Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

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.

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 lip 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 analvsis 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.

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.

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 t~ 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（n2 log~）. Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore, with the change of t~ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.

ON THE LATTICE PATH METHOD IN CONVOLUTION-TYPE COMBINATORIAL IDENTITIES(Ⅱ)—THE WEIGHTED COUNTING FUNCTION METHOD ON LATTICE PATHS

An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.

INVERSE POWER METHOD AND WEIGHTED SOBOLEV SPACES

1. Introduction This paper is a continuation of the paper [5]. Now we want to treat the problem

A WEIGHTED PENALTY FINITE ELEMENT METHOD FOR THE ANALYSIS OF POWER-LAW FLUID FLOW PROBLEMS

In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.

An Information Entropy-Based Methodology to Construct the Avulsion Threshold in the Tail Reach of the Estuarine Alluvial Plain

Channel avulsion is a natural phenomenon that occurs abruptly on alluvial river deltas,which can affect the channel stability.The causes for avulsion could be generally categorized as topography-and flood-driven factors.However,previous studies on avulsion thresholds usually focused on topography-driven factors due to the centurial or millennial avulsion timescales of the world’s most deltas,but neglected the impacts of flood-driven factors.In the current study,a novel demarcation equation including the two driven factors was proposed,with the decadal timescale of avulsion being considered in the Yellow River Estuary(YRE).In order to quantify the contributions of different factors in each category,an entropy-based methodology was used to calculate the contributing weights of these factors.The factor with the highest weight in each category was then used to construct the demarcation equation,based on avulsion datasets associated with the YRE.An avulsion threshold was deduced according to the demarcation equation.This avulsion threshold was then applied to conduct the risk assessment of avulsion in the YRE.The results show that:two dominant factors cover respectively geomorphic coefficient representing the topography-driven factor and fluvial erosion intensity representing the flood-driven factor,which were thus employed to define a two dimensional mathematical space in which the demarcation equation can be obtained;the avulsion threshold derived from the equation was also applied in the risk assessment of avulsion;and the avulsion threshold proposed in this study is more accurate,as compared with the existing thresholds.

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.

Fracture propagation and evolution law of indirect fracturing in the roof of broken soft coal seams

Indirect fracturing in the roof of broken soft coal seams has been demonstrated to be a feasible technology.In this work,the No.5 coal seam in the Hancheng block was taken as the research object.Based on the findings of true triaxial hydraulic fracturing experiments and field pilot under this technology and the cohesive element method,a 3D numerical model of indirect fracturing in the roof of broken soft coal seams was established,the fracture morphology propagation and evolution law under different conditions was investigated,and analysis of main controlling factors of fracture parameters was conducted with the combination weight method,which was based on grey incidence,analytic hierarchy process and entropy weight method.The results show that“士”-shaped fractures,T-shaped fractures,cross fractures,H-shaped fractures,and“干”-shaped fractures dominated by horizontal fractures were formed.Different parameter combinations can form different fracture morphologies.When the coal seam permeability is lower and the minimum horizontal principal stress difference between layers and fracturing fluid injection rate are both larger,it tends to form“士”-shaped fractures.When the coal seam permeability and minimum horizontal principal stress between layers and perforation position are moderate,cross fractures are easily generated.Different fracture parameters have different main controlling factors.Engineering factors of perforation location,fracturing fluid injection rate and viscosity are the dominant factors of hydraulic fracture shape parameters.This study can provide a reference for the design of indirect fracturing in the roof of broken soft coal seams.

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.

Modelling of debris-flow susceptibility and propagation: a case study from Northwest Himalaya

The geological and geographical position of the Northwest Himalayas makes it a vulnerable area for mass movements particularly landslides and debris flows. Mass movements have had a substantial impact on the study area which is extending along Karakorum Highway(KKH) from Besham to Chilas. Intense seismicity, deep gorges, steep terrain and extreme climatic events trigger multiple mountain hazards along the KKH, among which debris flow is recognized as the most destructive geohazard. This study aims to prepare a field-based debris flow inventory map at a regional scale along a 200 km stretch from Besham to Chilas. A total of 117 debris flows were identified in the field, and subsequently, a point-based debris-flow inventory and catchment delineation were performed through Arc GIS analysis. Regional scale debris flow susceptibility and propagation maps were prepared using Weighted Overlay Method(WOM) and Flow-R technique sequentially. Predisposing factors include slope, slope aspect, elevation, Topographic Roughness Index(TRI), Topographic Wetness Index(TWI), stream buffer, distance to faults, lithology rainfall, curvature, and collapsed material layer. The dataset was randomly divided into training data(75%) and validation data(25%). Results were validated through the Receiver Operator Characteristics(ROC) curve. Results show that Area Under the Curve(AUC) using WOM model is 79.2%. Flow-R propagation of debris flow shows that the 13.15%, 22.94%, and 63.91% areas are very high, high, and low susceptible to debris flow respectively. The propagation predicated by Flow-R validates the naturally occurring debris flow propagation as observed in the field surveys. The output of this research will provide valuable input to the decision makers for the site selection, designing of the prevention system, and for the protection of current infrastructure.

Integrated Analysis of Water Quality in Artificial Fishponds Using WQI and GIS in South-East Sierra Leone

Artificial fishponds play a pivotal role in global aquaculture, serving as a source of livelihood and nourishment for many communities. Ensuring the sustained health and productivity of Fishes in these environments relies heavily on water quality management. This assessment was done to determine the water quality of ten artificial fishponds in the south-eastern part of Sierra Leone using twelve physicochemical factors (pH, BOD, EC, TDS, turbidity, COD, Fe2+, Mg2+, Ca2+, NH3, , and alkalinity) to find out the Water Quality Index (WQI) and spatial distribution of respective parameters. The assessment of artificial fishponds using WQI and Inverse Distant Weighting (IDW) integration represents a relatively underexplored area within the domain of environmental water resources. The WQI was determined using the “Weighted Arithmetic Water Quality Index’’ method. The results of WQI in the study area range from 65.05 to 147.26. Several locations have water quality deemed unsuitable for consumption, while others range from good to very poor. It is essential to address and improve water quality in locations categorized as unsuitable for consumption and very poor to ensure safe and healthy water sources. It was also clear from the calculation that the smaller the mean concentration value of the pH as compared to the ideal value (7), the smaller the WQI value and the better the water quality. To keep the artificial fishpond water in good condition, mass domestic use should be controlled, and draining of surrounding organic matter should be stopped in ponds Bo_001, Kenema_001, and Kenema_002.

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.

Comprehensive Evaluation Model of Livable City Based on Fuzzy Comprehensive Evaluation Method

This paper firstly introduced the degree of livability of a city from the social civilization,economic affluence,environmental beauty,resource carrying capacity,and life convenience. Based on the principle of the fuzzy comprehensive evaluation,it analyzed the connection between influencing factors,and established a comprehensive evaluation model for calculation of the livability index of a city. Finally,it obtained the relative livability of each city and the ranking of livability of each city.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.