Structural Setting of the South-West Cameroon Using Satellite Potential Field Derived from SGG-UGM-2 Gravity Data

This study aims to improve knowledge of the structure of southwest Cameroon based on the analysis and interpretation of gravity data derived from the SGG-UGM-2 model. A residual anomaly map was first calculated from the Bouguer anomaly map, which is strongly affected by a regional gradient. The residual anomaly map generated provides information on the variation in subsurface density, but does not provide sufficient information, hence the interest in using filtering with the aim of highlighting the structures affecting the area of south-west Cameroon. Three interpretation methods were used: vertical gradient, horizontal gradient coupled with upward continuation and Euler deconvolution. The application of these treatments enabled us to map a large number of gravimetric lineaments materializing density discontinuities. These lineaments are organized along main preferential directions: NW-SE, NNE-SSW, ENE-WSW and secondary directions: NNW-SSE, NE-SW, NS and E-W. Euler solutions indicate depths of up to 7337 m. Thanks to the results of this research, significant information has been acquired, contributing to a deeper understanding of the structural composition of the study area. The resulting structural map vividly illustrates the major tectonic events that shaped the geological framework of the study area. It also serves as a guide for prospecting subsurface resources (water and hydrocarbons). .

Application of Image Enhancement Techniques to Potential Field Data

In this paper the application of image enhancement techniques to potential field data is briefly described and two improved enhancement methods are introduced. One method is derived from the histogram equalization technique and automatically determines the color spectra of geophysical maps. Colors can be properly distributed and visual effects and resolution can be enhanced by the method. The other method is based on the modified Radon transform and gradient calculation and is used to detect and enhance linear features in gravity and magnetic images. The method facilites the detection of line segments in the transform domain. Tests with synthetic images and real data show the methods to be effective in feature enhancement.

Mobile robot path planning method combined improved artificial potential field with optimization algorithm

To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method combining the IAPFM with optimization algorithm （trust region algorithm） is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot＇s velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.

A new edge recognition technology based on the normalized vertical derivative of the total horizontal derivative for potential field data

Edge detection and enhancement techniques are commonly used in recognizing the edge of geologic bodies using potential field data. We present a new edge recognition technology based on the normalized vertical derivative of the total horizontal derivative which has the functions of both edge detection and enhancement techniques. First, we calculate the total horizontal derivative （THDR） of the potential-field data and then compute the n-order vertical derivative （VDRn） of the THDR. For the n-order vertical derivative, the peak value of total horizontal derivative （PTHDR） is obtained using a threshold value greater than 0. This PTHDR can be used for edge detection. Second, the PTHDR value is divided by the total horizontal derivative and normalized by the maximum value. Finally, we used different kinds of numerical models to verify the effectiveness and reliability of the new edge recognition technology.

A-E equation of potential field transformations in the wavenumber domain and its application

A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.

Virtual local target method for avoiding local minimum in potential field based robot navigation

A novel robot navigation algorithm with global path generation capability is presented. Local minimum is a most intractable but is an encountered frequently problem in potential field based robot navigation.Through appointing appropriately some virtual local targets on the journey, it can be solved effectively. The key concept employed in this algorithm are the rules that govern when and how to appoint these virtual local targets. When the robot finds itself in danger of local minimum, a virtual local target is appointed to replace the global goal temporarily according to the rules. After the virtual target is reached, the robot continues on its journey by heading towards the global goal. The algorithm prevents the robot from running into local minima anymore. Simulation results showed that it is very effective in complex obstacle environments.

Dynamic collision avoidance for cooperative fixed-wing UAV swarm based on normalized artificial potential field optimization

Cooperative path planning is an important area in fixed-wing UAV swarm.However,avoiding multiple timevarying obstacles and avoiding local optimum are two challenges for existing approaches in a dynamic environment.Firstly,a normalized artificial potential field optimization is proposed by reconstructing a novel function with anisotropy in each dimension,which can make the flight speed of a fixed UAV swarm independent of the repulsive/attractive gain coefficient and avoid trapping into local optimization and local oscillation.Then,taking into account minimum velocity and turning angular velocity of fixed-wing UAV swarm,a strategy of decomposing target vector to avoid moving obstacles and pop-up threats is proposed.Finally,several simulations are carried out to illustrate superiority and effectiveness.

Cooperative Search of UAV Swarm Based on Ant Colony Optimization with Artificial Potential Field

An ant colony optimization with artificial potential field(ACOAPF)algorithm is proposed to solve the cooperative search mission planning problem of unmanned aerial vehicle(UAV)swarm.This algorithm adopts a distributed architecture where each UAV is considered as an ant and makes decision autonomously.At each decision step,the ants choose the next gird according to the state transition rule and update its own artificial potential field and pheromone map based on the current search results.Through iterations of this process,the cooperative search of UAV swarm for mission area is realized.The state transition rule is divided into two types.If the artificial potential force is larger than a threshold,the deterministic transition rule is adopted,otherwise a heuristic transition rule is used.The deterministic transition rule can ensure UAVs to avoid the threat or approach the target quickly.And the heuristics transition rule considering the pheromone and heuristic information ensures the continuous search of area with the goal of covering more unknown area and finding more targets.Finally,simulations are carried out to verify the effectiveness of the proposed ACOAPF algorithm for cooperative search mission of UAV swarm.

Collision avoidance planning in multi-robot system based on improved artificial potential field and rules

For real-time and distributed features of multi-robot system,the strategy of combining the improved artificial potential field method and the rules based on priority is proposed to study the collision avoidance planning in multi-robot systems. The improved artificial potential field based on simulated annealing algorithm satisfactorily overcomes the drawbacks of traditional artificial potential field method,so that robots can find a local collision-free path in the complex environment. According to the movement vector trail of robots,collisions between robots can be detected,thereby the collision avoidance rules can be obtained. Coordination between robots by the priority based rules improves the real-time property of multi-robot system. The combination of these two methods can help a robot to find a collision-free path from a starting point to the goal quickly in an environment with many obstacles. The feasibility of the proposed method is validated in the VC-based simulated environment.

Size dependency and potential field influence on deriving mechanical properties of carbon nanotubes using molecular dynamics

A thorough understanding on the mechanical properties of carbon nanotube （CNT） is essential in extending the advanced applications of CNT based systems. However, conducting experiments to estimate mechanical properties at this scale is extremely challenging. Therefore, development of mechanistic models to estimate the mechanical properties of CNTs along with the integration of existing continuum mechanics concepts is critically important. This paper presents a comprehensive molecular dynamics simulation study on the size dependency and potential function influence of mechanical properties of CNT. Commonly used reactive bond order （REBO） and adaptive intermolecular reactive bond order （A1REBO） potential functions were considered in this regard. Young＇s modulus and shear modulus of CNTs are derived by integrating classical continuum mechanics concepts with molecular dynamics simulations. The results indicate that the potential function has a significant influence on the estimated mechanical properties of CNTs, and the influence of potential field is much higher when studying the torsional behaviour of CNTs than the tensile behaviour.

Solution to reinforcement learning problems with artificial potential field

A novel method was designed to solve reinforcement learning problems with artificial potential field.Firstly a reinforcement learning problem was transferred to a path planning problem by using artificial potential field(APF),which was a very appropriate method to model a reinforcement learning problem.Secondly,a new APF algorithm was proposed to overcome the local minimum problem in the potential field methods with a virtual water-flow concept.The performance of this new method was tested by a gridworld problem named as key and door maze.The experimental results show that within 45 trials,good and deterministic policies are found in almost all simulations.In comparison with WIERING's HQ-learning system which needs 20 000 trials for stable solution,the proposed new method can obtain optimal and stable policy far more quickly than HQ-learning.Therefore,the new method is simple and effective to give an optimal solution to the reinforcement learning problem.

Analyzing gravity anomaly variations before the 2016 Ms6.4 earthquake in Menyuan,Qinghai with an interpolation/cutting potential field separation technique

We evaluated 2011-2015 mobile relative gravity data from the Hexi monitoring network that covers the epicenter of the 2016 Menyuan Ms6.4 earthquake, Qinghai Province, China and examined the spatiotemporal characteristics of the gravity field at the focal depth. In addition, we assessed the regional gravity field and its variation the half-year before the earthquake. We use first different interpolation algorithms to build a grid for the gravity data and then introduce potential field interpolation-cutting separation techniques and adaptive noise filtering. The results suggest that the gravity filed at the focal depth of 11.12 km separated from the total gravity field at about -400-150 ×10^-8 m/s^2 in the second half of 2015, which is larger than that in the same period in 2011 to 2014 （±30×10^-8 m/s^2）. Moreover, at the same time, the gravity field changed fast from September 2014 to May 2015 and May 2015 to September 2015, reflecting to some extent material migration deep in the crust before the Menyuan earthquake.

Higher-Order Line Element Analysis of Potential Field with Slender Heterogeneities

Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.

Abnormality Degree Detection Method Using Negative Potential Field Group Detectors

Online monitoring methods have been widely used in many major devices, however the normal and abnormal states of equipment are estimated mainly based on the monitoring results whether monitored parameters exceed the setting thresholds. Using these monitoring methods may cause serious false positive or false negative results. In order to precisely monitor the state of equipment, the problem of abnormality degree detection without fault sample is studied with a new detection method called negative potential field group detectors（NPFG-detectors）. This method achieves the quantitative expression of abnormality degree and provides the better detection results compared with other methods. In the process of Iris data set simulation, the new algorithm obtains the successful results in abnormal detection. The detection rates for 3 types of Iris data set respectively reach 100%, 91.6%, and 95.24% with 50% training samples. The problem of Bearing abnormality degree detection via an abnormality degree curve is successfully solved.

An improved potential field method for mobile robot navigation

In order to overcome the inherent oscillation problem of potential field methods(PFMs) for autonomous mobile robots in the presence of obstacles and in narrow passages,an enhanced potential field method that integrates Levenberg-Marquardt(L-M) algorithm and k-trajectory algorithm into the basic PFMs is proposed and simulated.At first,the mobile robot navigation function based on the basic PFMs is established by choosing Gaussian model.Then,the oscillation problem of the navigation function is investigated when a mobile robot nears obstacles and passes through a long and narrow passage,which can cause large computation cost and system instability.At last,the L-M algorithm is adopted to modify the search direction of the navigation function for alleviating the oscillation,while the k-trajectory algorithm is applied to further smooth trajectories.By a series of comparative experiments,the use of the L-M algorithm and k-trajectory algorithm can greatly improve the system performance with the advantages of reducing task completion time and achieving smooth trajectories.

Potential fields of merging and splitting filaments in air

Two interacting light filaments with different initial phases propagating in air are investigated numerically by using a ray tracing method. The evolution of the rays of a filament is governed by a potential field. During propagation, the two potential wells of the two filaments can merge into one or repel each other, depending on the initial phase difference between the two filaments. The study provides a simple description of the interacting filaments.

Edge detection using directional eigenvalues of potential field gradient tensor data

Edge detection of potential field interpretation is an important task. The traditional edge detection methods have poor ability in outlining weak amplitude anomalies clearly. The resolved edges position is blurred.We purposed new edge detection methods based on directional eigenvalues of potential field gradient tensor for the causative sources. In order to balance strong and weak amplitude anomalies simultaneously,we present one normalization method using different orders of vertical derivatives to improve the new filters. The presented filters were tested on synthetic and real potential field data to verify its feasibility. All of the results have shown that the new edge detection methods can not only display the sources edges precisely and clearly,but also bring out more geological subtle details.

NOVEL APPROACH FOR ROBOT PATH PLANNING BASED ON NUMERICAL ARTIFICIAL POTENTIAL FIELD AND GENETIC ALGORITHM

A novel approach for collision-free path planning of a multiple degree-of-freedom （DOF） articulated robot in a complex environment is proposed. Firstly, based on visual neighbor point （VNP）, a numerical artificial potential field is constructed in Cartesian space, which provides the heuristic information, effective distance to the goal and the motion direction for the motion of the robot joints. Secondly, a genetic algorithm, combined with the heuristic rules, is used in joint space to determine a series of contiguous configurations piecewise from initial configuration until the goal configuration is attained. A simulation shows that the method can not only handle issues on path planning of the articulated robots in environment with complex obstacles, but also improve the efficiency and quality of path planning.

Application of wavelet transform modulus maxima in boundary detection of potential fields

This study presents the use of the method of wavelet transform modulus maxima(WTMM) to detect boundaries of potential field sources.The boundaries of causative sources can be judged by calculating the local modulus maxima of wavelet coefficients at different scales.For the potential field data with noise,the detected boundaries at small scales are easy to be distorted by noise,however,at large scales,the noise can be suppressed greatly and presents more accurate boundary detection results.Therefore,we can get a better boundary judgment by considering the detected boundaries at all scales.Applying the WTMM method to synthetic models and a real data set of Meishan iron deposit,both get a good effect.

ON THE STABILITY ESTIMATION OF ANALYTIC CONTINUATION FOR POTENTIAL FIELD

This paper discusses the stability of solutions to a class of Cauchy problems for Laplace equations under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamoto's methods for solving ill-posed problems respectively, the stability estimations of weighted Holder type and logarithmic type, have been obtained accordingly.