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Mathematics
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Applied Mathematical Modeling and Intelligent Algorithms
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Applied Mathematical Modeling and Intelligent Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 6073

Special Issue Editors

Dr. Tianyu Zhao

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Guest Editor
College of Sciences, Northeastern University, Shenyang 110819, China
Interests: theoretical modeling; rotor dynamics; nonlinear vibration
Special Issues, Collections and Topics in MDPI journals
Dr. Long Chen

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Guest Editor
School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
Interests: aerodynamics; animal flight; flapping wing; vortex dynamics; micro air vehicles
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The resolution of numerous contemporary engineering issues necessitates the application of mathematical modeling techniques and intelligent algorithms, such as in the field of mechanical engineering, civil engineering, aerospace, biological engineering, and so on. This Special Issue focuses on the application of mathematical modeling and intelligent algorithms. The scope of this Special Issue includes, but is not limited to, the following topics:

  1. Theoretical modeling;
  2. Free and forced vibrations;
  3. Computational fluid dynamics;
  4. Nonlinear analysis;
  5. Functionally graded material;
  6. Deep learning; 
  7. Optimization; 
  8. Structural design;
  9. Biomechanics;
  10. Fault diagnosis.

All colleagues are welcome to contribute high-quality papers.

Dr. Tianyu Zhao
Dr. Long Chen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • modeling
  • applied mathematics
  • vibration
  • algorithm
  • biomechanics
  • additive manufacturing

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

16 pages, 608 KiB  
Article
Regression of Likelihood Probability for Time-Varying MIMO Systems with One-Bit ADCs
by Tae-Kyoung Kim and Moonsik Min
Mathematics 2024, 12(24), 3957; https://doi.org/10.3390/math12243957 - 17 Dec 2024
Viewed by 687
Abstract
This study proposes a regression-based approach for calculating the likelihood probability in time-varying multi-input multi-output (MIMO) systems using one-bit analog-to-digital converters. These time-varying MIMO systems often face performance challenges because of the difficulty in tracking changes in the likelihood probability. To address this [...] Read more.
This study proposes a regression-based approach for calculating the likelihood probability in time-varying multi-input multi-output (MIMO) systems using one-bit analog-to-digital converters. These time-varying MIMO systems often face performance challenges because of the difficulty in tracking changes in the likelihood probability. To address this challenge, the proposed method leverages channel statistics and decoded outputs to refine the likelihood. An optimization problem is then formulated to minimize the mean-squared error between the true and refined likelihood probabilities. A linear regression approach is derived to solve this problem, and a regularization technique is applied to further optimize the calculation. The simulation results indicate that the proposed method improves reliability by effectively tracking temporal variations in the likelihood probability and outperforms conventional methods in terms of performance. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling and Intelligent Algorithms)
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28 pages, 16178 KiB  
Article
A High-Feasibility Real-Time Trajectory-Planning Method for Parafoils Based on a Flexible Dynamic Model
by Jiaming Yu, Hao Sun, Qinglin Sun, Mingwei Sun and Zengqiang Chen
Mathematics 2024, 12(24), 3913; https://doi.org/10.3390/math12243913 - 11 Dec 2024
Viewed by 1006
Abstract
Effective trajectory planning is critical for achieving precise autonomous navigation and safe landing of parafoil delivery systems. However, current parafoil trajectory planning still faces challenges in ensuring consistency between actual system behavior and algorithmic real-time performance. Due to the strong fluid–structure interaction (FSI) [...] Read more.
Effective trajectory planning is critical for achieving precise autonomous navigation and safe landing of parafoil delivery systems. However, current parafoil trajectory planning still faces challenges in ensuring consistency between actual system behavior and algorithmic real-time performance. Due to the strong fluid–structure interaction (FSI) between the flexible canopy and airflow, traditional dynamic models based on point mass and rigid-body assumptions often lack aerodynamic accuracy. These models produce planned trajectories in simulation environments that are inconsistent with the actual system’s behavior and cannot directly provide an effective reference for airdrop experiments. Additionally, traditional planning methods require a significant amount of time to calculate complex dynamic models and generate fixed trajectories in advance. These methods not only fail to provide usable results in a short period of time, but also cannot prevent the accumulation of tracking errors by adjusting the target trajectory in real time. To address these issues, this paper proposes a flexible 8-degree-of-freedom (8-DOF) dynamic model based on the FSI method, utilizing the actual aerodynamic parameters of the canopy to achieve improved consistency with the behavior of the actual system. The Soft Actor–Critic (SAC) algorithm is then employed to achieve real-time trajectory planning for parafoil airdrop systems, addressing the real-time planning performance limitations of traditional algorithms. The airdrop experiments validate that the simulation trajectories generated using this model demonstrate higher consistency with actual flight trajectories, providing more accurate references for pre-flight trajectory optimization. Moreover, the proposed method enables real-time trajectory planning and dynamically adjusts target trajectories based on the current position and attitude of the parafoil, effectively mitigating the accumulation of errors. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling and Intelligent Algorithms)
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41 pages, 9529 KiB  
Article
Study on the Vibration Characteristics of the Helical Gear-Rotor-Bearing Coupling System of a Wind Turbine with Composite Faults
by Hongyuan Zhang, Shuo Li and Hongyun Sun
Mathematics 2024, 12(9), 1410; https://doi.org/10.3390/math12091410 - 4 May 2024
Cited by 1 | Viewed by 2474
Abstract
As the core component of the wind turbine generation gearbox, the gear-rotor-bearing transmission system typically operates in harsh environments, inevitably leading to the occurrence of composite faults in the system, which exacerbates system vibration. Therefore, it is necessary to study the vibration characteristics [...] Read more.
As the core component of the wind turbine generation gearbox, the gear-rotor-bearing transmission system typically operates in harsh environments, inevitably leading to the occurrence of composite faults in the system, which exacerbates system vibration. Therefore, it is necessary to study the vibration characteristics of wind turbine helical gear-rotor-bearing transmission systems with composite faults. This paper uses an improved energy method to calculate the theoretical time-varying mesh stiffness of a helical gear with a root crack failure. On the premise of considering the time-varying meshing stiffness of the faulty helical gear, the gear eccentric fault, and the nonlinear support force of the faulty bearing, a multi-degree-of-freedom helical gear-rotor-bearing transmission system with compound faults was established by using the lumped parameter method. The dynamic model of the system was solved based on the Runge–Kutta method, and the vibration response of the system under healthy conditions, single faults with gear eccentricity, single faults with tooth root cracks, and coupled bearing composite faults were simulated and analyzed. The results show that the simulation results based on KISSsoft software 2018 version verify the effectiveness of the improved energy method; the existence of single faults and composite faults will cause the fault characteristics in the time domain and frequency domain responses. In this paper, the influence of a single fault and a complex fault on the time domain and frequency domain of the system is mainly discovered through the fault study of the helical rotor-bearing system, and the influence of the fault degree on the vibration of the gear motion system is discussed. The greater the degree of the fault, the more vibration of the system occurs; accordingly, when the system is under the coupling of tooth root crack and bearing fault, there is a significant difference compared with the healthy system and the single fault system. The system vibration has obvious time domain and frequency domain signal characteristics, including periodic pulse impacts caused by gear faults and time domain impact caused by bearing. The fault characteristic frequencies can also be found in the frequency domain. In this paper, the fault study of a helical gear of wind turbine generation provides a reference for the theoretical analysis of the vibration characteristics of the helical gear-rotor-bearing system under various fault conditions, lays a solid foundation for the simulation and subsequent diagnosis of the composite fault signal of the system, and provides help for the fault diagnosis of wind turbine gearboxes in the future. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling and Intelligent Algorithms)
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16 pages, 6884 KiB  
Article
Gradient Weakly Sensitive Multi-Source Sensor Image Registration Method
by Ronghua Li, Mingshuo Zhao, Haopeng Xue, Xinyu Li and Yuan Deng
Mathematics 2024, 12(8), 1186; https://doi.org/10.3390/math12081186 - 15 Apr 2024
Cited by 3 | Viewed by 1041
Abstract
Aiming at the nonlinear radiometric differences between multi-source sensor images and coherent spot noise and other factors that lead to alignment difficulties, the registration method of gradient weakly sensitive multi-source sensor images is proposed, which does not need to extract the image gradient [...] Read more.
Aiming at the nonlinear radiometric differences between multi-source sensor images and coherent spot noise and other factors that lead to alignment difficulties, the registration method of gradient weakly sensitive multi-source sensor images is proposed, which does not need to extract the image gradient in the whole process and has rotational invariance. In the feature point detection stage, the maximum moment map is obtained by using the phase consistency transform to replace the gradient edge map for chunked Harris feature point detection, thus increasing the number of repeated feature points in the heterogeneous image. To have rotational invariance of the subsequent descriptors, a method to determine the main phase angle is proposed. The phase angle of the region near the feature point is counted, and the parabolic interpolation method is used to estimate the more accurate main phase angle under the determined interval. In the feature description stage, the Log-Gabor convolution sequence is used to construct the index map with the maximum phase amplitude, the heterogeneous image is converted to an isomorphic image, and the isomorphic image of the region around the feature point is rotated by using the main phase angle, which is in turn used to construct the feature vector with the feature point as the center by the quadratic interpolation method. In the feature matching stage, feature matching is performed by using the sum of squares of Euclidean distances as a similarity metric. Finally, after qualitative and quantitative experiments of six groups of five pairs of different multi-source sensor image alignment correct matching rates, root mean square errors, and the number of correctly matched points statistics, this algorithm is verified to have the advantage of robust accuracy compared with the current algorithms. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling and Intelligent Algorithms)
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