ON THE REGULARIZATION METHOD OF THE FIRST KIND OFFREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

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.

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

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.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Analysis of variable coefficient advection-diffusion problems via complex variable reproducing kernel particle method

The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method.

三维二十面体准晶弹性半平面周期接触问题研究

借助平面弹性复变方法,研究了周期刚性压头作用下三维二十面体准晶弹性半平面的周期有限摩擦和周期粘结接触问题.从应力、位移分量的复变函数形式表达式出发,利用半平面Hilbert核积分公式、Plemelj公式,得到两类周期接触问题的解答.针对周期有限摩擦接触问题,得到了三类周期刚性压头(直水平、直倾斜和圆形基底)作用在准晶体半平面上接触应力的封闭解.针对半平面周期粘结接触问题,求得接触边界上作用周期尖劈形位移时接触应力的显式解答.当不考虑相位子场的作用时,文中求得的理论结果可退化到正交各向异性材料平面弹性周期接触问题的对应结果.数值算例说明准晶弹性常数对接触应力分布规律及大小的影响.本文结论可为分析准晶材料压痕实验结果及准晶材料性能提供一定理论依据.

复杂场景下一种改进的单目标跟踪算法研究

针对部分复杂场景下目标跟踪存在跟踪框漂移问题,基于孪生候选区域生成网络(SiamRPN),融合通道注意力模块和选择核心模块(SK Module),提出一种单目标跟踪算法CAKSiamRPN。特征提取部分引入高效通道注意模块(ECAM)和基于标准化的通道注意力模块(NCAM),在不降低通道维度的情况下,摒弃相似信息,突出显著特征,关注并提取特定信息;在候选区域生成网络(RPN)嵌入SK Module,增强全局信息嵌入,减少填充操作的影响。将改进算法与SiamRPN及其它经典单目标跟踪算法在OTB100和UAV123数据集上进行实验对比。实验结果表明:跟踪精度和成功率明显提高,能更好地适应复杂场景,具有更强的鲁棒性。

乳清浓缩蛋白对松仁蛋白溶解度及其乳液稳定性的影响

为研究蛋白质-蛋白质相互作用对松仁蛋白(PKP)溶解度、结构和乳液性质的影响,以PKP和乳清浓缩蛋白(WPC)为研究对象,采用pH循环法制备PK P-WPC复合蛋白,利用SD S-PAGE、内源性荧光光谱、紫外-可见光谱、圆二色谱、荧光探针和ζ-电位等方法分析了复合蛋白结构特性和表面特性,再以PK P-WPC复合蛋白为原料,分别制备了油相体积分数为3%、10%和50%的乳液,并对制备的乳液性质进行了检测。结果表明:当WPC与PKP的质量比为1.0∶1.0,且体系pH值经历由7.0到12.0再回到7.0时的1次pH循环后,PKP的水溶性可从48.53%提高到92.43%。SD S-PAGE结果显示,PK P-WPC复合蛋白完整保留了PKP和WPC的亚基。内源性荧光光谱、紫外-可见光谱和圆二色谱结果表明,静电相互作用、疏水相互作用和氢键是驱动PKP和WPC相互作用的主要作用力,PKP与WPC相互作用使复合蛋白具有较高的结构韧性,抵抗酸诱导的构象折叠;WPC的加入改变了PKP的二级结构,α-螺旋、β-转角和无规卷曲结构的含量增加,而β-折叠结构相对含量降低。PK P-WPC复合蛋白具有较高的表面电荷(-34.74 mV)来抵抗蛋白质的聚集。与由PKP制备的乳液相比,由PK P-WPC制备的乳液平均粒径和乳层析指数减小,ζ-电位绝对值增大,稳定性显著提高。乳液的性质因油相体积分数的不同而有较大的差异。油相体积分数为3%的复合乳液液滴小且分布均匀,稳定性好于油相体积分数为10%和50%的复合乳液。通过pH循环法,通过添加WPC,提高了PKP的溶解度,获得了稳定性较佳的PKP乳液,研究可为新型蛋白产品的研发提供理论基础,拓宽松仁蛋白在加工食品中的应用范围,推动PK P-WPC双蛋白乳液研究的发展。

A New Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.

Air Traffic Operation Complexity Analysis Based on Metrics System

In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was utilized to reduce the dimensionality of metrics,therefore to extract crucial information in the metrics.The hierarchical clustering method was used to analyze the complexity of different airspace.Fourteen sectors of Guangzhou Area Control Center were taken as samples.The operation complexity of traffic situation in each sector was calculated based on real flight radar data.Clustering analysis verified the feasibility and rationality of the method,and provided a reference for airspace operation and management.

Interior-point algorithm based on general kernel function for monotone linear complementarity problem

A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.

A Modified Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function

This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.

基于模拟串行端口的虚拟设备通信技术研究

MBSE是复杂系统设计的重要范式,尤其对于大型嵌入式系统设计具有重大意义;但在MBSE的虚拟验证环节,针对节点的串行端口的互联通信仍缺乏有效灵活的手段;为解决该问题,提出了一种基于Linux系统内核驱动的串行端口模拟方式,实现了基于模拟串行端口的多虚拟设备间的通信技术;分析了标准串行端口的内核驱动架构,进行规范的驱动设计,构建模拟串行端口,以模拟设备替代真实硬件设备;实验验证了模拟的串行端口的功能可用性,且具备平均456.98 Mbps的最大传输速率,满足物理串行端口的速率范围要求;利用该模拟串行端口,实现了虚拟设备间的双向串行通信实验,能够支持嵌入式子系统间串行通信模拟的需要。

正交结合熵权TOPSIS法优化酶解棕榈粕的条件

为改善棕榈粕的营养价值,本试验利用正交结合熵权TOPSIS法对甘露聚糖酶、酸性蛋白酶和纤维素酶组成的复合酶水解棕榈粕的条件进行了优化。以棕榈粕为原料,还原糖、三氯乙酸可溶蛋白含量为指标,筛选了复合酶的组成和各酶的最适浓度;采用单因素试验获得料水比、复合酶酶解时间、酶解pH值以及酶解温度的最适条件;在单因素试验基础上,利用正交试验结合熵权TOPSIS方法获得最佳酶解条件。结果:复合酶组成和含量分别为酸性蛋白酶250 U/g、甘露聚糖酶45 U/g、纤维素酶160 U/g;各因素最适条件为料水比1∶3、酶解时间24 h、pH值4.8、温度37℃;最佳酶解条件为料水比1∶2、酶解时间24 h、pH值4.8、温度42℃。结论:复合酶在料水比1∶2、时间24 h、pH值4.8、温度42℃条件下水解棕榈粕,反应后还原糖含量达到65.29 mg/g,酸溶蛋白含量达到3.86%,粗纤维降解至8.58%。

改进KFDA分类器在电力变压器故障诊断中的应用

针对变压器故障中数据呈现非线性,故障类型复杂,神经网络存在局部极值等问题,提出了一种改进的核Fisher(KFDA)诊断方法。在核Fisher的基础上,用欧氏距离对类间距离进行加权,一定程度上降低了数据投影重叠的问题,提升分类性能。另外,针对单一核函数的不足,采用了复合核函数,使其具有更好的非线性处理数据能力。经实验验证,KFDA分类器不存在局部最值,具有识别正确率高等优点,是一种有效的故障诊断方法。

一种支持向量逐步回归机算法研究

支持向量机是解决非线性问题的重要工具,对多元线性回归模型和支持向量机的原始形式进行比较,拟定从样本子集的多元线性回归模型出发,逐步搜索支持向量,提出了一种建立支持向量回归机的快速算法,以降低核矩阵的规模从而降低解凸二次规划的复杂度;最后,分析了该算法的复杂度,并提供了一个算例。

复双球垒域上具有离散局部全纯核的线性奇异积分方程

利用 Cn空间中复双球垒域上具有离散局部全纯核的奇异积分的“椭圆”邻域挖法的柯西主值及立体角系数方法 ,讨论了一类具有相应核的线性奇异积分方程和方程组 ,证明了此奇异积分方程与一 Fredholm方程等价 ,并且其特征方程存在唯一解 .

基于优化核函数带宽SVDD的机械振动预警模型

基于高斯核函数的支持向量数据描述(SVDD),因其具有良好的异常检测性能,常被用于机械振动故障预警领域,但其性能的好坏受限于核函数带宽的取值是否适宜。为此,针对常规高斯核函数支持向量数据描述(SVDD)存在需要负类样本训练模型、计算量大、不收敛、不适用于小数值数据等问题,提出了一种不需要专家经验知识和负类样本训练SVDD超球体的优化核函数带宽计算方法,构建了基于优化SVDD核函数带宽的机械振动故障预警模型。首先,根据空间矩阵复杂度的信息熵,量化表征核函数带宽的取值对SVDD超球体的影响;然后,采用粒子群优化(PSO)算法寻找空间矩阵复杂度最大时对应的核函数带宽σ取值,实现了目标函数的快速收敛目的;综合考虑惩罚参数对SVDD超球体描述边界的影响,引入惩罚参数对寻优结果进行了修正,完成了对历史正常运行状态数据驱动的机械振动故障预警模型的构建任务;最后,应用辛辛那提大学智能维护中心轴承试验数据集等6项公开实验室数据和4项工程案例数据,对上述方法的实用性和可靠性进行了验证,并将其结果与采用常规方法所得结果进行了对比验证。研究结果表明:与常规方法相比,采用优化核函数带宽计算方法训练出的机械振动故障预警模型的合格率为100%,超球体描述边界拟合良好,并且不存在不收敛的问题。

复高斯小波核函数的支持向量机研究

针对基于常用核函数的支持向量机在非线性系统参数辨识及预测方面的不足之处,构建了一种新的核函数——复高斯小波函数核函数。首先证明了新构建的核函数的正确性,即满足Mercy条件,表明其可以作为核函数;然后构建基于该核函数的支持向量机,并将该支持向量机用于非线性系统的辨识和未知部分的预测。通过与常用核函数构建的支持向量机的仿真结果进行对比,验证了该方法的正确性和有效性。

基于模糊核学习矢量量化的Sammon非线性映射算法

提出了一种基于可靠稳定的模糊核学习矢量量化(FKLVQ)聚类的Sammon非线性映射新算法。该方法通过Mercer核,将数据空间映射到高维特征空间,并在此特征空间上进行FKLVQ学习获取数据空间有效且稳定的聚类权矢量,然后在特征空间和输出空间上仅针对各空间的数据样本和它们各自的聚类权矢量进行Sammon非线性核映射。这样既降低了计算的复杂度,又使数据空间和输出空间上数据点与聚类中心间的距离信息保持相似。仿真结果验证了该方法的可靠性和稳定性。