Ellipsoidal Model Research Articles

A Calculation Method of Magnetic Anomaly Field Distribution of Ellipsoid with Arbitrary Posture

The ellipsoidal magnetization model has a wide range of application scenarios. For example, in aviation magnetic field prospecting, mineral prospecting, seabed prospecting, and UXO (unexploded ordnance) detection. However, because the existing ellipsoid magnetization formula is relatively complicated, the detection model is usually replaced by a dipole. Such a model increases the error probability and poses a significant challenge for subsequent imaging and pattern recognition. Based on the distribution of ellipsoid gravity potential and magnetic potential, the magnetic anomaly field distribution equation generated by the ellipsoid is deduced by changing the aspect ratio, making the ellipsoid equivalent to a sphere. The result of formula derivation shows that the two magnetic anomaly fields are consistent. This paper uses COMSOL finite element software to model UXO, ellipsoids, and spheres and analyzes magnetic anomalies. The conclusion shows that the ellipsoid model can completely replace the UXO model when the error range of 1nT is satisfied. Finally, we established two sets of ellipsoids and calculated the magnetic anomalous field distributions on different planes using deduction formulas and finite element software. We compared the experimental results and found that the relative error of the two sets of data was within [Formula: see text]‰. Error analysis found that the error distribution is standardized and conforms to the normal distribution. The above mathematical analysis and finite element simulation prove that the calculation method is simple and reliable and provides a magnetic field distribution equation for subsequent UXO inversion.

The fractal cylinder process: Existence and connectivity phase transitions

We consider a semi-scale invariant version of the Poisson cylinder model which in a natural way induces a random fractal set. We show that this random fractal exhibits an existence phase transition for any dimension d≥2, and a connectivity phase transition whenever d≥4. We determine the exact value of the critical point of the existence phase transition, and we show that the fractal set is almost surely empty at this critical point. A key ingredient when analysing the connectivity phase transition is to consider a restriction of the full process onto a subspace. We show that this restriction results in a fractal ellipsoid model which we describe in detail, as it is key to obtaining our main results. In addition we also determine the almost sure Hausdorff dimension of the fractal set.

A Novel Method to Predict the Maximum Electric Fields in Different Body Parts Exposed to Uniform Low-Frequency Magnetic Field

Thepermissible external field strength described in international exposure guidelines and standards was derived under the assumption that humans are exposed to a uniform field in free space. However, realistic field distributions are partial body exposure to the nonuniform field. Thus, the permissible field strength has overconservative values when applying the spatial peak strength to practical compliance assessment. In this study, we discuss the relationship between the uniform external magnetic field strength and induced electric field in different body part models to help set the permissible field strength for nonuniform magnetic field exposure. We proposed a formula for estimating induced electric field from the electromotive force of cuboid models based on Faraday's law. Then, we applied the formula to homogeneous ellipsoidal and homogeneous realistically shaped models. Furthermore, we investigated the effect of model inhomogeneity to confirm the difference in the induced electric field in anatomical body models. The homogeneous ellipsoidal model was comparable to the homogeneous realistically shaped model, whereas the model inhomogeneity led to an approximately 1.5 times increase in the computed maximum electric field strength.

A four-point direction search heuristic algorithm applied to facility location on plane, sphere, and ellipsoid surfaces

A facility location problem (FLP) refers to the best location for establishing a facility to optimally connect and meet the requirements of the demand points. In a supply chain on the earth’s surface, the cost function essentially includes a distance metric to compute the objective function. If the data points are located in a small area, Euclidean Distance (ED) can be considered. When the data points are fairly separated on the earth’s surface, ED cannot give a correct estimate and we have to opt for either a spherical model or an ellipsoidal model. This paper proposes a simple four-point direction search algorithm and a model which can be used for locating a facility on a plane, sphere, and ellipsoid model of earth. The main advantage of the proposed algorithm is that it can be used with any distance metric without changing the algorithm.

Tertiary lymphoid structures (TLS) identification and density assessment on H&E-stained digital slides of lung cancer.

Tertiary lymphoid structures (TLS) are ectopic aggregates of lymphoid cells in inflamed, infected, or tumoral tissues that are easily recognized on an H&E histology slide as discrete entities, distinct from lymphocytes. TLS are associated with improved cancer prognosis but there is no standardised method available to quantify their presence. Previous studies have used immunohistochemistry to determine the presence of specific cells as a marker of the TLS. This has now been proven to be an underestimate of the true number of TLS. Thus, we propose a methodology for the automated identification and quantification of TLS, based on H&E slides. We subsequently determined the mathematical criteria defining a TLS. TLS regions were identified through a deep convolutional neural network and segmentation of lymphocytes was performed through an ellipsoidal model. This methodology had a 92.87% specificity at 95% sensitivity, 88.79% specificity at 98% sensitivity and 84.32% specificity at 99% sensitivity level based on 144 TLS annotated H&E slides implying that the automated approach was able to reproduce the histopathologists’ assessment with great accuracy. We showed that the minimum number of lymphocytes within TLS is 45 and the minimum TLS area is 6,245μm2. Furthermore, we have shown that the density of the lymphocytes is more than 3 times those outside of the TLS. The mean density and standard deviation of lymphocytes within a TLS area are 0.0128/μm2 and 0.0026/μm2 respectively compared to 0.004/μm2 and 0.001/μm2 in non-TLS regions. The proposed methodology shows great potential for automated identification and quantification of the TLS density on digital H&E slides.

Determining the specific surface area of coarse aggregate based on sieving curve via image-analysis approach

Coarse aggregate composes the highest volume in concrete and affects the fresh and hardened performance significantly. To analyze the distribution status of coarse aggregate in cementitious system, the specific surface area (SSA) stays one of the essential parameters but relatively complicated to be determined by traditional ways. Due to the easy acquirement of the sieving characteristics in coarse aggregate, its relationship with SSA is explored and established in the present study. Initially, 20 coarse aggregate samples are obtained by quartering method with similar sieving curves of the same patch. Then, SSA of the samples is evaluated experimentally via paste-wrapping method. Afterwards, the shape parameters of individual aggregate samples are analyzed via image-analysis approach. Herein, cylindrical, prismatic and ellipsoid models, in total 11 models, are utilized to simulate the SSA of the selected samples. Results show that the cylindrical model adopting the parameter of average feret diameter best describes the SSA in comparison with the experimental results. On account of the relationship between the surface area/volume and diameter of the samples, a numerical method of SSA is established using the sieving characteristics of coarse aggregate, thus providing an effective and simple solution in determining the SSA of coarse aggregate in concrete.

Bi-level optimization approach for robust mean-variance problems

Portfolio Optimization is based on the efficient allocation of several assets, which can get heavily affected by the uncertainty in input parameters. So we must look for such solutions which can give us steady results in uncertain conditions too. Recently, the uncertainty based optimization problems are being dealt with robust optimization approach. With this development, the interest of researchers has been shifted toward the robust portfolio optimization. In this paper, we study the robust counterparts of the uncertain mean-variance problems under box and ellipsoidal uncertainties. We convert those uncertain problems into bi-level optimization models and then derive their robust counterparts. We also solve a problem using this methodology and compared the optimal results of box and ellipsoidal uncertainty models with the nominal model.

Welding-induced Residual Stresses in U-Ribs of a Steel Bridge Deck

To calculate the welding-induced residual stresses in U-ribs of the steel deck plate and conduct quantitative analysis of influential factors, the U-ribs of steel deck plate of Xinghai Bay Bridge was taken as the research object. In the ABAQUS finite element software, the local models of U-ribs of steel deck plate were established. Nodal body force loads, i.e., heat generation rate, of the double ellipsoidal heat source models were applied via the compiled subsidiary Dflux program. The welding process of the v-groove welds was simulated, to obtain the residual stresses distribution in the top plate and U-rib plates. The influence of thickness of top plate and angle of welding groove on the residual stresses in the U-ribs were studied. The results show that the welding-induced residual stresses calculated by the numerical method proposed in this paper agree well with the experimental data. The maximum residual stresses in the top plates and the U-rib plates all occur near the welds, which exceeds the yielding limitation of the material. As the thickness of top plate increases, the maximum values of residual stresses in the top plates and U-ribs increase. However, with the increase of groove angle, the maximum values of residual stresses in the top plates and U-rib plates decrease.

A non-probabilistic uncertainty analysis method based on ellipsoid possibility model and its applications in multi-field coupling systems

Non-probabilistic methods are usually more appropriate and feasible than probabilistic methods to quantify and propagate uncertainty with small samples in many engineering problems. However, some non-probabilistic methods are easily affected by an outlier in uncertainty quantification and only estimate the bounds of output responses in a feasible region in uncertainty propagation. Moreover, some such methods ignore the situation that its sample points have the characteristic of clustering to the center, which significantly affects the accuracy of uncertainty quantification and propagation. In this study, a novel non-probabilistic uncertainty analysis method is proposed to solve the situation and obtain detailed information within the response interval during the process of uncertainty propagation for some problems with small samples. First, an ellipsoid possibility model (EPM) including multiple ellipsoid domains is established using the estimated covariance matrix and predefined scaling rule, which takes into consideration the distribution characteristic of the sample points. The possibilities of all established ellipsoid domains can be calculated by transforming the oblique ellipsoid space into the standard ellipsoid space. Then, two uncertainty propagation approaches based on the established EPM are presented to obtain the interval of an uncertain response and the possibility on all the possible values of the system response, respectively. Finally, the calculation results based on the proposed uncertainty analysis method are in good agreement with those of the MCS in three numerical examples and two engineering applications. The comparison results with three traditional non-probabilistic methods demonstrate that the proposed non-probabilistic uncertainty analysis method is accurate and practical.

Boundary conditions for two-temperature Navier-Stokes equations for a polyatomic gas

We previously derived the two-temperature Navier-Stokes system (a set of compressible Navier-Stokes equations with the translational and internal temperatures) for a polyatomic gas with slow relaxation of the internal modes from the ellipsoidal statistical model of the Boltzmann equation. In this paper, the appropriate boundary conditions for the two-temperature Navier-Stokes system are derived. The results are presented in a form that is applicable to practical applications immediately.

Dynamic evolution simulation of sintering pool in selective laser sintering walnut shell/Co-PES composite

In view of the difficulties in the observation of sintering pool and too many factors influencing the dynamic evolution process of sintering pool during the selective laser sintering (SLS) process of biomass composite materials, the structural morphology of sintering pool during the SLS process of walnut shell/Co-PES (WSPC) powder and its dynamic evolution process were studied. Based on the DFLUX subprogram, a moving double ellipsoid heat source model was established. Considering heat conduction, heat radiation, heat convection and thermophysical parameters changing with temperature, the three-dimensional finite element model of WSPC powder was numerically simulated in the process of SLS. Through numerical simulation analysis, the surface shape of sintering pool is circularand the cross section one is deep bowl, and the sintering forming process is a process in which the sintering pool is continuously superposed along the sintering direction. By comparing the experimental results with the numerical simulated results, the experimental results are in good agreement with the simulated results. The dynamic evolution law of sintering pool during SLS process of WSPC powder and the change law that sintering pool size increases with the increase of preheating temperature and laser power and the decrease of scanning speed were obtained.

Adoption of Snake Variable Model-Based Method in Segmentation and Quantitative Calculation of Cardiac Ultrasound Medical Images.

This paper intends to explore the effect of the enhanced snake variable model in the segmentation of cardiac ultrasound images and its adoption in quantitative measurement of cardiac cavity. First, the basic principles of the traditional snake model and the gradient vector flow (GVF) snake model are explained. Then, an ellipsoid model is constructed to obtain the initial contour of the heart based on the three-dimensional volume of cardiac ultrasound image, and a discretized triangular mesh model is generated. Finally, the vortical gradient vector flow (VGVF) external force field is introduced and combined with the greedy algorithm to process the deformation of the initial ellipsoid contour of the heart. The segmentation effect is quantitatively evaluated regarding the area overlap rate (AOR) and the mean contour distance (MCD). The results show that the VGVF snake model can segment the deep recessed area of the “U-shaped map” in contrast to the traditional snake model and the GVF snake model. After being applied to ultrasonic image segmentation, the VGVF snake model obtains the segmentation result that is close to the doctor's manual segmentation result, and the average AOR and MCD are 97.4% and 3.2, respectively. The quantitative evaluation of the cardiac cavity is carried out based on the segmentation results, and the measurement of the volume change of the left ventricle within a cardiac cycle is realized. To sum up, VGVF snake model is superior to the traditional snake and GVF snake models in terms of ultrasonic image segmentation, which realizes the three-dimensional segmentation and quantitative calculation of the cardiac cavity.

Rapid algorithm for covariance ellipsoid model based collision warning of space objects

The recent decades have witnessed a tremendous growth in the number of satellites and debris in space, leading to an increasingly high risk of collision between space objects. Collision warning aims at assessing the collision risk between space objects and attempts to identify possible collisions in order for satellites to perform evasive maneuvers in advance. Current collision warning methods are based on the computation of collision probability and comparison with some tolerance threshold. Such a threshold is usually set according to experience. In contrast, this paper proposes to use covariance ellipsoid with a user defined Mahalanobis distance to represent the most possible region in which the relative position vector distributes. Zero vector represents the collision event, and once it enters this ellipsoid, a collision warning occurs. A collision warning function along with a definite threshold is then formulated based on this criterion. Moreover, in order to rapidly predict the possible collision intervals, a self-adaptive Hermite interpolation technique is applied to approximate the collision warning function by piecewise cubic polynomials for efficient roots finding. Finally, the proposed collision warning criterion has been evaluated in several collision scenarios. Comparison experiments are also conducted with the brute force method and analytical propagators. The simulation shows that the calculation of collision warning interval based on the proposed criterion is effective, and the self-adaptive Hermite interpolation method performs high efficiency and accuracy.

Controlled Process of Crystallization in Weld Pool

In this report the problem of control of solidification crack formation in welded plates is considered. In this problem the welding source is determined in dependence on the preset configuration and curvature of the rear part weld pool. A double ellipsoid model of weld pool with preset semi-axes may be used for the first approximation of preset weld pool configuration. It is an inverse problem which may be more efficiently solved as optimal control problem. The Function of welding source as a controlling function obtained in the result of solution is determined in a class of piecewise continuous functions which is more common class and the continuous-smooth functions are special partial case of common class. Recent methods of optimal control which use for solution of optimal control problems require to present the controlling functions in class of piecewise constant functions. Laser influence, electron beam, plasma, arc and submerged arc are the welding sources with high concentrated energy. A mathematical models of these welding sources may be introduced in class of piecewise continuous function with an efficient accuracy.

How incoherent measurement succeeds: Coordination and success in the measurement of the earth's polar flattening

The development of nineteenth-century geodetic measurement challenges the dominant coherentist account of metric success. Coherentists argue that measurements of a parameter are successful if their numerical outcomes convergence across varying contextual constraints. Aiming at numerical convergence, in turn, offers an operational aim for scientists to solve problems of coordination. Geodesists faced such a problem of coordination between two indicators of the earth's polar flattening, which were both based on imperfect ellipsoid models. While not achieving numerical convergence, their measurements produced novel data that grounded valuable theoretical hypotheses. Consequently, they ought to be regarded as epistemically successful. This insight warrants a dynamic revision of coherentism, which allows to judge the success of a metric based on both its coherence and fruitfulness. On that view, scientific measurement aims to coordinate theoretical definitions and produce novel data and theoretical insights.

Ellipsoid non-probabilistic reliability analysis of the crack growth fatigue of a new titanium alloy used in deep-sea manned cabin

Reliability analysis of crack growth fatigue of titanium alloy is one of the important guarantees for the safety of deep-sea manned cabin. However, the traditional probabilistic fatigue reliability analysis methods often need accurate parameter statistics information. In this paper, under the condition of the limited test data, a first-order approximate ellipsoid non-probabilistic reliability analysis method for fatigue crack growth of a titanium alloy was proposed. A limit state equation of the crack growth correction model, considering the small crack effect, is formulated according to the fatigue life model. The uncertain parameters are constructed by the interval model, normal distribution, and Khachiyan algorithm. The different limit state equations are obtained by changing the coefficient κ. The first-order approximation and Monte Carlo methods are used to solve the reliability of the ellipsoid model. Calculations demonstrate that the results of the ellipsoid non-probabilistic reliability method are more conservative than that of the probabilistic reliability method. When κ is less than or equal to 2, the Khachiyan algorithm is preferred to build the ellipsoid model, and when κ is greater than 2, the interval model is preferred. Through parameter sensitivity analysis, the uncertain parameters KC, n, m, A, and ΔKthR are found to significantly affect the crack growth rate.

Welding simulation of circumferential weld joint using TIG welding process

Circumferential weld joints are commonly used in marine engineering, nuclear power plant, aerospace industry. In this welding simulation of circumferential weld joint using Tungsten inert gas welding (TIG) process was done. In TIG welding joint the high temperature is induced due to which there is high distortion and residual stress. For that developing a good welding joint in controlled residual stress and deformation we are using the Welding simulation Finite element methodology. A SS304 material with TIG welding is selected as experimental and combination of Finite Element Analysis (FEM) using the MSC marc software to predict the temperature, residual stresses and distortion with varying cylindrical thickness, voltage, pressure and efficiency. Using finite element simulations, the welding heat input is varied by modifying welding parameters (such as welding current and welding speed) to study the effect on residual stresses. The aim of this research is to provide information to verify the validity of current process circumferential manufacturing technology for thin-walled pipes, in order to prevent the failure of these structures in operation due to these inherent stresses. The study's welding heat source model is the Double Ellipsoidal Heat Source Model, which is the best heat source model of welding simulation.

A Tri-Satellite Interference Source Localization Method for Eliminating Mirrored Location.

With the increase in satellite communication interference, the tri-satellite time difference of arrival (TDOA) localization technique, which is an effective method to determine the location of the interference using sensors or antennas, has been developed rapidly. The location of the interference source is determined through the intersection of the TDOA lines of position (LOP). However, when the two TDOA LOP have two mirrored intersection points, it is theoretically difficult to determine the real location. Aiming at this problem, a method for eliminating mirrored location based on multiple moment TDOA is proposed in this paper. First, the TDOA results are measured at multiple moments using the cross-ambiguity function (CAF), and the localization equation set is established based on the World Geodetic System (WGS)-84 earth ellipsoid model. Then, the initial location result can be obtained by solving the equation set through the Newton iteration method. Finally, the high-precision location result after eliminating the mirrored location is obtained after the single moment localization based on the initial location. Simulation experiments and real measured data processing results verify the effectiveness of the proposed method. It still has good robustness under the condition of large measurement errors and deviations from the prior initial values.

Simulation of the influence of Lode parameter on ductile fracture using an ellipsoidal void model

The influence of the Lode parameter μ on ductile fracture is simulated using an ellipsoidal void model proposed previously by the author, and is analyzed using an elementary theory proposed in this study. The equivalent strain at fracture calculated using the ellipsoidal void model in the case of μ=+1 is almost identical to that in the case of μ=-1. The equivalent strain at fracture calculated using the ellipsoidal void model in the case of μ=±1 is larger than that in the case of μ=0. The void shape and the void configuration at fracture calculated using the ellipsoidal void model significantly depend on the stress triaxiality but scarcely depend on the Lode parameter. The proposed elementary theory indicates that the equivalent strain at fracture in the case of μ=±1 is 2/3 times larger than that in the case of μ=0. The equivalent strain at fracture analyzed using the elementary theory almost agrees with that calculated using the ellipsoidal void model.

Diameter-Based Volumetric Models May Inadequately Calculate Jugular Paraganglioma Volume Following Sub-Total Resection.

As gross total resection of jugular paragangliomas (JPs) may result in cranial nerve deficits, JPs are increasingly managed with subtotal resection (STR) with postoperative radiological monitoring. However, the validity of commonly used diameter-based models that calculate postoperative volume to determine residual tumor growth is dubious. The purpose of this study was to assess the accuracy of these models compared to manual volumetric slice-by-slice segmentation. A senior neuroradiologist measured volumes via slice-by-slice segmentation of JPs pre- and postoperatively from patients who underwent STR from 2007 to 2019. Volumes from three linear-based models were calculated. Models with absolute percent error (APE) > 20% were considered unsatisfactory based on a common volumetric definition for residual growth. Bland-Altman plots were used to evaluate reproducibility, and Wilcoxon matched-pairs signed rank test evaluated model bias. Twenty-one patients were included. Median postoperative APE exceeded the established 20% threshold for each of the volumetric models as cuboidal, ellipsoidal, and spherical model APE were 63%, 28%, and 27%, respectively. The postoperative cuboidal model had significant systematic bias overestimating volume (p = 0.002) whereas the postoperative ellipsoidal and spherical models lacked systematic bias (p = 0.11 and p = 0.82). Cuboidal, ellipsoidal, and spherical models do not provide accurate assessments of postoperative JP tumor volume and may result in salvage therapies that are unnecessary or inappropriately withheld due to inaccurate assessment of residual tumor growth. While more time-consuming, slice-by-slice segmentation by an experienced neuroradiologist provides a substantially more accurate and precise measurement of tumor volume that may optimize clinical management.