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Applications of Advanced Mathematical Method for Modeling, Predicting, Controlling, and...
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Applications of Advanced Mathematical Method for Modeling, Predicting, Controlling, and Optimizing the Dynamical System in Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 2337

Special Issue Editors

Dr. Lei Zhou

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Guest Editor
Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technolgy, Clear Water Bay, Hong Kong
Interests: fluid dynamics; wind engineering; data-driven methods
Dr. Zhanbiao Zhang

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Guest Editor
School of Civil Engineering, Dalian University of Technology, Dalian, China
Interests: bridge engineering; wind engineering; bluff body aerodynamics; computational fluid dynamics; fluid-structure interaction
Dr. Haiquan Jing

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Guest Editor
School of Civil Engineering, Central South University, Changsha 410075, China
Interests: fluid structure interaction; bridge wind engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Mingjie Zhang

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Guest Editor
Department of Structural Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Interests: wind engineering; bridge engineering; flow-induced vibration; bluff body aerodynamics; wind tunnel test; reduced-order modeling; system identification
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex dynamic systems ubiquitously exist in the natural, science, and engineering world, such as wind and flexible structure coupled systems, soil and civil structure coupled systems, ocean engineering structures subjected to wind, wave, and water, etc. It is a significant but also great challenge to establish an accurate and refined mathematical model to describe such a multi-physics, multi-scale, high-dimensional, and non-linear problem. Notably, a well-developed mathematical model can not only reveal the physical essence contained in practical engineering but also provide a fast prediction and efficient control strategy to ensure design optimization and structural safety. Thanks to the rapid development of numerical algorithms, computer science and devices, the digital twin, advanced numerical simulation method, data-driven method, and artificial intelligence (AI) emerge today as new solutions and perspectives to solve these challenges.

This Special Issue aims to collect state-of-the-art mathematical methods that are applied in the field of engineering to reveal the physical mechanism of this complex dynamical system. Therefore, papers aimed at using new mathematic theories, methods, and algorithms to model, control, predict, and optimize the physical essence contained in various engineering application scenarios is highly welcomed in this Special Issue. The novel mathematical methodology includes but is not limited to digital twin, the reduced-order model method, artificial intelligence, and probabilistic approaches. The fields of interest involve fluid mechanics, solid mechanics, reliability modeling and system optimization, civil engineering systems and structures, ocean engineering structures, renewable energy, transportation engineering, etc.

Dr. Lei Zhou
Dr. Zhanbiao Zhang
Dr. Haiquan Jing
Dr. Mingjie Zhang
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

  • reduced-order modeling
  • wind and structure
  • computational fluid dynamics
  • structural mechanics
  • material mechanics
  • mathematic modelling
  • machine learning
  • multi-physics simulation
  • numerical method
  • data-driven method

Published Papers (3 papers)

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Research

17 pages, 4204 KiB  
Article
Investigating the Influence of Non-Uniform Characteristics of Layered Foundation on Ground Vibration Using an Efficient 2.5D Random Finite Element Method
by Shaofeng Yao, Liang Yue, Wei Xie, Sen Zheng, Shuo Tang, Jinglong Liu and Wenkai Wang
Mathematics 2024, 12(10), 1488; https://doi.org/10.3390/math12101488 - 10 May 2024
Viewed by 323
Abstract
High-speed train operation may cause vibration near track facilities and propagate far through the ground, affecting people’s lives, work, and normal use of precision instruments in an urban environment. An efficient numerical method is proposed to calculate the non-uniform ground vibration under a [...] Read more.
High-speed train operation may cause vibration near track facilities and propagate far through the ground, affecting people’s lives, work, and normal use of precision instruments in an urban environment. An efficient numerical method is proposed to calculate the non-uniform ground vibration under a moving high-speed railway load. The theory of stochastic variables is used to describe the soil spatial variability of the non-uniform layered elastic ground, and the coupled 2.5D random finite element method (FEM) is proposed to reduce the computational cost without losing accuracy. Vibration propagation and attenuation of the non-uniform layered ground are investigated and the effect of train speed and soil non-homogeneity are analyzed. Results show that (1) at cross speed and high speed, the homogeneity coefficient of the layered ground has the most important influence on the ground vibration amplitude; (2) the upward acceleration is much larger than the downward acceleration at most speeds, and at cross speed and high speed, the acceleration amplitude decreases with the increase in the homogeneity coefficient; (3) as train speed increases from 60 m/s to 130 m/s, the influencing range of the homogeneity coefficient increases to 10 m from 2 m; and (4) the phenomenon of an in increase in local rebound can be observed in the velocity and acceleration attenuation curve at cross speed when the ground soil has a weaker homogeneity. Full article
(This article belongs to the Special Issue Applications of Advanced Mathematical Method for Modeling, Predicting, Controlling, and Optimizing the Dynamical System in Engineering)
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14 pages, 285 KiB  
Article
Optimal Corrective Maintenance Policies via an Availability-Cost Hybrid Factor for Software Aging Systems
by Huixia Huo
Mathematics 2024, 12(5), 694; https://doi.org/10.3390/math12050694 - 27 Feb 2024
Viewed by 414
Abstract
Availability is an important index for the evaluation of the performance of software aging systems. Although the corrective maintenance increases the system availability, the associated cost may be very high; therefore, the balancing of availability and cost during the corrective maintenance phase is [...] Read more.
Availability is an important index for the evaluation of the performance of software aging systems. Although the corrective maintenance increases the system availability, the associated cost may be very high; therefore, the balancing of availability and cost during the corrective maintenance phase is a critical issue. This paper investigates optimal corrective maintenance policies via an availability-cost hybrid factor for software aging systems. The system is described by a group of coupled differential equations, where the multiplier effect of the repair rate on a system variable is bilinear term. Our aim is to drive an optimal repair rate that ensures a balance between the maximal system availability and the minimal repair cost. In a finite time interval [0,T], we rigorously discuss the state space of the system and prove the existence of the optimal repair rate, and then derive the first-order necessary optimality conditions by applying a variational inequality with the adjoint variables. Full article
(This article belongs to the Special Issue Applications of Advanced Mathematical Method for Modeling, Predicting, Controlling, and Optimizing the Dynamical System in Engineering)
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23 pages, 37180 KiB  
Article
Wake Control of Flow Past Twin Cylinders via Small Cylinders
by Jinghua Yang, Bo Peng, Ying Zhao and Hongfu Zhang
Mathematics 2023, 11(10), 2261; https://doi.org/10.3390/math11102261 - 11 May 2023
Viewed by 1200
Abstract
The drag and lift force of a twin-cylinder structure are often greater than those of a single cylinder, causing serious structural safety problems. However, there are few studies on the passive control of twin cylinders. The study aimed to investigate the performance of [...] Read more.
The drag and lift force of a twin-cylinder structure are often greater than those of a single cylinder, causing serious structural safety problems. However, there are few studies on the passive control of twin cylinders. The study aimed to investigate the performance of passive drag reduction measures using small cylinders on twin cylinders at a Reynolds number of 100. The effects of small cylinder height (HD/D = 0~1.0, D is the side length of the twin cylinder) and cross-sectional shape on fluid force and flow structures were studied by direct numerical simulations. The control mechanism was analyzed using high-order dynamic mode decomposition (HODMD). The results showed that significant drag reduction occurred in the co-shedding state, particularly when the gap length of the twin cylinders L/D = 6.0. The small control cylinders with HD = 0.6, by contrast, showed the best performance in reducing the mean drag and fluctuating lift of the twin cylinders. It reduced the mean drag of the upstream cylinder (UC) by 2.58% and the downstream cylinder (DC) by more than 62.97%. The fluctuating lift coefficient for UC (DC) was also decreased by more than 70.41% (59.74%). The flow structures showed that when the flow hit UC under the action of small control cylinders, a virtual missile-like aerodynamic shape was formed at the leading edge of UC. In this way, the gap vortex consisted of two asymmetric steady vortices and the vortex length significantly increased. This was also confirmed by HODMD. The coherence modes in the gap were suppressed and thus the interaction between gap flow and wake flow was mitigated, which resulted in the fluid force reduction. Full article
(This article belongs to the Special Issue Applications of Advanced Mathematical Method for Modeling, Predicting, Controlling, and Optimizing the Dynamical System in Engineering)
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