits further investigation. Our results contribute to knowledge of snake muscles specifically and multiarticular muscle systems generally, providing a foundation for future comparisons across species and bioinspired multiarticular systems.

A pulmonary vein atlas for radiotherapy planning

Background and PurposeCardiac arrhythmia is a recognised potential complication of thoracic radiotherapy, but the responsible cardiac substructures for arrhythmogenesis have not been identified. Arrhythmogenic tissue is commonly located in the pulmonary veins (PVs) of cardiology patients with arrhythmia, however these structures are not currently considered organs-at-risk during radiotherapy planning. A standardised approach to their delineation was developed and evaluated. Materials and MethodsThe gross and radiological anatomy relevant to atrial fibrillation was derived from cardiology and radiology literature by a multidisciplinary team. A region of interest and contouring instructions for radiotherapy computed tomography scans were iteratively developed and subsequently evaluated. Radiation oncologists (n = 5) and radiation technologists (n = 2) contoured the PVs on the four-dimensional planning datasets of five patients with locally advanced lung cancer treated with 1.8–2.75 Gy fractions. Contours were compared to reference contours agreed by the researchers using geometric and dosimetric parameters. ResultsThe mean dose to the PVs was 35% prescription dose. Geometric and dosimetric similarity of the observer contours with reference contours was fair, with an overall mean Dice of 0.80 ± 0.02. The right superior PV (mean DSC 0.83 ± 0.02) had better overlap than the left (mean DSC 0.80 ± 0.03), but the inferior PVs were equivalent (mean DSC of 0.78). The mean difference in mean dose was 0.79 Gy ± 0.71 (1.46% ± 1.25). ConclusionA PV atlas with multidisciplinary approval led to reproducible delineation for radiotherapy planning, supporting the utility of the atlas in future clinical radiotherapy cardiotoxicity research encompassing arrhythmia endpoints.

Scale-up and Economic Assessment of Biofunctional Particles Synthesis for Bilirubin Removal

The scale-up and the economic feasibility of the synthesis of St-MMA-GMA-PEGMA particles biofunctionalized with HSA were studied. First, the geometrical similarity of laboratory and pilot plant reactors was checked to develop the scale up of the process according to a criterion of partial similarity. The selected criterion was constant Re number. Then, a reaction in the pilot plant scale was carried out, confirming the suitability of the scale-up criterion, since particles with similar characteristics (same particle size with a deviation of just 6%) and functional groups were obtained. Finally, the design of an industrial plant able to produce 581 Tm/year of HSA functionalized St-MMA-GMA-PEGMA particles was addressed. The economic feasibility of this plant was confirmed by a value of internal rate of return (IRR) of 14.8% and a net present value (NPV) of 5452 M€, with a payback time between six and seven years, for the price of a cartridge 25% lower than that from the current treatments for bilirubin removal from patients with liver failure.

Parameter recommendation for injection molding based on similarity analysis of injection molded parts

Injection molding is a widespread manufacturing process for producing complex plastic shapes. The process is controlled by a large number of parameters, which show interactions with each other. Thereby the determination of an optimal operating point during sampling is a resource-consuming and demanding task. The data, which is generated during sampling, is usually not used for subsequent sampling processes. In the context of Industry 4.0, manufacturing companies attempt to optimize production efficiency to save time and resources and remain competitive. Machine learning methods offer great potential to analyze correlations in already generated data in order to predict optimal parameters of the operating point for newly developed parts, which can only be determined with high experimental effort.The aim of the investigations is to provide a method for recommending setting parameters of the injection molding machine for new injection molds. This method is intended to make a significant contribution to reducing the elaborate tests during sampling. For this purpose, a concept was developed that, in the first step, calculates the geometric similarity of the new mold to a known database with part information from molds that have already been sampled (here: 743 parts). In the second step, the new injection mold is assigned to a cluster containing geometrically similar parts. Since the information on the robust operating point is known for each part of the database, this information is used to calculate the operating point for the new part. The applied case-based reasoning method provides the machine operator with a recommended operating point for a new injection mold without the need to carry out elaborate tests beforehand. Since the operating point of an injection molding machine consists of several parameters, the investigations were initially focused on the flow rate, which is one of the key parameters for controlling the injection phase.

Mathematical aspects of distortion calibration for digital cameras

Nowadays, most human processes are automated by means of computerization. This process has not spared the automotive industry. The latest developments in this field give promise that in the near future, cars will be completely autonomous. However, before that, there is an urgent need to address a number of issues, such as increasing the angle of view for greater coverage of the road with minimal space curvature. It is known that when the angle of view increases, so does the distortion (a mismatch in geometric similarity between an object and its image). This mismatch significantly reduces the accuracy of recognition algorithms. To solve this problem, this paper proposes a calibration method for cameras. The paper deals with mathematical aspects of distortion and the method of calibration of automobile chambers, and calibration errors. The method of static calibration without the use of points at infinity using static templates is proposed. A conventional camera has a small field of view (about 80 degrees). Such angle of view does not provide full scanning of the space; as a result, some of the necessary information remains outside the field of view, which is crucial for automotive industry because road signs, pedestrians, traffic lights might be missed. Therefore, in case of car cameras, the angle of view is increased by introducing distortion aberration. In this case, the field of view increases, yet the geometric similarity between the object and its image is affected. This, in turn, can affect the accuracy of computer vision algorithms. In order to keep the field of view angle large and the similarity between the subject and the object, it is necessary to calibrate the camera. In this paper, a calibration method for wide-angle car cameras is proposed and considered.

Effects of body size and countermeasure exercise on estimates of life support resources during all-female crewed exploration missions

Employing a methodology reported in a recent theoretical study on male astronauts, this study estimated the effects of body size and aerobic countermeasure (CM) exercise in a four-person, all-female crew composed of individuals drawn from a stature range (1.50- to 1.90-m) representative of current space agency requirements (which exist for stature, but not for body mass) upon total energy expenditure (TEE), oxygen (O2) consumption, carbon dioxide (CO2) and metabolic heat (Hprod) production, and water requirements for hydration, during space exploration missions. Assuming geometric similarity across the stature range, estimates were derived using available female astronaut data (mean age: 40-years; BMI: 22.7-kg·m−2; resting VO2 and VO2max: 3.3- and 40.5-mL·kg−1·min−1) on 30- and 1080-day missions, without and with, ISS-like countermeasure exercise (modelled as 2 × 30-min aerobic exercise at 75% VO2max, 6-day·week−1). Where spaceflight-specific data/equations were not available, terrestrial equivalents were used. Body size alone increased 24-h TEE (+ 30%), O2 consumption (+ 60%), CO2 (+ 60%) and Hprod (+ 60%) production, and water requirements (+ 17%). With CM exercise, the increases were + 25–31%, + 29%, + 32%, + 38% and + 17–25% across the stature range. Compared to the previous study of theoretical male astronauts, the effect of body size on TEE was markedly less in females, and, at equivalent statures, all parameter estimates were lower for females, with relative differences ranging from -5% to -29%. When compared at the 50th percentile for stature for US females and males, these differences increased to − 11% to − 41% and translated to larger reductions in TEE, O2 and water requirements, and less CO2 and Hprod during 1080-day missions using CM exercise. Differences between female and male theoretical astronauts result from lower resting and exercising O2 requirements (based on available astronaut data) of female astronauts, who are lighter than male astronauts at equivalent statures and have lower relative VO2max values. These data, combined with the current move towards smaller diameter space habitat modules, point to a number of potential advantages of all-female crews during future human space exploration missions.

Shaking table test of multiple-type isolation control strategies for high-rise structure based on friction pendulum

Given the difficulties associated with deploying isolation technique in high-rise structures, this article conducts a comprehensive comparison of three operating systems: friction pendulum system (FPS) base isolation form: FPS-B, FPS inter-story isolation form: FPS-I, and FPS hybrid isolation form: FPS-H. A 9-layer scaled test model is constructed by using third generation benchmark model, and the accompanying FPS model is created and fabricated using the geometric similarity criterion. Considering four typical ground motions and four peak ground acceleration (PGA), the structural seismic responses of the three control systems were analyzed. The result demonstrates that FPS-H technology greatly decreases the superstructure’ top floor acceleration and even the substructure's acceleration impact in both mild and major earthquakes. The working mechanism of FPS-H technology in terms of vibration reduction is similar to the conjunction of tuned mass damper (TMD) and FPS-B structure. The inertia force of superstructure suppresses the substructure since superstructure has FPS inter-story isolation form, and even the substructure is an FPS-B form that can extend the structural period and segregate earthquake energy. The FPS-H technology, which reduces the acceleration response of the structure's 1st -order mode and restrains the dynamic reaction of the high-order mode by changes the dynamic characteristics of whole structure, is primarily responsible for the long-period structure's effective damping.

Dimensionless Groups by Entropic Similarity: I - Diffusion, Chemical Reaction and Dispersion Processes.

Since the time of Buckingham in 1914, dimensional analysis and similarity arguments based on dimensionless groups have served as powerful tools for the analysis of systems in all branches of science and engineering. Dimensionless groups are generally classified into those arising from geometric similarity, based on ratios of length scales; kinematic similarity, based on ratios of velocities or accelerations; and dynamic similarity, based on ratios of forces. We propose an additional category of dimensionless groups based on entropic similarity, defined by ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes. Since all processes involving work against friction, dissipation, diffusion, dispersion, mixing, separation, chemical reaction, gain of information or other irreversible changes are driven by (or must overcome) the second law of thermodynamics, it is appropriate to analyze them directly in terms of competing entropy-producing and transporting phenomena and the dominant entropic regime, rather than indirectly in terms of forces. In this study, entropic groups are derived for a wide variety of diffusion, chemical reaction and dispersion processes relevant to fluid mechanics, chemical engineering and environmental engineering. It is shown that many dimensionless groups traditionally derived by kinematic or dynamic similarity (including the Reynolds number) can also be recovered by entropic similarity-with a different entropic interpretation-while many new dimensionless groups can also be identified. The analyses significantly expand the scope of dimensional analysis and similarity arguments for the resolution of new and existing problems in science and engineering.

Application of the similarity theory to analysis of photocatalytic hydrogen production and photocurrent generation

In this research some methods of the similarity theory were quantitatively applied to the description of the relationship between the efficiencies of the photocatalytic hydrogen production and photocurrent generation for the first time. Two possible similarity criteria, namely, such as the ratio of the number of electrons involved in the photocatalytic reaction to the generation of photocurrent ones and the ratio of energies transformed in the case of photocatalytic hydrogen evolution to the photocurrent, were obtained by the dimensional analysis. The literature data allow checking the first criterion. The application of the first possible similarity criterion to the samples with different chemical nature, solid solutions, series, in which the synthesis time or the ratio of catalyst components, electrolyte amount or its nature is changed, was analyzed. It was shown that the ratio of electrons may serve as the similarity criterion only under the conditions of geometric and physical similarities.

A new Voronoi diagram-based approach for matching multi-scale road networks

Object matching is a key technology for map conflation, data updating, and data quality assessment. This article proposed a new Voronoi diagram-based approach for matching multi-scale road networks (VAMRN). Using this method, we first created Voronoi diagrams of the road network using the strategy of discretizing road lines into points and adding dense points to special road intersection segments. Then, we used the Voronoi diagram of road segment to find matching candidates. Finally, we obtained matching results by judging the geometric similarity metrics we designed and a heuristic combination optimization strategy. The experimental results demonstrated that the VAMRN outperformed two existing methods in generality and matching quality. The F-measures of VAMRN were 18.4, 29.6, 3.8, and 7.6% higher than the buffer growing method, and 4.5, 2.8, 1.8, and 6.1% higher than the probabilistic relaxation method. And the time performance is improved by more than 90% over the probabilistic relaxation method.

A pair of deep learning auto-contouring models for prostate cancer patients injected with a radio-transparent versus radiopaque hydrogel spacer.

Absorbable hydrogel spacer injected between prostate and rectum is gaining popularity for rectal sparing. The spacer alters patient anatomy and thus requires new auto-contouring models. To report the development and comprehensive evaluation of two deep-learning models for patients injected with a radio-transparent (model I) versus radiopaque (model II) spacer. Model I was trained and cross-validated by 135 cases with transparent spacer and tested on 24 cases. Using refined training methods, model II was trained and cross-validated by the same dataset, but with the Hounsfield Unit distribution in the spacer overridden by that obtained from ten cases with opaque spacer. Model II was tested on 64 cases. The models auto-contour eight regions of interest (ROIs): spacer, prostate, proximal seminal vesicles (SVs), left and right femurs, bladder, rectum, and penile bulb. Qualitatively, each auto contour (AC), as well as the composite set, was assessed against manual contour (MC), by a radiation oncologist using a 1 (accepted directly or after minor editing), 2 (accepted after moderate editing), 3 (accepted after major editing), and 4 (rejected) scoring scale. The efficiency gain was characterized by the mean score as nearly complete [1-1.75], substantial (1.75-2.5], meaningful (2.5-3.25], and no (3.25-4.00]. Quantitatively, the geometric similarity between AC and MC was evaluated by dice similarity coefficient (DSC) and mean distance to agreement (MDA), using tolerance recommended by AAPM TG-132 Report. The results by the two models were compared to examine the outcome of the refined training methods. The large number of testing cases for model II allowed further investigation of inter-observer variability in clinical dataset. The correlation between score and DSC/MDA was studied on the ROIs with 10 or more counts of each acceptable score (1, 2, 3). For model I/model II: the mean score was 3.63/1.30 for transparent/opaque spacer, 2.71/2.16 for prostate, 3.25/2.44 for proximal SVs, 1.13/1.02 for both femurs, 2.25/1.25 for bladder, 3.00/2.06 for rectum, 3.38/2.42 for penile bulb, and 2.79/2.20 for the composite set; the mean DSC was 0.52/0.84 for spacer, 0.84/0.85 for prostate, 0.60/0.62 for proximal SVs, 0.94/0.96 for left femur, 0.95/0.96 for right femur, 0.91/0.95 for bladder, 0.81/0.84 for rectum, and 0.65/0.65 for penile bulb; and the mean MDA was 2.9/0.9mm for spacer, 1.9/1.7mm for prostate, 2.4/2.3mm for proximal SVs, 0.8/0.5mm for left femur, 0.7/0.5mm for right femur, 1.5/0.9mm for bladder, 2.3/1.9mm for rectum, and 2.2/2.2mm for penile bulb. Model II showed significantly improved scores for all ROIs, and metrics for spacer, femurs, bladder, and rectum. Significant inter-observer variability was only found for prostate. Highly linear correlation between the score and DSC was found for the two qualified ROIs (prostate and rectum). The overall efficiency gain was meaningful for model I and substantial for model II. The ROIs meeting the clinical deployment criteria (mean score below 3.25, DSC above 0.8, and MDA below 2.5mm) included prostate, both femurs, bladder and rectum for both models, and spacer for model II.

Geometric similarity invariants of Cowen-Douglas operators

In 1978, M. J. Cowen and R.G. Douglas introduced a class of operators B_n(\Omega) (known as Cowen-Douglas class of operators) and associated a Hermitian holomorphic vector bundle to such an operator. They gave a complete set of unitary invariants in terms of the curvature and its covariant derivatives. At the same time they asked whether one can use geometric ideas to find a complete set of similarity invariants of Cowen-Douglas operators. We give a partial answer to this question. In this paper, we show that the curvature and the second fundamental form completely determine the similarity orbit of a norm dense class of Cowen-Douglas operators. As an application we show that uncountably many (non-similar) strongly irreducible operators in B_n(\mathbb{D}) can be constructed from a given operator in B_1(\mathbb{D}) . We also characterize a class of strongly irreducible weakly homogeneous operators in B_n(\mathbb{D}) .

Comparative analysis of energy losses in hydrogen and helium turbo-expanders for hydrogen liquefiers

Liquid hydrogen plays an essential role in the large-scale hydrogen energy development. Claude cycle is the baseline process for most industrial hydrogen liquefactions. The hydrogen turbo-expander is the crucial component, determining the system efficiency and reliability. In this paper, a hydrogen turbo-expander is designed by using a mean-line method with loss models which have been validated against experimental data of helium turbo-expanders. Geometrical and velocity field similarity can be achieved between a hydrogen turbo-expander and a helium turbo-expander by selecting the same specific speed and the characteristic ratio. CFD simulations are performed to illustrate the internal flow field and loss mechanisms in helium and hydrogen turbo-expanders. The CFD predictions of passage efficiencies agree well with that by the loss models, demonstrating the mean-line design method and loss models can be used to guide the preliminary design of hydrogen turbo-expanders. The CFD simulation results show that the passage efficiency of hydrogen turbo-expander is 1.88% higher than that of helium expander. Due to a higher sound speed and a lower viscosity, the hydrogen turbo-expander has smaller nozzle loss, incidence loss and impeller passage compared with the helium turbo-expander. The lower viscosity of hydrogen results in a higher tip leakage flow, and the tip leakage accounts for 1.09% and 1.23% of total mass flow in helium and hydrogen turbo-expanders, respectively. Since the cross flow over the blade tips can increase the vortices and secondary flow losses in impeller passages, it is necessary to reduce tip clearance in the design of hydrogen turbo-expanders.

Revealing Free Energy Landscape From MD Data via Conditional Angle Partition Tree.

Deciphering the free energy landscape of biomolecular structure space is crucial for understanding many complex molecular processes, such as protein-protein interaction, RNA folding, and protein folding. A major source of current dynamic structure data is Molecular Dynamics (MD) simulations. Several methods have been proposed to investigate the free energy landscape from MD data, but all of them rely on the assumption that kinetic similarity is associated with global geometric similarity, which may lead to unsatisfactory results. In this paper, we proposed a new method called Conditional Angle Partition Tree to reveal the hierarchical free energy landscape by correlating local geometric similarity with kinetic similarity. Its application on the benchmark alanine dipeptide MD data showed a much better performance than existing methods in exploring and understanding the free energy landscape. We also applied it to the MD data of Villin HP35. Our results are more reasonable on various aspects than those from other methods and very informative on the hierarchical structure of its energy landscape.

Unsupervised Learning for Salient Object Detection via Minimization of Bilinear Factor Matrix Norm

Saliency detection is an important but challenging task in the study of computer vision. In this article, we develop a new unsupervised learning approach for the saliency detection by an intrinsic regularization model, in which the Schatten-2/3 norm is integrated with the nonconvex sparse l2/3 norm. The l2/3 -norm is shown to be capable of detecting consistent values among sparse foreground by using image geometrical structure and feature similarity, while the Schatten-2/3 norm can capture the lower rank of background by matrix factorization. To improve effective performance of separation for Schatten-2/3-norm and l2/3 -norm, a Laplacian regularization is adopted to the foreground for the smoothness. The proposed model essentially converts the required nonconvex optimization problem into the convex one, conducted by splitting the objective function based on singular value decomposition on one much smaller factor matrix and then optimized by using the alternating direction method of the multiplier. The convergence of the proposed algorithm is discussed in detail. Extensive experiments on three benchmark datasets demonstrate that our unsupervised learning approach is very competitive and appears to be more consistent across various salient objects than the current existing approaches.

Shaking table test on suspend-dome structure with the center-hung scoreboard under three-dimensional seismic

In order to meet the demand of watching games, the LED display, i.e., the center-hung scoreboard, has been widely used in large stadiums. To investigate the mechanical properties of the suspend-dome structure with the center-hung scoreboard under the action of earthquake, a dynamic scaled model with a geometric similarity ratio of 1:20 was designed. And the shaking table test was performed to study the seismic performance under the actions of 8 degree frequent, seismic precautionary and rare earthquakes. The acceleration, displacement and internal force responses under three-dimensional seismic were analyzed. The results show that the Z-directional acceleration amplification factors of the reticulated shell vertex region are significant and decrease fastest under actions of rare earthquakes, which is the weak point of the model. The influence of the center-hung scoreboard on the structure cannot be ignored in the study of seismic performance. The vertical displacement is the largest in the center and gradually decreases from inside to outside. The maximum displacement under actions of frequent earthquakes is 2.061 mm. The maximum displacement under actions of seismic precautionary earthquakes is 1/556, the maximum displacement under actions of rare earthquakes is 1/242, both of which satisfy the requirement of seismic specifications. The maximum internal force of the ring rod first decreases and then increases from the center to the surroundings. The internal force of the radial rod gradually increases from the edge to the center. Under actions of rare earthquakes, the center-hung scoreboard has more influence on the internal force of the rod. The accuracy of the finite element modeling method is verified by comparing the simulation results and test results of the scaled model, and the reliability of the scaled model is verified by comparing the simulation results of the scaled model and the prototype structure. The structure does not collapse under actions of 8 degree rare earthquakes and does not show apparent failure. The seismic principle that “the structure hasn’t damaged under frequent earthquake, repairable under precautionary earthquake, and doesn’t collapse under rare earthquake” is reached, thus the structural design of the Lanzhou Olympic Sports Complex is reasonable.