A Simple Weighted Integration Method for Calculating Surface Tension Force to Suppress Parasitic Flow in the Level Set Approach

Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved method for calculating the surface tension based on the level set approach is proposed, in which the contribution of not only the center node but also the rest area of a control volume to the calculation of surface tension is considered in a balanced manner. The weighted integration method (WIM) is more consistent with the concept of a banded in- terface in the level set method. It is applied to the temporal evolution of a two-dimensional neutrally buoyant liquid drop and a buoyancy driven deformable bubble in an immiscible fluid for the validation of WIM. The results show that the parasitic flows are evidently suppressed by the weighted integration method. The weight factors for WIM in 3-D cases are also suggested.

Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

加权的熔化算法，能在 multi-sensordata 熔化的区域被使用，基于加权的最不方形的方法被推进。一个加权的熔化算法，在重量系数之间的关系和测量噪音在被建立，被注意测量噪音的关联建议。然后，一个简化加权的熔化算法在假设上被推出测量噪音是 uncorrelated。另外，一个算法，它装由用大小做测量噪音的评价在简化算法调整重量系数，被介绍。它被多传感器系统的精确性能基于另外的算法基于这些算法比多传感器系统的好的模拟和实验证明。

A redundant subspace weighting procedure for clock ensemble

A redundant-subspace-weighting(RSW)-based approach is proposed to enhance the frequency stability on a time scale of a clock ensemble.In this method,multiple overlapping subspaces are constructed in the clock ensemble,and the weight of each clock in this ensemble is defined by using the spatial covariance matrix.The superimposition average of covariances in different subspaces reduces the correlations between clocks in the same laboratory to some extent.After optimizing the parameters of this weighting procedure,the frequency stabilities of virtual clock ensembles are significantly improved in most cases.

A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS

In this paper,a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample.The elastic-plastic solutions of the crack tip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field,to calculate the plastic stress intensity factors,are also developed.Therefore,a complete analysis based on the calculation both for the crack tip field and for the whole crack body field is provided.

Indoor air quality risk assessment on the Canadian campus by a multilevel integrated weighted average method

Increasing incidents of indoor air quality(IAQ) related complaints lead us to the fact that IAQ has become a significant occupational health and environmental issue. However, how to effectively evaluate IAQ under different scale of multiple indicators is still a challenge. The traditional single-indicator method is subjected to uncertainties in assessing IAQ due to different subjectivity on good or bad quality and scalar differences of data set. In this study, a multilevel integrated weighted average IAQ method including initial walking through assessment(IWA) and two-layers weighted average method are developed and applied to evaluate IAQ of the laboratory building at the University of Regina in Canada. Some important chemical parameters related to IAQ in terms of volatile organic compounds(VOCs), methanol(HCHO), carbon dioxide(CO2), and carbon monoxide(CO) are evaluated based on 5 months continuous monitoring data. The new integrated assessment result can not only indicates the risk of an individual parameter, but also able to quantify the overall IAQ risk on the sampling site. Finally, some recommendations based on the result are proposed to address sustainable IAQ practices in the sampling area.

Criteria for Weighted Moving-Mean Method

The moving-mean method is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-mean, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordinary global mean. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-mean and global-mean criteria hold. Among these three criteria, the local-mean one has the strongest adaptability, which is suggested for your usage.

Dynamic Equivalent Method of Motor Loads for Power Systems Based on the Weighted

Dynamic equivalence can not only largely reduce the system size and the computation time but also stress the dominant features of the system [1]-[3]. This paper firstly recommends the basic concept of dynamic equivalent and the status of both domestic and abroad development in this area. The most existing equivalent methods usually only deal with static load models and neglect the dynamic characteristics of loads such as induction motors. In addition, the existing polymerization method which is based on the frequency domain algorithm of induction electric machines parameters takes a long time to equivalent for the large system, then the new method based on the weighted is proposed. Then, the basic steps for dynamic equivalence with the weighted method are introduced as follows. At first, the clustering criterion of motor loads based on time domain simulation is given. The motors with similar dynamic characteristics are classified into one group. Then, the simplication of the buses of motors in same group and network is carried out. Finally, parameters of the equivalent motor are calculated and the equivalent system is thus obtained based on the weighted. This aggregation method is applied to the simple distribution system of 4 generators. Simulation results show that the method can quickly obtain polymerization parameters of generator groups and the aggregation model retains the dynamic performance of the original model with good accuracy, the active and reactive power fitting error is smaller as well.

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods,i.e.,preconditioned generalized accelerated overrelaxation(GAOR) methods,is proposed to solve linear systems based on a class of weighted linear least squares problems.The convergence and comparison results are obtained.The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods.Furthermore,the effectiveness of the proposed methods is shown in the numerical experiment.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

Weighted Nuclear Norm Minimization-Based Regularization Method for Image Restoration

Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.

A weight's agglomerative method for detecting communities in weighted networks based on weight's similarity

This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge's weights distribute uniformly but at random between them. It can describe the steady connections between nodes or some similarity between nodes' functions effectively. In order to detect the community structure efficiently,a threshold coefficient κ to evaluate the equivalence of edges' weights and a new weighted modularity based on the weight's similarity are proposed. Then,constructing the weighted matrix and using the agglomerative mechanism,it presents a weight's agglomerative method based on optimizing the modularity to detect communities. For a network with n nodes,the algorithm can detect the community structure in time O(n 2 log n 2 ). Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore,with the change of κ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.

Application of Weighted Average Method in Evaluation System for Rural Cadre Distance Education

We elaborate the application method,process and effect of weighted average method in the examination and evaluation system for modern distance education of rural party members and cadres.The study shows that this method reflects the evaluation results objectively and comprehensively and plays a remarkable role in establishing and improving the examination and evaluation system,thus will have an important reference value for the development of modern distance education of rural party members and cadres in the future.

Gaussian Weighted Trajectory Method Ⅳ： No Rainbow Effect in Practice

Gaussian 加权的轨道方法(GWTM ) 在随机的阶段近似是古典 S 矩阵理论(CSMT ) 的实际实现，是的 CSMT 第一并且分子的碰撞的最简单的半古典作品途径，在七十年代初发展了。很不过精神上关门到完全古典的描述，到为不同 degrees-of-freedom 的量子化的某程度的 GWTM 报道在这些过程包含了。当 CSMT 可以给分叉的期末考试时，说分布，在与散布理论的橡皮的彩虹效果的关系， GWTM 从来没导致过如此的一场数学大祸。现在的笔记的目标是解释这发现。

Modified Wiener method in diffusion weighted image denoising

To denoise the diffusion weighted images (DWIs) featured as multi-boundary, which was very important for the calculation of accurate DTIs (diffusion tensor magnetic resonance imaging), a modified Wiener filter was proposed. Through analyzing the widely accepted adaptive Wiener filter in image denoising fields, which suffered from annoying noise around the edges of DWIs and in turn greatly affected the denoising effect of DWIs, a local-shift method capable of overcoming the defect of the adaptive Wiener filter was proposed to help better denoising DWIs and the modified Wiener filter was constructed accordingly. To verify the denoising effect of the proposed method, the modified Wiener filter and adaptive Wiener filter were performed on the noisy DWI data, respectively, and the results of different methods were analyzed in detail and put into comparison. The experimental data show that, with the modified Wiener method, more satisfactory results such as lower non-positive tensor percentage and lower mean square errors of the fractional anisotropy map and trace map are obtained than those with the adaptive Wiener method, which in turn helps to produce more accurate DTIs.

Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves

The multiple patterns of internal solitary wave interactions(ISWI)are a complex oceanic phenomenon.Satellite remote sensing techniques indirectly detect these ISWI,but do not provide information on their detailed structure and dynamics.Recently,the authors considered a three-layer fluid with shear flow and developed a(2+1)Kadomtsev-Petviashvili(KP)model that is capable of describing five types of oceanic ISWI,including O-type,P-type,TO-type,TP-type,and Y-shaped.Deep learning models,particularly physics-informed neural networks(PINN),are widely used in the field of fluids and internal solitary waves.However,the authors find that the amplitude of internal solitary waves is much smaller than the wavelength and the ISWI occur at relatively large spatial scales,and these characteristics lead to an imbalance in the loss function of the PINN model.To solve this problem,the authors introduce two weighted loss function methods,the fixed weighing and the adaptive weighting methods,to improve the PINN model.This successfully simulated the detailed structure and dynamics of ISWI,with simulation results corresponding to the satellite images.In particular,the adaptive weighting method can automatically update the weights of different terms in the loss function and outperforms the fixed weighting method in terms of generalization ability.

Weighted-Tau Rank:一种采用加权Kendall Tau的面向排序的协同过滤算法

已知的面向排序的协同过滤算法主要有两个缺点:计算用户相似度时只考虑用户对同一产品对的偏好是否一致,而忽略了用户对产品对的偏好程度以及该偏好在用户间的流行度;进行偏好融合和排序时需要中间步骤来构建价值函数然后才能利用贪婪算法产生推荐列表。为解决上述问题:我们利用类TF-IDF加权策略对用户的偏好程度及偏好流行度进行综合考量,使用加权的Kendall Tau相关系数计算用户间的相似度;进行偏好融合与排序时则使用基于投票的舒尔茨方法直接产生推荐列表。在两个电影数据集上,本文提出的算法在评测指标NDCG上的效果要明显优于其他流行的协同过滤算法。

Identifying influential spreaders in complex networks based on entropy weight method and gravity law

In complex networks,identifying influential spreader is of great significance for improving the reliability of networks and ensuring the safe and effective operation of networks.Nowadays,it is widely used in power networks,aviation networks,computer networks,and social networks,and so on.Traditional centrality methods mainly include degree centrality,closeness centrality,betweenness centrality,eigenvector centrality,k-shell,etc.However,single centrality method is onesided and inaccurate,and sometimes many nodes have the same centrality value,namely the same ranking result,which makes it difficult to distinguish between nodes.According to several classical methods of identifying influential nodes,in this paper we propose a novel method that is more full-scaled and universally applicable.Taken into account in this method are several aspects of node’s properties,including local topological characteristics,central location of nodes,propagation characteristics,and properties of neighbor nodes.In view of the idea of the multi-attribute decision-making,we regard the basic centrality method as node’s attribute and use the entropy weight method to weigh different attributes,and obtain node’s combined centrality.Then,the combined centrality is applied to the gravity law to comprehensively identify influential nodes in networks.Finally,the classical susceptible-infected-recovered(SIR)model is used to simulate the epidemic spreading in six real-society networks.Our proposed method not only considers the four topological properties of nodes,but also emphasizes the influence of neighbor nodes from the aspect of gravity.It is proved that the new method can effectively overcome the disadvantages of single centrality method and increase the accuracy of identifying influential nodes,which is of great significance for monitoring and controlling the complex networks.

Comprehensive evaluation of the transformer oil-paper insulation state based on RF-combination weighting and an improved TOPSIS method

The accurate identification of the oil-paper insulation state of a transformer is crucial for most maintenance strategies.This paper presents a multi-feature comprehensive evaluation model based on combination weighting and an improved technique for order of preference by similarity to ideal solution(TOPSIS)method to perform an objective and scientific evaluation of the transformer oil-paper insulation state.Firstly,multiple aging features are extracted from the recovery voltage polarization spectrum and the extended Debye equivalent circuit owing to the limitations of using a single feature for evaluation.A standard evaluation index system is then established by using the collected time-domain dielectric spectrum data.Secondly,this study implements the per-unit value concept to integrate the dimension of the index matrix and calculates the objective weight by using the random forest algorithm.Furthermore,it combines the weighting model to overcome the drawbacks of the single weighting method by using the indicators and considering the subjective experience of experts and the random forest algorithm.Lastly,the enhanced TOPSIS approach is used to determine the insulation quality of an oil-paper transformer.A verification example demonstrates that the evaluation model developed in this study can efficiently and accurately diagnose the insulation status of transformers.Essentially,this study presents a novel approach for the assessment of transformer oil-paper insulation.

Benefit allocation model of distributed photovoltaic power generation vehicle shed and energy storage charging pile based on integrated weighting-Shapley method

In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley integrated-empowerment benefit-distribution method.First,through literature survey and expert interview to identify the risk factors at various stages of the project,a dynamic risk-factor indicator system is developed.Second,to obtain a more meaningful risk-calculation result,the subjective and objective weights are combined,the weights of the risk factors at each stage are determined by the expert scoring method and entropy weight method,and the interest distribution model based on multi-dimensional risk factors is established.Finally,an example is used to verify the rationality of the method for the benefit distribution of the charging-pile project.The results of the example indicate that the limitations of the Shapley method can be reasonably avoided,and the applicability of the model for the benefit distribution of the charging-pile project is verified.