Fully Completed Spherical Fuzzy Approach-Based Z Numbers(PHIModel)for Enhanced Group Expert Consensus

This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex scenarios.In such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations.This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers.Subsequently,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies.Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input.Further,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions.The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision outcomes.Additionally,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Numerical study of plasmas start-up by electron cyclotron waves in NCST spherical tokamak and CN-H1 stellarator

According to the physics of tokamak start-up,this study constructs a zero-dimensional(0D)model applicable to electron cyclotron(EC)wave assisted start-up in NCST spherical torus(spherical tokamak)and CN-H1 stellarators.Using the constructed 0D model,the results obtained in this study under the same conditions are compared and validated against reference results for pure hydrogen plasma start-up in tokamak.The results are in good agreement,especially regarding electron temperature,ion temperature and plasma current.In the presence of finite Ohmic electric field in the spherical tokamak,a study on the EC wave assisted start-up of the NCST plasma at frequency of 28 GHz is conducted.The impact of the vertical magnetic field B_(v)on EC wave assisted start-up,the relationship between EC wave injection power P_(inj),Ohmic electric field E,and initial hydrogen atom density n_(H0)are explored separately.It is found that under conditions of Ohmic electric field lower than ITER(~0.3 V m^(-1)),EC wave can expand the operational space to achieve better plasma parameters.Simulating the process of28 GHz EC wave start-up in the CN-H1 stellarator plasma,the plasma current in the zerodimensional model is replaced with the current in the poloidal coil of the stellarator.Plasma startup can be successfully achieved at injection powers in the hundreds of kilowatts range,resulting in electron densities on the order of 10^(17)-10^(18)m^(-3).

Three-dimensional magnetotelluric modeling in the spherical and Cartesian coordinate systems:A comparative study

With the increase in the coverage area of magnetotelluric data,three-dimensional magnetotelluric modeling in spherical coordinates and its differences with respect to traditional Cartesian modeling have gradually attracted attention.To fully understand the influence of the Earth’s curvature and map projection deformations on Cartesian modeling,qualitative and quantitative analyses based on realistic three-dimensional models need to be examined.Combined with five representative map projections,a type of model conversion method that transforms the original spherical electrical conductivity model to Cartesian coordinates is described in this study.The apparent resistivity differences between the spherical western United States electrical conductivity model and the corresponding five Cartesian models are then compared.The results show that the cylindrical equal distance map projection has the smallest error.A meridian convergence correction resulting from the deformation of the map projection is introduced to rotate the Cartesian impedance tensor from grid north to geographic north,which reduces differences from the spherical results.On the basis of the magnetotelluric field data,the applicability of the Cartesian coordinate system to western and contiguous United States models is quantitatively evaluated.Precise interpretations of the contiguous United States model were found to require spherical coordinates.

A Simple but Accurate Ultraviolet Limb-Scan Spherically-Layered Radiative-Transfer-Model Based on Single-Scattering Physics

Here we present a study focusing on atmospheric limb-scattered radiative characteristics in the ultraviolet band by using a limb-scan spherically-layered radiative-transfer-model based on the single-scattering approximation, which was developed by the present authors. We have applied an accurate numerical integration technique involving an auto-adaptive modified-space step, which assured high accuracy and simplification. Comparisons were made to the newly released spherical radiative transfer model, SCIATRAN2.0, which was developed by Institute of Remote Sensing/Institute of Environmental Physics （IUP/IFE） at University of Bremen and to measurements collected via an ultraviolet spectrometer on the Solar Mesospheric Explorer （SME） satellite, which was launched in October, 1981. Preliminary results indicate that the present model provides a good interpretation of the earth-limb scattered ultraviolet radiance, and thus, is suitable for the study of the ultraviolet-limb radiative-transfer problem with high accuracy.

Research on the nonlinear spherical percolation model with quadratic pressure gradient and its percolation characteristics

For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spheri-cal flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the ef-fect of wellbore storage. By variable substitu-tion, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the nu-merical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear per-colation type curves in shape and characteris-tics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical off-set of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the in-fluence of the quadratic pressure gradient is very distinct, especially for the low permeabil-ity and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in res-ervoir, therefore the research on nonlinear per-colation theory should be strengthened and reinforced.

Mechanism and Method of Testing Fracture Toughness and Impact Absorbed Energy of Ductile Metals by Spherical Indentation Tests

To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were frst investigated through fnite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is diferent from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the diference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modifed. The quasi-static fracture toughness determined from the modifed CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The efectiveness of the newly proposed method was verifed through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.

Simulation for MSS-2 low-perigee elliptical orbit satellites:an example of lithospheric magnetic field modelling

A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.

Numerical Modeling of a Spherical Buoy Moored by a Cable in Three Dimensions

Floating facilities have been studied based on the static analysis of mooring cables over the past decades. To analyze the floating system of a spherical buoy moored by a cable with a higher accuracy than before, the dynamics of the cables are considered in the construction of the numerical modeling. The cable modeling is established based on a new element frame through which the hydrodynamic loads are expressed efficiently. The accuracy of the cable modeling is verified with an experiment that is conducted by a catenary chain moving in a water tank. In addition, the modeling of a spherical buoy is established with respect to a spherical coordinate in three dimensions, which can suffers the gravity, the variable buoyancy and Froude-Krylov loads. Finally, the numerical modeling for the system of a spherical buoy moored by a cable is established, and a virtual simulation is proceeded with the X- and Y-directional linear waves and the X-directional current. The comparison with the commercial simulation code Proteus DS indicates that the system is accurately analyzed by the numerical modeling. The tensions within the cable, the motions of the system, and the relationship between the motions and waves are illustrated according to the defined sea state. The dynamics of the cables should be considered in analyzing the floating system of a spherical buoy moored by a cable.

Dynamic Modeling and Analysis of 4UPS-UPU Spatial Parallel Mechanism with Spherical Clearance Joint

Clearance between the moving joints is unavoidable in real working process. At present, many researches are mainly focused on dynamics of plane revolute joint in plane mechanism, but few on dynamics of spatial spherical joint clearance in spatial parallel mechanism. In this paper, a general method is proposed for establishing dynamic equations of spatial parallel mechanism with spatial spherical clearance by Lagrange multiplier method. The kinematic model and contact force model of the spherical joint clearance were established successively. Lagrange multiplier method was used to deduce the dynamics equation of 4 UPS-UPU mechanism with spherical clearance joint systematically. The influence of friction coefficient on dynamics response of 4 UPS-UPU mechanism with spherical clearance joint was analyzed. Non-linear characteristics of clearance joint and moving platform were analyzed by Poincare map, phase diagram, and bifurcation diagram. The results show that variation of friction coefficient and clearance value had little effect on stability of the mechanism, but the chaotic phenomenon was found at spherical clearance joint. The research has theoretical guiding significance for improving the dynamic performance and avoiding of chaos of parallel mechanisms including spherical joint clearance.

Modeling and verification of comprehensive errors of real-time wear-depth detecting for spherical plain bearing tester

Because of various error factors,the detecting errors in the real-time experimental data of the wear depth affect the accuracy of the detecting data.The self-made spherical plain bearing tester was studied,and its testing principle of the wear depth of the spherical plain bearing was introduced.Meanwhile,the error factors affecting the wear-depth detecting precision were analyzed.Then,the comprehensive error model of the wear-depth detecting system of the spherical plain bearing was built by the multi-body system theory(MBS).In addition,the thermal deformation of the wear-depth detecting system caused by varying the environmental temperature was detected.Finally,according to the above experimental parameters,the thermal errors of the related parts of the comprehensive error model were calculated by FEM.The results show that the difference between the simulation value and the experimental value is less than 0.005 mm,and the two values are close.The correctness of the comprehensive error model is verified under the thermal error experimental conditions.

Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.

Establishment of European Regional Ionosphere Model Based on Spherical Harmonic Functions

In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.

Multi-level spherical moments based 3D model retrieval

In this paper a novel 3D model retrieval method that employs multi-level spherical moment analysis and relies on voxelization and spherical mapping of the 3D models is proposed. For a given polygon-soup 3D model, first a pose normalization step is done to align the model into a canonical coordinate frame so as to define the shape representation with respect to this orientation. Afterward we rasterize its exterior surface into cubical voxel grids, then a series of homocentric spheres with their center superposing the center of the voxel grids cut the voxel grids into several spherical images. Finally moments belonging to each sphere are computed and the moments of all spheres constitute the descriptor of the model. Experiments showed that Euclidean distance based on this kind of feature vector can distinguish different 3D models well and that the 3D model retrieval system based on this arithmetic yields satisfactory performance.

Static Force-Based Modeling and Parameter Estimation for a Deformable Link Composed of Passive Spherical Joints With Preload Forces

To balance the contradiction between higher flexibility and heavier load bearing capacity,we present a novel deformable manipulator which is composed of active rigid joints and deformable links.The deformable link is composed of passive spherical joints with preload forces between socket-ball surfaces.To estimate the load bearing capacity of a deformable link,we present a static force-based model of spherical joint with preload force and analyze the static force propagation in the deformable link.This yields an important result that the load bearing capacity of a spherical joint only depends on its radius,preload force,and static friction coefficient.We further develop a parameter estimation method to estimate the product of preload force and static friction coefficient.The experimental results validate our model.80.4%of percentage errors on the maximum payload mass prediction are below 15%.

Constitutive model for casting magnesium alloy involving spherical void evolution

Casting magnesium alloys are highly heterogeneous materials inevitably containing numerous voids.These voids will evolve during material deformation and markedly affect material behaviors,so it is important to investigate the equation of the void evolution and the constitutive relation involving the void evolution.By assuming the voids in casting magnesium alloys were spherical,the growth equation of the voids was obtained from the incompressibility and continuity conditions of material matrix. Through combining the obtained void-growth equation with the void-nucleation equation relative to the increment of intrinsic-time measure,the evolution equation of the voids was presented.By introducing the presented void-evolution equation to a nonclassical elastoplastic constitutive equation,a constitutive model involving the void evolution was put forward.The corresponding numerical algorithm and finite element procedure of the model were developed and applied to the analysis of the elastoplastic response and the porosity change of casting magnesium alloy ZL305.Computed results show satisfactory agreement with those of the corresponding experiments.

Finite Element Modeling of Shop Built Spherical Pressure Vessels

This work builds on an earlier work done which used global coordinates where a large number of elements were needed to form a convergence of results for shop built spherical pressure vessels. In this work area coordinates were used. Any action that leads to an inability on the part of a structure to function as intended is known as failure. This research, therefore, investigates stresses developed in a shop built carbon steel spherical storage vessels using finite element approach as the analytical tool. 3-D finite element modeling using 3-node shallow triangular element with five degrees of freedom at each node is employed. These five degrees of freedom are the essential nodal degrees of freedom without the sixth in-plane rotation. The resulting equations from finite element analysis are coded using FORTRAN 90 computer programme. Spherical storage vessels are subjected to various internal loading pressures while nodal displacements, strains and the corresponding maximum Von-mises stresses are determined. The calculated maximum Vonmises stresses are compared with the yield strength of the shell plate material. Using specified safety factor, safety internal pressures with the corresponding shell thicknesses for shop built spherical pressure vessels are determined. The finite element modeling carried out in this research can be used to predict in-service stresses, strains, and deformations of shop built spherical pressure vessels using Von-mises yield stress as the failure criteria. The results obtained were validated by analytical method and it showed there was no significant difference (P > 0.05) with values obtained through analytical method.

Spherical-Cymbal换能器位移特性研究

提出了一种新型高位移性能的球冠钹型(Spherical-Cymbal)压电复合换能器。Spherical-Cymbal换能器由厚度方向极化的压电陶瓷薄圆片夹持在两个球形金属端帽间制成,每个金属端帽内表面均有一个浅球冠形空腔,球形金属端帽起机械放大作用,它将压电陶瓷薄圆片的微小径向位移转换并放大为垂直其表面的较大的轴向位移。在变形假设条件下,建立了Spherical-Cymbal换能器的位移简化模型。数值计算结果表明,Spherical-Cymbal换能器比钹型(Cymbal)换能器具有更好的位移特性,某给定几何尺寸Spherical-Cymbal换能器的轴向位移是无端帽压电陶瓷薄圆片轴向位移的43.7倍,是相同尺寸Cymbal换能器轴向位移的1.1倍。

Spherical-Cymbal换能器端帽自由胀形过程建模

为掌握Spherical-Cymbal换能器端帽自由胀形的成形规律,在端帽材料选定、几何尺寸(包括外径D、空腔底部直径dc和厚度te)及胀形压边力不变且线性加载等约束条件下,采用ANSYS/LS-DYNA软件对几种不同加载终压P下端帽的自由胀形成形过程进行了数值模拟。通过非线性曲线拟合分别得到了加载后端帽中心高度与加载终压(HP-P)、卸载回弹量与加载终压(ΔH-P)及卸载后端帽中心高度与加载终压(H-P)之间关系的数学模型。实验结果表明,在以上约束条件下,所建数学模型揭示了Spherical-Cymbal换能器端帽的自由胀形成形规律,可用于指导实际生产。