Accuracy analysis of gradient reconstruction on isotropic unstructured meshes and its effects on inviscid flow simulation

The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically.Mathematical derivations reveal that,for gradient reconstruction based on the Green-Gauss theorem(the GG methods),if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process,which rarely occurs,second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate gradient.However,gradient reconstruction based on the least-squares approach(the LSQ methods)is at least first-order on arbitrary unstructured grids.Verifications are performed on typical isotropic grid stencils by analyzing the relationship between the discretization error of gradient reconstruction and the discretization error of the face midpoint value approximation of a given analytic function.Meanwhile,the numerical accuracy of gradient reconstruction methods is examined with grid convergence study on typical isotropic grids.Results verify the phenomenon of accuracy degradation for the GG methods when the face midpoint value condition is not satisfied.The LSQ methods are proved to be at least first-order on all tested isotropic grids.To study gradient accuracy effects on inviscid flow simulation,solution errors are quantified using the Method of Manufactured Solutions(MMS)which was validated before adoption by comparing with an exact solution case,i.e.,the 2-dimensional(2D)inviscid isentropic vortex.Numerical results demonstrate that the order of accuracy(OOA)of gradient reconstruction is crucial in determining the OOA of numerical solutions.Solution accuracy deteriorates seriously if gradient reconstruction does not reach first-order.

Optimization-based image reconstruction in x-ray computed tomography by sparsity exploitation of local continuity and nonlocal spatial self-similarity

The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography（CT） reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts.To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated.The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alternating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation.

Enlarged Gradient Observability for Distributed Parabolic Systems: HUM Approach

This paper is focused on studying an important concept of the system analysis, which is the regional enlarged observability or constrained observability of the gradient for distributed parabolic systems evolving in the spatial domain Ω We will explore an approach based on the Hilbert Uniqueness Method (HUM), which can reconstruct the initial gradient state between two prescribed functions f1 and f2 only in a critical subregion ω of Ω without the knowledge of the state. Finally, the obtained results are illustrated by numerical simulations.

Gradient Observability for Semilinear Hyperbolic Systems: Sectorial Approach

The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient reconstruction is achieved following sectorial approach combined with fixed point techniques. The obtained results lead to an algorithm which can be implemented numerically.

Sensors and Regional Gradient Observability of Hyperbolic Systems

This paper presents a method to deal with an extension of regional gradient observability developed for parabolic system [1,2] to hyperbolic one. This concerns the reconstruction of the state gradient only on a subregion of the system domain. Then necessary conditions for sensors structure are established in order to obtain regional gradient observability. An approach is developed which allows the reconstruction of the system state gradient on a given subregion. The obtained results are illustrated by numerical examples and simulations.

A FAST CONVERGING SPARSE RECONSTRUCTION ALGORITHM IN GHOST IMAGING

A fast converging sparse reconstruction algorithm in ghost imaging is presented. It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex optimization. Tests using experimental data show that, compared with the algorithm of Gradient Projection for Sparse Reconstruction (GPSR), the proposed algorithm yields better results with less computation work.

Kinetic equilibrium reconstruction for the NBI-and ICRH-heated H-mode plasma on EAST tokamak

The equilibrium reconstruction is important to study the tokamak plasma physical processes.To analyze the contribution of fast ions to the equilibrium,the kinetic equilibria at two time-slices in a typical H-mode discharge with different auxiliary heatings are reconstructed by using magnetic diagnostics,kinetic diagnostics and TRANSP code.It is found that the fast-ion pressure might be up to one-third of the plasma pressure and the contribution is mainly in the core plasma due to the neutral beam injection power is primarily deposited in the core region.The fast-ion current contributes mainly in the core region while contributes little to the pedestal current.A steep pressure gradient in the pedestal is observed which gives rise to a strong edge current.It is proved that the fast ion effects cannot be ignored and should be considered in the future study of EAST.

Sectorial Approach of the Gradient Observability of the Hyperbolic Semilinear Systems Intern and Boundary Cases

The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.

基于知识模糊迁徙的城市污水处理膜污染决策

针对城市污水处理膜污染难以精准决策的问题,提出一种基于知识模糊迁徙的膜污染决策方法。首先,结合城市污水处理运行过程数据和运行经验,利用模糊规则的形式实现膜污染决策知识的表达;其次,提出一种知识重构机制(knowledge reconstruction mechanism,KRM),动态平衡源域与目标域之间的准确性和多样性,并采用知识迁徙的方法完成决策知识重构;最后,建立一种基于数据和知识驱动的区间二型模糊神经网络(data-knowledge-driven interval type-2 fuzzy neural network,DK-IT2FNN)的决策模型,利用模糊规则设计模型参数,采用迁徙梯度下降算法动态调整网络权值,提高决策精度。实验结果表明,该模型能够实现膜污染的精准决策。

基于梯度惩罚Wasserstein生成对抗网络的数字岩心重建

文章针对三维Wasserstein生成对抗网络(Wasserstein generative adversarial networks,WGAN)重建数字岩心的梯度不稳定问题,提出一种基于带梯度惩罚的Wasserstein生成对抗网络(Wasserstein generative adversarial networks with gradient penalty,WGAN-GP)三维数字岩心重建算法。首先利用卷积神经网络构建生成网络学习真实样本的分布,然后再构建判别网络以区分重建样本和真实样本。由于WGAN的权值裁剪导致权重分散不均匀,WGAN-GP增加了梯度惩罚项,使得梯度分布更加均匀并加快网络收敛速度,让训练更加稳定。实验通过孔隙度、比表面积和欧拉特性的对比表明,相比于WGAN算法,WGAN-GP三维数字岩心重建算法能更加有效地重现岩石的三维孔隙结构特征。

桥梁实景三维高斯辐射场建模

实景三维和数字孪生已成为桥梁运维和管理的重要基础,然而面对桥梁的复杂几何结构,现有三维建模方法存在原始数据采集量大、建模效率低、模型细节缺失或变形等问题。对此,本文研究了一种基于3D高斯辐射场的桥梁实景三维重建方法。利用3D高斯函数对采集图像生成的稀疏点云构建高斯辐射场,并基于随机梯度下降对辐射场参数进行自适应优化,通过可微光栅渲染对三维模型进行实时可视化,从而实现高质量桥梁三维重建和渲染。试验探讨了不同图像分辨率,以及各项参数变化对桥梁建模的影响,并与传统方法作对比,为进一步针对桥梁的应用提供理论和技术支撑,推动桥梁复杂结构的高效、准确实景三维重建。

联邦学习深度梯度反演攻防研究进展

联邦学习作为一种“保留数据所有权,释放数据使用权”的分布式机器学习方法,打破了阻碍大数据建模的数据孤岛。然而,联邦学习在训练过程中只交换梯度而不交换训练数据的特点并不能保证用户训练数据的机密性。近年来新型的深度梯度反演攻击表明,敌手可从共享梯度中重建用户的私有训练数据,从而对联邦学习的私密性产生了严重威胁。随着梯度反演技术的演进,敌手从深层网络恢复大批量原始数据的能力不断增强,甚至对加密梯度的隐私保护联邦学习(PPFL)发起了挑战。而有效的针对性防御方法主要基于扰动变换,旨在混淆梯度、输入或特征以隐藏敏感信息。该文首先指出了隐私保护联邦学习的梯度反演漏洞,并给出了梯度反演威胁模型。之后从攻击范式、攻击能力、攻击对象3个角度对深度梯度反演攻击进行详细梳理。随后将基于扰动变换的防御方法依据扰动对象的不同分为梯度扰动、输入扰动、特征扰动3类,并对各类方法中的代表性工作进行分析介绍。最后,对未来研究工作进行展望。

基于各向异性滤波的无人机红外图像超分辨率重建方法

为提高无人机红外图像分辨率,研究基于各向异性滤波的无人机红外图像超分辨率重建方法。基于人眼视觉特性自适应设定图像内边缘区域与平滑区域梯度阈值,在此设定下通过各向异性扩散滤波方法去除初始红外图像内平滑区域噪声,并保留与增强图像内边缘区域细节信息,获得去噪后红外图像,向生成对抗网络内输入此图像,经其中生成模型与判别模型的博弈学习,获得最终超分辨率重建红外图像输出。结果显示,该方法具有较高的图像边缘细节保护能力与背景噪声去除能力,综合消噪效果较好,可获得分辨率高、视觉呈现清晰的超分辨率重建红外图像,保障无人机巡检中红外图像的辨识精度与效率。

一种基于WT⁃MMGR超像素技术的图像分割算法

在图像处理领域,谱聚类算法被广泛应用于图像分割任务。但对于背景复杂、色彩界限不明显的图像,传统的谱聚类算法往往无法准确地将目标物体分割出来,同时需要耗费大量的计算资源和时间。因此设计一种基于多尺度形态学梯度重构的分水岭超像素的改进谱聚类算法,它利用多尺度形态学梯度重构的分水岭超像素算法作为谱聚类算法的预处理步骤,将超像素处理所得的结果作为谱聚类的输入,以达到谱聚类算法的运算量目的。验证算法实验结果表明,所提出的改进谱聚类算法在图像分割任务中具有较好的边缘贴合度,并且程序的运行速率得到了显著提升。

基于压缩感知的加速近端梯度下降法

运用图像处理技术对卫星、侦察机和无人机侦察获取的图像进行校正和去噪等处理,可以提高战场环境影像和打击目标图像清晰度,有利于提升战场侦察监视效能。基于压缩感知技术能够以远小于奈奎斯特采样率从少量的测量值中重构出原信号的基本原理,提出了一种基于压缩感知的加速近端梯度下降(DAPG)图像去噪重构算法,并证明了该算法的收敛性。试验结果表明,与4种传统算法相比,该算法重构的图像有效提高了清晰度,其目标特征更加明显。

随机梯度追踪算法的硬件架构设计

压缩感知能够有效降低信号的采样速率,但信号恢复需要大量的复杂计算,这给用于重构的专用电路的面积和功耗带来挑战。以牺牲计算精度和增加计算时长为代价的情况下,随机计算能够大幅度减少算术操作过程中的功耗和硬件成本。这一特性使得随机计算在计算密集型电路设计中得到广泛应用。基于随机计算范式,设计了一种使用简单逻辑门搭建的向量内积计算电路,进一步构建了随机梯度追踪算法的硬件架构。相较于传统的二进制计算电路,该架构在Slices资源的使用上减少了83%。对信号长度为256、稀疏度为8的信号进行重构测试,结果显示其重构信噪比达到了18.99 dB,充分验证了该方案的有效性和灵活性。

深度残差网络下的电缆隧道低压故障检测

针对数据梯度消失导致电缆隧道低压故障检测结果精度不高的问题,提出了一种基于深度残差网络的电缆隧道低压故障检测方法。该方法对电缆隧道低压回路电流进行分析,建立深度残差网络,通过初始化学习得到线路电流故障特征值,并在权重层中引入激活函数,结合传递梯度进行特征重构,有效避免了梯度消失问题,输出信号特征,通过过零率判别得出故障检测结果。实验结果表明:应用所提方法得出的故障检测结果表现出的高频系数衰减比值图像呈现均值变化且较为密集,检测结果精度较高,满足了电缆隧道低压回路的现实运维需求。

自适应光学系统的实时模式复原算法

分析了自适应光学系统中实时模式复原算法的基本原理 ,建立了一种新型的传感器本征模复原算法。与常用的直接斜率法相比 ,这种模式复原算法可以有效减小探测噪声对复原计算过程的影响 ,提高系统的闭环稳定性和校正效果。在 6 1单元自适应光学系统上实现了这种模式复原算法 。

基于形态学梯度重构和标记提取的分水岭图像分割

为了解决传统分水岭算法的过分割问题,提出一种使用形态学梯度重构和标记提取技术进行图像预处理的分水岭图像分割方法。该方法基于多尺度概念,进行梯度重构时采用了不同尺寸的结构元素,在对重构后的各梯度图像的区域极小值进行标记后,将各标记点的并集作为最终标记图像,用其修改梯度图像,然后进行分水岭变换,实现图像的区域分割。实验结果表明,该方法既能有效解决分水岭算法的过分割问题,又保留了各尺度下的重要目标,并且可以根据图像特点和具体的分割要求,调整分割过程中所选参数,得到满意的图像分割效果。