Significant advancements have been achieved in the field of Single Image Super-Resolution(SISR)through the utilization of Convolutional Neural Networks(CNNs)to attain state-of-the-art performance.Recent efforts have e...Significant advancements have been achieved in the field of Single Image Super-Resolution(SISR)through the utilization of Convolutional Neural Networks(CNNs)to attain state-of-the-art performance.Recent efforts have explored the incorporation of Transformers to augment network performance in SISR.However,the high computational cost of Transformers makes them less suitable for deployment on lightweight devices.Moreover,the majority of enhancements for CNNs rely predominantly on small spatial convolutions,thereby neglecting the potential advantages of large kernel convolution.In this paper,the authors propose a Multi-Perception Large Kernel convNet(MPLKN)which delves into the exploration of large kernel convolution.Specifically,the authors have architected a Multi-Perception Large Kernel(MPLK)module aimed at extracting multi-scale features and employ a stepwise feature fusion strategy to seamlessly integrate these features.In addition,to enhance the network's capacity for nonlinear spatial information processing,the authors have designed a Spatial-Channel Gated Feed-forward Network(SCGFN)that is capable of adapting to feature interactions across both spatial and channel dimensions.Experimental results demonstrate that MPLKN outperforms other lightweight image super-resolution models while maintaining a minimal number of parameters and FLOPs.展开更多
In recent years,deep learning has been introduced into the field of Single-pixel imaging(SPI),garnering significant attention.However,conventional networks still exhibit limitations in preserving image details.To addr...In recent years,deep learning has been introduced into the field of Single-pixel imaging(SPI),garnering significant attention.However,conventional networks still exhibit limitations in preserving image details.To address this issue,we integrate Large Kernel Convolution(LKconv)into the U-Net framework,proposing an enhanced network structure named U-LKconv network,which significantly enhances the capability to recover image details even under low sampling conditions.展开更多
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.展开更多
This paper aims to develop a nonrigid registration method of preoperative and intraoperative thoracoabdominal CT images in computer-assisted interventional surgeries for accurate tumor localization and tissue visualiz...This paper aims to develop a nonrigid registration method of preoperative and intraoperative thoracoabdominal CT images in computer-assisted interventional surgeries for accurate tumor localization and tissue visualization enhancement.However,fine structure registration of complex thoracoabdominal organs and large deformation registration caused by respiratory motion is challenging.To deal with this problem,we propose a 3D multi-scale attention VoxelMorph(MAVoxelMorph)registration network.To alleviate the large deformation problem,a multi-scale axial attention mechanism is utilized by using a residual dilated pyramid pooling for multi-scale feature extraction,and position-aware axial attention for long-distance dependencies between pixels capture.To further improve the large deformation and fine structure registration results,a multi-scale context channel attention mechanism is employed utilizing content information via adjacent encoding layers.Our method was evaluated on four public lung datasets(DIR-Lab dataset,Creatis dataset,Learn2Reg dataset,OASIS dataset)and a local dataset.Results proved that the proposed method achieved better registration performance than current state-of-the-art methods,especially in handling the registration of large deformations and fine structures.It also proved to be fast in 3D image registration,using about 1.5 s,and faster than most methods.Qualitative and quantitative assessments proved that the proposed MA-VoxelMorph has the potential to realize precise and fast tumor localization in clinical interventional surgeries.展开更多
Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional...Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere S^(d-1).We established that the large deviation principle for{sup_(x∈S^(d-1))|fn(x)-fn(-x)|,n≥1}holds if the kernel function is a function with bounded variation,and the density function f of the random variables is continuous and symmetric.展开更多
Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learnin...Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learning have attracted widespread attention.Most existing methods use 3×3 small kernel convolution to extract image features and embed the watermarking.However,the effective perception fields for small kernel convolution are extremely confined,so the pixels that each watermarking can affect are restricted,thus limiting the performance of the watermarking.To address these problems,we propose a watermarking network based on large kernel convolution and adaptive weight assignment for loss functions.It uses large-kernel depth-wise convolution to extract features for learning large-scale image information and subsequently projects the watermarking into a highdimensional space by 1×1 convolution to achieve adaptability in the channel dimension.Subsequently,the modification of the embedded watermarking on the cover image is extended to more pixels.Because the magnitude and convergence rates of each loss function are different,an adaptive loss weight assignment strategy is proposed to make theweights participate in the network training together and adjust theweight dynamically.Further,a high-frequency wavelet loss is proposed,by which the watermarking is restricted to only the low-frequency wavelet sub-bands,thereby enhancing the robustness of watermarking against image compression.The experimental results show that the peak signal-to-noise ratio(PSNR)of the encoded image reaches 40.12,the structural similarity(SSIM)reaches 0.9721,and the watermarking has good robustness against various types of noise.展开更多
Graph convolutional networks(GCNs)have become a dominant approach for skeleton-based action recognition tasks.Although GCNs have made significant progress in modeling skeletons as spatial-temporal graphs,they often re...Graph convolutional networks(GCNs)have become a dominant approach for skeleton-based action recognition tasks.Although GCNs have made significant progress in modeling skeletons as spatial-temporal graphs,they often require stacking multiple graph convolution layers to effectively capture long-distance relationships among nodes.This stacking not only increases computational burdens but also raises the risk of over-smoothing,which can lead to the neglect of crucial local action features.To address this issue,we propose a novel multi-scale adaptive large kernel graph convolutional network(MSLK-GCN)to effectively aggregate local and global spatio-temporal correlations while maintaining the computational efficiency.The core components of the network include two multi-scale large kernel graph convolution(LKGC)modules,a multi-channel adaptive graph convolution(MAGC)module,and a multi-scale temporal self-attention convolution(MSTC)module.The LKGC module adaptively focuses on active motion regions by utilizing a large convolution kernel and a gating mechanism,effectively capturing long-distance dependencies within the skeleton sequence.Meanwhile,the MAGC module dynamically learns relationships between different joints by adjusting connection weights between nodes.To further enhance the ability to capture temporal dynamics,the MSTC module effectively aggregates the temporal information by integrating Efficient Channel Attention(ECA)with multi-scale convolution.In addition,we use a multi-stream fusion strategy to make full use of different modal skeleton data,including bone,joint,joint motion,and bone motion.Exhaustive experiments on three scale-varying datasets,i.e.,NTU-60,NTU-120,and NW-UCLA,demonstrate that our MSLK-GCN can achieve state-of-the-art performance with fewer parameters.展开更多
Aiming at the difficulty of fault identification caused by manual extraction of fault features of rotating machinery,a one-dimensional multi-scale convolutional auto-encoder fault diagnosis model is proposed,based on ...Aiming at the difficulty of fault identification caused by manual extraction of fault features of rotating machinery,a one-dimensional multi-scale convolutional auto-encoder fault diagnosis model is proposed,based on the standard convolutional auto-encoder.In this model,the parallel convolutional and deconvolutional kernels of different scales are used to extract the features from the input signal and reconstruct the input signal;then the feature map extracted by multi-scale convolutional kernels is used as the input of the classifier;and finally the parameters of the whole model are fine-tuned using labeled data.Experiments on one set of simulation fault data and two sets of rolling bearing fault data are conducted to validate the proposed method.The results show that the model can achieve 99.75%,99.3%and 100%diagnostic accuracy,respectively.In addition,the diagnostic accuracy and reconstruction error of the one-dimensional multi-scale convolutional auto-encoder are compared with traditional machine learning,convolutional neural networks and a traditional convolutional auto-encoder.The final results show that the proposed model has a better recognition effect for rolling bearing fault data.展开更多
In order to extract the richer feature information of ship targets from sea clutter, and address the high dimensional data problem, a method termed as multi-scale fusion kernel sparse preserving projection(MSFKSPP) ba...In order to extract the richer feature information of ship targets from sea clutter, and address the high dimensional data problem, a method termed as multi-scale fusion kernel sparse preserving projection(MSFKSPP) based on the maximum margin criterion(MMC) is proposed for recognizing the class of ship targets utilizing the high-resolution range profile(HRRP). Multi-scale fusion is introduced to capture the local and detailed information in small-scale features, and the global and contour information in large-scale features, offering help to extract the edge information from sea clutter and further improving the target recognition accuracy. The proposed method can maximally preserve the multi-scale fusion sparse of data and maximize the class separability in the reduced dimensionality by reproducing kernel Hilbert space. Experimental results on the measured radar data show that the proposed method can effectively extract the features of ship target from sea clutter, further reduce the feature dimensionality, and improve target recognition performance.展开更多
In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is buil...In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. There is no other special constraint concerning the force. In previous papers, the force was either helical or violating parity invariance. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the linear stage of the instability.展开更多
In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptot...In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.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
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth o...It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples,since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%～3% for sample size larger than 10~4. This approach can also be generalized easily to cases of variable kernel estimations.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
文摘Significant advancements have been achieved in the field of Single Image Super-Resolution(SISR)through the utilization of Convolutional Neural Networks(CNNs)to attain state-of-the-art performance.Recent efforts have explored the incorporation of Transformers to augment network performance in SISR.However,the high computational cost of Transformers makes them less suitable for deployment on lightweight devices.Moreover,the majority of enhancements for CNNs rely predominantly on small spatial convolutions,thereby neglecting the potential advantages of large kernel convolution.In this paper,the authors propose a Multi-Perception Large Kernel convNet(MPLKN)which delves into the exploration of large kernel convolution.Specifically,the authors have architected a Multi-Perception Large Kernel(MPLK)module aimed at extracting multi-scale features and employ a stepwise feature fusion strategy to seamlessly integrate these features.In addition,to enhance the network's capacity for nonlinear spatial information processing,the authors have designed a Spatial-Channel Gated Feed-forward Network(SCGFN)that is capable of adapting to feature interactions across both spatial and channel dimensions.Experimental results demonstrate that MPLKN outperforms other lightweight image super-resolution models while maintaining a minimal number of parameters and FLOPs.
文摘In recent years,deep learning has been introduced into the field of Single-pixel imaging(SPI),garnering significant attention.However,conventional networks still exhibit limitations in preserving image details.To address this issue,we integrate Large Kernel Convolution(LKconv)into the U-Net framework,proposing an enhanced network structure named U-LKconv network,which significantly enhances the capability to recover image details even under low sampling conditions.
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
基金Supported by National Natural Science Foundation of China(60675039)National High Technology Research and Development Program of China(863 Program)(2006AA04Z217)Hundred Talents Program of Chinese Academy of Sciences
基金supported in part by the National Natural Science Foundation of China[62301374]Hubei Provincial Natural Science Foundation of China[2022CFB804]+2 种基金Hubei Provincial Education Research Project[B2022057]the Youths Science Foundation of Wuhan Institute of Technology[K202240]the 15th Graduate Education Innovation Fund of Wuhan Institute of Technology[CX2023295].
文摘This paper aims to develop a nonrigid registration method of preoperative and intraoperative thoracoabdominal CT images in computer-assisted interventional surgeries for accurate tumor localization and tissue visualization enhancement.However,fine structure registration of complex thoracoabdominal organs and large deformation registration caused by respiratory motion is challenging.To deal with this problem,we propose a 3D multi-scale attention VoxelMorph(MAVoxelMorph)registration network.To alleviate the large deformation problem,a multi-scale axial attention mechanism is utilized by using a residual dilated pyramid pooling for multi-scale feature extraction,and position-aware axial attention for long-distance dependencies between pixels capture.To further improve the large deformation and fine structure registration results,a multi-scale context channel attention mechanism is employed utilizing content information via adjacent encoding layers.Our method was evaluated on four public lung datasets(DIR-Lab dataset,Creatis dataset,Learn2Reg dataset,OASIS dataset)and a local dataset.Results proved that the proposed method achieved better registration performance than current state-of-the-art methods,especially in handling the registration of large deformations and fine structures.It also proved to be fast in 3D image registration,using about 1.5 s,and faster than most methods.Qualitative and quantitative assessments proved that the proposed MA-VoxelMorph has the potential to realize precise and fast tumor localization in clinical interventional surgeries.
基金Supported by the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Program of Department of Education of Jiangxi Province of China(Grant Nos.GJJ190732,GJJ180737)the Natural Science Foundation Program of Jiangxi Province(Grant No.20202BABL211005).
文摘Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere S^(d-1).We established that the large deviation principle for{sup_(x∈S^(d-1))|fn(x)-fn(-x)|,n≥1}holds if the kernel function is a function with bounded variation,and the density function f of the random variables is continuous and symmetric.
基金supported,in part,by the National Nature Science Foundation of China under grant numbers 62272236in part,by the Natural Science Foundation of Jiangsu Province under grant numbers BK20201136,BK20191401in part,by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)fund.
文摘Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learning have attracted widespread attention.Most existing methods use 3×3 small kernel convolution to extract image features and embed the watermarking.However,the effective perception fields for small kernel convolution are extremely confined,so the pixels that each watermarking can affect are restricted,thus limiting the performance of the watermarking.To address these problems,we propose a watermarking network based on large kernel convolution and adaptive weight assignment for loss functions.It uses large-kernel depth-wise convolution to extract features for learning large-scale image information and subsequently projects the watermarking into a highdimensional space by 1×1 convolution to achieve adaptability in the channel dimension.Subsequently,the modification of the embedded watermarking on the cover image is extended to more pixels.Because the magnitude and convergence rates of each loss function are different,an adaptive loss weight assignment strategy is proposed to make theweights participate in the network training together and adjust theweight dynamically.Further,a high-frequency wavelet loss is proposed,by which the watermarking is restricted to only the low-frequency wavelet sub-bands,thereby enhancing the robustness of watermarking against image compression.The experimental results show that the peak signal-to-noise ratio(PSNR)of the encoded image reaches 40.12,the structural similarity(SSIM)reaches 0.9721,and the watermarking has good robustness against various types of noise.
基金supported in part by the National Natural Science Foundation of China under Grant No.61976127the Shandong Provincial Natural Science Foundation under Grant No.ZR2024MF030+1 种基金the Taishan Scholar Program of Shandong Province of China under Grant No.tsqn202306150the Key Research and Development Program of Shandong Province of China under Grant No.2025CXPT096.
文摘Graph convolutional networks(GCNs)have become a dominant approach for skeleton-based action recognition tasks.Although GCNs have made significant progress in modeling skeletons as spatial-temporal graphs,they often require stacking multiple graph convolution layers to effectively capture long-distance relationships among nodes.This stacking not only increases computational burdens but also raises the risk of over-smoothing,which can lead to the neglect of crucial local action features.To address this issue,we propose a novel multi-scale adaptive large kernel graph convolutional network(MSLK-GCN)to effectively aggregate local and global spatio-temporal correlations while maintaining the computational efficiency.The core components of the network include two multi-scale large kernel graph convolution(LKGC)modules,a multi-channel adaptive graph convolution(MAGC)module,and a multi-scale temporal self-attention convolution(MSTC)module.The LKGC module adaptively focuses on active motion regions by utilizing a large convolution kernel and a gating mechanism,effectively capturing long-distance dependencies within the skeleton sequence.Meanwhile,the MAGC module dynamically learns relationships between different joints by adjusting connection weights between nodes.To further enhance the ability to capture temporal dynamics,the MSTC module effectively aggregates the temporal information by integrating Efficient Channel Attention(ECA)with multi-scale convolution.In addition,we use a multi-stream fusion strategy to make full use of different modal skeleton data,including bone,joint,joint motion,and bone motion.Exhaustive experiments on three scale-varying datasets,i.e.,NTU-60,NTU-120,and NW-UCLA,demonstrate that our MSLK-GCN can achieve state-of-the-art performance with fewer parameters.
基金The National Natural Science Foundation of China(No.51675098)
文摘Aiming at the difficulty of fault identification caused by manual extraction of fault features of rotating machinery,a one-dimensional multi-scale convolutional auto-encoder fault diagnosis model is proposed,based on the standard convolutional auto-encoder.In this model,the parallel convolutional and deconvolutional kernels of different scales are used to extract the features from the input signal and reconstruct the input signal;then the feature map extracted by multi-scale convolutional kernels is used as the input of the classifier;and finally the parameters of the whole model are fine-tuned using labeled data.Experiments on one set of simulation fault data and two sets of rolling bearing fault data are conducted to validate the proposed method.The results show that the model can achieve 99.75%,99.3%and 100%diagnostic accuracy,respectively.In addition,the diagnostic accuracy and reconstruction error of the one-dimensional multi-scale convolutional auto-encoder are compared with traditional machine learning,convolutional neural networks and a traditional convolutional auto-encoder.The final results show that the proposed model has a better recognition effect for rolling bearing fault data.
基金supported by the National Natural Science Foundation of China (62271255,61871218)the Fundamental Research Funds for the Central University (3082019NC2019002)+1 种基金the Aeronautical Science Foundation (ASFC-201920007002)the Program of Remote Sensing Intelligent Monitoring and Emergency Services for Regional Security Elements。
文摘In order to extract the richer feature information of ship targets from sea clutter, and address the high dimensional data problem, a method termed as multi-scale fusion kernel sparse preserving projection(MSFKSPP) based on the maximum margin criterion(MMC) is proposed for recognizing the class of ship targets utilizing the high-resolution range profile(HRRP). Multi-scale fusion is introduced to capture the local and detailed information in small-scale features, and the global and contour information in large-scale features, offering help to extract the edge information from sea clutter and further improving the target recognition accuracy. The proposed method can maximally preserve the multi-scale fusion sparse of data and maximize the class separability in the reduced dimensionality by reproducing kernel Hilbert space. Experimental results on the measured radar data show that the proposed method can effectively extract the features of ship target from sea clutter, further reduce the feature dimensionality, and improve target recognition performance.
文摘In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. There is no other special constraint concerning the force. In previous papers, the force was either helical or violating parity invariance. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the linear stage of the instability.
文摘In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.
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 the National Science Foundation of China under Grant No.11273013by the Natural Science Foundation of Jilin Province under Grant No.20180101228JC
文摘It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples,since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%～3% for sample size larger than 10~4. This approach can also be generalized easily to cases of variable kernel estimations.
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.
