Applied Mathematical Modelling最新文献

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Tangential stiffness model of the joint surface considering contact angles between asperities based on fractal theory

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-12 DOI: 10.1016/j.apm.2025.116088

Yongchang Li, Guangpeng Zhang, Zhenyang Lv, Ke Chen

Based on fractal theory, the tangential contact model for a joint surface, taking into account the contact angle between asperities, was developed by incorporating Gorbatikh's contact angle probability distribution function. Mathematical expressions for the stages of a single asperity and the entire joint surface were derived. The quantitative effects of fractal parameters, friction coefficient, material properties, normal and tangential loading forces, and repeated loading on tangential stiffness were analyzed theoretically, and a dedicated testing platform was constructed to validate the accuracy of the model. The results show that the proposed model enhances stiffness prediction accuracy. The increase in contact stiffness is primarily determined by the fractal dimension and the number of repeated loadings. Tangential contact stiffness initially increases and then decreases with the fractal dimension D, reaching its maximum value when D = 2.6. Multiple loadings significantly improved stiffness, which gradually stabilized. After three loading cycles, the stiffness reached over 90 % of the maximum value, stabilizing at 1.21 times the initial loading stiffness when D > 2.6. This study provides a systematic analysis of the quantitative effects of various factors on tangential contact stiffness, offering both a theoretical foundation and practical guidance for optimizing the assembly process.

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引用次数: 0

Dual-quaternion-based kinematic calibration in robotic hand-eye systems: A new separable calibration framework and comparison

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-10 DOI: 10.1016/j.apm.2025.116076

Xiao Wang, Hanwen Song

The kinematic calibration of the robotic hand-eye system is formulated as solving the

A X = X B

problem, with calibration accuracy serving as the sole evaluation criterion. Whether the rotational and translational parts of the kinematic equations are calculated decoupled or not, being regarded as an important factor affecting the calibration accuracy, serves as a categorization criterion to form the separable and simultaneous methods. While it is widely acknowledged that both separable and simultaneous methods have distinct advantages and disadvantages, no definitive conclusions have been reached. This is primarily due to the challenges of isolating various influencing factors and the inherent coupling among them. This study addresses the problem within the theoretical framework of dual quaternion, excluding accuracy variations attributable to computational tools. First, a kinematic calibration framework is established by introducing the generalized conjugate formula, which accommodates existing simultaneous methods. Subsequently, a separable framework is proposed, incorporating Chasles' decoupling of the generalized conjugate formula. In the experiments, a pose optimization scheme based on permutations and combinations is developed. This scheme decouples the primary influencing factors and clarifies the applicability conditions of both separable and simultaneous methods. The proposed calibration scheme can be directly applied to robot motion planning.

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引用次数: 0

Mathematical models for truck-drone routing problem: Literature review 卡车-无人机路由问题的数学模型：文献综述

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-09 DOI: 10.1016/j.apm.2025.116074

He Luo , Jie Duan , Guoqiang Wang

The extensive literature on the truck-drone routing problem (TDRP) from 2015 to 2024 is synthesized, driven by significant advancements in the field. The increasing volume of research indicates a sustained interest in the practical applications of TDRP in everyday scenarios. Despite the gap between theory and practice, the rapid development highlights its multi-disciplinary importance. A comprehensive research framework is proposed, focusing on problem parameters, mathematical modeling, and effective approaches. TDRP is systematically organized and analyzed from a modeling perspective across three modes: one-truck and one-drone, one-truck and multi-drone, and multi-truck and multi-drone. The review then explores coordination modes, optimization objectives, solution approaches, practical applications, research gaps, and environmental benefits, while identifying key achievements, challenges, and future directions in TDRP.

引用次数: 0

Civil aircraft weight and center-of-gravity real-time estimation via the six-degree-of-freedom model with variable center of mass

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-07 DOI: 10.1016/j.apm.2025.116063

Shaobo Zhai , Guangwen Li , Penghui Huang , Mingshan Hou

This article addresses the issue of civil aircraft weight and center-of-gravity position real-time estimation using the six-degree-of-freedom model with variable center of mass, and derives the explicit expressions for aircraft weight and longitudinal center-of-gravity. Firstly, the nonlinear six-degree-of-freedom aircraft model with center-of-gravity variations is established, where the moment correction is considered. Subsequently, an aircraft weight estimation method via force analysis and an aircraft longitudinal center-of-gravity position estimation method via moment transformation are developed, and the acceleration correction is derived. Furthermore, a fuel system architecture is introduced, and the active center-of-gravity controller is designed. To assess the effectiveness of the proposed method, a series of numerical simulations are operated, integrating sensitivity analysis with quantitative calculation. The results demonstrate that the algorithm achieves consistent and reliable performance even under parameter perturbations, with the longitudinal center-of-gravity position estimation error remaining within ±2 % of the mean aerodynamic chord (MAC).

{"title":"Civil aircraft weight and center-of-gravity real-time estimation via the six-degree-of-freedom model with variable center of mass","authors":"Shaobo Zhai , Guangwen Li , Penghui Huang , Mingshan Hou","doi":"10.1016/j.apm.2025.116063","DOIUrl":"10.1016/j.apm.2025.116063","url":null,"abstract":"<div><div>This article addresses the issue of civil aircraft weight and center-of-gravity position real-time estimation using the six-degree-of-freedom model with variable center of mass, and derives the explicit expressions for aircraft weight and longitudinal center-of-gravity. Firstly, the nonlinear six-degree-of-freedom aircraft model with center-of-gravity variations is established, where the moment correction is considered. Subsequently, an aircraft weight estimation method via force analysis and an aircraft longitudinal center-of-gravity position estimation method via moment transformation are developed, and the acceleration correction is derived. Furthermore, a fuel system architecture is introduced, and the active center-of-gravity controller is designed. <strong><em>To assess the effectiveness of the proposed method, a series of numerical simulations are operated, integrating sensitivity analysis with quantitative calculation. The results demonstrate that the algorithm achieves consistent and reliable performance even under parameter perturbations, with the longitudinal center-of-gravity position estimation error remaining within ±2 % of the mean aerodynamic chord (MAC).</em></strong></div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"144 ","pages":"Article 116063"},"PeriodicalIF":4.4,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Metamaterial-based vibration suppression stories (VSSs) for mitigating train-induced structural vibrations in multi-story and high-rise buildings

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-07 DOI: 10.1016/j.apm.2025.116075

Feifei Sun , Chao Zeng , Wenhan Yin , Jiaqi Wen

With the rapid development of urban rail transit systems, the issues of structural vibration and re-radiated noise in adjacent buildings have become increasingly prominent. This paper investigates the feasibility of a novel metamaterial-based Vibration Suppression Stories (VSSs) for mitigating train-induced structural vibrations from the perspective of vibration propagation. A Lumped Parameter Model (LPM) has been developed to accurately predict the dynamic behavior of single-span multi-story and high-rise buildings under vertical ground excitations induced by train operations. The validity of this model has been confirmed through finite element analysis of a 12-story building. Additionally, an in-depth analysis has been conducted on the attenuation zone characteristics of an infinite controlled structure equipped with VSS oscillators. A closed-form analytical expression has been derived to provide insight into the general attenuation behavior of dual-oscillator metamaterials. The results show that the VSSs perform well in the high-frequency range. Furthermore, the local resonance of the beam-restrained floor slabs enhances the vibration attenuation capacity of the VSSs in the frequency range above the slab's natural frequency. To quantitatively evaluate the vibration attenuation performance of the VSS, vibration transmission and response history analyses are performed on a 12-story building equipped with three VSSs. The results indicate that the VSSs significantly suppress target peak responses, particularly for high-frequency global vibrations. This research presents a new and effective approach for addressing train-induced vibration issues in buildings.

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引用次数: 0

Moment-based Hermite model for asymptotically small non-Gaussianity

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-07 DOI: 10.1016/j.apm.2025.116061

Vincent Denoël

The third degree Moment-based Hermite model, which expresses a random variable as a cubic transformation of a standard normal variable, offers versatility in engineering applications. While its probability density function is not directly tractable, it is more complex to compute than the Gram-Charlier series, which, despite its simplicity, suffers from limitations such as positivity and unimodality issues, restricting its range of applicability. This paper presents two asymptotic analyses of the cubic Moment-based Hermite model for slight non-Gaussianity (i.e. small skewness and excess coefficients, “small” being understood in the sense of perturbation methods), showing that it asymptotically converges to the fourth cumulant Gram-Charlier model, while offering a slightly broader domain of applicability with minimal additional computational cost. Additionally, the paper derives, mathematically, a non empirical expression for the monotone limit of the original cubic translation model, and validates the theoretical findings through numerical simulations.

引用次数: 0

Image reconstruction method for segmental limited-angle CT based on coupled relative structure

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-07 DOI: 10.1016/j.apm.2025.116066

Changcheng Gong , Qiang Song , Jianxun Liu

Reducing scanning time or radiation doses is a primary demand in computed tomography (CT) imaging. Few-view CT and limited-angle CT are considered as two effective imaging ways to meet this demand. However, they both face different challenges in practical applications, such as difficulties in technical implementation and image reconstruction. This study focuses on a special imaging strategy called segmental limited-angle (SLA) CT, where the scanning angular range is composed of multiple segments. This strategy helps to avoid difficulties in technical implementation and reduces the complexity of CT reconstruction. However, SLA projections inherit the properties of limited-angle projections, and the reconstructed images may encounter pronounced shading artifacts. This paper proposes a reconstruction model based on coupled relative structure (CRS) and presents an algorithm to solve this model. The CRS method utilizes mutual structure features between the prior image and target image to guide image reconstruction, rather than relying solely on the prior image. To demonstrate its effectiveness, we conduct numerical simulation experiments and real CT data experiments. The reconstruction results indicate that the target image can inherit prior structures and keep away from reconstruction errors that may be introduced by inconsistent structures. Compared to other methods, the images reconstructed by our method are closer to the reference images.

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引用次数: 0

Modeling and controlling spatiotemporal malware propagation in mobile Internet of Things

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-06 DOI: 10.1016/j.apm.2025.116042

Huiying Cao , Da-Tian Peng , Dengxiu Yu

The mobility of devices in mobile Internet of Things (IoT) enables dynamic interactions, facilitating the spatiotemporal malware propagation. However, few studies have focused on accurately modeling and effectively controlling this form of malware propagation. To address this issue, we propose a theoretical framework that integrates patch-malware spreading dynamics with optimal patch allocation policy. First, we establish a novel temporal multilayer network comprising a central node, a patch dissemination layer, and a malware propagation layer. The hybrid patching process is implemented by the integration of the central node and the patch dissemination layer. In the malware propagation layer, the mobility of IoT devices is modeled as a diffusion process across multiple areas. Next, we design a dynamic spreading model to capture the evolution of malware propagation and analytically derive the invasion threshold. The threshold indicates that malware propagation is significantly influenced by both the patching process and the topological structure of mobile IoT. Furthermore, considering the central host's capacity and patch effectiveness, we develop an optimization algorithm to determine the optimal patch allocation policy under resource constraints. This algorithm significantly outperforms traditional centrality-based methods in malware mitigation. Finally, we analyze the impact of device mobility, the connectivity of the patch dissemination layer, the device distribution, the central node's capacity, and the patch effectiveness on malware propagation. Our study provides a theoretical foundation for predicting and controlling malware spreading in mobile IoT.

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引用次数: 0

Neural fractional differential equations

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-06 DOI: 10.1016/j.apm.2025.116060

C. Coelho , M. Fernanda P. Costa , L.L. Ferrás

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours. This property is useful in systems where variables do not respond to changes instantaneously, but instead exhibit a strong memory of past interactions. Having this in mind, and drawing inspiration from Neural Ordinary Differential Equations (Neural ODEs), we propose the Neural FDE, a novel deep neural network framework that adjusts a FDE to the dynamics of data. This work provides a comprehensive overview of the numerical method employed in Neural FDEs and the Neural FDE architecture. The numerical outcomes suggest that, despite being more computationally demanding, the Neural FDE may outperform the Neural ODE in modelling systems with memory or dependencies on past states, and it can effectively be applied to learn more complex dynamical systems.

引用次数: 0

Backstepping adaptive observer tracking strategy for gear transmission system under nonlinear constraints

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-03-06 DOI: 10.1016/j.apm.2025.116065

Zhu Yang , Meng Li , Yong Chen

In this paper, the tracking control problem of gear transmission servo system with full-state constraints is studied, in which nonlinear dead zone and disturbance are considered. A backstepping tracking control strategy based on barrier Lyapunov function is proposed. First, a dynamic model of the gear transmission system considering nonlinear dead zone was established. Then, a disturbance observer based on sliding mode and adaptive gain is proposed to approximate the dead zone and disturbance. Thirdly, to address the issue of full-state constraints, a backstepping control method based on a barrier Lyapunov function is proposed, wherein the barrier Lyapunov function is used to constrain the states. In addition, a radial basis function neural network is proposed to fit the nonlinear term in the backstepping process. Finally, the effectiveness of the control algorithm is verified by simulation and experiment.

引用次数: 0

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