Applied Mathematical Modelling最新文献_第4页

An evolutionary isogeometric topology optimization method for multi-material viscoelastic damping structures 多材料粘弹性阻尼结构的演化等几何拓扑优化方法

IF 5 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-31 DOI: 10.1016/j.apm.2026.116787

Hongshuo Fan, Jianli Liu, Tao Nie, Jingui Yu, Peng Li, Jianzhong Yang, Zhaohui Xia

引用次数: 0

Fisher-based inaccuracy measure in terms of survival function: Applications in reliability and image segmentation 基于生存函数的fisher不准确性度量：在可靠性和图像分割中的应用

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-29 DOI: 10.1016/j.apm.2026.116797

Omid Kharazmi , Femin Yalcin

In this paper, we introduce a cumulative version of the Fisher-based inaccuracy information measure in both model-based and parameter-based forms, formulated in terms of the survival function. We establish results related to aging concepts in survival analysis and reliability engineering and, in particular, derive several results concerning the connections between the proposed inaccuracy information measure and fundamental stochastic orderings, including the usual stochastic order, hazard rate order, and dispersive order. Furthermore, we derive upper bounds for the proposed inaccuracy measure under arithmetic and geometric mixture survival models and extend the classical Gini coefficient through a weighted formulation, obtaining explicit expressions for this measure in terms of the equilibrium distribution. The behavior of the cumulative residual Fisher-based inaccuracy measure is also examined for convoluted and proportional hazard-convoluted survival functions under increasing and decreasing failure rate assumptions commonly used in reliability analysis.

In addition, two applications of the proposed measure are presented. The first concerns image quality assessment, where Gaussian noise is added to an image at varying signal-to-noise ratios (SNRs) to simulate different noise levels. The second application incorporates the measure into a novel image segmentation algorithm. The performance of the proposed algorithm is evaluated against benchmark unsupervised methods, including Otsu’s thresholding and K-means clustering, using supervised ground-truth-based metrics such as the Adjusted Rand Index (ARI), Accuracy, Recall, F1-score, Dice coefficient, and Jaccard index.

在本文中，我们以基于模型和基于参数的形式介绍了基于费雪的不准确性信息度量的累积版本，并以生存函数的形式表述。我们在生存分析和可靠性工程中建立了与老化概念相关的结果，特别是得出了关于所提出的不准确信息度量与基本随机顺序之间的联系的几个结果，包括通常的随机顺序，风险率顺序和分散顺序。此外，我们在算术和几何混合生存模型下推导了不准确性度量的上界，并通过加权公式扩展了经典基尼系数，得到了该度量的均衡分布的显式表达式。在可靠性分析中常用的故障率增加和减少的假设下，对卷积和比例危险-卷积生存函数的累积残差费雪误差度量也进行了检验。此外，还介绍了该方法的两种应用。第一个涉及图像质量评估，其中高斯噪声以不同的信噪比（SNRs）添加到图像中，以模拟不同的噪声水平。第二种应用是将该测量并入一种新的图像分割算法中。该算法的性能根据基准无监督方法进行评估，包括Otsu的阈值和K-means聚类，使用基于监督的基于事实的指标，如调整后的兰德指数（ARI）、准确性、召回率、f1分数、骰子系数和Jaccard指数。

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引用次数: 0

Physics-informed Kolmogorov-Arnold networks for multi-material elasticity problems in electronic packaging 电子封装中多材料弹性问题的物理信息Kolmogorov-Arnold网络

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-28 DOI: 10.1016/j.apm.2026.116793

Yanpeng Gong , Yida He , Yue Mei , Xiaoying Zhuang , Fei Qin , Timon Rabczuk

This paper proposes a Physics-Informed Kolmogorov-Arnold Network for analyzing elasticity problems in multi-material electronic packaging structures. The method replaces traditional Multi-Layer Perceptrons with Kolmogorov-Arnold Networks within an energy-based Physics-Informed Neural Network framework. By constructing admissible displacement fields satisfying essential boundary conditions and optimizing network parameters through numerical integration, the proposed method effectively handles material property discontinuities. Unlike traditional methods that require domain decomposition and interface constraints for multi-material problems, Kolmogorov-Arnold Networks’ trainable B-spline activation functions provide inherent piecewise characteristics. This capability stems from B-splines’ local support, which enables effective approximation of discontinuities despite their individual smoothness. Consequently, this approach enables accurate approximation across the entire domain using a single network and simplifying the computational framework. Numerical experiments demonstrate that the proposed method achieves excellent accuracy and robustness in multi-material elasticity problems, validating its practical potential for electronic packaging analysis. Source codes are available at https://github.com/yanpeng-gong/PIKAN-MultiMaterial.

本文提出了一种基于物理的Kolmogorov-Arnold网络，用于分析多材料电子封装结构中的弹性问题。该方法在基于能量的物理信息神经网络框架内用Kolmogorov-Arnold网络取代了传统的多层感知器。该方法通过构造满足基本边界条件的容许位移场，并通过数值积分优化网络参数，有效地处理了材料性质不连续问题。不同于传统方法需要对多材料问题进行区域分解和界面约束，Kolmogorov-Arnold网络的可训练b样条激活函数提供了固有的分段特征。这种能力源于b样条的局部支持，它可以有效地逼近不连续点，尽管它们的个体是光滑的。因此，这种方法可以使用单个网络在整个领域进行精确的近似，并简化了计算框架。数值实验表明，该方法在多材料弹性问题中具有良好的精度和鲁棒性，验证了其在电子封装分析中的应用潜力。源代码可从https://github.com/yanpeng-gong/PIKAN-MultiMaterial获得。

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引用次数: 0

Observation position selection model for distributed dynamic load identification to minimize error 基于最小误差的分布式动载荷识别观测位置选择模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-28 DOI: 10.1016/j.apm.2026.116790

Yinshen Wang, Jinhui Jiang, Wenxu Cui, Yi Cai

Distributed dynamic load identification is a technique used to identify dynamic loads applied to structures through dynamic responses, and it is a typical inverse problem. Current research mainly focuses on identification methods, with little attention given to the selection of observation positions during the measurement of dynamic responses. The difficulty in analyzing the impact of observation positions on the identification results lies in the fact that the regularization methods and the inherent randomness of noise must also be considered during the identification process, making it challenging to draw sufficient theoretical conclusions. This work theoretically derives the impact of observation positions on the upper bound of identification result errors, under the premise of a fixed number of observation positions. Based on this, an observation position selection model aimed at minimizing identification errors is proposed. Finally, the effectiveness of this model in reducing identification errors is verified through simulations and experiments. Experimental results show that the proposed observation position selection model reduced the mean identification error by 37.12 % and the maximum error by 10.56 %.

分布式动荷载识别是一种通过动力响应识别作用在结构上的动荷载的技术，是典型的反问题。目前的研究主要集中在识别方法上，很少关注动态响应测量过程中观测位置的选择。分析观测位置对识别结果影响的难点在于，在识别过程中还必须考虑正则化方法和噪声固有的随机性，难以得出充分的理论结论。在观测位置个数固定的前提下，从理论上推导了观测位置对识别结果误差上界的影响。在此基础上，提出了一种以最小识别误差为目标的观测位置选择模型。最后，通过仿真和实验验证了该模型在减少识别误差方面的有效性。实验结果表明，所提出的观测位置选择模型将平均识别误差降低了37.12%，最大识别误差降低了10.56%。

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引用次数: 0

Accelerated engineering of band gaps and topological interface states in one-dimensional metamaterials via deep learning 基于深度学习的一维超材料带隙和拓扑界面态加速工程

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-28 DOI: 10.1016/j.apm.2026.116792

Xue-Qian Zhang , Yi-Da Liu , Xiao-Shuang Li , Tian-Xue Ma , Yue-Sheng Wang , Zhuo Zhuang

Metamaterials exhibit unique sound insulation capabilities within band gaps. Topological interface states in metamaterials are robust against external perturbations, enabling sound enhancement. However, designing a pair of metamaterials with specified band gaps, especially the topological interface state frequency, remains a challenging problem, and few studies directly design the topological interface state frequency. In this work, deep learning approaches are used for the engineering of one-dimensional metamaterials with high design freedoms. The considered one-dimensional metamaterials are composed of periodic solid scatterers embedded in the air background, whose unit cell is divided into a matrix with 32 × 32 pixels. First, the variational autoencoder is applied to reduce the dimensionality of unit cell images, allowing accurate reconstruction of images with different numbers of scatterers. Subsequently, the multilayer perceptron and the tandem neural network are used to realize the property prediction and customized design of one-dimensional metamaterials, respectively. The correlation coefficients for the property prediction and inverse design are more than 97%. The unit cell images of one-dimensional metamaterials with specific band gap properties could be successfully and instantaneously designed. Importantly, the implementation of a ”one-to-many” design of metamaterial pairs with specific topological interface state frequencies is realized. This study demonstrates the broad application prospects of deep learning approaches in the field of metamaterial design and provides new ideas and methods for the intelligent design of artificially functional materials.

超材料在带隙内表现出独特的隔声能力。超材料中的拓扑界面态对外部扰动具有鲁棒性，从而实现了声音增强。然而，设计具有特定带隙的一对超材料，特别是具有特定拓扑界面状态频率的超材料，仍然是一个具有挑战性的问题，很少有研究直接设计拓扑界面状态频率。在这项工作中，深度学习方法被用于具有高设计自由度的一维超材料的工程。所考虑的一维超材料由嵌入在空气背景中的周期性固体散射体组成，其单位胞被划分为32 × 32像素的矩阵。首先，采用变分自编码器降低单元格图像的维数，实现不同散射体数量的图像精确重建。随后，利用多层感知器和串联神经网络分别实现了一维超材料的性能预测和定制设计。性能预测与反设计的相关系数均大于97%。具有特定带隙特性的一维超材料的单元胞图像可以成功地、即时地设计出来。重要的是，实现了具有特定拓扑界面状态频率的超材料对的“一对多”设计。本研究展示了深度学习方法在超材料设计领域的广阔应用前景，为人工功能材料的智能设计提供了新的思路和方法。

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引用次数: 0

Artificial neural network analysis of size-dependent dynamic characteristics of reinforced nanoplates with integrated thermal-magneto-electro-elastic layers 热-磁-电弹性集成层增强纳米板尺寸相关动态特性的人工神经网络分析

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-27 DOI: 10.1016/j.apm.2026.116791

Qingya Li , Tengfei Mao , Juan Ma , Haochen Liu , Ming Liu , Jian Liu , Ye Yuan , Peter Wriggers , Phutphalla Kong

Emerging innovative materials with multifunctionality are revolutionizing the design, development, and manufacturing of electronics. Through a novel machine learning approach, this study addresses computational challenges in modeling size-dependent free vibration of smart sandwich nanoplates with a carbon nanotube-reinforced core and multifunctional thermal-magneto-electro-elastic face sheets supported by a Winkler-Pasternak foundation. A nonlocal strain gradient theory plate model quantifies dual-scale effects of nonlocal and material length scale parameters, while incorporating carbon nanotube interphase layer and agglomeration effects, as well as the multiphysics field couplings in the thermal–magneto–electro–elastic layer. To overcome the prohibitive computational cost of traditional Galerkin-based solution in high-dimensional parametric spaces, a backpropagation neural network surrogate is developed for predicting natural frequencies. Verification studies validate the accuracy of the proposed machine-learning-based surrogate approach against analytical solutions. Additionally, extensive parametric analyses using the surrogate evaluate the impact of key factors, including nonlocal and material length scale parameters, boundary conditions, carbon nanotube agglomeration states, electric voltage, magnetic potentials, thermal gradients, and elastic foundation parameters, on the free vibration response. The backpropagation neural network surrogate model enables a systematic statistical evaluation of parameter interactions and sensitivity trends, providing new insights into the relationships among multiphysics variables that influence the size-dependent dynamic behavior of smart, multifunctional nanoplates.

具有多种功能的新兴创新材料正在彻底改变电子产品的设计、开发和制造。通过一种新颖的机器学习方法，本研究解决了智能三明治纳米板的尺寸依赖自由振动建模的计算挑战，该三明治纳米板具有碳纳米管增强核心和多功能热磁电弹性面片，由Winkler-Pasternak基础支撑。非局部应变梯度理论板模型量化了非局部和材料长度尺度参数的双尺度效应，同时考虑了碳纳米管界面层和团聚效应，以及热-磁-电弹性层中的多物理场耦合。为了克服传统的基于伽辽金方法在高维参数空间中计算成本过高的问题，提出了一种反向传播神经网络替代方法来预测固有频率。验证研究验证了针对分析解决方案提出的基于机器学习的替代方法的准确性。此外，使用替代方法进行了广泛的参数分析，评估了关键因素对自由振动响应的影响，包括非局部和材料长度尺度参数、边界条件、碳纳米管团聚状态、电压、磁势、热梯度和弹性基础参数。反向传播神经网络代理模型能够对参数相互作用和灵敏度趋势进行系统的统计评估，为影响智能多功能纳米片尺寸依赖动态行为的多物理场变量之间的关系提供新的见解。

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引用次数: 0

From discrete fracture network-resolved flow to effective permeability: A corrector-theory homogenization approach 从离散裂缝网络分解流到有效渗透率：一种校正理论的均匀化方法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-27 DOI: 10.1016/j.apm.2026.116795

K. Martins, R. Quevedo, D. Roehl, Celso Romanel

This study presents a rigorous mathematical approach to upscaling hydraulic properties of fractured porous media using corrector theory within the framework of homogenization of partial differential equations (PDE). The work details the numerical analogy of the limit transition applied to the mass conservation equation governed by Darcy’s law in a d-dimensional domain stochastically populated with (d-1)-dimensional sub-manifolds representing fractures. Using the finite volume method with the Two Point Flux Approximation (TPFA) and the Projection-Based Embedded Fracture Model (pEDFM) operators, the governing PDE (incorporating exchange terms between the rock matrix and fractures as well as fracture-fracture interactions) is solved in a representative cell problem. The homogenized permeability is then computed through a semi-empirical method involving the stationary corrector equation in the limit as

ε \to 0

. Finally, a comparison with the widely used Oda method and the Double Porosity – Double Permeability method is provided, highlighting the advantages and differences of the proposed approach at two different scales: the plug and reservoir scales.

本文在偏微分方程均质化的框架下，提出了一种严格的数学方法来提高裂缝性多孔介质的水力性能。该工作详细介绍了极限跃迁的数值模拟，应用于由达西定律控制的质量守恒方程，在随机填充（d-1）维子流形表示裂缝的d维域中。采用有限体积法，结合两点通量近似（TPFA）和基于投影的嵌入裂缝模型（pEDFM）算子，在代表性单元问题中求解控制PDE（包括岩石基质与裂缝之间的交换项以及裂缝-裂缝相互作用）。在ε→0的极限条件下，采用平稳校正方程，采用半经验方法计算均匀渗透率。最后，与广泛应用的Oda方法和双孔双渗方法进行了比较，突出了该方法在桥塞和储层两种不同尺度上的优势和差异。

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引用次数: 0

A nonlocal thermoelastic theory for porous media based on the modified Green-Lindsay model 基于修正Green-Lindsay模型的多孔介质非局部热弹性理论

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-27 DOI: 10.1016/j.apm.2026.116794

Xiaoya Li, Zixin Wang, Bo Ning, Xingyu Song

To investigate the influence of strain rate and size effect on the thermeolastic response for porous media, this work develops a nonlocal poro-thermoelastic model in the context of modified Green-Lindsay (MGL) model that concurrently integrates mechanical and thermal nonlocal effects. The transient responses of a one-dimensional semi-infinite porous medium subjected to ramp-type heating are obtained by using the method of Laplace transform technique and numerical inversion. The influences of different poro-thermoelastic theories ramp-heating time, mechanical and thermal nonlocal parameters, and pore effect on the thermoelastic response are discussed and illustrated graphically. This study can provide some theoretical guidance for the thermo-mechanical design and optimization of porous structures.

为了研究应变率和尺寸效应对多孔介质热塑性响应的影响，本文在改进的Green-Lindsay （MGL）模型的基础上建立了一个非局部孔隙热弹性模型，该模型同时集成了力学和热非局部效应。采用拉普拉斯变换技术和数值反演方法，得到了一维半无限多孔介质在斜坡加热作用下的瞬态响应。讨论了不同的孔隙热弹性理论对热弹性响应的影响，并图解说明了斜坡加热时间、力学和热非局部参数以及孔隙效应。该研究可为多孔结构的热力学设计和优化提供一定的理论指导。

引用次数: 0

A model-based calibration method for improving end-effector positioning accuracy of wheeled mobile manipulators 一种提高轮式移动机械臂末端执行器定位精度的模型标定方法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-27 DOI: 10.1016/j.apm.2026.116796

Tianyu Liu , Lizhao Wang , Hanlei Zhao , Xiaohui Jia , Xinxu Ma , Tiejun Li , Jinyue Liu

The end-effector positioning of wheeled mobile manipulators during the manipulation process is dependent on the accuracy of the underlying mathematical model. However, errors in the model parameters caused by faulty calibration directly degrade the positioning accuracy of the end-effector. Although existing kinematic calibration methods can reduce the end-effector positioning errors, calibration methods for non-kinematic errors, such as those arising from flexibility deformation, remain underdeveloped. To address this problem, this paper proposes a comprehensive model-based calibration method for wheeled mobile manipulators that aims to improve the end-effector positioning accuracy by accounting for deformation errors from both the chassis tires and the arm joints, as well as structural errors in the arm rigid links. The effectiveness and generalizability of the calibration method are verified through experiments conducted across different prototype configurations and under various load conditions. The results show that the absolute positioning accuracy of the end-effector can be improved by at least 92.83% after calibration. This method can provide a reliable theoretical basis for the practical calibration of wheeled mobile manipulators in engineering applications.

轮式移动机械臂在操作过程中末端执行器的定位取决于底层数学模型的准确性。然而，由于标定错误导致的模型参数误差直接降低了末端执行器的定位精度。虽然现有的运动学标定方法可以减小末端执行器的定位误差，但针对柔性变形等非运动学误差的标定方法还不发达。针对这一问题，本文提出了一种基于模型的轮式移动机械臂综合标定方法，该方法考虑了底盘轮胎和机械臂关节的变形误差以及机械臂刚性环节的结构误差，提高了末端执行器的定位精度。通过不同原型配置和不同载荷条件下的实验，验证了该标定方法的有效性和通用性。结果表明，经标定后，末端执行器的绝对定位精度至少提高了92.83%。该方法可为工程应用中轮式移动机械手的实际标定提供可靠的理论依据。

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引用次数: 0

Self-triggered cooperative autonomous tracking and landing control for UAV-USV systems with prescribed performance 具有规定性能的UAV-USV系统自触发协同自主跟踪与着陆控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-01-25 DOI: 10.1016/j.apm.2026.116788

Zhijie Bian , Baofeng Pan , Guibing Zhu , Changjian Yan

This work addresses the control problem for autonomous shipboard landing of quadrotor unmanned aerial vehicles (UAVs), and proposes a self-triggered robust adaptive control scheme with prescribed performance. The control design incorporates the effects of model parameter uncertainties and external disturbances acting on the UAV, as well as spatial constraints at the landing point on the unmanned surface vessel (USV) and the influence of relative vertical motion between the USV and UAV during the landing process. To tackle the multi-dimensional spatial constraints and ensure a smooth transition during landing, a hyperbolic tangent-based guidance mechanism is proposed, and establish the stage-switching criteria for the autonomous shipboard landing. Furthermore, a novel error transformation method is introduced to guarantee that the landing process does not violate the spatial constraints of the UAV-USV system, while simultaneously ensuring both transient and steady-state tracking performance. To mitigate the effects of model parameter uncertainties and external disturbances, a single-parameter learning mechanism is developed, enabling the integrated online compensation of composite uncertainties formed by model parameters and external disturbances. Concurrently, a parallel self-triggering mechanism is incorporated into the controller-actuator channel to reduce the control signal transmission frequency and alleviate actuator wear. The boundedness of all signals in the closed-loop system is analyzed and rigorously proven using Lyapunov-based stability theory. Finally, comparative simulation results demonstrate the effectiveness and practicality of the developed control scheme.

针对四旋翼无人机自主登舰的控制问题，提出了一种具有规定性能的自触发鲁棒自适应控制方案。控制设计结合了模型参数不确定性和作用于无人机的外部干扰的影响，以及无人水面舰艇（USV）着陆点的空间约束和着陆过程中USV与无人机之间相对垂直运动的影响。为解决舰载自主着舰过程中的多维空间约束和平稳过渡问题，提出了一种基于双曲切线的制导机构，建立了舰载自主着舰的阶段切换准则。在此基础上，提出了一种新的误差变换方法，以保证着陆过程不违反UAV-USV系统的空间约束，同时保证瞬态和稳态跟踪性能。为了减轻模型参数不确定性和外部干扰的影响，开发了一种单参数学习机制，实现了模型参数和外部干扰形成的复合不确定性的在线综合补偿。同时，在控制器-执行器通道中加入并联自触发机构，降低控制信号传输频率，减轻执行器磨损。利用基于李雅普诺夫的稳定性理论，分析并严格证明了闭环系统中所有信号的有界性。最后，通过仿真对比验证了该控制方案的有效性和实用性。

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引用次数: 0