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Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems 一些一维边值问题的高阶有限元方法
Pub Date : 2023-01-16 DOI: 10.37256/rrcs.2120232118
Baiying Dong, Zhilin Li, Juan Ruiz-Álvarez
In this paper, third-order compact and fourth-order finite element methods (FEMs) based on simple modifications of traditional FEMs are proposed for solving one-dimensional Sturm-Liouville boundary value problems (BVPs). The key idea is based on interpolation error estimates. A simple posterior error analysis of the original piecewise linear finite element space leads to a third-order accurate solution in the L2 norm, second-order in the H1, and the energy norm. The novel idea is also applied to obtain a fourth-order FEM based on the quadratic finite element space. The basis functions in the new fourth-order FEM are more compact compared with that of the classic cubic basis functions. Numerical examples presented in this paper have confirmed the convergence order and analysis. A generalization to a class of nonlinear two-point BVPs is also discussed and tested.
本文在对传统有限元法进行简单修改的基础上,提出了求解一维Sturm-Liouville边值问题的三阶紧凑有限元法和四阶紧凑有限元法。关键思想是基于插值误差估计。对原始分段线性有限元空间进行简单的后验误差分析,可以得到L2范数的三阶精确解,H1和能量范数的二阶精确解。该方法还应用于基于二次元空间的四阶有限元计算。与经典的三次基函数相比,新的四阶有限元基函数更加紧凑。文中给出的数值算例验证了该方法的收敛阶数和分析结果。讨论并验证了一类非线性两点bvp的推广。
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引用次数: 0
Design and Application of Virtual Flexible Simulation Experiment Teaching Platform for Relay Protection 继电保护虚拟柔性仿真实验教学平台的设计与应用
Pub Date : 2023-01-06 DOI: 10.37256/rrcs.2120232119
Z. Dou, Ke Peng, Yajing Wang, Zhenmei Li, Qinqin Wei
Abstract: Power system relay protection (PSRP) is a comprehensive course in electrical engineering undergraduate stage, which has a very strong engineering application. However, due to the influence of many factors, such as the power system security, high experimental cost, limited course hours, insufficient open conditions, and so on, traditional experimental teaching combined with hardware is difficult to meet the needs of students in various scenarios anytime and anywhere. Therefore, a low-cost virtual flexible simulation experiment teaching platform (VFSETP) is developed. The platform uses Simulink to build the simulation model of power system primary system and uses graphical user interface (GUI) to design the human-computer interaction interface. Through the communication between GUI and Simulink model, the protection experiments in various scenarios are successfully simulated. The VFSETP has many advantages such as simple interface, good visualization effect, and simple operation. The teachers can easily use it for classroom demonstration, and the students can use it for verification, analysis, expansion, and exploration of experiments in a variety of application scenarios without relying on the laboratory environment. This experimental mode is very conducive to the understanding of knowledge and the cultivation of practical innovation ability. The results of the student survey show that the design method and application mode of the platform can provide a reference for similar courses.
摘要:电力系统继电保护(PSRP)是电气工程本科阶段的一门综合性课程,具有很强的工程应用性。然而,由于电力系统安全、实验成本高、课时有限、开放条件不足等诸多因素的影响,传统的结合硬件的实验教学难以满足学生随时随地各种场景的需求。为此,开发了一种低成本的虚拟柔性仿真实验教学平台。该平台采用Simulink建立电力系统主系统仿真模型,采用图形用户界面(GUI)设计人机交互界面。通过GUI和Simulink模型之间的通信,成功地模拟了各种场景下的保护实验。VFSETP具有界面简单、可视化效果好、操作简单等优点。教师可以方便地使用它进行课堂演示,学生可以使用它在各种应用场景下进行实验的验证、分析、扩展和探索,而不依赖于实验室环境。这种实验模式非常有利于对知识的理解和实践创新能力的培养。学生调查结果表明,该平台的设计方法和应用模式可以为同类课程提供参考。
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引用次数: 0
A Note on Reinforcement Learning 关于强化学习的说明
Pub Date : 2022-11-16 DOI: 10.37256/rrcs.1220222153
Ying Tan
In the past decade, deep reinforcement learning (DRL) has drawn much attention in theoretical research, meanwhile, it has seen huge success across multiple application areas, such as combinatorial optimization, recommender systems, autonomous driving, intelligent healthcare system and robotics. As one of three basic machine learning paradigms, reinforcement learning concerns with how intelligent agents learn in an interactive environment through trial and error to maximize the total cumulative reward of the agents. Even though many progresses of reinforcement learning have been presented, there are still many challenging research topics due to the complexity of the problems.
在过去的十年中,深度强化学习(DRL)在理论研究中备受关注,同时在组合优化、推荐系统、自动驾驶、智能医疗系统和机器人等多个应用领域取得了巨大的成功。作为三种基本的机器学习范式之一,强化学习关注智能代理如何在交互式环境中通过试错学习以最大化代理的总累积奖励。尽管强化学习已经取得了许多进展,但由于问题的复杂性,仍然存在许多具有挑战性的研究课题。
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引用次数: 0
Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme 三维非线性平流扩散方程的准变网格高分辨率隐式压缩格式数字模拟
Pub Date : 2022-06-21 DOI: 10.37256/rrcs.1120211466
Navnit Jha, P. Lin
A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.
本文给出了求解三维二阶非线性抛物型偏微分方程的一种带拟变量网格的两级隐式紧化公式。新的19点紧化方案在可变网格步长和均匀间隔网格点上具有空间和时间上的四阶和二阶精度。我们还开发了一种算子分裂技术来实现交替方向隐式(ADI)方案,用于计算三维平流扩散方程。Thomas算法在最小的计算时间内计算由ADI步骤产生的每个三对角矩阵。算子分裂形式是无条件稳定的。由于空间网格参数根据解值的行为调整网格位置,因此以较低的计算和存储成本实现了精度的提高。将新方法成功地应用于Navier-Stokes方程、平流-扩散方程和Burger方程的计算实例,证实了新高阶隐式紧化格式的有序性、准确性和鲁棒性。本文的主要工作重点是在拟变量网格网络上得到了一种四阶格式,并与同类的均匀网格高阶紧凑格式相比具有优越性。
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引用次数: 2
Learning Pinball TWSVM efficiently using Privileged Information and their applications 利用特权信息高效学习弹球TWSVM及其应用
Pub Date : 2022-06-16 DOI: 10.37256/rrcs.1120211325
R. Rastogi, Aman Pal, Suresh Chandra
In any learning framework, an expert knowledge always plays a crucial role. But, in the field of machine learning, the knowledge offered by an expert is rarely used. Moreover, machine learning algorithms (SVM based) generally use hinge loss function which is sensitive towards the noise. Thus, in order to get the advantage from an expert knowledge and to reduce the sensitivity towards the noise, in this paper, we propose a fast and novel Twin Support Vector Machine classifier based on privileged information with pinball loss function which has been termed as Pin-TWSVMPI where expert's knowledge is in the form of privileged information. The proposed Pin-TWSVMPI incorporates privileged information by using correcting function so as to obtain two nonparallel decision hyperplanes. Further, in order to make computations more efficient and fast, we use Sequential Minimal Optimization (SMO) technique for obtaining the classifier and have also shown its application for Pedestrian detection and Handwritten digit recognition. Further, for UCI datasets, we first implement a procedure which extracts privileged information from the features of the dataset which are then further utilized by Pin-TWSVMPI to which lead to enhancement in classification accuracy with comparatively lesser computational time.
在任何学习框架中,专业知识总是起着至关重要的作用。但是,在机器学习领域,专家提供的知识很少被使用。此外,机器学习算法(基于支持向量机)通常使用对噪声敏感的铰链损失函数。因此,为了充分利用专家知识的优势,降低对噪声的敏感性,本文提出了一种基于特权信息的双支持向量机分类器,该分类器采用弹球损失函数,将专家知识以特权信息的形式表示,称为Pin-TWSVMPI。提出的Pin-TWSVMPI算法利用校正函数将特权信息融合,从而得到两个非平行决策超平面。此外,为了提高计算效率和速度,我们使用顺序最小优化(SMO)技术来获得分类器,并展示了其在行人检测和手写数字识别中的应用。此外,对于UCI数据集,我们首先实现了一个程序,从数据集的特征中提取特权信息,然后由Pin-TWSVMPI进一步利用,从而以相对较少的计算时间提高分类精度。
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引用次数: 1
Multi-label Minimax Probability Machine with Multi-manifold Regularisation 具有多流形正则化的多标签极大极小概率机
Pub Date : 2021-12-30 DOI: 10.37256/rrcs.1120211193
Sambhav Jain, R. Rastogi
Semi-supervised learning i.e., learning from a large number of unlabelled data and exploiting a small percentage of labelled data has attracted centralised attention in recent years. Semi-supervised problem is handled mainly using graph based Laplacian and Hessian regularisation methods. However, neither the Laplacian method which leads to poor generalisation nor the Hessian energy can properly forecast the data points beyond the range of the domain. Thus, in this paper, the Laplacian-Hessian semi-supervised method is proposed, which can both predict the data points and enhance the stability of Hessian regulariser. In this paper, we propose a Laplacian-Hessian Multi-label Minimax Probability Machine, which is Multi-manifold regularisation framework. The proposed classifier requires mean and covariance information; therefore, assumptions related to the class conditional distributions are not required; rather, a upper bound on the misclassification probability of future data is obtained explicitly. Furthermore, the proposed model can effectively utilise the geometric information via a combination of Hessian-Laplacian manifold regularisation. We also show that the proposed method can be kernelised on the basis of a theorem similar to the representer theorem for handling non-linear cases. Extensive experimental comparisons of our proposed method with related multi-label algorithms on well known multi-label datasets demonstrate the validity and comparable performance of our proposed approach.
半监督学习,即从大量未标记数据中学习并利用一小部分标记数据,近年来引起了人们的关注。半监督问题的处理主要采用基于图的拉普拉斯正则化和Hessian正则化方法。然而,广义性差的拉普拉斯方法和黑森能量都不能很好地预测超出域范围的数据点。因此,本文提出了Laplacian-Hessian半监督方法,该方法既能预测数据点,又能提高Hessian正则器的稳定性。本文提出了一种多流形正则化框架——Laplacian-Hessian多标签极大极小概率机。该分类器需要均值和协方差信息;因此,不需要与类条件分布相关的假设;相反,明确地得到了未来数据误分类概率的上界。此外,该模型通过结合Hessian-Laplacian流形正则化,可以有效地利用几何信息。我们还表明,所提出的方法可以基于一个类似于处理非线性情况的表征定理的定理进行核化。在已知的多标签数据集上,我们提出的方法与相关的多标签算法进行了广泛的实验比较,证明了我们提出的方法的有效性和可比较的性能。
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引用次数: 0
Linked List Elimination from Hashing Methods 从哈希方法中消除链表
Pub Date : 2021-11-19 DOI: 10.37256/rrcs.1120211145
Mahmoud Naghibzadeh, B. Naghibzadeh
Hashing has been used for decades in many fields such as encryption, password verification, and pattern search. Hash systems consist mainly of three components: the hash function, the hash table, and the linked lists that are attached to the hash table. One of the major benefits of using a hash function is reduction in the runtime of the hash-based software systems. However, their linked lists are a major source of time consumption. In this paper, an innovative method is proposed to remove all the linked lists attached to the hash table and collect the necessary information in a one-dimensional array. The method can be used to create an index for the human genome. The human genome is the size of a million-page book with no index, and it is difficult to find the needed information. The proposed method transforms list search operations with linear time complexity into array searches with logarithmic time complexity. In a sample problem, finding inversions in genomic sequences, the proposed indexing system is compared with traditional hashing systems with linked lists. It is demonstrated that, in addition to time complexity reduction, the proposed method reduces the space required for the hash system to one half of what is used by linked list based methods.
哈希已经在许多领域使用了几十年,比如加密、密码验证和模式搜索。哈希系统主要由三个部分组成:哈希函数、哈希表和附加在哈希表上的链表。使用散列函数的主要好处之一是减少基于散列的软件系统的运行时。然而,它们的链表是时间消耗的主要来源。本文提出了一种新颖的方法,将哈希表上的链表全部移除,并在一维数组中收集必要的信息。该方法可用于创建人类基因组索引。人类基因组是一本没有索引的百万页的书,很难找到所需的信息。该方法将具有线性时间复杂度的列表搜索操作转换为具有对数时间复杂度的数组搜索操作。在一个寻找基因组序列倒排的示例问题中,将所提出的索引系统与传统的链表哈希系统进行了比较。结果表明,除了降低时间复杂度外,所提出的方法还将哈希系统所需的空间减少到基于链表的方法所使用空间的一半。
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引用次数: 0
A Simple and Efficient Technique to Generate Bounded Solutions for the Generalized Assignment Problem: A Guide for OR Practitioners 广义分配问题有界解的一种简单有效的生成方法:OR实践者指南
Pub Date : 2021-11-01 DOI: 10.37256/rrcs.1120211039
Francis J. Vasko, Anthony Dellinger, Yun Lu, Bryan McNally, Myung Soon Song
The generalized assignment problem (GAP) is a NP-hard problem that has a large and varied number of important applications in business and industry. Approximate solution approaches for the GAP do not require excessive computation time, but typically there are no guarantees on solution quality. In this article, a methodology called the simple sequential increasing tolerance (SSIT) matheuristic that iteratively uses any general-purpose integer programming software is discussed. This methodology uses a sequence of increasing tolerances in conjunction with optimization software to generate a solution that is guaranteed to be within a specified percentage of the optimum in a short time. SSIT requires no problem-specific coding and can be used with any commercial optimization software to generate bounded solutions in a timely manner. Empirically, SSIT is tested on 51 GAP instances (24 medium and 27 large) in the literature. The performance of CPLEX versus Gurobi on these 51 GAP test instances is also statistically analyzed.
广义分配问题(GAP)是一类np困难问题,在商业和工业中有着广泛而多样的重要应用。GAP的近似解方法不需要过多的计算时间,但通常不能保证解的质量。在本文中,讨论了一种称为简单顺序递增容差(SSIT)数学的方法,它迭代地使用任何通用的整数编程软件。该方法使用一系列不断增加的公差,并结合优化软件来生成解决方案,保证在短时间内达到最优的指定百分比。SSIT不需要特定于问题的编码,可以与任何商业优化软件一起使用,以及时生成有界的解决方案。在经验上,SSIT在51个GAP实例(24个中型和27个大型)上进行了测试。CPLEX与Gurobi在这51个GAP测试实例上的性能也进行了统计分析。
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引用次数: 4
Hybridization of Convolutional Neural Networks with Wavelet Architecture for COVID-19 Detection 基于小波结构的卷积神经网络杂交检测新冠肺炎
Pub Date : 2021-10-27 DOI: 10.37256/rrcs.1120211112
R. Manavalan, S. Priya
Coronavirus disease is an infectious disease caused by perilous viruses. According to the World Health Organization (WHO) updated reports, the number of people infected with Coronavirus-2019 (COVID-19) and death rate rises rapidly every day. The limited number of COVID-19 test kits available in hospitals could not meet with the demand of daily growing cases. The ability to diagnose COVID-19 suspected cases accurately and quickly is essential for prompt quarantine and medical treatment. The goal of this research is to implement a novel system called Convolution Neural Network with Wavelet Transformation (CNN-WT) to assist radiologists for the automatic COVID-19 detection through chest X-ray images to counter the outbreak of SARS-CoV-2. The proposed CNN-WT method employing X-ray imaging has the potential to be very beneficial for the medical sector in dealing with mass testing circumstances in pandemics like COVID-19. The dataset used for experimentation consists of 219 chest X-Ray images with confirmed COVID-19 cases and 219 images of healthy people. The suggested model's efficacy is evaluated using 5-fold cross-validation. The CNN-WT model yielded an average accuracy of 98.63%, which is 1.36% higher than the general CNN architecture.
冠状病毒病是一种由危险病毒引起的传染病。根据世界卫生组织(世卫组织)的最新报告,2019冠状病毒感染人数和死亡率每天都在迅速上升。医院现有的新冠病毒检测试剂盒数量有限,无法满足日益增长的病例需求。准确、快速诊断新冠肺炎疑似病例的能力对于及时隔离和医疗至关重要。本研究的目标是实现一种新颖的小波变换卷积神经网络(CNN-WT)系统,帮助放射科医生通过胸部x线图像自动检测COVID-19,以应对SARS-CoV-2的爆发。采用x射线成像的CNN-WT方法对于医疗部门处理COVID-19等流行病的大规模测试环境非常有益。用于实验的数据集包括219张确诊COVID-19病例的胸部x射线图像和219张健康人的图像。采用5倍交叉验证评估建议模型的有效性。CNN- wt模型的平均准确率为98.63%,比一般CNN架构提高了1.36%。
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引用次数: 0
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