An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the ex...An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.展开更多
In this paper,the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional multi-term fractional-order PDEs wit...In this paper,the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional multi-term fractional-order PDEs with variable coefficients.The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem.The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by threevariable shifted Jacobi polynomials are compared with the exact solutions.Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm.Lastly,several numerical examples are presented to test the superiority and efficiency of the proposed method.展开更多
In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obt...In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.展开更多
This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions...This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions for temporal discretization and the Lagrangian polynomials are used for spatial discretization. An efficient spectral approximation of the weak solution is established. The main work is the demonstration of the well-posedness for the weak problem and the derivation of a posteriori error estimates for the spectral Galerkin approximation. Extensive numerical experiments are presented to perform the validity of a posteriori error estimators, which support our theoretical results.展开更多
By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the m...By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the multi-term time-fractional sub-diffusion equation or diffusion-wave equation,the mixed case contains a special time-space coupled derivative,which leads to many difficulties in numerical analysis.Firstly,a fully discrete scheme is established by using nonconforming finite element method(FEM)in spatial direction and L1 approximation coupled with Crank-Nicolson(L1-CN)scheme in temporal direction.Furthermore,the fully discrete scheme is proved to be unconditional stable.Besides,convergence and superclose results are derived by using the properties of EQ^(ROT)_(1) nonconforming finite element.What's more,the global superconvergence is obtained via the interpolation postprocessing technique.Finally,several numerical results are provided to demonstrate the theoretical analysis on anisotropic meshes.展开更多
The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which...The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which contains a time-space coupled derivative.The nonconforming EQ^(rot)_(1)element and Raviart-Thomas element are employed for spatial discretization,and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization.Firstly,based on some significant lemmas,the unconditional stability analysis of the fully-discrete scheme is acquired.With the assistance of the interpolation operator I_(h)and projection operator Rh,superclose and convergence results of the variable u in H^(1)-norm and the flux~p=k_(5)(x)ru(x,t)in L^(2)-norm are obtained,respectively.Furthermore,the global superconvergence results are derived by applying the interpolation postprocessing technique.Finally,the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
当前大语言模型的兴起为自然语言处理、搜索引擎、生命科学研究等领域的研究者提供了新思路,但大语言模型存在资源消耗高、推理速度慢,难以在工业场景尤其是垂直领域应用等方面的缺点。针对这一问题,提出了一种多尺度卷积神经网络(convo...当前大语言模型的兴起为自然语言处理、搜索引擎、生命科学研究等领域的研究者提供了新思路,但大语言模型存在资源消耗高、推理速度慢,难以在工业场景尤其是垂直领域应用等方面的缺点。针对这一问题,提出了一种多尺度卷积神经网络(convolutional neural network,CNN)与双向长短期记忆神经网络(long short term memory,LSTM)融合的唐卡问句分类模型,本文模型将数据的全局特征与局部特征进行融合实现唐卡问句分类任务,全局特征反映数据的本质特点,局部特征关注数据中易被忽视的部分,将二者以拼接的方式融合以丰富句子的特征表示。通过在Thangka数据集与THUCNews数据集上进行实验,结果表明,本文模型相较于Bert模型在精确度上略优,在训练时间上缩短了1/20,运算推理时间缩短了1/3。在公开数据集上的实验表明,本文模型在文本分类任务上也表现出了较好的适用性和有效性。展开更多
针对传统卷积神经网络故障诊断方法提取特征不丰富,容易丢失故障敏感信息,且在单一尺度处理方法限制实际复杂工况下故障特性的深度挖掘问题,提出了注意力机制的多尺度卷积神经网络和双向长短期记忆(bi-directional long short-term memo...针对传统卷积神经网络故障诊断方法提取特征不丰富,容易丢失故障敏感信息,且在单一尺度处理方法限制实际复杂工况下故障特性的深度挖掘问题,提出了注意力机制的多尺度卷积神经网络和双向长短期记忆(bi-directional long short-term memory,BiLSTM)网络融合的迁移学习故障诊断方法。该方法首先应用不同尺寸池化层和卷积核捕获振动信号的多尺度特征;然后引入多头自注意力机制自动地给予特征序列中的不同部分不同的权重,进一步加强特征表示的能力;其次利用BiLSTM结构引入双向性质提取特征前后之间的内部关系实现信息的逐层传递;最后利用多核最大均值差异减小源域和目标域在预训练模型中各层上的概率分布差异并利用少量标记的目标域数据再对模型进行训练。试验结果表明,所提方法在江南大学(JNU)、德国帕德博恩大学(PU)公开轴承数据集上平均准确率分别为98.43%和97.66%,该方法在重庆长江轴承股份有限公司自制的轴承故障数据集上也表现出了极高的准确率和较快的收敛速度,为有效诊断振动旋转部件故障提供了实际依据。展开更多
精准的分布式光伏短期发电功率预测有助于电力系统运行与功率就地平衡。该文提出一种基于BIRCH(balanced iterative reducing and clustering using hierarchies)相似日聚类的L-Transformer(LSTM-Transformer)模型进行短期光伏功率预测...精准的分布式光伏短期发电功率预测有助于电力系统运行与功率就地平衡。该文提出一种基于BIRCH(balanced iterative reducing and clustering using hierarchies)相似日聚类的L-Transformer(LSTM-Transformer)模型进行短期光伏功率预测。首先使用BIRCH无监督聚类算法对历史数据聚类得到3种典型天气,根据聚类结果划分测试集对模型进行训练。为提高不同天气类型下的预测精度,采用双层架构的L-Transformer模型,首层通过长短期记忆网络(long short term memory,LSTM)的门控单元机制捕捉时间序列中的长期依赖关系;次层结合Transformer模型的自注意力机制聚焦于当前任务更关键的特征量,通过多注意力头与光伏数据特征量相结合生成向量,注意力头并行计算,从而高效、精确地预测短期光伏功率。实测数据验证结果表明L-Transformer模型对于不同天气类型功率预测泛化性优异、精确度高,气象数据波动大时鲁棒性强。展开更多
基金National Natural Science Foundation of China(No.11371087)
文摘An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.
基金This work was supported by the Collaborative Innovation Center of Taiyuan Heavy Machinery Equipment,Postdoctoral Startup Fund of Taiyuan University of Science and Technology(20152034)the Natural Science Foundation of Shanxi Province(201701D221135)National College Students Innovation and Entrepreneurship Project(201710109003)and(201610109007).
文摘In this paper,the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional multi-term fractional-order PDEs with variable coefficients.The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem.The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by threevariable shifted Jacobi polynomials are compared with the exact solutions.Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm.Lastly,several numerical examples are presented to test the superiority and efficiency of the proposed method.
文摘In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.
基金supported by the State Key Program of National Natural Science Foundation of China(Nos.11931003)National Natural Science Foundation of China(Nos.41974133)。
文摘This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions for temporal discretization and the Lagrangian polynomials are used for spatial discretization. An efficient spectral approximation of the weak solution is established. The main work is the demonstration of the well-posedness for the weak problem and the derivation of a posteriori error estimates for the spectral Galerkin approximation. Extensive numerical experiments are presented to perform the validity of a posteriori error estimators, which support our theoretical results.
基金National Natural Science Foundation of China(No.11971416)Scientific Research Innovation Team of Xuchang University(No.2022CXTD002)+3 种基金Foundation for University Key Young Teacher of Henan Province(No.2019GGJS214)Key Scientific Research Projects in Universities of Henan Province(Nos.21B110007,22A110022)National Natural Science Foundation of China(International cooperation key project:No.12120101001)Australian Research Council via the Discovery Project(DP190101889).
文摘By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the multi-term time-fractional sub-diffusion equation or diffusion-wave equation,the mixed case contains a special time-space coupled derivative,which leads to many difficulties in numerical analysis.Firstly,a fully discrete scheme is established by using nonconforming finite element method(FEM)in spatial direction and L1 approximation coupled with Crank-Nicolson(L1-CN)scheme in temporal direction.Furthermore,the fully discrete scheme is proved to be unconditional stable.Besides,convergence and superclose results are derived by using the properties of EQ^(ROT)_(1) nonconforming finite element.What's more,the global superconvergence is obtained via the interpolation postprocessing technique.Finally,several numerical results are provided to demonstrate the theoretical analysis on anisotropic meshes.
基金The work is supported by the National Natural Science Foundation of China(Nos.11971416 and 11871441)the Scientific Research Innovation Team of Xuchang University(No.2022CXTD002)the Foundation for University Key Young Teacher of Henan Province(No.2019GGJS214).
文摘The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusionwave equation with spatial variable coefficient,which contains a time-space coupled derivative.The nonconforming EQ^(rot)_(1)element and Raviart-Thomas element are employed for spatial discretization,and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization.Firstly,based on some significant lemmas,the unconditional stability analysis of the fully-discrete scheme is acquired.With the assistance of the interpolation operator I_(h)and projection operator Rh,superclose and convergence results of the variable u in H^(1)-norm and the flux~p=k_(5)(x)ru(x,t)in L^(2)-norm are obtained,respectively.Furthermore,the global superconvergence results are derived by applying the interpolation postprocessing technique.Finally,the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
文摘当前大语言模型的兴起为自然语言处理、搜索引擎、生命科学研究等领域的研究者提供了新思路,但大语言模型存在资源消耗高、推理速度慢,难以在工业场景尤其是垂直领域应用等方面的缺点。针对这一问题,提出了一种多尺度卷积神经网络(convolutional neural network,CNN)与双向长短期记忆神经网络(long short term memory,LSTM)融合的唐卡问句分类模型,本文模型将数据的全局特征与局部特征进行融合实现唐卡问句分类任务,全局特征反映数据的本质特点,局部特征关注数据中易被忽视的部分,将二者以拼接的方式融合以丰富句子的特征表示。通过在Thangka数据集与THUCNews数据集上进行实验,结果表明,本文模型相较于Bert模型在精确度上略优,在训练时间上缩短了1/20,运算推理时间缩短了1/3。在公开数据集上的实验表明,本文模型在文本分类任务上也表现出了较好的适用性和有效性。
文摘针对传统卷积神经网络故障诊断方法提取特征不丰富,容易丢失故障敏感信息,且在单一尺度处理方法限制实际复杂工况下故障特性的深度挖掘问题,提出了注意力机制的多尺度卷积神经网络和双向长短期记忆(bi-directional long short-term memory,BiLSTM)网络融合的迁移学习故障诊断方法。该方法首先应用不同尺寸池化层和卷积核捕获振动信号的多尺度特征;然后引入多头自注意力机制自动地给予特征序列中的不同部分不同的权重,进一步加强特征表示的能力;其次利用BiLSTM结构引入双向性质提取特征前后之间的内部关系实现信息的逐层传递;最后利用多核最大均值差异减小源域和目标域在预训练模型中各层上的概率分布差异并利用少量标记的目标域数据再对模型进行训练。试验结果表明,所提方法在江南大学(JNU)、德国帕德博恩大学(PU)公开轴承数据集上平均准确率分别为98.43%和97.66%,该方法在重庆长江轴承股份有限公司自制的轴承故障数据集上也表现出了极高的准确率和较快的收敛速度,为有效诊断振动旋转部件故障提供了实际依据。
文摘精准的分布式光伏短期发电功率预测有助于电力系统运行与功率就地平衡。该文提出一种基于BIRCH(balanced iterative reducing and clustering using hierarchies)相似日聚类的L-Transformer(LSTM-Transformer)模型进行短期光伏功率预测。首先使用BIRCH无监督聚类算法对历史数据聚类得到3种典型天气,根据聚类结果划分测试集对模型进行训练。为提高不同天气类型下的预测精度,采用双层架构的L-Transformer模型,首层通过长短期记忆网络(long short term memory,LSTM)的门控单元机制捕捉时间序列中的长期依赖关系;次层结合Transformer模型的自注意力机制聚焦于当前任务更关键的特征量,通过多注意力头与光伏数据特征量相结合生成向量,注意力头并行计算,从而高效、精确地预测短期光伏功率。实测数据验证结果表明L-Transformer模型对于不同天气类型功率预测泛化性优异、精确度高,气象数据波动大时鲁棒性强。
