Reliability Engineering & System Safety最新文献_第6页

An analysis and reliability-based optimization design method of trajectory accuracy for industrial robots considering parametric uncertainties 考虑参数不确定性的工业机器人轨迹精度分析和基于可靠性的优化设计方法

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-11-04 DOI: 10.1016/j.ress.2024.110626

Chenxin Su , Bo Li , Wei Zhang , Wei Tian , Wenhe Liao

To address the challenges of poor trajectory accuracy in industrial robots, which has emerged as a technological bottleneck hindering further robots’ applications in high-precision manufacturing industries, this paper proposes a method for the analysis and reliability-based optimization design for industrial robots’ trajectory accuracy considering parametric uncertainties. Firstly, the dynamic equation of an articulated industrial robot with six degrees of freedom is derived, incorporating the Stribeck joint friction model, followed by the uncertain parameter identification of this dynamic model. Subsequently, an uncertainty simulation system for the robot is established based on the constructed dynamic model and the sensitivity of system uncertain parameters to the robot trajectory accuracy is analyzed, where 10 key parameters are obtained among 54 uncertain parameters. Finally, a reliability-based multi-objective optimization design methodology is proposed synthesizing the robot trajectory accuracy, manufacturing cost, and quality loss, to achieve tolerance design of the robot's parameters, and enables minimizing costs and quality losses while ensuring the robot's trajectory accuracy reliability. The performance and practicality of the proposed method were validated using a six-degree-of-freedom rotary joint serial industrial robot as an example.

针对工业机器人轨迹精度差这一阻碍机器人在高精密制造业进一步应用的技术瓶颈，本文提出了一种考虑参数不确定性的工业机器人轨迹精度分析和基于可靠性的优化设计方法。首先，结合 Stribeck 关节摩擦模型，推导出具有六个自由度的关节型工业机器人的动态方程，然后对该动态模型进行不确定参数识别。随后，基于构建的动态模型建立了机器人不确定性仿真系统，分析了系统不确定性参数对机器人轨迹精度的敏感性，在 54 个不确定性参数中得到了 10 个关键参数。最后，综合机器人轨迹精度、制造成本和质量损失，提出了基于可靠性的多目标优化设计方法，实现了机器人参数的容差设计，在保证机器人轨迹精度可靠性的同时，使成本和质量损失最小化。以六自由度旋转关节串行工业机器人为例，验证了所提方法的性能和实用性。

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引用次数: 0

The Spectral Representation Method: A framework for simulation of stochastic processes, fields, and waves 频谱表示法：模拟随机过程、场和波的框架

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-11-02 DOI: 10.1016/j.ress.2024.110522

George Deodatis , Michael Shields

The Spectral Representation Method (SRM) was developed in the 1970s to simulate Gaussian stochastic processes and fields from a Fourier series expansion according to the Spectral Representation Theorem. Since those early developments, the SRM has continuously evolved into a comprehensive framework for the simulation of stochastic processes, fields, and waves with a rigorous theoretical foundation. Its major advantages are conceptual simplicity and computational efficiency. In the 1990s, much of the theory for simulation of Gaussian stochastic processes, fields, and waves was firmly established and early methods for simulation of non-Gaussian processes, fields, and waves were introduced. In the 2000s and 2010s, methods that coupled the SRM with Translation Process Theory were improved to enable efficient and accurate simulations of stochastic processes, fields, and waves with strongly non-Gaussian marginal probability distributions. More recently, the SRM was extended for higher-order non-Gaussian processes, fields, and waves by extending the Fourier stochastic expansion to include non-linear wave interactions derived from higher-order spectra. This paper reviews the key theoretical developments related with the SRM and provides the relevant algorithms necessary for its practical implementation for the simulation of stochastic processes, fields, and waves that can be either stationary or non-stationary, homogeneous or non-homogeneous, one-dimensional or multi-dimensional, scalar or multi-variate, Gaussian or non-Gaussian, or any combination thereof. The paper concludes with some brief remarks addressing the open research challenges in SRM-based theory and simulations.

频谱表示法（SRM）开发于 20 世纪 70 年代，用于根据频谱表示定理通过傅里叶级数展开模拟高斯随机过程和场。自早期开发以来，SRM 不断发展成为模拟随机过程、场和波的综合框架，并具有严格的理论基础。其主要优势在于概念简单和计算高效。20 世纪 90 年代，模拟高斯随机过程、场和波的大部分理论已经牢固确立，并引入了模拟非高斯过程、场和波的早期方法。在 2000 年代和 2010 年代，将 SRM 与平移过程理论相结合的方法得到了改进，从而能够高效、准确地模拟具有强非高斯边际概率分布的随机过程、场和波。最近，通过扩展傅立叶随机扩展，SRM 被扩展用于高阶非高斯过程、场和波，以包括从高阶频谱衍生的非线性波相互作用。本文回顾了与 SRM 相关的主要理论发展，并提供了实际应用 SRM 仿真随机过程、场和波所需的相关算法，这些过程、场和波可以是静态或非静态的，均质或非均质的，一维或多维的，标量或多变量的，高斯或非高斯的，或它们的任意组合。最后，本文简要论述了基于 SRM 的理论和模拟方面尚待解决的研究难题。

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引用次数: 0

Knowledge-informed FIR-based cross-category filtering framework for interpretable machinery fault diagnosis under small samples 基于知识的 FIR 跨类别滤波框架，用于小样本下可解释的机械故障诊断

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-31 DOI: 10.1016/j.ress.2024.110610

Rui Liu , Xiaoxi Ding , Shenglan Liu , Hebin Zheng , Yuanyaun Xu , Yimin Shao

Relying on sufficient training data, the existing fault diagnosis methods rarely focus on the methodological interpretability and the data scarcity in real industrial scenarios simultaneously. Motivated by this issue, we deeply reexamined the intrinsic characteristics of fault signals and the guiding significance of classical signal-processing methods for feature enhancement. From the perspective of multiscale modes, this study tailors multiple learnable knowledge-informed finite impulse response (FIR) filtering kernels to extract sensitive modes for explainable feature enhancement. On this foundation, a knowledge-informed FIR-based cross-category filtering (FIR-CCF) framework is further proposed for interpretable small-sample fault diagnosis. With the consideration of the mode complexity, a cross-category filtering strategy is explored to further enhance feature expressions for identifying single state. To be special, this strategy divides a multi-class recognition process into multiple two-class recognition task. A multi-task learning is then presented where multiple binary-class base learners (BCBLearners) that consists of a feature extractor and a two-class classifier is established to seek discriminate mode features for each type of state. Eventually, all feature extractors are fixed and a multi-class classifier is established and to fuse all mode features for high-precision multi-class identification via ensemble learning. As a variant of signal-processing-collaborated deep learning frameworks, the FIR-CCF method fully exploits the strengths of signal-processing methods in interpretability and feature extraction. Three experimental cases highlight the superiority and significant improvement of the FIR-CCF framework over other five state-of-the-art diagnosis methods and three ablation models. Specially, extensive visualization is implemented to place in-depth insight into how the FIR-CCF framework works. It can be also foreseen that the signal-processing-collaborated deep learning framework shows enormous potential in interpretable fault diagnosis for knowledge-informed artificial intelligence. Related source codes will be available at: https://github.com/BITS/FIR-CCF-main.

依赖于充足的训练数据，现有的故障诊断方法很少同时关注方法的可解释性和实际工业场景中数据的稀缺性。基于这一问题，我们重新深入研究了故障信号的内在特征以及经典信号处理方法对特征增强的指导意义。本研究从多尺度模式的角度出发，定制了多个可学习的知识信息有限脉冲响应（FIR）滤波核，以提取敏感模式，从而实现可解释的特征增强。在此基础上，进一步提出了基于知识的 FIR 跨类别滤波（FIR-CCF）框架，用于可解释的小样本故障诊断。考虑到模式的复杂性，探索了一种跨类别滤波策略，以进一步增强识别单一状态的特征表达。比较特殊的是，该策略将多类识别过程分为多个两类识别任务。然后提出了一种多任务学习方法，即建立由特征提取器和两类分类器组成的多个二元类基础学习器（BCBLearners），以寻求每类状态的判别模式特征。最后，固定所有特征提取器，建立多类分类器，通过集合学习融合所有模式特征，实现高精度多类识别。作为信号处理协同深度学习框架的一种变体，FIR-CCF 方法充分发挥了信号处理方法在可解释性和特征提取方面的优势。三个实验案例凸显了 FIR-CCF 框架相对于其他五种最先进诊断方法和三种消融模型的优越性和显著改进。特别值得一提的是，为了深入了解 FIR-CCF 框架是如何工作的，我们采用了广泛的可视化方法。可以预见，信号处理-协作深度学习框架在知识型人工智能的可解释故障诊断方面展现出巨大潜力。相关源代码请访问：https://github.com/BITS/FIR-CCF-main。

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引用次数: 0

Physics-informed machine learning for system reliability analysis and design with partially observed information 利用部分观测信息进行系统可靠性分析和设计的物理信息机器学习

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-30 DOI: 10.1016/j.ress.2024.110598

Yanwen Xu , Parth Bansal , Pingfeng Wang , Yumeng Li

Constructing a high-fidelity predictive model is crucial for analyzing complex systems, optimizing system design, and enhancing system reliability. Although Gaussian Process (GP) models are well-known for their capability to quantify uncertainty, they rely heavily on data and necessitate a large representative dataset to establish a high-fidelity predictive model. Physics-informed Machine Learning (PIML) has emerged as a way to integrate prior physics knowledge and machine learning models. However, current PIML methods are generally based on fully observed datasets and mainly suffer from two challenges: (1) effectively utilize partially available information from multiple sources of varying dimensions and fidelity; (2) incorporate physics knowledge while maintaining the mathematical properties of the GP-based model and uncertainty quantification capability of the predictive model. To overcome these limitations, this paper proposes a novel physics-informed machine learning method that incorporates physics prior knowledge and multi-source data by leveraging latent variables through the Bayesian framework. This method effectively utilizes partially available limited information, significantly reduces the need for costly fully observed data, and improves prediction accuracy while maintaining the model property of uncertainty quantification. The developed approach has been demonstrated with two case studies: the vehicle design problem and the battery capacity loss prediction. The case study results demonstrate the effectiveness of the proposed model in complex system design and optimization while propagating uncertainty with limited fully observed data.

构建高保真预测模型对于分析复杂系统、优化系统设计和提高系统可靠性至关重要。尽管高斯过程（GP）模型以其量化不确定性的能力而闻名，但它们在很大程度上依赖于数据，因此需要一个具有代表性的大型数据集来建立高保真预测模型。物理信息机器学习（PIML）作为一种整合先验物理知识和机器学习模型的方法应运而生。然而，目前的 PIML 方法一般基于完全观测数据集，主要面临两个挑战：(1) 有效利用来自不同维度和保真度的多个来源的部分可用信息；(2) 结合物理知识，同时保持基于 GP 的模型的数学特性和预测模型的不确定性量化能力。为了克服这些局限性，本文提出了一种新颖的物理信息机器学习方法，该方法通过贝叶斯框架利用潜在变量，将物理先验知识和多源数据结合起来。该方法有效地利用了部分可用的有限信息，大大减少了对成本高昂的完全观测数据的需求，并在保持不确定性量化模型特性的同时提高了预测精度。所开发的方法通过两个案例研究得到了验证：车辆设计问题和电池容量损失预测。案例研究结果证明了所提出的模型在复杂系统设计和优化中的有效性，同时利用有限的完全观测数据传播不确定性。

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引用次数: 0

Employing the cluster of node cut sets to improve the robustness of the network measured by connectivity 利用节点切割集群来提高以连通性衡量的网络鲁棒性

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-30 DOI: 10.1016/j.ress.2024.110612

Wei Wei, Guobin Sun, Peng Li, Qinghui Zhang

Protection of critical nodes or edges can help defend networks from failures caused by natural disasters or intended attacks. Node protection becomes the only way when edge protection is not possible, where node connectivity is usually used to measure network robustness due to its effectiveness. Although simple, node connectivity-oriented node consolidation optimization is still NP-hard, especially when dealing with large numbers of nodes. To address the problem, by leveraging the mapping between nodes and traversal trees, per-node cluster of node cut sets is used to identify nominee nodes, which are then conditionally consolidated through a extended dual tree-based selection process. Experimental results show that in small graphs with tens of nodes where the optimal algorithm is applicable, an acceleration ratio of more than

1 0^{5}

(at most

1 0^{6}

) is observed at the expense of about 6% extra cost. In large graphs with millions of nodes, the proposed algorithm can help promote node connectivity of more than 99.9% of node pairs, which is far better than commonly used heuristics. Its inherent ready-for-paralleling capability paves the way for more speedups.

保护关键节点或边缘有助于保护网络免受自然灾害或蓄意攻击造成的故障。当边缘保护无法实现时，节点保护就成了唯一的办法，而节点连通性因其有效性通常被用来衡量网络的鲁棒性。面向节点连通性的节点整合优化虽然简单，但仍是 NP 难题，尤其是在处理大量节点时。为了解决这个问题，我们利用节点和遍历树之间的映射关系，使用节点切割集的每个节点簇来识别提名节点，然后通过扩展的基于对偶树的选择过程有条件地合并这些节点。实验结果表明，在适用最优算法的数十个节点的小型图中，加速比超过 105（最多 106），而额外成本约为 6%。在拥有数百万节点的大型图中，所提出的算法可以帮助促进 99.9% 以上节点对的节点连接，远远优于常用的启发式算法。其固有的可并行能力为更快的速度铺平了道路。

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引用次数: 0

Distribution reconstruction and reliability assessment of complex LSFs via an adaptive Non-parametric Density Estimation Method 通过自适应非参数密度估计法重建复杂 LSF 的分布和可靠性评估

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-30 DOI: 10.1016/j.ress.2024.110609

Quanfu Yu , Jun Xu

Complex limit state functions (LSFs), often characterized by strong nonlinearity, non-smoothness, or discontinuity, pose challenges for structural reliability analysis in engineering practices. Conventional methods for uncertainty propagation and reliability assessment may struggle to handle these issues effectively. This paper introduces a novel approach to adaptively reconstruct the unknown distributions of complex LSFs. The Non-parametric Density Estimation Method based on Harmonic Transform (NDEM-HT) is employed as the tool for this purpose. An adaptive strategy is then proposed to determine the number of harmonic moments required in NDEM-HT for achieving high accuracy. Specifically, the Adaptive Kernel Density Estimation (AKDE) method is also adopted to provide an initial estimation of the rough distribution. Subsequently, the optimal number of harmonic moments is determined by minimizing the relative entropy between the distributions obtained by AKDE and NDEM-HT. The efficacy of the proposed method is demonstrated through five numerical examples, considering various types of complex LSFs. Comparative results are also provided employing MCS along with both conventional and state-of-the-art methods.

复杂的极限状态函数（LSFs）通常具有很强的非线性、非平稳性或不连续性，给工程实践中的结构可靠性分析带来了挑战。传统的不确定性传播和可靠性评估方法可能难以有效处理这些问题。本文介绍了一种自适应重建复杂 LSF 未知分布的新方法。为此，本文采用了基于谐波变换的非参数密度估计方法（NDEM-HT）作为工具。然后提出了一种自适应策略，以确定 NDEM-HT 所需的谐波矩数量，从而实现高精度。具体来说，还采用了自适应核密度估计（AKDE）方法来提供粗略分布的初始估计。随后，通过最小化 AKDE 和 NDEM-HT 所得分布之间的相对熵，确定谐波矩的最佳数量。考虑到各种类型的复杂 LSF，通过五个数值示例展示了所提方法的功效。此外，还提供了 MCS 与传统方法和最先进方法的比较结果。

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引用次数: 0

Health management of power batteries in low temperatures based on Adaptive Transfer Enformer framework 基于自适应转移执行器框架的低温下动力电池健康管理

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-29 DOI: 10.1016/j.ress.2024.110613

Bingyang Chen , Xingjie Zeng , Chao Liu , Yafei Xu , Heling Cao

Accurate State of Charge (SOC) estimation is essential for extending battery life and improving the safety of battery management systems. However, many existing methods face challenges, including a lack of sufficient samples in specific driving modes, overlooking hidden factors such as low temperatures, and experiencing negative transfer in transfer learning. This paper introduces the Adaptive Transfer Enformer (ATE) Framework, which integrates an Enhanced Transformer (Enformer) model with Adaptive Transfer Learning (ATL). The Enformer incorporates Multilevel Residual Attention (MRA) and Pattern Dynamic Decomposition (PDD), forming the backbone of the pre-trained model. MRA addresses gradient vanishing issues due to limited samples and captures the underlying relationships at each time point. PDD dynamically learns temporal trends, hidden factors, and their interactions. ATL provides an effective feature learning strategy to promote positive transfer in SOC estimation. Experimental results on two public datasets with added noise show that the proposed method improves average accuracy compared to state-of-the-art methods. Additionally, results from nine transfer scenarios demonstrate the strong generalization and noise resistance capabilities of the ATE Framework.

准确的充电状态（SOC）估计对于延长电池寿命和提高电池管理系统的安全性至关重要。然而，许多现有方法都面临着挑战，包括在特定驾驶模式下缺乏足够的样本、忽略低温等隐藏因素以及在转移学习中出现负转移等。本文介绍了自适应转移执行器（ATE）框架，该框架集成了增强变压器（Enformer）模型和自适应转移学习（ATL）。Enformer 融合了多级残留注意力（MRA）和模式动态分解（PDD），构成了预训练模型的骨干。MRA 解决了由于样本有限而导致的梯度消失问题，并捕捉了每个时间点的潜在关系。PDD 动态学习时间趋势、隐藏因素及其相互作用。ATL 提供了一种有效的特征学习策略，以促进 SOC 估计中的正迁移。在两个添加了噪声的公共数据集上的实验结果表明，与最先进的方法相比，所提出的方法提高了平均准确率。此外，九个转移场景的结果表明 ATE 框架具有很强的泛化和抗噪能力。

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引用次数: 0

Preventive maintenance strategy for multi-component systems in dynamic risk assessment 动态风险评估中的多组件系统预防性维护战略

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-29 DOI: 10.1016/j.ress.2024.110611

Chengjie Zhang, Zhigeng Fang, Wenjie Dong

As the system operates, the system risk level will also dynamically change. In this paper, a dynamic risk assessment of the system is carried out by considering the system reliability and system risk losses, both of which vary over time. Then, based on the system risk level, different maintenance measures are applied to the components that have reached the preventive maintenance thresholds, including medium repair, major repair, and replacement. If the system risk is relatively light, low-cost medium repair will be adopted to save maintenance resources. Thus, a novel maintenance optimization strategy for multi-component systems considering the system risk level and aiming to minimize maintenance costs is proposed. Finally, the feasibility and effectiveness of the model are verified through a numerical case of the air conditioning temperature regulation subsystem.

随着系统的运行，系统风险水平也会发生动态变化。本文通过考虑随时间变化的系统可靠性和系统风险损失，对系统进行动态风险评估。然后，根据系统风险等级，对达到预防性维护阈值的部件采取不同的维护措施，包括中修、大修和更换。如果系统风险相对较轻，则采用低成本的中修，以节省维护资源。因此，针对多组件系统提出了一种考虑系统风险水平、以最小化维护成本为目标的新型维护优化策略。最后，通过空调温度调节子系统的数值案例验证了该模型的可行性和有效性。

引用次数: 0

A new reliability health status assessment model for complex systems based on belief rule base 基于信念规则库的复杂系统可靠性健康状况评估新模型

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-29 DOI: 10.1016/j.ress.2024.110614

Mingyuan Liu, Wei He, Ning Ma, Hailong Zhu, Guohui Zhou

In complex systems, health status assessment identifies system conditions and potential issues. However, large uncertainties and variations make efficient model construction challenging. The belief rule base (BRB), which addresses uncertainty through data-driven and knowledge-driven methods, is widely used for health status assessment of complex systems. Current BRB modeling methods focus primarily on accuracy, leaving a gap in research on reliability. Therefore, a reliable BRB (RE-BRB), which enables effective modeling for complex system health assessment under high reliability requirements, is proposed in this paper. First, a systematic reliability analysis of the BRB is performed, and the reliability criteria are defined. Second, the model parameters of the RE-BRB are optimized via the nondominated sorting whale optimization algorithm with reliability constraints (NSWOA), and the reliability of the model is ensured. In addition, a perturbation analysis of the RE-BRB model is conducted to identify the perturbation thresholds. The perturbation thresholds acceptable to the model provide guidance for managers in making decisions. Last, using the WD615 diesel engine and flywheel bearing as examples, this method achieves reliable system health status assessment by accurately assessing system status, incorporating the ability to address external perturbations and providing an easily interpretable output process.

在复杂系统中，健康状况评估可确定系统状况和潜在问题。然而，巨大的不确定性和变化使得高效的模型构建面临挑战。信念规则库（BRB）通过数据驱动和知识驱动的方法来解决不确定性问题，被广泛应用于复杂系统的健康状况评估。目前的信念规则库建模方法主要侧重于准确性，在可靠性方面的研究还存在空白。因此，本文提出了一种可靠的 BRB（RE-BRB），它能在高可靠性要求下为复杂系统健康状况评估进行有效建模。首先，对 BRB 进行了系统的可靠性分析，并定义了可靠性标准。其次，通过带可靠性约束的无支配排序鲸优化算法（NSWOA）优化 RE-BRB 的模型参数，确保模型的可靠性。此外，还对 RE-BRB 模型进行了扰动分析，以确定扰动阈值。模型可接受的扰动阈值可为管理人员提供决策指导。最后，以 WD615 柴油发动机和飞轮轴承为例，该方法通过准确评估系统状态、结合处理外部扰动的能力以及提供易于解释的输出过程，实现了可靠的系统健康状态评估。

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引用次数: 0

Toward the resilience of UAV swarms with percolation theory under attacks 利用渗流理论实现无人机群在攻击下的复原力

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety

Pub Date : 2024-10-29 DOI: 10.1016/j.ress.2024.110608

Tianzhen Hu , Yan Zong , Ningyun Lu , Bin Jiang

Unmanned aerial swarms have been widely applied across various domains. The security of swarms against attacks has been of significance. However, there still exists a lack of quantitatively assessing the unmanned swarm resilience against attacks. Thus, this work adopts the percolation theory to mathematically analyse the resilience of the unmanned aerial swarms after random attacks. In addition to the typically used popularity in the preferential attachment, distance of neighbours is taken into account for modelling unmanned swarms, which is missing in the literature. This improved preferential attachment-based swarm model offers a more precise and realistic description of swarm behaviours. In addition, an attack model is proposed, which can be a description of dynamic attacks. Moreover, this study also utilizes the percolation theory to assess the resilience of swarms after the random attacks. Finally, the simulation results show that the resilience derived using percolation theory aligns with the improved swarm model. The proposed swarm model maintains

79 %

resilience when

20 %

of the UAVs are attacked under random attacks, and even

69.4 %

resilience when

20 %

of the UAVs are attacked under initial betweenness-based attacks.

无人机群已广泛应用于各个领域。无人机群抵御攻击的安全性一直具有重要意义。然而，目前仍缺乏对无人机群抗击攻击能力的定量评估。因此，本研究采用渗流理论，从数学角度分析无人机群在受到随机攻击后的恢复能力。除了在优先附着中通常使用的流行性外，在模拟无人机群时还考虑了邻居的距离，这在文献中是缺失的。这种基于优先附着的改进型蜂群模型能更精确、更真实地描述蜂群行为。此外，还提出了一种攻击模型，可用于描述动态攻击。此外，本研究还利用渗流理论来评估蜂群在受到随机攻击后的恢复能力。最后，模拟结果表明，利用渗滤理论得出的复原力与改进后的蜂群模型一致。当 20% 的无人机受到随机攻击时，所提出的蜂群模型能保持 79% 的恢复力；当 20% 的无人机受到基于初始间隙度的攻击时，所提出的蜂群模型甚至能保持 69.4% 的恢复力。

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引用次数: 0