This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend...This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.展开更多
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-tri...An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.展开更多
A meshless approach, called the rigid-plastic reproducing kernel particle method （RKPM）, is presented for three-dimensional （3D） bulk metal forming simulation. The approach is a combination of RKPM with the flow t...A meshless approach, called the rigid-plastic reproducing kernel particle method （RKPM）, is presented for three-dimensional （3D） bulk metal forming simulation. The approach is a combination of RKPM with the flow theory of 3D rigid-plastic mechanics. For the treatments of essential boundary conditions and incompressibility constraint, the boundary singular kernel method and the modified penalty method are utilized, respectively. The arc-tangential friction model is employed to treat the contact conditions. The compression of rectangular blocks, a typical 3D upsetting operation, is analyzed for different friction conditions and the numerical results are compared with those obtained using commercial rigid-plastic FEM （finite element method） software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures which are unavoidable in conventional FEM and can provide results that are in good agreement with finite element predictions.展开更多
On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is present...On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.展开更多
The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, d...The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.展开更多
An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in th...An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.展开更多
The application field of the Internet of Things(IoT)involves all aspects,and its application in the fields of industry,agriculture,environment,transportation,logistics,security and other infrastructure has effectively...The application field of the Internet of Things(IoT)involves all aspects,and its application in the fields of industry,agriculture,environment,transportation,logistics,security and other infrastructure has effectively promoted the intelligent development of these aspects.Although the IoT has gradually grown in recent years,there are still many problems that need to be overcome in terms of technology,management,cost,policy,and security.We need to constantly weigh the benefits of trusting IoT products and the risk of leaking private data.To avoid the leakage and loss of various user data,this paper developed a hybrid algorithm of kernel function and random perturbation method based on the algorithm of non-negative matrix factorization,which realizes personalized recommendation and solves the problem of user privacy data protection in the process of personalized recommendation.Compared to non-negative matrix factorization privacy-preserving algorithm,the new algorithm does not need to know the detailed information of the data,only need to know the connection between each data;and the new algorithm can process the data points with negative characteristics.Experiments show that the new algorithm can produce recommendation results with certain accuracy under the premise of preserving users’personal privacy.展开更多
This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)metho...This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.展开更多
In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE metho...In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.展开更多
The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact...The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials.展开更多
Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning m...Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning methods, especially kernel methods with Support Vector Machines （SVMs） are very popular and effective tools. In the perspective of kernel matrix, a technique namely Eigen- matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy has a lot of nice properties which deserve more exploration. This paper investigates the major role of Eigen-matrix translation in classification. The authors propose that its importance lies in the dimension reduction of predictor attributes within the data set. This is very important when the dimension of features is huge. The authors show by numerical experiments on real biological data sets that the proposed framework is crucial and effective in improving classification accuracy. This can therefore serve as a novel perspective for future research in dimension reduction problems.展开更多
Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected ...Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.展开更多
The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of...The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of Near-Infrared Reflectance(NIR)analysis is practical,relatively easy to implement,and becoming one of the most popular methods for conducting food quality based on NIR data.The k-NN is often named k nearest neighbor classifier when it is used for classifying categorical variables,while it is called k-nearest neighbor regression when it is applied for predicting noncategorical variables.The objective of this paper is to use the functional Near-Infrared Reflectance(NIR)spectroscopy approach to predict some chemical components with some modern statistical models based on the kernel and k-Nearest Neighbour procedures.In this paper,three NIR spectroscopy datasets are used as examples,namely Cookie dough,sugar,and tecator data.Specifically,we propose three models for this kind of data which are Functional Nonparametric Regression,Functional Robust Regression,and Functional Relative Error Regression,with both kernel and k-NN approaches to compare between them.The experimental result shows the higher efficiency of k-NN predictor over the kernel predictor.The predictive power of the k-NN method was compared with that of the kernel method,and several real data sets were used to determine the predictive power of both methods.展开更多
This paper investigates the nonlinear boundary value problem resulting from the exact reduction of the Navier-Stokes equations for unsteady magnetohydrodynamic boundary layer flow over the stretching/shrinking permeab...This paper investigates the nonlinear boundary value problem resulting from the exact reduction of the Navier-Stokes equations for unsteady magnetohydrodynamic boundary layer flow over the stretching/shrinking permeable sheet submerged in a moving fluid.To solve this equation,a numerical method is proposed based on a Laguerre functions with reproducing kernel Hilbert space method.Using the operational matrices of derivative,we reduced the problem to a set of algebraic equations.We also compare this work with some other numerical results and present a solution that proves to be highly accurate.展开更多
Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric meth...Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.展开更多
A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means ...A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.展开更多
During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the fi...During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.展开更多
Aiming at the problem of soft sensing modeling for chemical process with strong nonlinearity and complexity,a soft sensing modeling method based on kernel-based orthogonal projections to latent structures(K-OPLS)is pr...Aiming at the problem of soft sensing modeling for chemical process with strong nonlinearity and complexity,a soft sensing modeling method based on kernel-based orthogonal projections to latent structures(K-OPLS)is proposed.Orthogonal projections to latent structures(O-PLS)is a general linear multi-variable data modeling method.It can eliminate systematic variations from descriptive variables(input)that are orthogonal to response variables(output).In the framework of O-PLS model,K-OPLS method maps descriptive variables to high-dimensional feature space by using“kernel technique”to calculate predictive components and response-orthogonal components in the model.Therefore,the K-OPLS method gives the non-linear relationship between the descriptor and the response variables,which improves the performance of the model and enhances the interpretability of the model to a certain extent.To verify the validity of K-OPLS method,it was applied to soft sensing modeling of component content of debutane tower base butane(C4),the quality index of the key product output for industrial fluidized catalytic cracking unit(FCCU)and H 2S and SO 2 concentration in sulfur recovery unit(SRU).Compared with support vector machines(SVM),least-squares support-vector machine(LS-SVM),support vector machine with principal component analysis(PCA-SVM),extreme learning machine(ELM),kernel based extreme learning machine(KELM)and kernel based extreme learning machine with principal component analysis(PCA-KELM)methods under the same conditions,the experimental results show that the K-OPLS method has superior modeling accuracy and good model generalization ability.展开更多
A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a...A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.展开更多
基金supported by a grant from the National Science and Technology Council of the Republic of China(Grant Number:MOST 112-2221-E-006-048-MY2).
文摘This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
文摘An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.
基金This work was supported by the National Natural Science Foundation of China （No. 50275094）.
文摘A meshless approach, called the rigid-plastic reproducing kernel particle method （RKPM）, is presented for three-dimensional （3D） bulk metal forming simulation. The approach is a combination of RKPM with the flow theory of 3D rigid-plastic mechanics. For the treatments of essential boundary conditions and incompressibility constraint, the boundary singular kernel method and the modified penalty method are utilized, respectively. The arc-tangential friction model is employed to treat the contact conditions. The compression of rectangular blocks, a typical 3D upsetting operation, is analyzed for different friction conditions and the numerical results are compared with those obtained using commercial rigid-plastic FEM （finite element method） software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures which are unavoidable in conventional FEM and can provide results that are in good agreement with finite element predictions.
基金supported by the National Natural Science Foundation of China (Grant No.10871124)the Innovation Program of Shanghai Municipal Education Commission,China (Grant No.09ZZ99)
文摘On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.
文摘The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.
基金supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Shanxi Province,China(Grant No.2013011022-6)
文摘An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.
基金the National Natural Science Foundation of Chinaunder Grant No.61772280by the China Special Fund for Meteorological Research in the Public Interestunder Grant GYHY201306070by the Jiangsu Province Innovation and Entrepreneurship TrainingProgram for College Students under Grant No.201910300122Y.
文摘The application field of the Internet of Things(IoT)involves all aspects,and its application in the fields of industry,agriculture,environment,transportation,logistics,security and other infrastructure has effectively promoted the intelligent development of these aspects.Although the IoT has gradually grown in recent years,there are still many problems that need to be overcome in terms of technology,management,cost,policy,and security.We need to constantly weigh the benefits of trusting IoT products and the risk of leaking private data.To avoid the leakage and loss of various user data,this paper developed a hybrid algorithm of kernel function and random perturbation method based on the algorithm of non-negative matrix factorization,which realizes personalized recommendation and solves the problem of user privacy data protection in the process of personalized recommendation.Compared to non-negative matrix factorization privacy-preserving algorithm,the new algorithm does not need to know the detailed information of the data,only need to know the connection between each data;and the new algorithm can process the data points with negative characteristics.Experiments show that the new algorithm can produce recommendation results with certain accuracy under the premise of preserving users’personal privacy.
基金the National Natural Science Foundation of China(Grant Nos.71961022,11902163,12265020,and 12262024)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant Nos.2019BS01011 and 2022MS01003)+5 种基金2022 Inner Mongolia Autonomous Region Grassland Talents Project-Young Innovative and Entrepreneurial Talents(Mingjing Du)2022 Talent Development Foundation of Inner Mongolia Autonomous Region of China(Ming-Jing Du)the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region Program(Grant No.NJYT-20-B18)the Key Project of High-quality Economic Development Research Base of Yellow River Basin in 2022(Grant No.21HZD03)2022 Inner Mongolia Autonomous Region International Science and Technology Cooperation High-end Foreign Experts Introduction Project(Ge Kai)MOE(Ministry of Education in China)Humanities and Social Sciences Foundation(Grants No.20YJC860005).
文摘This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Special Fund for Basic Scientific Research of Central Colleges of Chang’an University, China (Grant No. CHD2011JC080)
文摘In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.
基金Project /s50674002 supported by the National Natural Science Foundation of China
文摘The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials.
基金supported by Research Grants Council of Hong Kong under Grant No.17301214HKU CERG Grants,Fundamental Research Funds for the Central Universities+2 种基金the Research Funds of Renmin University of ChinaHung Hing Ying Physical Research Grantthe Natural Science Foundation of China under Grant No.11271144
文摘Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning methods, especially kernel methods with Support Vector Machines （SVMs） are very popular and effective tools. In the perspective of kernel matrix, a technique namely Eigen- matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy has a lot of nice properties which deserve more exploration. This paper investigates the major role of Eigen-matrix translation in classification. The authors propose that its importance lies in the dimension reduction of predictor attributes within the data set. This is very important when the dimension of features is huge. The authors show by numerical experiments on real biological data sets that the proposed framework is crucial and effective in improving classification accuracy. This can therefore serve as a novel perspective for future research in dimension reduction problems.
基金supported by Research Grant from the Kajima Foundation,JST CREST Grant No.JPMJCR1911,JapanJSPS KAKENHI(Nos.17K06633,21K04351).
文摘Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.
基金funding this work through the Research Groups Program under Grant Number R.G.P.1/189/41.I.M.A.and M.K.A.received the grant.
文摘The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of Near-Infrared Reflectance(NIR)analysis is practical,relatively easy to implement,and becoming one of the most popular methods for conducting food quality based on NIR data.The k-NN is often named k nearest neighbor classifier when it is used for classifying categorical variables,while it is called k-nearest neighbor regression when it is applied for predicting noncategorical variables.The objective of this paper is to use the functional Near-Infrared Reflectance(NIR)spectroscopy approach to predict some chemical components with some modern statistical models based on the kernel and k-Nearest Neighbour procedures.In this paper,three NIR spectroscopy datasets are used as examples,namely Cookie dough,sugar,and tecator data.Specifically,we propose three models for this kind of data which are Functional Nonparametric Regression,Functional Robust Regression,and Functional Relative Error Regression,with both kernel and k-NN approaches to compare between them.The experimental result shows the higher efficiency of k-NN predictor over the kernel predictor.The predictive power of the k-NN method was compared with that of the kernel method,and several real data sets were used to determine the predictive power of both methods.
文摘This paper investigates the nonlinear boundary value problem resulting from the exact reduction of the Navier-Stokes equations for unsteady magnetohydrodynamic boundary layer flow over the stretching/shrinking permeable sheet submerged in a moving fluid.To solve this equation,a numerical method is proposed based on a Laguerre functions with reproducing kernel Hilbert space method.Using the operational matrices of derivative,we reduced the problem to a set of algebraic equations.We also compare this work with some other numerical results and present a solution that proves to be highly accurate.
文摘Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.
基金Project supported by the 15th Plan for National Defence Preventive Research Project (Grant No.413030201)
文摘A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.
基金Item Sponsored by National Natural Science Foundation of China(50474016)
文摘During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.
基金National Natural Science Foundation of China(No.51467008)。
文摘Aiming at the problem of soft sensing modeling for chemical process with strong nonlinearity and complexity,a soft sensing modeling method based on kernel-based orthogonal projections to latent structures(K-OPLS)is proposed.Orthogonal projections to latent structures(O-PLS)is a general linear multi-variable data modeling method.It can eliminate systematic variations from descriptive variables(input)that are orthogonal to response variables(output).In the framework of O-PLS model,K-OPLS method maps descriptive variables to high-dimensional feature space by using“kernel technique”to calculate predictive components and response-orthogonal components in the model.Therefore,the K-OPLS method gives the non-linear relationship between the descriptor and the response variables,which improves the performance of the model and enhances the interpretability of the model to a certain extent.To verify the validity of K-OPLS method,it was applied to soft sensing modeling of component content of debutane tower base butane(C4),the quality index of the key product output for industrial fluidized catalytic cracking unit(FCCU)and H 2S and SO 2 concentration in sulfur recovery unit(SRU).Compared with support vector machines(SVM),least-squares support-vector machine(LS-SVM),support vector machine with principal component analysis(PCA-SVM),extreme learning machine(ELM),kernel based extreme learning machine(KELM)and kernel based extreme learning machine with principal component analysis(PCA-KELM)methods under the same conditions,the experimental results show that the K-OPLS method has superior modeling accuracy and good model generalization ability.
基金the National Natural Science Foundation of China （No. 50275059）.
文摘A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.
