Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted...Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.展开更多
Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
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 comp...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.展开更多
One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification ...One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.展开更多
This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations...This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.展开更多
Scour around a submerged square pile was realized experimentally in a steady flow to study the effects of flow depth on local scour.Flow depth to pile height ratios ranging from 1.5 to 5 in uniform sand and 2 to 5 in ...Scour around a submerged square pile was realized experimentally in a steady flow to study the effects of flow depth on local scour.Flow depth to pile height ratios ranging from 1.5 to 5 in uniform sand and 2 to 5 in non-uniform sand were tested in the approaching flow velocity to critical velocity(larger than which the sediment particle is motivated)ratios of 0.56 and 1.03,respectively.The influences of flow depth were investigated on the basis of analysis of the three-dimensional topography,temporal maximum scour depth,bed profile development,and equilibrium scour depth.Results showed that the maximum scour depth was at the upstream corners of the pile other than at the stagnation point.The evolutions of the maximum scour depth data in non-uniform sand were well fitted with a recent exponential function,which characterized the initial,developing,and equilibrium stages of scour depth.The scour hole slopes upstream of the pile were found to be parallel to each other in the process of each test and were mainly governed by the sediment repose underwater.The equilibrium scour depth varied slightly with flow depth when the submergence ratio was larger than 1 in uniform sand while it was 2 in non-uniform sand.The armoring effects of coarse sediment particles markedly reduced the sediment transport in non-uniform sand despite the 0.34 increment in non-uniformity.展开更多
In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and l...In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.展开更多
A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different...A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.展开更多
This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations in...This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.展开更多
The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power systemtomaintain reliable operation.With equal conductor spacing grounding grid design,the distribut...The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power systemtomaintain reliable operation.With equal conductor spacing grounding grid design,the distribution of the current in the grid is not uniform.Hence,unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing.This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors:the least-square curve fitting technique and the compression ratio techniquewith equal grid configuration for both square and rectangular grids.Particle Swarm Optimization(PSO)is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids.Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration.Simulation results are obtained by theMATLAB software developed.Percentage of improvement in ground potential rise,step voltage,touch voltage,and grid resistancewith variation in compression ratios are plotted.展开更多
Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsi...Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.展开更多
As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to intr...As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to introduce a new rock skeleton parameter which is the dry-rock VP/VS ratio squared(DVRS).In the process of fluid factor calculation or inversion,the existing methods take this parameter as a static constant,which has been estimated in advance,and then apply it to the fluid factor calculation and inversion.The fluid identification analysis based on a portion of the Marmousi 2 model and numerical forward modeling test show that,taking the DVRS as a static constant will limit the identification ability of fluid factor and reduce the inversion accuracy.To solve the above problems,we proposed a new method to regard the DVRS as a dynamic variable varying with depth and lithology for the first time,then apply it to fluid factor calculation and inversion.Firstly,the exact Zoeppritz equations are rewritten into a new form containing the fluid factor and DVRS of upper and lower layers.Next,the new equations are applied to the four parameters simultaneous inversion based on the generalized nonlinear inversion(GNI)method.The testing results on a portion of the Marmousi 2 model and field data show that dynamic DVRS can significantly improve the fluid factor identification ability,effectively suppress illusion.Both synthetic and filed data tests also demonstrate that the GNI method based on Bayesian deterministic inversion(BDI)theory can successfully solve the above four parameter simultaneous inversion problem,and taking the dynamic DVRS as a target inversion parameter can effectively improve the inversion accuracy of fluid factor.All these results completely verified the feasibility and effectiveness of the proposed method.展开更多
In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal positi...The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal position of the heated block on heat transfer enhancement. The Galerkin weighted residual finite element method is employed to computationally solve the governing equations of Navier-Stokes, thermal energy, and mass conservation. The enclosure consists of two square heated blocks strategically placed at different heights—firstly, one set is closer to the bottom surface;secondly, one set is nearer to the middle area and finally, one set is closer to the upper undulating surface of the enclosure. The wavy top wall’s thermal insulation, along with active heating of the bottom wall and blocks, generates a dynamic convective atmosphere. In addition, the left wall ascends as the right wall falls, causing the flow formed by the lid. The study investigates the impact of the Richardson number on many factors, such as streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers. These impacts are depicted through graphical illustrations. In all instances, two counter-rotating eddies were generated within the cage. Higher rotating speed consistently leads to improved performance, irrespective of other characteristics. Furthermore, an ideal amalgamation of the regulating factors would lead to increased heat transmission.展开更多
In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using t...In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.展开更多
工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小...工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小迭代修复和改进WGAN混合模型的时序数据修复方法.首先,在预处理阶段,保留异常数据,进行信息标注等处理,从而充分挖掘异常值与真实值之间的特征约束.其次,在噪声模块提出了近邻参数裁剪规则,用于修正最小迭代修复公式生成的噪声向量.将其传递至模拟分布模块的生成器中,同时设计了一个动态时间注意力网络层,用于提取时序特征权重并与门控循环单元串联组合捕捉不同步长的特征依赖,并引入递归多步预测原理共同提升模型的表达能力;在判别器中设计了Abnormal and Truth奖励机制和Weighted Mean Square Error损失函数共同反向优化生成器修复数据的细节和质量.最后,在公开数据集和真实数据集上的实验结果表明,该方法的修复准确度与模型稳定性显著优于现有方法.展开更多
基金supported by the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the National Natural Science Foundation of China(12071431)+1 种基金the Fundamental Research Funds for the Central Universities(lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
文摘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.
文摘One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.
文摘This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.
基金the support of the National Natural Science Foundation of China(Nos.51679223 and 51739010)the 111 Project(No.B14028),the Shangdong Provincial Key Laboratory of Ocean Engineering(No.kl oe202009)+1 种基金the Ningbo Natural Science Foundation(No.2021J096)a grant from the 7th Generation Ultra-Deepwater Drilling Rig Innovation Project。
文摘Scour around a submerged square pile was realized experimentally in a steady flow to study the effects of flow depth on local scour.Flow depth to pile height ratios ranging from 1.5 to 5 in uniform sand and 2 to 5 in non-uniform sand were tested in the approaching flow velocity to critical velocity(larger than which the sediment particle is motivated)ratios of 0.56 and 1.03,respectively.The influences of flow depth were investigated on the basis of analysis of the three-dimensional topography,temporal maximum scour depth,bed profile development,and equilibrium scour depth.Results showed that the maximum scour depth was at the upstream corners of the pile other than at the stagnation point.The evolutions of the maximum scour depth data in non-uniform sand were well fitted with a recent exponential function,which characterized the initial,developing,and equilibrium stages of scour depth.The scour hole slopes upstream of the pile were found to be parallel to each other in the process of each test and were mainly governed by the sediment repose underwater.The equilibrium scour depth varied slightly with flow depth when the submergence ratio was larger than 1 in uniform sand while it was 2 in non-uniform sand.The armoring effects of coarse sediment particles markedly reduced the sediment transport in non-uniform sand despite the 0.34 increment in non-uniformity.
基金Project supported by the National Natural Science Foundation of China(No.11571240)the Shenzhen Natural Science Fund of China(the Stable Support Plan Program No.20220805175116001)。
文摘In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.
文摘A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.
基金Supported by the NSF of Hubei Province(2022CFD042)。
文摘This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.
文摘The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power systemtomaintain reliable operation.With equal conductor spacing grounding grid design,the distribution of the current in the grid is not uniform.Hence,unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing.This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors:the least-square curve fitting technique and the compression ratio techniquewith equal grid configuration for both square and rectangular grids.Particle Swarm Optimization(PSO)is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids.Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration.Simulation results are obtained by theMATLAB software developed.Percentage of improvement in ground potential rise,step voltage,touch voltage,and grid resistancewith variation in compression ratios are plotted.
基金supported by the National Natural Science Foundation of China(6177202062202433+4 种基金621723716227242262036010)the Natural Science Foundation of Henan Province(22100002)the Postdoctoral Research Grant in Henan Province(202103111)。
文摘Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.
基金the National Natural Science Foundation of China(41904116,41874156,42074167 and 42204135)the Natural Science Foundation of Hunan Province(2020JJ5168)the China Postdoctoral Science Foundation(2021M703629)for their funding of this research.
文摘As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to introduce a new rock skeleton parameter which is the dry-rock VP/VS ratio squared(DVRS).In the process of fluid factor calculation or inversion,the existing methods take this parameter as a static constant,which has been estimated in advance,and then apply it to the fluid factor calculation and inversion.The fluid identification analysis based on a portion of the Marmousi 2 model and numerical forward modeling test show that,taking the DVRS as a static constant will limit the identification ability of fluid factor and reduce the inversion accuracy.To solve the above problems,we proposed a new method to regard the DVRS as a dynamic variable varying with depth and lithology for the first time,then apply it to fluid factor calculation and inversion.Firstly,the exact Zoeppritz equations are rewritten into a new form containing the fluid factor and DVRS of upper and lower layers.Next,the new equations are applied to the four parameters simultaneous inversion based on the generalized nonlinear inversion(GNI)method.The testing results on a portion of the Marmousi 2 model and field data show that dynamic DVRS can significantly improve the fluid factor identification ability,effectively suppress illusion.Both synthetic and filed data tests also demonstrate that the GNI method based on Bayesian deterministic inversion(BDI)theory can successfully solve the above four parameter simultaneous inversion problem,and taking the dynamic DVRS as a target inversion parameter can effectively improve the inversion accuracy of fluid factor.All these results completely verified the feasibility and effectiveness of the proposed method.
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
文摘The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal position of the heated block on heat transfer enhancement. The Galerkin weighted residual finite element method is employed to computationally solve the governing equations of Navier-Stokes, thermal energy, and mass conservation. The enclosure consists of two square heated blocks strategically placed at different heights—firstly, one set is closer to the bottom surface;secondly, one set is nearer to the middle area and finally, one set is closer to the upper undulating surface of the enclosure. The wavy top wall’s thermal insulation, along with active heating of the bottom wall and blocks, generates a dynamic convective atmosphere. In addition, the left wall ascends as the right wall falls, causing the flow formed by the lid. The study investigates the impact of the Richardson number on many factors, such as streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers. These impacts are depicted through graphical illustrations. In all instances, two counter-rotating eddies were generated within the cage. Higher rotating speed consistently leads to improved performance, irrespective of other characteristics. Furthermore, an ideal amalgamation of the regulating factors would lead to increased heat transmission.
文摘In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.
文摘工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小迭代修复和改进WGAN混合模型的时序数据修复方法.首先,在预处理阶段,保留异常数据,进行信息标注等处理,从而充分挖掘异常值与真实值之间的特征约束.其次,在噪声模块提出了近邻参数裁剪规则,用于修正最小迭代修复公式生成的噪声向量.将其传递至模拟分布模块的生成器中,同时设计了一个动态时间注意力网络层,用于提取时序特征权重并与门控循环单元串联组合捕捉不同步长的特征依赖,并引入递归多步预测原理共同提升模型的表达能力;在判别器中设计了Abnormal and Truth奖励机制和Weighted Mean Square Error损失函数共同反向优化生成器修复数据的细节和质量.最后,在公开数据集和真实数据集上的实验结果表明,该方法的修复准确度与模型稳定性显著优于现有方法.