耦合优化蚁群算法与P-Median model的选址模型设计

为节省城建部门对于公共体育设施的投入成本以及提高城市人民生活质量,以运动场所优化选址为例,提出一种新型设施选址模型。该模型主要基于P-Median model(最小化阻抗模型)根据需求点数量从全部候选设施选址中选择设施空间位置,让用户达到离自己最近设施距离成本总和最小的目的,对选址的基本原则和实际情况提出要求,构造目标函数用于优化后蚁群算法求解进行选址工作。优化蚁群算法实现基于Python语言模块,通过改进蚁群原始信息素,提升原有算法的收敛速度,求出目标函数最优解,可以很好地模拟对于运动场所的选址。用二者耦合进行优势互补所设计的选址模型来搜寻研究区蚁群信息素浓度残留最大的栅格像元,从而确定未被已有设施点服务半径覆盖的最佳设施点建立位置。实验结果表明,该新型选址模型相较于最小化阻抗模型与最大化覆盖模型,新增优化设施点使整体服务半径覆盖率分别高出10.42%和6.95%,适合求解较为精确且小规模空间下的选址问题。

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using Screw Theory

The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.

The damage to model concrete gravity dams subjected to water explosions

Over the past century,the safety of dams has gradually attracted attention from all parties.Research on the dynamic response and damage evolution of dams under extreme loads is the basis of dam safety issues.In recent decades,scholars have studied the responses of dams under earthquake loads,but there is still much room for improvement in experimental and theoretical research on small probability loads such as explosions.In this paper,a 50-m-high concrete gravity dam is used as a prototype dam,and a water explosion model test of a 2.5-m-high concrete gravity dam is designed.The water pressure and the acceleration response of the dam body in the test are analysed.The pressure characteristics and dynamic response of the dam body are assessed.Taking the dam damage test as an example,a numerical model of concrete gravity dam damage is established,and the damage evolution of the dam body is analysed.By combining experiments and numerical simulations,the damage characteristics of the dam body under the action of different charge water explosions are clarified.The integrity of the dam body is well maintained under the action of a small-quantity water explosion,and the dynamic response of the dam body is mainly caused by the shock wave.Both the shock wave and the bubble pulsation cause the dam body to accelerate,and the peak acceleration of the dam body under the action of the bubble pulsation is only one percent of the peak acceleration of the dam body under the action of the shock wave.When subjected to explosions in large quantities of water,the dam body is seriously damaged.Under the action of a shock wave,the dam body produces a secondary acceleration response,which is generated by an internal interaction after the dam body is damaged.The damage evolution process of the dam body under the action of a large-scale water explosion is analysed,and it is found that the shock wave pressure of the water explosion causes local damage to the dam body facing the explosion.After the peak value of the shock wave,the impulse continues to act on the dam body,causing cumulative damage and damage inside the dam body.

A Modified Gravity p-Median Model for Optimizing Facility Locations

The gravity p-median model is an important improvement to the widely-used p-median model. However, there is still a debate on its validity in empirical applications. Previous studies even doubt the significance of the gravity p-median model. Using a case study of tertiary hospitals in Shenzhen, China, this study re-examines the difference between the gravity p-median model with the p-median model, by decomposing the difference between the two models into gravity rule and variant attraction. This study also proposes a modified gravity p-median model by incorporating a distance threshold. The empirical results support the validity of the gravity p-median model, and also reveal that only when the attractions of candidate facility locations are variable will the gravity p-median model lead to different results with the p-median model. The difference between the modified gravity p-median model and the gravity p-median model is also examined. Moreover, the impacts of the distance-decay parameter and distance threshold on solutions are investigated. Results indicate that a larger distance-decay parameter tends to result in a more dispersed distribution of optimal facilities and a smaller average travel time, and a smaller distance threshold can better promote the spatial equity of facilities. The proposed method can also be applied in studies of other types of facilities or in other areas.

Spatial Analysis of Gravity Data in the Basement of the Yaoundé-Yoko Area from the Global Gravity Model: Implication on the Sanaga Fault (South-Cameroon)

In this work, gravity anomalies from the XGM2016 global gravity model are used to study the basement of the Yaounde, Yoko area. The aim is to locate the characteristic tectonic faults and to characterize the geometry of the basement of these localities in order to improve the knowledge of the structural and tectonic basement of the study area. Numerical filters (vertical gradient, horizontal gradient, upward continuation) and Euler deconvolution were applied to the gravity anomalies respectively for qualitative and quantitative analysis. The results of the qualitative analysis allowed us to establish the lineament map of the study area;ranging from 0 to 35 km depth. For the quantitative analysis, the work is done in two parts: 1) highlighting the distribution of depths of geological structures in the basement of the study area;2) 2D1/2 modeling of geological structures to highlight the geometry of the basement of Yaounde, Yoko area. Thus, from five suitably selected profiles, the established models reveal the presence of eight blocks of geological structures of different densities and analyze their implications on the Sanaga Fault. Moreover, the models show that the positive anomalies characteristics for the Sanaga Fault reflect the anomalous character due to the strong dominance of the shale intrusion in the basement.

Methodology for local correction of the heights of global geoid models to improve the accuracy of GNSS leveling

At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.

对中直接投资立地选择因素分析——Gravity Model分析

利用中国与对中直接投资12个主要国家(地区)的1990年至2006年的面板数据,通过重力模型实证分析对中直接投资的决定因素。结果表明,经济规模对直接投资的吸引起到正面的有益的影响,而距离的增加对直接投资的吸引则有负面影响,虚拟变量的说服力也很高。通过分析,得出两国间贸易额的影响比其他变量的影响更为显著的结果。

A High-Resolution Earth’s Gravity Field Model SGG-UGM-2 from GOCE,GRACE,Satellite Altimetry,and EGM2008

This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.

Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.

Spatial-temporal Evolution and Determinants of the Belt and Road Initiative: A Maximum Entropy Gravity Model Approach

The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.

3D Modelling from New and Existing Gravity Data of an Intrusive Body in the Northern Part of Kribi-Campo Sub-Basin in Cameroon

A new gravity survey was carried out in the northern part of the onshore Kribi- Campo sub-basin in Cameroon. The data were incorporated to the existing ones and then analyzed and modeled in order to elucidate the subsurface structure of the area. The area is characterized in its north-western part by considerably high positive anomalies indicative of the presence of a dense intrusive body. We find, 1) from the analysis of the gravity residual anomaly map, the high positive anomalies observed are the signature of a shallow dense structure;2) from the multi-scale analysis of the maxima of the horizontal gradient, the structure is confined between depths of 0.5 km and 5 km;3) from the quantitative interpretation of residual anomalies by spectral analysis, the depth to the upper surface of the intrusive body is not uniform, the average depth of the bottom is h1 = 3.6 km and the depths to particular sections of the roof of the intrusion are h2 = 1.6 km and h3 = 0.5 km;4) and the 3D modeling gives results that are suggestive of the presence of contacts between rocks of different densities at different depths and a dense intrusive igneous body in the upper crust of the Kribi zone. From the 3D model the dense intrusive igneous block is surrounded by sedimentary formations to the south-west and metamorphic formations to the north-east. Both formations have a density of about 2.74 g/cm3. The near surface portions of this igneous block lie at a depth range of 0.5 km to 1.5 km while its lower surface has a depth range of 3.6 km to 5.2 km. The shape of the edges and the bottom of the intrusive body are suggestive of the fact that it forms part of a broader structure underlying the Kribi-Campo sub-basin with a great influence on the sedimentary cover.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

Crustal structure of the western Indian shield: Model based on regional gravity and magnetic data

Regional surface gravity data and global satellite magnetic data have been utilized to generate a preliminary model of the crustal structure along a southwest-northeast profile （Gadra-Fatehpur） through western Rajasthan.The study area represents the western part of the Indian continental landmass which has undergone several major episodes of repeated subduction/collision,plume traces and rifting from Archaean to recent times.The temporal and spatial relationship between the various geotectonic provinces is quite complex,thereby limiting the emergence of a suitable crustal structure model for this region.Exposures of the Malani Igneous Suite （MIS）,a product of bimodal volcanism （～780 Ma）,and considered to be the third largest felsic magmatic province of the world,is evident along the profile and also to the southwest of the study area.The easternmost part of the profile is close to the DAFB （Delhi Aravalli Fold Belt）,a Proterozoic orogenic belt.This study probes the geometry of the different crustal units in terms of density and susceptibility variations in order to decipher the imprints of the major tectonic processes the region has undergone.In order to decipher the crustal geometry of the Gadra-Fatehpur profile,two NW-SE gravity and magnetic profile vertical sections （A-A＇ in the south and B-B＇ in the north） are modelled on the basis of the constraints provided from previous seismic models.The crustal model of the Gadra-Fatehpur profile is composed of alluvium,Tertiary sediments,MIS,Marwar Supergroup,low-density layers （LDLs） and the middle-lower crustal layers,with a distinct change in configuration from the southwest to northeast.The Moho dips from SW to NE,the MIS in the SW gives way to the thick pile of the Marwar Supergroup to the NE.The evolution of MIS has been suggested to have occurred as a consequence of delamination of the upper mantle.LDLs are incorporated in Gadra-Fatehpur model.In the SW,LDL （2550 kg/m3） lies below the MIS in the NE,another LDL （2604 kg/m3） is depicted below the mid-crustal layer.

Robust inversion analysis of local gravity anomalies caused by geological dislocation model of faults

Theoretical analysis and practical observations show that fault dislocations can change the gravity field around the fault. Gravity changes which were caused by the repeated dislocations over a long period of time were superimposed on the Bougeur gravity anomalies. These anomalies became the evidence of historical movement of fault as well as provide a way for the study of paleo earthquakes. This paper investigates inversion methods for the geological dislocation modeling of faults using the local Bouguer's gravity anomalies. To remove the effects of the irrelevant part of gravity anomalies to fault movements, we propose the robust nonlinear inversion method and set up the corresponding algorithm. Modeling examples indicate that the Marquardt's and Baye's least squares solutions depart from the true solution due to the attraction of gross errors in the data. The more seriously the data is contaminated, the more seriously the solutions are biased. In contrast, the proposed robust Marquardt's and Baye's inversion solutions can still maintain consistency with the solution without gross errors, even though 50 percent of the data is contaminated. This indicates that the proposed robust methods are effective. Using the proposed methods, we invert the geological dislocation models of the faults around the Erhai Lake in West Yunnan. The results show that the Northern Cangdong fault and the Erhai fault are normal dip slip faults with about 4 to 5 km dislocations; and that the Southern Cangdong fault has a less dip slip compared with the former two. A satisfactory fitting between the theoretical values of the inversion solution and the actual local gravity field is achievable.

Analyses on gravity variation before and after the Lijiang earthquake based on a finite rectangular dislocation model

The methods were discussed to calculate the gravity variation due to crustal deformation based on a model of dis-location on a finite rectangular plane. Taking the Lijiang MS=7.0 earthquake as an example the calculating princi-ple of fault parameters were determined, and the results were given. Of particular interests were the characteristics of the gravity variations in different dislocation types. With comparison between the calculated results and the practical measurements, it was found that the model could to some extent account for the observations. But it failed to give explanations to the more far spatial gravity variation.

A 3D Geological Model Constrained by Gravity and Magnetic Inversion and its Exploration Implications for the World-class Zhuxi Tungsten Deposit, South China

The Zhuxi tungsten deposit in Jiangxi Province,South China,contains a total W reserve of about 2.86 Mt at an average grade of 0.54 wt%WO3,representing the largest W deposit in the world.Numerous studies on the metallogeny of the deposit have included its timing,the ore-controlling structures and sedimentary host rocks and their implications for mineral exploration.However,the deep nappe structural style of Taqian-Fuchun metallogenic belt that hosts the W deposit,and the spatial shape and scale of deeply concealed intrusions and their sedimentary host rocks are still poorly defined,which seriously restricts the discovery of new deposits at depth and in surrounding areas of the W deposit.Modern 3 D geological modeling is an important tool for the exploration of concealed orebodies,especially in brownfield environments.There are obvious density contrast and weak magnetic contrast in the ore-controlling strata and granite at the periphery of the deposit,which lays a physical foundation for solving the 3 D spatial problems of the ore-controlling geological body in the deep part of the study area through gravity and magnetic modeling.Gravity data(1:50000)and aeromagnetic data(1:50000)from the latest geophysical surveys of 2016-2018 have been used,firstly,to carry out a potential field separation to obtain residual anomalies for gravity and magnetic interactive inversion.Then,on the basis of the analysis of the relationship between physical properties and lithology,under the constraints of surface geology and borehole data,human-computer interactive gravity and magnetic inversion for 18 cross-sections were completed.Finally,the 3 D geological model of the Zhuxi tungsten deposit and its periphery have been established through these 18 sections,and the spatial shape of the intrusions and strata with a depth of 5 km underground were obtained,initially realizing―transparency‖for ore-controlling bodies.According the analysis of the geophysical,geochemical,and geological characteristics of the Zhuxi tungsten deposit,we discern three principles for prospecting and prediction in the research area,and propose five new exploration targets in its periphery.

Comparative Study on Deformation Prediction Models of Wuqiangxi Concrete Gravity Dam Based on Monitoring Data

The deformation prediction models of Wuqiangxi concrete gravity dam are developed,including two statistical models and a deep learning model.In the statistical models,the reliable monitoring data are firstly determined with Lahitte criterion;then,the stepwise regression and partial least squares regression models for deformation prediction of concrete gravity dam are constructed in terms of the reliable monitoring data,and the factors of water pressure,temperature and time effect are considered in the models;finally,according to the monitoring data from 2006 to 2020 of five typical measuring points including J23(on dam section 24^(#)),J33(on dam section 4^(#)),J35(on dam section 8^(#)),J37(on dam section 12^(#)),and J39(on dam section 15^(#))located on the crest of Wuqiangxi concrete gravity dam,the settlement curves of the measuring points are obtained with the stepwise regression and partial least squares regression models.A deep learning model is developed based on long short-term memory(LSTM)recurrent neural network.In the LSTM model,two LSTMlayers are used,the rectified linear unit function is adopted as the activation function,the input sequence length is 20,and the random search is adopted.The monitoring data for the five typical measuring points from 2006 to 2017 are selected as the training set,and the monitoring data from 2018 to 2020 are taken as the test set.From the results of case study,we can find that(1)the good fitting results can be obtained with the two statistical models;(2)the partial least squares regression algorithm can solve the model with high correlation factors and reasonably explain the factors;(3)the prediction accuracy of the LSTM model increases with increasing the amount of training data.In the deformation prediction of concrete gravity dam,the LSTM model is suggested when there are sufficient training data,while the partial least squares regression method is suggested when the training data are insufficient.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.

A new high-precision gravity solid tidal model for Precision Gravity Measurement Facility

It is significant for establishing gravity datum to construct precise gravity solid tidal model,A simple method with relatively low performance is to interpolate tidal parameters from the global gravity solid tide models.A competitive approach is to determine local gravity solid tidal model by harmonic analysis using long-time serial gravity observations.In this paper a new high-precision gravity solid tidal model for Precision Gravity Measurement Facility is estimated from two co-site gravimeters in the cave laboratory using modern international standard data processing techniques,whose accuracy is evaluated further by comparing with previous publications.The results show that:(1)the determined gravity solid tidal models from two co-site gravimeters are in good agreement with each other,of which the maximum differences for amplitude factors and phase delays don’t exceed 0.01700%and 2.50990°,respectively.(2)the performance of the obtained gravity solid tidal model is 0.00411 for amplitude factors and 0.24120°for phase delays,which is a little better than that of previous publications using superconducting gravity data from Wuhan station.(3)our results and methods are corrective and effective.(4)our model is tiny different from that provided by Wuhan station,which implies that it is necessary to construct a gravity solid tidal model for Precision Gravity Measurement Facility,rather than just adopting existing models at Wuhan station.Our results are helpful in realizing the goal of Precision Gravity Measurement Facility.