Uniform Node Distribution Research Articles

A generalized uniform placement of alters on spherical surface (U-PASS) for visualizing general weighted networks

Network visualization is an important tool for extracting information from the structure and configuration of a network, especially when the network includes weighted edges and nodes with attribute information. Previous studies have demonstrated an effective visualization method that projects the network onto a spherical surface. In this work, we extend this method, known as Uniform Placement of Alters on Spherical Surface (U-PASS), to general weighted networks. This extension enables the uniform distribution of network nodes across multiple layers of concentric spheres. In addition, we discuss the lower bound of a criterion called generalized spherical cap discrepancy, which is used to evaluate the uniformity of node distribution on a collapsed spherical surface.

Analysis of the dynamic response for Kirchhoff plates by the element-free Galerkin method

Dynamic response analysis involves examining structural behavior under dynamic loading conditions. Transient dynamic analysis emerges as a method employed to assess the responses of deformable bodies. Due to the depth analysis of transient responses for thin plates, the associated error analysis work becomes particularly important. In this work, we conduct stability and convergence analysis of the element-free Galerkin (EFG) method for the dynamic response of Kirchhoff plate model. We start by discretizing the thin plate dynamics using the EFG method for the spatial domain and the central difference scheme for the temporal domain. Stability and convergence analysis for transient responses, including deflection and moment responses, are derived similarly to those in two-dimensional transient structural dynamic analysis. The key to the analysis is transforming the governing equations and clamped boundary conditions into a weak formulation with penalty terms using the penalty method. The main results demonstrate a significant correlation between the error estimate and both nodal spacing and time step size. Additionally, the continuity of the approximation functions and the selection of penalty factors significantly affect numerical accuracy. To validate the theoretical results, we conduct numerical experiments involving clamped square and L-shaped plates with uniform and nonuniform node distributions, as well as a perforated plate model. Furthermore, we investigate the impact of node influence domains and penalty factors on numerical accuracy, facilitating parameter selection for practical engineering applications.

Improving analytic approximations of TSP tour lengths with adjustment factors

Optimizing Traveling Salesman Problem (TSP) tours requires substantial computational effort, leading researchers to develop approximations relating tour length to the number of visited points, n. Existing models, such as the √nA predictor, effectively approximate tour lengths for large-capacity vehicles but sacrifice accuracy for small n values relevant for most practical applications. Consequently, this study addresses this gap by proposing models with uniform node distributions, which incorporate realistic factors, such as central vs. random starting points and various service zone shapes. These factors are then integrated into a single equation, enhancing applicability. Furthermore, the exponent of n is statistically estimated to be significantly different from 0.5, challenging previous studies. Our proposed model estimates TSP tour lengths more accurately, particularly for small n values, and maintains accuracy for large n values, with errors below 3.11% for up to 600 points. This model offers a more precise and versatile alternative to current models.

Resource Optimization Using a Step-by-Step Scheme in Wireless UWB Sensing and Localization Networks

Wireless localization and target sensing both rely on precise extraction of parameters such as signal amplitude, propagation delay, and Doppler shift from the received signals. Due to the high multi-path resolution and strong penetration, both localization and sensing can be achieved through identical UWB waveforms. In this paper, we try to properly allocate resources for localization and sensing to fully exploit the potential of UWB systems. Considering the complexity of the multi-slot networks, we derive the Fisher Information Matrix (FIM) expressions for single-slot and dual-slot integrated sensing and localization (ISAL) networks, respectively, and propose two resource optimization schemes, namely the step-by-stepscheme and the integrated scheme, respectively. The numerical results show that: (i) for the sensing-resource-limited networks with relatively uniform node distribution, the energy allocated to each step in the step-by-step scheme satisfies the relationship energy for clock offset < energy for radar localization < energy for target sensing; (ii) in the multi-slot ISAL networks, more energy will be allocated to the time slots where the networks are relatively sensing-resource-limited; (iii) the step-by-step scheme is more suitable for the sensing-resource-abundant networks, while the integrated scheme is more suitable for the sensing-resource-limited networks.

Low Order Modeling of a Biomass Throated Gasification Reactor

As first step towards the consideration of the associated control-estimator design problem, in this study the problem of drawing a low-order finite-dimensional DA model of the bi/tristable OPDE one of a spatially distributed throated biomass gasification reactors is addressed, with focus on the description of the practical steady state (SS) of highest conversion. The reactor is described by 15 nonlinear PDEs, which are numerically solved using finite differences to discretize the spatial domain. The number and placement of nodes along the axial direction of the reactor act as degrees of freedom that must be carefully chosen. In this study, a node location method, initially developed for a different class of reactors, is applied to the throated reactor. It was found that the desired SS can be effectively described by relocating some nodes using the adaptive mesh method, which results in a model order smaller than the case with an uniform node distribution. It was also observed that one must be mindful of the discretization near the air entrance, as excessive discretization in that zone can lead to poor descriptions of the desired SS or increase unnecessarily the model order (and consequently, the number of equations to be solved online). The results presented here lay the groundwork for improving the adaptive mesh location method to extend its application to throated gasifiers, thereby ensuring accurate numerical solutions for control and estimation tasks.

An ALE meshfree method for surface PDEs coupling with forced mean curvature flow

In this paper, we propose an arbitrary Lagrangian Eulerian (ALE) meshfree method that utilizes the radial basis function-finite difference (RBF-FD) method for solving diffusion-reaction equations on evolving surfaces. The surface evolution law is determined by a forced mean curvature flow (FMCF). We develop a parametric RBF-FD method to solving the FMCF, which has not been done previously in the framework of meshfree methods. The advantage of this parametric method is that it utilizes a suitable tangential velocity in the equation to maintain a fairly uniform distribution of nodes during the surface evolution. The tangential velocity also allows us to construct an ALE RBF-FD scheme for the surface PDEs, which performs better than the purely Lagrangian method. Furthermore, we discuss how to deal with the boundary conditions for both the FMCF and the PDEs on surfaces, and present a ghost node approach to efficiently discretize the boundary conditions. Some numerical experiments are shown, which not only demonstrate the effectiveness of the tangential velocity, but also illustrate two applications.

Mechanical equipment fault diagnosis based on wireless sensor network data fusion technology

Abstract To save network energy consumption and prolong network life cycle in complex mechanical fault diagnosis, a research method of data fusion routing protocol algorithm based on wireless sensor network (WSN) is proposed. The specific content of the method is as follows: First, the low-energy adaptive clustering hierarchy algorithm is analyzed and discussed. On this basis, the prim route fusion algorithm is proposed to realize the effective utilization of energy and prolong the life of the network. Then, the WSN is abstracted as an undirected graph. From the perspective of saving the energy of the whole network, several current algorithms for building fusion trees are compared. The experimental results show that the prim algorithm consumes energy only after 700 rounds of clustering, while the leach clustering algorithm consumes energy only after 500 rounds. This shows that applying the prim algorithm can reduce the energy consumption of the whole network and prolong the life cycle of the network. However, the algorithm is carried out on the premise of uniform distribution of nodes, and there is a certain gap with the specific application of WSN in mechanical fault diagnosis. In the comparison of node energy consumption, it is found that compared with using the shortest path tree, using the central point of graph algorithm can greatly save the energy consumption of the node and has better performance. Practice has proved that this method can effectively remove redundant data information and solve the problem of unreliable data collected by a single sensor node. It is more suitable for the specific application of WSN in mechanical fault diagnosis.

An analytic method for vibration analysis of non-uniformly coupled L-shaped plates with arbitrary boundary conditions

L-shaped plates are extensively utilized in practical engineering and plates are uniformly coupled in most previous studies. However, spot welding, riveting or bolting is also employed to link two plates and these connection types lead to non-uniform coupling conditions. In this regard, an analytic model is developed for vibration analysis of L-shaped plates with non-uniform coupling conditions. The system is decomposed into two independent rectangular plates, and both bending and in-plane vibrations are analyzed via the classic plate theory and superposition method. The artificial spring technique is adopted to deal with non-uniform continuity conditions and arbitrary uniform boundary conditions, and these conditions are assembled into the governing equation. Comparisons of natural frequencies of L-shaped plates with different boundary and coupling conditions are firstly made, and high accuracy and wide application of the developed model are demonstrated. Furthermore, influences of boundary conditions, coupling conditions, coupling angle and length of plates are investigated. Results reveal that out-of-plane and in-plane displacements are coupled in every plate of L-shaped plate systems. Uniform distribution of coupling nodes can efficiently increase natural frequencies and a few coupling nodes play the role of uniform rigid coupling conditions. Natural frequencies of L-shaped plates at a right angle are the maximum or very close to maximum one. Besides, present results can be used as benchmarks for future researchers.

Acceleration of RBF-FD meshless phase-field modelling of dendritic solidification by space-time adaptive approach

• A novel meshless approach for phase-field modelling of dendritic growth. • Reduction of discretisation-induced anisotropy by the scattered nodes. • Increase in computational efficiency by a space-time adaptive approach. A novel adaptive numerical approach is developed for an accurate and computationally efficient phase-field modelling of dendritic solidification. The adaptivity is based on the dynamic quadtree domain decomposition. A quadtree decomposes the computational domain into rectangular sub-domains of different sizes. Each sub-domain is extended to ensure overlap communication between neighbouring sub-domains. In each sub-domain, uniform distribution of computational nodes is generated. The product between the node density and the sub-domain area is fixed to ensure the h-adaptivity. The adaptive approach provides the highest density of computational nodes at the solid-liquid interface and the lowest density in the bulk of the phases. The meshless radial basis function generated finite difference (RBF-FD) method is applied for the spatial discretisation of the partial differential equations which arise from the phase-field model. The RBF-FD method is especially appealing since it allows straightforward spatial discretisation of partial differential equations on scattered node distributions. The use of scattered node distribution reduces the discretisation-induced anisotropy in the phase-field modelling of dendritic growth. The forward Euler scheme is used for temporal discretisation. The adaptive time-stepping is employed to speed up the calculations further. The performance of the novel numerical approach is tested for dendritic solidification of supercooled pure melts and supersaturated dilute binary alloys at arbitrary preferential growth directions. The impact of the numerical parameters on the accuracy and computational efficiency is thoroughly analysed. It is shown that the RBF-FD method, defined on scattered node distribution, together with the space-time adaptive approach, represents an accurate and efficient technique for solving the phase-field models of dendritic solidification.

Game theory based node clustering for cognitive radio wireless sensor networks

Cognitive radio wireless sensor networks (CRWSN) is a promising technology for developing bandwidth constrained applications. Future Internet of Things (IoT) applications may extensively use CRWSN. CRWSN consists of cognitive radio enabled sensor nodes which are energy constrained, in general. Hierarchical cluster based approach for overall network management is suitable for network stability and scalability. Thus node clustering is an important problem in CRWSN setup. Objective of this work is to develop a suitable node clustering algorithm for CRWSN, in which nodes are expected to be mobile. A node clustering protocol for CRWSN has been proposed in this paper. The proposed clustering protocol is based on evolutionary game theory (EGT). Initial clusters are formed through a simple partitioning approach. Eventually, initial clusters are merged to form the final clusters. After forming the clusters by the resourceful sink node, the cluster head nodes for respective clusters are determined. The sink node runs the EGT based algorithm to identify the most capable node as the cluster head. The strength of this approach is that while identifying the cluster head node, various parameters such as residual energy level, geographic location, mobility, and the probability of primary user (PU) arrival are considered. The clusters and therefore, the cluster head nodes are distributed uniformly in the geographical area. The proposed clustering protocol has been compared with LEACH, RARE and the spectrum aware clustering algorithm. The simulation results show that the proposed clustering protocol outperforms all these similar node clustering protocols. On average, the proposed protocol outperforms the benchmarks protocols by 25% in terms of number of high energy nodes selected as cluster head, by 37% in terms of uniform geographical distribution of cluster head nodes, by 23% in terms of total energy consumed during the simulation time, and by 27% in terms of network lifetime. The future scope of the work has been outlined.

Genetic Algorithm Energy Optimization in 3D WSNs with Different Node Distributions

Optimal node clustering in wireless sensor networks (WSNs) is a major issue in reducing energy consumption and extending network node life time and reliability measures. Many techniques for optimizing the node clustering process in WSN have been proposed in the literature. The metaheuristic algorithms are a subset of these techniques. Genetic algorithm (GA) is an evolutionary metaheuristic technique utilized to improve the network reliability and extending the network life time by optimizing the clustering process in the network. The GA dynamic clustering (GA-DC) algorithm is proposed in this paper to extend the network reliability and node life time of three dimensional (3D) WSN. The GA-DC algorithm made use of an improved fitness function that takes into account a variety of metrics such as energy expenditure per protocol round, clustering distance, and the number of long-distance wireless connections. There have been two types of simulation scenarios run. First, simulation results show that the GA-DC algorithm increases network life time by 80% and network throughput by 55% when compared to the well-known LEACH protocol. Second, simulation results show that the uniform node distribution outperforms the normal and exponential distributions in terms of network life time by 5.7% and 7%, network reliability by 4.2% and 76%, and data throughput by 10.85% and 19.54%, respectively

A Novel Static Cluster-Based Hierarchical Protocol for Wireless Sensor Networks

Wireless sensor networks have recently gained a lot of attention from the scientific community due to their very wide spectrum of applications. In such networks, the sensor nodes have limited resources. These constraints impose many challenges to the design of related protocols. Especially, routing protocols should be energy-efficient for the prolonged network lifetime. The LEACH protocol is the most popular energy-efficient hierarchical clustering protocol for WSNs that was proposed for reducing power consumption. However, LEACH suffers from several drawbacks such as the non uniform distribution of Cluster Head nodes, the possibility of choosing a low energy node as Cluster Head, etc. In this paper, an attempt is made to overcome this shortcoming by introducing a new hierarchical clustering protocol, called SCHP (Static Cluster-based Hierarchical Protocol). The SCHP protocol is based on a static cluster creation and an optimal cluster head selection. Simulation results show that the proposal guarantees better performance than the LEACH Protocol that is considered as the baseline in the literature. We used many metrics, as packet loss rate, end-to-end delay, and energy consumption to evaluate the efficiency of our proposal. We show also that the SCHP protocol can improve the network lifetime.

Design and Implementation of EOICHD Based Clustered Routing Protocol Variants for Wireless Sensor Networks

Efficient energy utilization and network life prolongation are primary objectives to be considered when designing a Wireless Sensor Network. Cluster-based routing protocols are most suitable for achieving such goals. Energy and Optimal Inter Cluster Head Distance (EOICHD) is a cluster-based hierarchical routing protocol inspired by the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol. EOICHD resolves the problems associated with LEACH protocol, such as selecting cluster head nodes in close proximity. By carefully selecting the cluster head nodes based on residual energy and optimal inter-cluster head distance, EOICHD ensures that selected cluster head nodes are separated by a certain optimal distance. This approach ensures uniform distribution of cluster head nodes across the entire network. The study of the EOICHD protocol presented so far is not sufficient. Hence, in this paper, we propose three variants of EOICHD protocol to understand its behavior in a better manner. A comparative analysis of all three EOICHD variants, LEACH and LEACH-central constrained (LEACH-C) protocol, is performed by considering comparative parameters such as alive nodes, cumulative network energy, data packets arrived at the base station, and stability of the network.

Path planning for mobile robots using Morphological Dilation Voronoi Diagram Roadmap algorithm

This paper presents Morphological Dilation Voronoi Diagram Roadmap (MVDRM) algorithm to address unsafe path computation accompanied by high time and space computation complexity problems of roadmap path planning methods in complex environments for mobile robots. Morphological dilation was employed to inflate the obstacles in the environment of the robot before computing the path to ensure safe path computation for the robots. To reduce time and space complexities in computing the path, a scale factor is introduced to provide sparse and uniform distribution of sample nodes in the environment of the robot for the computation of the roadmap. The purpose of this technique is to reduce the sample nodes and computation time to provide fast-path computation to aid robots to make quick decisions to avoid collision with obstacles. Simulation results using maps of different complexities demonstrate better performance of the proposed method compared to Probabilistic Roadmap (PRM) and conventional VD methods in terms of safe path computation as well as time and space computation complexities. Results indicate that the proposed method is 1.69 and 7.03 times faster than conventional VD and PRM methods, respectively. The proposed method is 88.32 times faster than VD and 1.08 times faster than PRM. The path computation success rate is 96.3% better than the PRM method. MVDRM is a promising roadmap path planning method for computing a safe and quick path for autonomous vehicles.

The Realistic 3D Group Mobility Model Based on Spiral Line for Aerial Backbone Network

For search and rescue (SAR), the group unmanned aerial vehicle (GUAV) can rapidly cover the disaster area, and it can provide reliable connectivity to victim by aerial backbone network (ABN). However, existing 3D aerial mobility model (3D AMM) cannot capture unique features of GUAV in SAR, especially smooth 3D trajectory and collision avoidance. In this paper, we develop realistic 3D aerial group mobility model based on spiral line (3D SLGM) for SAR. Firstly, we review some related works. Then, we introduce the mechanism of 3D SLGM, such as Z-Or-SLGM and Z-Non-SLGM. Furthermore, we analyze some mathematical features of 3D SLGM. In addition, we investigate key mobility features of 3D SLGM. Finally, we evaluate the network performance under 3D SLGM. The result shows that 3D SLGM has smooth 3D trajectory and uniform distribution of spatial nodes in 3D space. With the collided rate of 0%, 3D SLGM merely takes about 1.4 minutes to cover 100% of the target area of 200 m*200 m. Besides, the network under 3D SLGM can approach the throughput of 0.45 Mb/s, the end-to-end delay of 3.2 ms and the loss packets rate of 0%. We believe that 3D SLGM, as a significant supplement of 3D AMM, can provide many helpful guidelines in the design and analysis of authentic ABN.

Centroid-Based Routing protocol with moving sink node for uniform and non-uniform distribution of wireless sensor nodes

A routing protocol called ‘Centroid-Based Routing (CBR)’ is proposed to optimize the total system energy for a given wireless sensor network. We have designed the CBR protocol to optimize the battery life of the sensor nodes, by using a mobile Sink Node (SN). In CBR, several clusters are formed for the sensor nodes and each cluster is assigned a ‘Cluster Head (CH)’ node, and these CHs act as a local Base Station. The SN moves to a coordinate point (Xc, Yc) which we call a ‘Centroid Point (CP)’ to collect data from the CH nodes. This ‘CP’ is dependent on the coordinates of all the CHs and also on their residual or remaining energy left over at any given round. This way the CH nodes have to pump a balanced amount of energy to send and receive data from SN, which makes the nodes last for a longer period. The simulation results imply that the CBR model is much efficient compared to other existing models in terms of energy utilization and network lifetime for the non-uniformly distributed sensor nodes in a given network area.

An Efficient Nodes Failure Recovery Management Algorithm for Mobile Sensor Networks

Wireless sensor networks are not prone to harsh environments and may fail due to various reasons. Failure of sensor nodes causes partitioning of network into various small segments and restricts the communication of nodes. Due to the significant importance of restoration mechanisms, many approaches have been proposed in the literature so far. However, these approaches do not focus on uniform distribution of sensor nodes before the occurrence of failure. This paper fulfills the shortcoming in the literature by proposing a Uniform Distribution and Recovery Algorithm (UDRA) in two parts. The first part (prefailure algorithm) focuses on preparing the mobile sensor nodes to be ready for the failure beforehand by maintaining half of their communication distance between them. Also, it uses a novel method of directional matrix based on one-hop information. By using this method, each mobile node declares itself as cut-vertex (CV), intermediate node, or leaf node. The second part of the algorithm (postfailure algorithm) gives complete recovery procedure in the network by its recovery nodes. The extensive simulations prove that the proposed algorithm supersedes the existing approaches.

Performance Evaluations of PC5-based Cellular-V2X Mode 4 for Feasibility Analysis of Driver Assistance Systems with Crash Warning.

This paper presents the communication performance of PC5-based Cellular-Vehicle-to-Everything mode 4 (called mode 4) to measure the feasibility of a Crash Warning System (called CWS). The CWS requires nodes (e.g., cars or pedestrians) to update its location information ten times per second. This requirement provides us with a channel congestion problem. To investigate feasibility in terms of channel congestion, we evaluated communication performance in various crash scenarios by computer simulation. One of the serious scenarios is a crowded environment like large intersections. In the uniform node distribution, in which we evaluated average performance, mode 4 accommodated 26% fewer nodes than the expected one; in a realistic node distribution, mode 4 achieved 55% worse performance than the CWS requirements. Our results highlighted the need for performance improvements of mode 4 for CWS in practical uses.

Phase field modelling of dendritic solidification by using an adaptive meshless solution procedure

A novel numerical procedure is developed for modelling two-dimensional dendritic solidification in dilute binary alloys. The evolution of the phases and the solute concentration is described by the partial differential equations, obtained from the phase field model. The meshless radial basis function-generated finite difference (RBF-FD) method is used for the spatial discretisation of the partial differential equations. The forward Euler scheme is used for the time-stepping. In order to reduce the computational cost, an adaptive procedure is developed, based on the quad-tree strategy, ensuring the highest density of the computational nodes at the solid-liquid interface. In the procedure, the computational domain is divided into overlapping sub-domains which can be dynamically refined or coarsened. The regular or scattered node distribution with constant node density is used for discretisation of each sub-domain. The h-adaptive procedure is ensured by the constant product between the area of a sub-domain and the computational node density. The accuracy and speedup in comparison to the solution on a uniform node distribution are assessed by solving the benchmark problem for dendritic solidification in dilute binary alloys. The main originality of the model represents the first use of RBF-FD method for the spatial discretisation of the PF equations in combination with adaptive solution procedure. The RBF-FD method can be used on unstructured node distributions, which is especially advantageous in the solution of PF model for dendritic growth, since the solution is very sensitive to the regularity of the node distribution. The developed spatial-temporal-adaptive numerical model represents an accurate and computationally efficient tool for the prediction of the dendrite morphology and micro-segregation during the solidification in binary alloys.

A New Hybrid Finite Element Method: Electromagnetic Propagation in Bent Waveguides

A new hybrid finite element method (HFEM) was developed, using basis functions of first and second order, to analyse the electromagnetic wave propagation in three types of waveguides: disk waveguides, ring waveguides and cylindrical waveguides. For validation purposes, results obtained with the HFEM method were compared with those obtained with a recursive finite element method (RFEM) and with two different analytical methods. The domain discretization effect on the results of the new HFEM method was examined using either a uniform distribution of nodes or a Delaunay distribution method. The results show that the Delaunay method, used in the mesh definition, is important, not only to assure the reliability of the method but also to significantly reduce the computation time and memory consumption. Also, the influence of the distance between the fictitious boundary and the waveguide core was analysed showing an important effect on the result numerical accuracy. In conclusion, results show that the new hybrid finite element method presented has a significant advantage on calculation time over the recursive finite element method.