CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods

We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.

Relaxed Stability Criteria for Delayed Generalized Neural Networks via a Novel Reciprocally Convex Combination

Dear Editor,This letter examines the stability issue of generalized neural networks(GNNs) with time-varying delay based on a novel reciprocally convex combination(RCC). By considering a new matrix polynomial, the proposed novel reciprocally convex method leads to a tight bound for integral inequality combination and encompasses several existing approaches as special cases.

DOUBLE INERTIAL PROXIMAL GRADIENT ALGORITHMS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS

In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.

基于改进凸内逼近法的主动配电网有功-无功协调优化

以风电、光伏为代表的分布式电源接入配电网后容易导致系统电压波动变大以及局部电压越限。以二阶锥优化为代表的松弛技术在优化时为了保证松弛后解的精确,约束条件极为严苛并且在功率的极端注入下容易导致对偶间隙增大。针对上述问题,该文提出基于改进凸内逼近法的主动配电网有功-无功优化方法。首先,基于支路潮流方程定义与支路电流、节点电压和视在功率流相关的非线性项的凸包,并与剩余线性元素结合形成凸内部近似,建立完善的数学模型;进一步提出网络容许性判据以及引入KKT条件收缩最优解的对偶间隙。最后,基于IEEE 33系统及PG&E69节点系统,利用Yalmip等平台求得电网中各有功、无功决策变量的出力区间,验证所提方法的稳定、精确与高效性。

一种结构不确定分析的改进多维平行六面体模型

多维平行六面体模型是一种能够同时考虑相关变量和独立变量的非概率凸集模型,更适用于工程结构中常见的多源不确定性问题。为更加有效合理地度量结构不确定性,提出一种改进多维平行六面体模型。通过定义区间变量的相关角和边缘区间,给出模型不确定域的显式表达式,进而给出依据实验样本点构建多维平行六面体模型的方法。3个算例分析结果表明,改进多维平行六面体模型能够较好地反映区间变量之间的相关性,是一种比传统多维平行六面体模型更为紧凑合理的模型。

基于凸型线圈双向电磁力加载的管件电磁翻边成形

传统线圈电磁力单一导致管件翻边角度不佳。本文提出采用凸型线圈管件翻边的方法,通过设计新型线圈,同时为管件翻边提供双向电磁力。建立了两组模型,分别采用传统线圈和凸型线圈驱动管件发生电磁翻边成形,探讨分析了两组管件模型翻边成形过程中的电磁力矢量以及变形速率的变化。结果表明,凸型线圈加载管件翻边时提供的双向电磁力极大地提高了管件变形的流动性,从而提高了翻边角度。此外,相同放电参数下基于凸型线圈的管件翻边角度较传统线圈提高了1.25倍。显然,新型线圈能够在一定程度上改善管件电磁翻边的质量问题,为电磁翻边成形的工业化应用提供更多可能。

计及UPFC最优配置的电力系统鲁棒调度协同优化策略

统一潮流控制器(UPFC)应用于潮流调控时,计及UPFC调控参数的交流潮流计算是非凸、非线性问题,且多台装置间的非线性交叉耦合特性也会直接影响优化配置方案。为此,基于UPFC的潮流调控特性,构建了计及UPFC的松弛型交流潮流二阶锥规划模型;计及风电的不确定性,协同考虑UPFC的规划和电力系统的调度问题,建立了计及UPFC最优配置的电力系统鲁棒协同优化模型,并采用列和约束生成算法进行求解。以IEEE RTS-24节点系统为算例进行仿真分析,结果表明所提协同优化策略有效提升了UPFC配置方案的适应性,提高了系统运行经济性和风电消纳能力,增强了系统运行调控的灵活性。

一种面向多任务的无人机辅助的通信网络资源分配与轨迹优化研究

装载各种有效荷载的无人机(UAV)能够实现传感、通信和计算等多任务,因而常被部署到数据采集(DA)和辅助计算等领域。但是到目前为止,绝大多数研究仅专注于单一功能的无人机辅助的通信网络资源分配与轨迹优化,对于面向多任务的资源分配和轨迹优化问题还未解决。为此,该文提出一种综合考虑无人机数据采集、数据广播以及计算任务卸载的无人机辅助的通信网络资源优化的分配策略,旨在通过联合优化传输占空比、用户发射功率与无人机轨迹,在满足目标位置采集数据实时广播的前提下,最大化用户卸载量。为了解决多变量耦合优化问题,提出了基于块坐标下降(BCD)和连续凸逼近(SCA)的高效迭代优化算法,将耦合优化问题分解为3个子问题进行迭代优化。最后,大量仿真结果表明,该算法在公平性和总卸载计算量方面都优于其他测试方案。

天津滨海地热田北部深部地热资源赋存规律

【研究目的】天津地热资源丰富,目前已开发的深部地热资源大部分位于“隆中凸”构造区域,而位于“坳中凸”构造区域的地热资源勘查和研究程度基本尚属空白,揭示其深部地热赋存规律可为滨海新区及京津冀地区寻找深部地热资源及勘探与开发提供重要参考。【研究方法】本文以黄骅坳陷宁河凸起中的桥沽地区为研究区,以近期新发现的资源禀赋最好的蓟县系雾迷山组热储层为研究对象,通过分析区域地质资料、大地电磁测深(MT)、钻孔测温和物探测井等资料,系统总结了研究区地质构造、地温场和深部地热资源赋存特征。【研究结果】雾迷山组储层的热储温度高(90~120℃),出水量大于100 m^(3)/h,埋藏相对较浅(2200~2800 m)。区内地质构造条件复杂,断裂构造发育,汉沽断裂为研究区重要的导热、导水通道;地温场呈现“两高夹一低”展布特征与两处背斜构造空间位置相对应;热源以壳源热为主、幔源热次之,大气降水为主要热水来源,热传输机制以热传导型为主。【结论】综合研究区深部地热赋存规律,建立了深部地热资源概念模型,明确了“坳中凸”深部地热找矿新思路。

交错凸齿式宽苗带小麦精量排种器设计与试验

针对外槽轮式小麦宽苗带排种器排量不稳定和苗带内种子分布均匀性较差的问题,该研究设计了一种交错凸齿式宽苗带小麦精量排种器。通过连续充种分析和排量计算,确定凸齿高度和凸齿角度是影响排量一致性和排种均匀性的关键参数。应用离散元法对上述关键参数进行中心旋转组合仿真试验,结果表明,对排量一致性、排种均匀性影响显著性程度由大到小的因素分别依次为凸齿角、凸齿高、作业速度,且均具有交互影响。借助响应面分析,得出凸齿高5 mm、凸齿角75°时的排量一致性和排种均匀性较优,平均变异系数分别为2.27%和7.61%。对该参数组合排种器进行样机试制,并进行台架试验,台架试验结果表明,排种一致性和均匀性变异系数与仿真值误差均低于5%,说明仿真优化结果可靠、准确。田间对比试验结果表明,播量120、150和180 kg/hm~2时,交错凸齿式宽苗带小麦精量排种器的播量一致性、纵向播种均匀性和横向播种均匀性变异系数分别较外槽轮式排种器降低0.99、3.01和9.38个百分点,满足小麦宽苗带播种农艺要求。研究结果可为提高排种均匀性的小麦排种装置设计提供参考。

基于非凸与不可分离正则化算法的电容层析成像图像重建

搅拌器内两相混合是化工生产中常见的现象,电容层析成像(ECT)技术主要对两相分布进行可视化重构,以达到监测的目的。受稀疏贝叶斯学习的启发,提出了一种非凸与不可分离正则化(NNR)算法重建ECT图像。在稀疏先验的基础上引入矩阵低秩特性,采用最大后验估计在潜在空间中提出一个新的优化问题,利用对偶变量将潜在空间的目标函数映射到原始空间进行迭代求解,用来恢复同时稀疏与低秩的矩阵。与凸近似L1范数相比,NNR算法可获得更准确的重建图像,同时比非凸可分离方法更容易收敛到全局最优解。为验证NNR算法的重建效果,通过数值仿真与静态实验的方法分别与其他5种算法进行重建对比。结果表明:NNR算法可以有效减少重建伪影,提升中心物体的重建质量,为搅拌器内两相分布提供了高质量的重建算法。

Drag Coefficient of a Non-Convex Polygonal Plate during Free Fall

Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.

基于机器视觉的芯片字符区域分割和定位算法

芯片表面的字符对分选具有重要意义,对字符的定位是分选工作的关键步骤。为了提高分选工作定位效率和定位精度,提出了一种基于改进的区域生长算法和凸包检测算法分割和定位芯片表面字符区域方法。首先,对采集图像进行预处理操作,利用改进的Canny算法获取无干扰图像边缘,将图像边缘作为区域生长法的种子点并以图像自适应阈值作为生长准则分割图像,使用最大内接矩形算法粗定位字符区域;其次,采用Harris角点检测算法获取字符角点分布位置;最后,筛选角点并提取关键点,利用一种改进的凸包检测算法定位字符区域。经过实验验证,所设计的算法能够完整的分割和定位芯片表面字符区域,定位精度和效率较原有方法提升5.3%和15.4%,满足实际工业生产的要求。

基于空间稀疏先验的冲击载荷识别频域非凸稀疏正则化方法

复合材料因其强度高、刚度高、密度小等优点而广泛应用于航空、航天等领域。但由于其抗冲击性差,监测作用于复合材料结构上的冲击载荷对于结构快速检测损伤十分重要。经典的Tikhonov正则化方法在欠定情况下求解载荷识别问题时容易在载荷非加载区识别出虚假力;近年来兴起的L1范数稀疏正则化方法在识别冲击载荷时常低估载荷的幅值。为了突破这些方法的局限以实现更高精度的冲击载荷识别,该研究基于冲击载荷的空间稀疏先验,提出一种新的冲击载荷识别频域非凸稀疏正则化方法。所提出的方法结合了广义极小极大凹惩罚项的非凸优势以及非凸保凸的特性,利用向前向后分裂算法进行凸优化求解,既避免了非凸优化容易收敛到局部最优解的问题,又促进了解的稀疏。分别在复合材料梁和复合材料层合板上开展了冲击载荷试验验证,试验结果表明,无论在正定还是欠定的情况下,所提出方法能在精准定位冲击位置的同时重构冲击载荷的时间历程,且该方法在促进解稀疏和识别载荷幅值方面的表现都优于L1正则化方法,其中幅值识别精度能比L1正则化提升50%以上。

硬件损伤条件下无人机辅助的NOMA-IRS网络资源分配算法

探讨了在硬件损伤条件下,如何通过搭载在无人机上的智能反射面(IRS)有效支持基于非正交多址接入(NOMA)技术的网络,以加快多用户数据的传输速率。提出了一种全面优化策略实现整个通信系统的最大传输速率,包括联合调整串行干扰消除的解码策略、IRS的反射配置、无人机的空间位置以及基站的发射功率。由于该问题是一个非凸问题,提出使用块坐标下降方法来实现优化的一种迭代算法,将原始的非凸问题细分为3个子问题,并通过结合惩罚函数法、半正定松弛技术和连续凸近似法来解决这些子问题。仿真结果表明:提出的算法在系统总速率方面相比随机部署无人机、未使用IRS辅助的NOMA策略,系统速率有显著提升。