Chaos Solitons & Fractals最新文献_第7页

Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model 非线性动态振动行为模型的积分谐振负导数反馈抑制控制策略

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-25 DOI: 10.1016/j.chaos.2024.115686

H.S. Bauomy , A.T. EL-Sayed , F.T. El-Bahrawy

One of the major problems in robotics research has been developing an actuator system for extremely dynamic-legged robots. High torque density and the capacity to control dynamic physical interactions are two design requirements for high-speed locomotion that are challenging for conventional actuators used in manufacturing applications to meet. To address this system and apply the desired control to reach the best stability position, the robot's foot was simulated with the Van der Pol equations, applied the required control, and studied that application. This work describes the actions of a new novel control mechanism known as the Integral Resonant Negative Derivative Feedback (IRNDF) controller, which reduces the vibration response of a double Van der Pol oscillator subjected to external excitations. This unique controller combines integral resonant control (IRC) and negative derivative feedback (NDF) controllers to provide a new controller effect for double Van der Pol oscillators. The multiple scale perturbation technique (MSPT) has been applied to solve the controlled system analytically. The MATLAB and MAPLE programs have been used to complete and clarify all of the numerical talks. The frequency response curves have been used to study the impact that altering the parameter values had on the amplitude. The controlled system vibration amplitude is governed by frequency-response equations (FREs), which have been constructed. In the vibration system, the IRC, NDF, and IRNDF controllers were compared to see which one was the best. Numerical results show that the unique IRNDF controller is the best at reducing oscillations and decreasing amplitude values. The effects of the effective parameters on the controlled system have been identified. The frequency-response equation that was derived has been used to plot the various response curves for the framework that show the stable and unstable zones when the controller is off and on. Lastly, excellent agreement between the derived numerical findings and the analytical ones was observed. Lastly, utilizing time histories and response curves to compare analytical and numerical solutions was fascinating and significant.

机器人研究中的一个主要问题是为极动态的足式机器人开发致动器系统。高扭矩密度和控制动态物理交互的能力是高速运动的两个设计要求，而制造应用中使用的传统致动器很难满足这两个要求。为了解决这一系统问题，并应用所需的控制来达到最佳稳定位置，我们用范德尔波尔方程对机器人的脚进行了模拟，应用了所需的控制，并对该应用进行了研究。这项工作描述了一种称为积分谐振负偏差反馈（IRNDF）控制器的新型控制机制的作用，它可以降低双范德波尔振荡器在外部激励下的振动响应。这种独特的控制器结合了积分谐振控制（IRC）和负导数反馈（NDF）控制器，为双范德波尔振荡器提供了一种新的控制器效应。多尺度扰动技术（MSPT）被用于对控制系统进行分析求解。MATLAB 和 MAPLE 程序用于完成和阐明所有的数值讨论。频率响应曲线用于研究改变参数值对振幅的影响。受控系统的振动振幅受频率响应方程（FRE）控制，该方程已经构建。在振动系统中，对 IRC、NDF 和 IRNDF 控制器进行了比较，以确定哪种控制器最好。数值结果表明，独特的 IRNDF 控制器在减少振荡和降低振幅值方面效果最佳。有效参数对控制系统的影响已经确定。得出的频率响应方程用于绘制框架的各种响应曲线，显示控制器关闭和开启时的稳定区和不稳定区。最后，观察到推导出的数值结果与分析结果非常一致。最后，利用时间历程和响应曲线来比较分析和数值解决方案是非常有意义的。

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引用次数: 0

Data driven cost-sensitive boosted tree for interpretable banking systemic risk prediction 数据驱动的成本敏感提升树，用于可解释的银行系统性风险预测

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-25 DOI: 10.1016/j.chaos.2024.115664

Meng Xia , Zhijie Wang , Wanan Liu

Systemic risk (SR) in the banking sector poses a significant threat to both the financial system and the real economy. Its inherent characteristics of nonlinearity, non-equilibrium, and interconnectedness make it challenging to analyze using conventional statistical methods. In this paper, a cost-sensitive gradient boosting tree algorithm, FLXGBoost, is proposed for predicting SR. FLXGBoost considers the boosted tree, XGBoost as the base framework, boosting trees as the fundamental framework, guaranteeing the robustness of SR prediction. Additionally, to tackle the challenge of extreme data imbalance prevalent in SR prediction tasks, a cost-aware loss function, focal loss, is embedded into the boosted tree to enable FLXGBoost a risk-aware fashion. Moreover, a tree-derived interpretable algorithm SHAP is incorporated into this cost-sensitive solution, making FLXGBoost an accurate and interpretable risk-aware model. Experimental results on a financial risk prediction dataset pertaining to banking SR evince the capacity of FLXGBoost to significantly reduce the misclassification rate of risk banks, thereby mitigating substantial losses attributed to erroneous predictions of risky scenarios. Moreover, compared with classical imbalanced machine learning-based SR prediction approaches, the diverse evaluation metrics of FLXGBoost show that it is a competitive solution for accurate SR prediction. Besides, the explanatory analysis further demonstrates that FLXGBoost is a promising solution to address the issue of biased predictions in imbalanced banking SR in the interpretation perspective.

银行业的系统性风险（SR）对金融体系和实体经济都构成了重大威胁。其固有的非线性、非平衡性和相互关联性等特点使其很难用传统的统计方法进行分析。本文提出了一种成本敏感梯度提升树算法 FLXGBoost，用于预测 SR。FLXGBoost 以提升树 XGBoost 为基础框架，以提升树为基本框架，保证了 SR 预测的鲁棒性。此外，为了应对 SR 预测任务中普遍存在的数据极度不平衡的挑战，在助推树中嵌入了成本感知损失函数--焦点损失，使 FLXGBoost 成为一种风险感知方式。此外，这种成本敏感型解决方案中还包含了一种由树衍生的可解释算法 SHAP，从而使 FLXGBoost 成为一种准确且可解释的风险感知模型。在银行 SR 金融风险预测数据集上的实验结果表明，FLXGBoost 能够显著降低风险银行的误分类率，从而减少因错误预测风险情况而造成的重大损失。此外，与基于不平衡机器学习的传统 SR 预测方法相比，FLXGBoost 的各种评价指标表明，它是一种具有竞争力的准确 SR 预测解决方案。此外，解释性分析进一步表明，从解释角度来看，FLXGBoost 是解决不平衡银行 SR 中偏差预测问题的一种有前途的解决方案。

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引用次数: 0

Dynamic characteristics and conversion process of solitons in a Mamyshev oscillator 马迈雪夫振荡器中孤子的动态特性和转换过程

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-24 DOI: 10.1016/j.chaos.2024.115667

Yuhe Dong, Xingliang Li, Mengmeng Han, Shumin Zhang, Chaoran Wang

The Mamyshev oscillator (MO) can produce not only a single pulse (SP) but also multi-pulses (MPs). However, most of the research focuses on increasing the output pulse energy and reducing the pulse width, and only some studies reveal the characteristics of MPs output. More research is needed on achieving the conversion from MPs to SP by adjusting the oscillator parameters and determining what intermediate states will be experienced in the conversion process. Here, we study the dynamic characteristics of soliton and the conversion process between different output states of ultrafast MO. By adjusting the gain saturation energy and filter interval, we obtain the relationship between the number of MPs outputs and the oscillator parameters and observe the intermediate process from MPs pulsation to SP. The research results reveal the dynamic characteristics of non-equilibrium optical solitons, assisting in optimizing MO design.

马梅雪夫振荡器（MO）不仅能产生单脉冲（SP），还能产生多脉冲（MP）。然而，大多数研究都集中在增加输出脉冲能量和减小脉冲宽度上，只有一些研究揭示了 MPs 输出的特性。在通过调整振荡器参数实现从 MP 到 SP 的转换以及确定转换过程中会出现哪些中间状态方面，还需要进行更多的研究。在此，我们研究了孤子的动态特性以及超快 MO 不同输出状态之间的转换过程。通过调整增益饱和能量和滤波器间隔，我们得到了 MPs 输出数量与振荡器参数之间的关系，并观察了从 MPs 脉动到 SP 的中间过程。研究成果揭示了非平衡光孤子的动态特性，有助于优化 MO 的设计。

引用次数: 0

Study on a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions 研究非线性物理学中的（3+1）维 B 型 Kadomtsev-Petviashvili 方程：多重孤子解、块解和呼吸波解

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115668

Abdul-Majid Wazwaz

In this work, we study an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equations that appear in many nonlinear physics applications. We show that this extended equation retains its complete integrability via Painlevé analysis. We explore multiple soliton solutions by using the Hirota bilinear method. Moreover, we derive lump solutions where two numerical examples are tested. Breather wave solutions were also explored by using a variety of distinct schemes. We also determine other traveling wave solutions, rational solutions, periodic solutions, exponential solutions, ratio of trigonometric or hyperbolic functions, and others.

在这项工作中，我们研究了在许多非线性物理应用中出现的扩展 (3+1)-dimensional B 型 Kadomtsev-Petviashvili (BKP) 方程。我们通过 Painlevé 分析表明，这个扩展方程保持了其完全的可整性。我们利用 Hirota 双线性方法探索了多重孤子解。此外，我们还推导出了块解，并对两个数值实例进行了测试。我们还使用各种不同的方案探索了呼吸波解决方案。我们还确定了其他行波解、有理解、周期解、指数解、三角函数或双曲函数的比值等。

引用次数: 0

Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations 基于对称组的域分解，增强物理信息神经网络求解偏微分方程的能力

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115658

Ye Liu , Jie-Ying Li , Li-Sheng Zhang , Lei-Lei Guo , Zhi-Yong Zhang

Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain, but the lack of efficient tools for dealing with the interfaces between two adjacent sub-domains heavily hinders the training effects, even leads to the discontinuity of the learned solutions. In this paper, we propose a symmetry group based domain decomposition strategy to enhance the PINN for solving the forward and inverse problems of the PDEs possessing a Lie symmetry group. Specifically, for the forward problem, we first deploy the symmetry group to generate the dividing-lines having known solution information which can be adjusted flexibly and are used to divide the whole training domain into a finite number of non-overlapping sub-domains, then utilize the PINN and the symmetry-enhanced PINN methods to learn the solutions in each sub-domain and finally stitch them to the overall solution of PDEs. For the inverse problem, we first utilize the symmetry group acting on the data of the initial and boundary conditions to generate labeled data in the interior domain of PDEs and then find the undetermined parameters as well as the solution by only training the neural networks in a sub-domain. Consequently, the proposed method can predict high-accuracy solutions of PDEs which are failed by the vanilla PINN in the whole domain and the extended PINN in the same sub-domain. Numerical results of the Korteweg–de Vries equation with a translation symmetry and the nonlinear viscous fluid equation with a scaling symmetry show that the accuracies of the learned solutions are improved largely.

物理信息神经网络（PINN）难以准确高效地求解整个域中的偏微分方程（PDE），但由于缺乏有效工具来处理相邻两个子域之间的界面，严重影响了训练效果，甚至导致所学解的不连续性，域分解为解决这一困境提供了有效途径。本文提出了一种基于对称组的域分解策略，以增强 PINN 解决具有 Lie 对称组的 PDE 正演和反演问题的能力。具体来说，对于正向问题，我们首先利用对称组生成具有已知解信息的分割线，这些分割线可以灵活调整，用于将整个训练域划分为有限个不重叠的子域，然后利用 PINN 和对称增强 PINN 方法学习每个子域中的解，最后将其拼接到 PDE 的整体解中。对于逆问题，我们首先利用对称组对初始条件和边界条件数据的作用，在 PDE 的内部域生成标注数据，然后仅在一个子域中训练神经网络，就能找到未确定的参数和解。因此，所提出的方法可以高精度地预测虚PINN在整个域和扩展PINN在同一子域中失效的PDE解。具有平移对称性的 Korteweg-de Vries 方程和具有缩放对称性的非线性粘性流体方程的数值结果表明，学习到的解的精确度有了很大提高。

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引用次数: 0

Chaos and regularities in cavity assisted two-channel nonlinear coupler 空腔辅助双通道非线性耦合器中的混沌与规律性

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115650

Firoz Chogle , Seba Sara Varghese , Abdel-Baset M.A. Ibrahim , Awadhesh Prasad , Hichem Eleuch

This paper presents a study of the dynamical behavior in a cavity-assisted two-channel Kerr nonlinear directional coupler. Applying a deterministic periodic laser pump to a two-channel coupled system led to a range of dynamic behaviors, encompassing periodicity, quasiperiodicity, chaoticity and hyperchaoticity. This is confirmed by the exploration of the Lyapunov exponents, Poincaré sections and bifurcation diagrams for resonance and low cavity detuning. For low cavity detuning, chaos arises when the laser pump’s amplitude is large. This is due to higher interactions between photons and the cavity, resulting in more photons inside and higher nonlinearity. On the other hand, the reduced interactions in high cavity detuning displayed regular behavior which is explained qualitatively.

本文研究了腔体辅助双通道克尔非线性定向耦合器的动态行为。将确定性周期激光泵浦应用于双通道耦合系统会产生一系列动态行为，包括周期性、准周期性、混沌性和超混沌性。对共振和低腔失谐的 Lyapunov 指数、Poincaré 截面和分岔图的研究证实了这一点。对于低腔失谐，当激光泵浦的振幅较大时就会出现混乱。这是由于光子与腔体之间的相互作用增强，导致腔内光子增多，非线性增强。另一方面，在高腔失谐情况下，相互作用的减少显示出有规律的行为，这一点可以得到定性的解释。

引用次数: 0

Application of hybrid strategies of complex network attack and defense games 复杂网络攻防博弈混合策略的应用

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115662

Zhe Li, Jin Liu, Jiaqi Ren, Yibo Dong, Weili Li

Critical infrastructure networks serve as the backbone of modern society’s operations, and the application of game theory to safeguard these networks against deliberate attacks under resource constraints is of paramount importance. Regrettably, the existing body of research on hybrid attack and defense strategies for nodes and edges is notably scarce, despite the ubiquity of such strategies in practical contexts. Current understanding regarding the establishment of a cost constraint model within the framework of hybrid attack and defense strategies, the strategic inclinations of both adversarial and defensive parties under varying cost constraint coefficients, and the influence of resource allocation ratios on equilibrium outcomes remains limited. Consequently, this study constructs a game-theoretic model for the engagement of critical infrastructure networks under non-uniform cost constraints, incorporating hybrid attack and defense strategies for nodes and edges, and conducts an equilibrium analysis across a range of cost constraint coefficients and resource allocation ratios. The findings reveal that when resource availability is limited, both attackers and defenders are inclined towards a strategy of concentrated resource allocation; in contrast, under most circumstances, defenders exhibit a preference for an equitable distribution of resources.

关键基础设施网络是现代社会运行的支柱，应用博弈论来保护这些网络免受资源限制下的蓄意攻击至关重要。令人遗憾的是，尽管节点和边缘的混合攻击和防御策略在实际环境中无处不在，但现有的相关研究却十分匮乏。目前，人们对在混合攻防策略框架内建立成本约束模型、不同成本约束系数下敌对双方和防御方的策略倾向以及资源分配比率对均衡结果的影响等方面的了解仍然有限。因此，本研究构建了非均匀成本约束下关键基础设施网络交战的博弈论模型，纳入了节点和边的混合攻防策略，并对一系列成本约束系数和资源分配比率进行了均衡分析。研究结果表明，当资源可用性有限时，攻击方和防御方都倾向于集中分配资源的策略；相反，在大多数情况下，防御方都表现出公平分配资源的偏好。

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引用次数: 0

Particle swarm optimization with historical return decay enhances cooperation in public goods games with investment risks 带有历史收益衰减的粒子群优化技术可增强具有投资风险的公共产品博弈中的合作

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115665

Hongwei Kang , Xin Li , Yong Shen, Xingping Sun, Qingyi Chen

In the realm of spatial public goods games, heterogeneous investment has emerged as a potent mechanism to enhance cooperative behavior. Savvy investors dynamically adjust their investment levels to optimize returns based on environmental conditions and personal circumstances. This study delves into the evolution of cooperation within a spatial public goods game framework, characterized by heterogeneous investment and associated risks, conducted on a square lattice. We introduce the investors (I) with heterogeneous investment, who updates his investment amount according to the current environment of the game and his own historical experience. We introduce a particle swarm optimization algorithm with decaying historical returns to fine-tune the investment levels of investors. Furthermore, a risk mechanism inspired by the ultimatum game is integrated into the model. This paper investigates the impact of the risk threshold

θ

on cooperative behavior and examines the influence of the risk decay factor

α

on cooperation. Additionally, it analyzes the investment behavior of investors in scenarios where two types of investors coexist. Finally, this study explores the effects of the historical best payoff decay factor

β

and the self-learning rate

c_{1}

on cooperative behavior. This research contributes to a nuanced understanding of heterogeneous investment behaviors in public goods games under specified risk mechanisms, providing novel insights into the intricate dynamics of cooperation in complex systems.

在空间公共产品博弈领域，异质投资已成为加强合作行为的有效机制。精明的投资者会根据环境条件和个人情况动态调整投资水平，以优化收益。本研究深入探讨了空间公共物品博弈框架下的合作演化，该博弈以异质投资和相关风险为特征，在正方形网格上进行。我们引入了异质投资的投资者（I），他根据当前博弈环境和自己的历史经验更新自己的投资额。我们引入了一种粒子群优化算法，利用衰减历史收益来微调投资者的投资水平。此外，受最后通牒博弈启发的风险机制也被整合到了模型中。本文研究了风险阈值 θ 对合作行为的影响，并探讨了风险衰减因子 α 对合作的影响。此外，本文还分析了在两类投资者并存的情况下投资者的投资行为。最后，本研究探讨了历史最佳回报衰减因子 β 和自学率 c1 对合作行为的影响。这项研究有助于深入理解特定风险机制下公共物品博弈中的异质投资行为，为复杂系统中错综复杂的合作动态提供了新的见解。

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引用次数: 0

Identifying influential nodes in social networks via improved Laplacian centrality 通过改进的拉普拉斯中心性识别社交网络中的有影响力节点

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115675

Xiaoyu Zhu , Rongxia Hao

Identifying influential nodes in social networks has significant applications in terms of social analysis and information dissemination. How to capture the crucial features of influential nodes without increasing the computational complexity is an urgent issue to be solved in the context of big data. Laplacian centrality (LC) measures nodal influence by computing nodes' degree, making it extremely low complexity. However, there is still significant room for improvement. Consequently, we propose the improved Laplacian centrality (ILC) to identify influential nodes based on the concept of self-consistent. Identifying results on 9 real networks prove that ILC is superior to LC and other 6 classical measures in terms of ranking accuracy, top-k nodes identification and discrimination capability. Moreover, the computational complexity of ILC has not significantly increased compared to LC, and remains the linear order of magnitude O(m). Additionally, ILC has excellent robustness and universality such that there is no need to adjust parameters according to different network structures.

识别社交网络中的有影响力节点在社会分析和信息传播方面有着重要的应用。如何在不增加计算复杂度的情况下捕捉有影响力节点的关键特征，是大数据背景下亟待解决的问题。拉普拉斯中心度（Laplacian centrality，LC）通过计算节点的度数来衡量节点的影响力，因此复杂度极低。然而，该方法仍有很大的改进空间。因此，我们提出了改进的拉普拉斯中心度（ILC），基于自洽概念来识别有影响力的节点。9 个真实网络的识别结果证明，ILC 在排序准确性、前 k 节点识别和判别能力方面都优于 LC 和其他 6 种经典度量方法。此外，与 LC 相比，ILC 的计算复杂度并没有显著增加，仍然是线性数量级 O(m)。此外，ILC 还具有出色的鲁棒性和通用性，无需根据不同的网络结构调整参数。

引用次数: 0

Improving resilience of cyber physical power networks against Time Synchronization Attacks (TSAs) using deep learning and spline interpolation with real-time validation 利用深度学习和带实时验证的样条插值提高网络物理电力网络抵御时间同步攻击（TSA）的能力

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-22 DOI: 10.1016/j.chaos.2024.115647

Soma Bhattacharya, Ebha Koley, Subhojit Ghosh

The integration of high-speed communication networks and synchrophasors into smart grids has significantly improved real-time monitoring and control accuracy. However, the increased reliance on communication infrastructure has also heightened the vulnerability of the power networks to cyber intrusions. Synchronized phasor data and GPS time-stamping used by Phasor Measurement Units (PMUs), make them prime targets for cyber intrusions. Among the different types of intrusions in smart grids, Time Synchronization Attacks (TSA), because of their impact and easier execution, are widely employed by intruders to disrupt grid operations. Such attacks aim at spoofing GPS signals, thereby altering voltage and current phasor information across the network. The same leads to malfunction of the operations executed at the control center. The present work aims to develop a secured and resilient mechanism against TSAs in smart grids. In this regard, a two-stage mechanism based on deep learning and spline interpolation is proposed. The first stage employs an LSTM-based classifier to detect TSAs in the cyber layer. Post-TSA detection, the second stage uses spline interpolation to filter out malicious data. The filtering allows for the restoration of the actual pre-TSA data acquired from PMUs. The proposed TSA detection and correction scheme has been validated extensively across various TSA scenarios on IEEE 9, 14, and 57 bus systems. Majority of the reported works of TSA detection have been validated using offline numerical simulations, which have limitations in replicating practical TSA dynamics. To address the same, the proposed scheme has been validated using a real-time testbed comprising of a digital simulator, real PMU, GPS receiver, and a data acquisition module with a communication interface.

将高速通信网络和同步传感器集成到智能电网中，大大提高了实时监测和控制精度。然而，对通信基础设施的依赖性增加也加剧了电力网络面对网络入侵的脆弱性。相位测量单元 (PMU) 使用的同步相位数据和 GPS 时间戳使其成为网络入侵的主要目标。在智能电网的各种入侵类型中，时间同步攻击（TSA）因其影响大、执行容易而被入侵者广泛用来破坏电网运行。此类攻击旨在欺骗 GPS 信号，从而改变整个网络的电压和电流相位信息。这同样会导致控制中心执行的操作出现故障。本研究旨在开发一种针对智能电网中的 TSA 的安全且有弹性的机制。为此，我们提出了一种基于深度学习和样条插值的两阶段机制。第一阶段采用基于 LSTM 的分类器来检测网络层中的 TSA。检测出 TSA 后，第二阶段使用样条插值法过滤恶意数据。通过过滤，可以恢复从 PMU 获取的 TSA 前的实际数据。提议的 TSA 检测和校正方案已在 IEEE 9、14 和 57 总线系统的各种 TSA 场景中得到广泛验证。大多数 TSA 检测报告都是通过离线数值模拟进行验证的，这在复制实际 TSA 动态方面存在局限性。为了解决这一问题，我们使用实时测试平台对所提出的方案进行了验证，该测试平台由数字模拟器、真实 PMU、GPS 接收器和带通信接口的数据采集模块组成。

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引用次数: 0