Mathematical Problems in Aerospace

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

Deadline for manuscript submissions: closed (30 March 2023) | Viewed by 33968

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Special Issue Editors


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Guest Editor
State Key Laboratory of Astronautic Dynamics, Xi’an Satellite Control Center, Xi’an, China
Interests: AI in aerospace

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Guest Editor
Department of Engineering Mechanics, Dalian University of Technology, No.2 Linggong Road, Ganjingzi District, Dalian City 116024, China
Interests: the theory and computation of optimal control and their applications in aerospace

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Guest Editor
College of Astronautics, Nanjing Agricultural University, Nanjing, China
Interests: astrodynamics; orbit design and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Mathematical problem in aerospace becomes a hot issue in recent years and has received more and more attention, and deeply affects the development of many fields, such as aerodynamics, astrodynamics, deep space exploration, space environment, manned space flight, etc. Notwithstanding the enormous efforts of mathematicians, natural scientists, and engineers, many major issues remain unresolved. Therefore, there is an urgent need to comprehensively introduce major mathematical problems in aerospace to help people refer to and conduct further in-depth research. This special issue is planned to provide an overview of the latest major mathematical problems in aerospace and their applications in different fields. The purpose of this special issue is to provide a partial contribution to the mathematical theory, computational methods and other issues involved in aerospace. Potential topics include, but are not limited to:

Rocket propulsion;

Planetary atmosphere;

Deep space exploration;

Aerodynamics;

Astrodynamics;

Guidance, navigation, and control;

Manned space flight;

Plume of spacecraft and aircraft;

Thermophysical of spacecraft and aircraft;

Debris, dust, meteoroid, asteroid, comet, planet;

Boundary of the Solar system;

Space environment.

Prof. Dr. Yu Jiang
Prof. Dr. Haijun Peng
Dr. Hongwei Yang
Guest Editors

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Keywords

  • Astrodynamics
  • Dynamical system
  • Space environment
  • Invariant manifold
  • Guidance, navigation, and control
  • Aerospace
  • Celestial Mechanics
  • Planetary Science

Published Papers (20 papers)

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19 pages, 1505 KiB  
Article
Polynomial Chaos Expansion-Based Enhanced Gaussian Process Regression for Wind Velocity Field Estimation from Aircraft-Derived Data
by Marius Marinescu, Alberto Olivares, Ernesto Staffetti and Junzi Sun
Mathematics 2023, 11(4), 1018; https://doi.org/10.3390/math11041018 - 16 Feb 2023
Cited by 1 | Viewed by 1269
Abstract
This paper addresses the problem of spatiotemporal wind velocity field estimation for air traffic management applications. Using data obtained from aircraft, the eastward and northward components of the wind velocity field inside a specific air space are calculated as functions of time. Both [...] Read more.
This paper addresses the problem of spatiotemporal wind velocity field estimation for air traffic management applications. Using data obtained from aircraft, the eastward and northward components of the wind velocity field inside a specific air space are calculated as functions of time. Both short-term wind velocity field forecasting and wind velocity field reconstruction are performed. Wind velocity data are indirectly obtained from the states of the aircraft flying in the relevant airspace, which are broadcast by the ADS-B and Mode-S aircraft surveillance systems. The wind velocity field is estimated by combining two data-driven techniques: the polynomial chaos expansion and the Gaussian process regression. The former approximates the global behavior of the wind velocity field, whereas the latter approximates the local behavior. The eastward and northward wind components of the wind velocity field must be estimated, which causes the problem to be a multiple-output problem. This method enables the estimation of the wind velocity field at any spatiotemporal location using wind velocity observations from any spatiotemporal location, eliminating the need for spatial and temporal grids. Moreover, since the method proposed in this article allows for the probability distributions of the estimates to be computed, it causes the computation of the confidence intervals to be possible. Furthermore, since the method presented in this paper allows for data assimilation, it can be used online to continuously update the wind velocity field estimation. The method is tested on different wind scenarios and different training-test data configurations, by means of which the consistency between the results of the wind velocity field forecasting and the wind velocity field reconstruction is checked. Finally, the ERA5 meteorological reanalysis data of the European Centre for Medium-Range Weather Forecasts are used to validate the proposed technique. The results show that the method is able to reliably estimate the wind velocity field from aircraft-derived data. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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19 pages, 6999 KiB  
Article
The Shape Entropy of Small Bodies
by Yanshuo Ni, He Zhang, Junfeng Li, Hexi Baoyin and Jiaye Hu
Mathematics 2023, 11(4), 878; https://doi.org/10.3390/math11040878 - 9 Feb 2023
Viewed by 1761
Abstract
The irregular shapes of small bodies usually lead to non-uniform distributions of mass, which makes dynamic behaviors in the vicinities of small bodies different to that of planets. This study proposes shape entropy (SE) as an index that compares the shapes of small [...] Read more.
The irregular shapes of small bodies usually lead to non-uniform distributions of mass, which makes dynamic behaviors in the vicinities of small bodies different to that of planets. This study proposes shape entropy (SE) as an index that compares the shapes of small bodies and spheres to describe the shape of a small body. The results of derivation and calculation of SE in two-dimensional and three-dimensional cases show that: SE is independent of the size of geometric figures but depends on the shape of the figures; the SE difference between a geometric figure and a circle or a sphere, which is the limit of SE value, reflects the difference between this figure and a circle or a sphere. Therefore, the description of shapes of small bodies, such as near-spherical, ellipsoid, and elongated, can be quantitatively described via a continuous index. Combining SE and the original inertia index, describing the shape of small bodies, can define the shapes of small bodies and provide a reasonably simple metric to describe a complex shape that is applicable to generalized discussion and analysis rather than highly detailed work on a specific, unique, polyhedral model. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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19 pages, 4802 KiB  
Article
Non-Cooperative Target Attitude Estimation Method Based on Deep Learning of Ground and Space Access Scene Radar Images
by Chongyuan Hou, Rongzhi Zhang, Kaizhong Yang, Xiaoyong Li, Yang Yang, Xin Ma, Gang Guo, Yuan Yang, Lei Liu and Feng Zhou
Mathematics 2023, 11(3), 745; https://doi.org/10.3390/math11030745 - 2 Feb 2023
Cited by 1 | Viewed by 1458
Abstract
Determining the attitude of a non-cooperative target in space is an important frontier issue in the aerospace field, and has important application value in the fields of malfunctioning satellite state assessment and non-cooperative target detection in space. This paper proposes a non-cooperative target [...] Read more.
Determining the attitude of a non-cooperative target in space is an important frontier issue in the aerospace field, and has important application value in the fields of malfunctioning satellite state assessment and non-cooperative target detection in space. This paper proposes a non-cooperative target attitude estimation method based on the deep learning of ground and space access (GSA) scene radar images to solve this problem. In GSA scenes, the observed target satellite can be imaged not only by inverse synthetic-aperture radar (ISAR), but also by space-based optical satellites, with space-based optical images providing more accurate attitude estimates for the target. The spatial orientation of the intersection of the orbital planes of the target and observation satellites can be changed by fine tuning the orbit of the observation satellite. The intersection of the orbital planes is controlled to ensure that it is collinear with the position vector of the target satellite when it is accessible to the radar. Thus, a series of GSA scenes are generated. In these GSA scenes, the high-precision attitude values of the target satellite can be estimated from the space-based optical images obtained by the observation satellite. Thus, the corresponding relationship between a series of ISAR images and the attitude estimation of the target at this moment can be obtained. Because the target attitude can be accurately estimated from the GSA scenes obtained by a space-based optical telescope, these attitude estimation values can be used as training datasets of ISAR images, and deep learning training can be performed on ISAR images of GSA scenes. This paper proposes an instantaneous attitude estimation method based on a deep network, which can achieve robust attitude estimation under different signal-to-noise ratio conditions. First, ISAR observation and imaging models were created, and the theoretical projection relationship from the three-dimensional point cloud to the ISAR imaging plane was constructed based on the radar line of sight. Under the premise that the ISAR imaging plane was fixed, the ISAR imaging results, theoretical projection map, and target attitude were in a one-to-one correspondence, which meant that the mapping relationship could be learned using a deep network. Specifically, in order to suppress noise interference, a UNet++ network with strong feature extraction ability was used to learn the mapping relationship between the ISAR imaging results and the theoretical projection map to achieve ISAR image enhancement. The shifted window (swin) transformer was then used to learn the mapping relationship between the enhanced ISAR images and target attitude to achieve instantaneous attitude estimation. Finally, the effectiveness of the proposed method was verified using electromagnetic simulation data, and it was found that the average attitude estimation error of the proposed method was less than 1°. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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23 pages, 1306 KiB  
Article
Approximations for Secular Variation Maxima of Classical Orbital Elements under Low Thrust
by Zhaowei Wang, Lin Cheng and Fanghua Jiang
Mathematics 2023, 11(3), 744; https://doi.org/10.3390/math11030744 - 2 Feb 2023
Cited by 2 | Viewed by 1341
Abstract
The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. [...] Read more.
The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. Specifically, two steps organize the contribution of this study. First, combined with functional approximations, a set of analytical expressions for the variation maxima of orbital elements over one orbital revolution are derived. Second, the secular approximations for the variation maxima of the inclination and the right ascension of the ascending node are derived and expressed explicitly. An iterative algorithm is given to obtain the secular variation maxima of the other orbital elements the orbital elements other than the inclination and right ascension of the ascending node. Numerical simulations for approximating the variation maxima and a preliminary application in estimation of the velocity increment are given to demonstrate the efficiency and accuracy of the proposed method. Compared with the indirect method used alone for low-thrust trajectory optimization, the computation burden of the proposed method is reduced by over five orders of magnitude, and the computational accuracy is still high. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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24 pages, 10465 KiB  
Article
Deep Neural Network-Based Footprint Prediction and Attack Intention Inference of Hypersonic Glide Vehicles
by Jingjing Xu, Changhong Dong and Lin Cheng
Mathematics 2023, 11(1), 185; https://doi.org/10.3390/math11010185 - 29 Dec 2022
Cited by 4 | Viewed by 1601
Abstract
In response to the increasing threat of hypersonic weapons, it is of great importance for the defensive side to achieve fast prediction of their feasible attack domain and online inference of their most probable targets. In this study, an online footprint prediction and [...] Read more.
In response to the increasing threat of hypersonic weapons, it is of great importance for the defensive side to achieve fast prediction of their feasible attack domain and online inference of their most probable targets. In this study, an online footprint prediction and attack intention inference algorithm for hypersonic glide vehicles (HGVs) is proposed by leveraging the utilization of deep neural networks (DNNs). Specifically, this study focuses on the following three contributions. First, a baseline multi-constrained entry guidance algorithm is developed based on a compound bank angle corridor, and then a dataset containing enough trajectories for the following DNN learning is generated offline by traversing different initial states and control commands. Second, DNNs are developed to learn the functional relationship between the flight state/command and the corresponding ranges; on this basis, an online footprint prediction algorithm is developed by traversing the maximum/minimum ranges and different heading angles. Due to the substitution of DNNs for multiple times of trajectory integration, the computational efficiency for footprint prediction is significantly improved to the millisecond level. Third, combined with the predicted footprint and the hidden information in historical flight data, the attack intention and most probable targets can be further inferred. Simulations are conducted through comparing with the state-of-the-art algorithms, and results demonstrate that the proposed algorithm can achieve accurate prediction for flight footprint and attack intention while possessing significant real-time advantage. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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19 pages, 6608 KiB  
Article
Design of Ganymede-Synchronous Frozen Orbit around Europa
by Xuxing Huang, Bin Yang, Shuang Li, Jinglang Feng and Josep J. Masdemont
Mathematics 2023, 11(1), 41; https://doi.org/10.3390/math11010041 - 22 Dec 2022
Cited by 1 | Viewed by 1416
Abstract
A Ganymede-synchronous frozen orbit around Europa provides a stable spatial geometry between a Europa probe and a Ganymede lander, which facilitates the observation of Ganymede and data transmission between probes. However, the third-body gravitation perturbation of Ganymede continues to accumulate and affect the [...] Read more.
A Ganymede-synchronous frozen orbit around Europa provides a stable spatial geometry between a Europa probe and a Ganymede lander, which facilitates the observation of Ganymede and data transmission between probes. However, the third-body gravitation perturbation of Ganymede continues to accumulate and affect the long-term evolution of the Europa probe. In this paper, the relative orbit of Ganymede with respect to Europa is considered to accurately capture the perturbation potential. The orbital evolution behaviors of the Europa probe under the non-spherical gravitation of Europa and the third-body gravitation of Jupiter and Ganymede are studied based on a double-averaging framework. Then, the initial orbital conditions of the Ganymede-synchronous frozen orbit are developed. A station-keeping maneuver was performed to maintain the orbital elements to achieve the Ganymede-synchronous and frozen behaviors. A numerical simulation showed that the consumption for orbital maintenance is acceptable. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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28 pages, 15028 KiB  
Article
Associated Fault Diagnosis of Power Supply Systems Based on Graph Matching: A Knowledge and Data Fusion Approach
by Laifa Tao, Haifei Liu, Jiqing Zhang, Xuanyuan Su, Shangyu Li, Jie Hao, Chen Lu, Mingliang Suo and Chao Wang
Mathematics 2022, 10(22), 4306; https://doi.org/10.3390/math10224306 - 17 Nov 2022
Cited by 3 | Viewed by 1469
Abstract
With the rapid development of more-electric and all-electric aircraft, the role of power supply systems in aircraft is becoming increasingly prominent. However, due to the complex coupling within the power supply system, a fault in one component often leads to parameter abnormalities in [...] Read more.
With the rapid development of more-electric and all-electric aircraft, the role of power supply systems in aircraft is becoming increasingly prominent. However, due to the complex coupling within the power supply system, a fault in one component often leads to parameter abnormalities in multiple components within the system, which are termed associated faults. Compared with conventional faults, the diagnosis of associated faults is difficult because the fault source is hard to trace and the fault mode is difficult to identify accurately. To this end, this paper proposes a graph-matching approach for the associated fault diagnosis of power supply systems based on a deep residual shrinkage network. The core of the proposed approach involves supplementing the incomplete prior fault knowledge with monitoring data to obtain a complete cluster of associated fault graphs. The association graph model of the power supply system is first constructed based on a topology with characteristic signal propagation and the associated measurements of typical components. Furthermore, fault propagation paths are backtracked based on the Warshall algorithm, and abnormal components are set to update and enhance the association relationship, establishing a complete cluster of typical associated fault mode graphs and realizing the organic combination and structured storage of knowledge and data. Finally, a deep residual shrinkage network is used to diagnose the associated faults via graph matching between the current state graph and the historical graph cluster. The comparative experiments conducted on the simulation model of an aircraft power supply system demonstrate that the proposed method can achieve high-precision associated fault diagnosis, even under circumstances where there are an insufficient number of samples and missing parameters. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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24 pages, 912 KiB  
Article
A Unified Multi-Objective Optimization Framework for UAV Cooperative Task Assignment and Re-Assignment
by Xiaohua Gao, Lei Wang, Xichao Su, Chen Lu, Yu Ding, Chao Wang, Haijun Peng and Xinwei Wang
Mathematics 2022, 10(22), 4241; https://doi.org/10.3390/math10224241 - 13 Nov 2022
Cited by 6 | Viewed by 1422
Abstract
This paper focuses on cooperative multi-task assignment and re-assignment problems when multiple unmanned aerial vehicles (UAVs) attack multiple known targets. A unified multi-objective optimization framework for UAV cooperative task assignment and re-assignment is studied in this paper. In order to simultaneously optimize the [...] Read more.
This paper focuses on cooperative multi-task assignment and re-assignment problems when multiple unmanned aerial vehicles (UAVs) attack multiple known targets. A unified multi-objective optimization framework for UAV cooperative task assignment and re-assignment is studied in this paper. In order to simultaneously optimize the losses and benefits of the UAVs, we establish a multi-objective optimization model. The amount of tasks that each UAV can perform and the number of attacks on each target are limited according to the ammunition capacity of each UAV and the value of each target. To solve this multi-objective optimization problem, a multi-objective genetic algorithm suitable for UAV cooperative task assignment is constructed based on the NSGA-II algorithm. At the same time, a selection strategy is used to assist decision-makers in choosing one or more solutions from the Pareto-optimal front. Moreover, to deal with emergencies such as UAV damage and to detect of new targets, a task re-assignment algorithm based on the contract network protocol (CNP) is developed. It can be implemented in real-time while only slightly sacrificing the ability to seek the optimal solution. Simulation results demonstrate that the methods developed in this paper are effective. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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25 pages, 5609 KiB  
Article
An Improved Optimization Algorithm for Aeronautical Maintenance and Repair Task Scheduling Problem
by Changjiu Li, Yong Zhang, Xichao Su and Xinwei Wang
Mathematics 2022, 10(20), 3777; https://doi.org/10.3390/math10203777 - 13 Oct 2022
Cited by 7 | Viewed by 1843
Abstract
The maintenance of carrier-based aircraft is a critical factor restricting the availability of aircraft fleets and their capacity to sortie and operate. In this study, an aeronautical maintenance and repair task scheduling problem for carrier-based aircraft fleets in hangar bays is investigated to [...] Read more.
The maintenance of carrier-based aircraft is a critical factor restricting the availability of aircraft fleets and their capacity to sortie and operate. In this study, an aeronautical maintenance and repair task scheduling problem for carrier-based aircraft fleets in hangar bays is investigated to improve the maintenance efficiency of aircraft carrier hangar bays. First, the operational process of scheduling aeronautical maintenance tasks is systematically analyzed. Based on maintenance resource constraints and actual maintenance task requirements, a wave availability index and load balance index for the maintenance personnel are proposed for optimization. An aeronautical maintenance task scheduling model is formulated for carrier-based aircraft fleets. Second, model abstraction is performed to simulate a multi-skill resource-constrained project scheduling problem, and an improved teaching-learning-based optimization algorithm is proposed. The algorithm utilizes a serial scheduling generation scheme based on resource constraint advancement. Finally, the feasibility and effectiveness of the modeling and algorithm are verified by using simulation cases and algorithm comparisons. The improved teaching-learning-based optimization algorithm exhibits improved solution stability and optimization performance. This method provides theoretical support for deterministic aeronautical maintenance scheduling planning and reduces the burden associated with manual scheduling and planning. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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20 pages, 13633 KiB  
Article
The Fast Generation of the Reachable Domain for Collision-Free Asteroid Landing
by Yingjie Zhao, Hongwei Yang and Jincheng Hu
Mathematics 2022, 10(20), 3763; https://doi.org/10.3390/math10203763 - 12 Oct 2022
Cited by 2 | Viewed by 1101
Abstract
For the mission requirement of collision-free asteroid landing with a given time of flight (TOF), a fast generation method of landing reachable domain based on section and expansion is proposed. First, to overcome the difficulties of trajectory optimization caused by anti-collision path constraints, [...] Read more.
For the mission requirement of collision-free asteroid landing with a given time of flight (TOF), a fast generation method of landing reachable domain based on section and expansion is proposed. First, to overcome the difficulties of trajectory optimization caused by anti-collision path constraints, a two-stage collision-free trajectory optimization model is used to improve the efficiency of trajectory optimization. Second, the velocity increment under a long TOF is analyzed to obtain the distribution law of the reachable domain affected by the TOF, and the generation problem of the reachable domain is transformed into the solution problem of the initial boundary and the continuous boundary. For the initial boundary, the section method is used to acquire a point on the boundary as the preliminary reachable domain boundary. The solution of continuous boundary is based on the initial boundary continuously expanding the section into the reachable domain until the boundary is continuous. Finally, the proposed method is applied to the asteroids 101955 Bennu and 2063 Bacchus. The simulation results show that this method can quickly and accurately obtain the reachable domain of collision-free asteroid landing in a given TOF and is applicable to different initial positions. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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25 pages, 9869 KiB  
Article
Stability Analysis on the Moon’s Rotation in a Perturbed Binary Asteroid
by Yunfeng Gao, Bin Cheng, Yang Yu, Jing Lv and Hexi Baoyin
Mathematics 2022, 10(20), 3757; https://doi.org/10.3390/math10203757 - 12 Oct 2022
Cited by 2 | Viewed by 1046
Abstract
Numerical calculation provides essential tools for deep space exploration, which are indispensable to mission design and planetary research. In a specific case of binary asteroid defense such as the DART mission, an accurate understanding of the possible dynamical responses and the system’s stability [...] Read more.
Numerical calculation provides essential tools for deep space exploration, which are indispensable to mission design and planetary research. In a specific case of binary asteroid defense such as the DART mission, an accurate understanding of the possible dynamical responses and the system’s stability and engineers’ prerequisite. In this paper, we discuss the numeric techniques for tracking the year-long motion of the secondary after being perturbed, based upon which its rotational stability is analyzed. For long-term simulations, we compared the performances of several integrating schemes in the scenario of a post-impact full two-body system, including low- and high-order Runge–Kutta methods, and a symplectic integrator that combines the finite element method with a symplectic integral format. For rotational stability analysis of the secondary, we focus on the rotation of the secondary around its long-axis. We calculated a linearised error propagation matrix and found that, in the case of tidal locking of the secondary to the primary, the rotation is stable; as the perturbation amplitude of the spin angular velocity of the secondary increases, the rotation will lose stability and will be prone to being unstable in the long-axis direction of the secondary. Furthermore, we investigated the one-year-long influences of the non-spherical perturbations of the primary and the secondary. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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22 pages, 3793 KiB  
Article
Simultaneous-Fault Diagnosis of Satellite Power System Based on Fuzzy Neighborhood ζ-Decision-Theoretic Rough Set
by Laifa Tao, Chao Wang, Yuan Jia, Ruzhi Zhou, Tong Zhang, Yiling Chen, Chen Lu and Mingliang Suo
Mathematics 2022, 10(19), 3414; https://doi.org/10.3390/math10193414 - 20 Sep 2022
Cited by 4 | Viewed by 1250
Abstract
Due to the increasing complexity of the entire satellite system and the deteriorating orbital environment, multiple independent single faults may occur simultaneously in the satellite power system. However, two stumbling blocks hinder the effective diagnosis of simultaneous-fault, namely, the difficulty of obtaining the [...] Read more.
Due to the increasing complexity of the entire satellite system and the deteriorating orbital environment, multiple independent single faults may occur simultaneously in the satellite power system. However, two stumbling blocks hinder the effective diagnosis of simultaneous-fault, namely, the difficulty of obtaining the simultaneous-fault data and the extremely complicated mapping of the simultaneous-fault modes to the sensor data. To tackle the challenges, a fault diagnosis strategy based on a novel rough set model is proposed. Specifically, a novel rough set model named FNζDTRS by introducing a concise loss function matrix and fuzzy neighborhood relationship is proposed to accurately mine and characterize the relationship between fault and data. Furthermore, an attribute rule-based fault matching strategy is designed without using simultaneous-fault data as training samples. The numerical experiments demonstrate the effectiveness of the FNζDTRS model, and the diagnosis experiments performed on a satellite power system illustrate the superiority of the proposed approach. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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24 pages, 7283 KiB  
Article
SMoCo: A Powerful and Efficient Method Based on Self-Supervised Learning for Fault Diagnosis of Aero-Engine Bearing under Limited Data
by Zitong Yan and Hongmei Liu
Mathematics 2022, 10(15), 2796; https://doi.org/10.3390/math10152796 - 6 Aug 2022
Cited by 15 | Viewed by 2475
Abstract
Vibration signals collected in real industrial environments are usually limited and unlabeled. In this case, fault diagnosis methods based on deep learning tend to perform poorly. Previous work mainly used the unlabeled data of the same diagnostic object to improve the diagnostic accuracy, [...] Read more.
Vibration signals collected in real industrial environments are usually limited and unlabeled. In this case, fault diagnosis methods based on deep learning tend to perform poorly. Previous work mainly used the unlabeled data of the same diagnostic object to improve the diagnostic accuracy, but it did not make full use of the easily available unlabeled signals from different sources. In this study, a signal momentum contrast for unsupervised representation learning (SMoCo) based on the contrastive learning algorithm—momentum contrast for unsupervised visual representation Learning (MoCo)—is proposed. It can learn how to automatically extract fault features from unlabeled data collected from different diagnostic objects and then transfer this ability to target diagnostic tasks. On the structure, SMoCo increases the stability by adding batch normalization to the multilayer perceptron (MLP) layer of MoCo and increases the flexibility by adding a predictor to the query network. Using the data augmentation method, SMoCo performs feature extraction on vibration signals from both time and frequency domains, which is called signal multimodal learning (SML). It has been proved by experiments that after pre-training with artificially injected fault bearing data, SMoCo can learn a powerful and robust feature extractor, which can greatly improve the accuracy no matter the target diagnostic data with different working conditions, different failure modes, or even different types of equipment from the pre-training dataset. When faced with the target diagnosis task, SMoCo can achieve accuracy far better than other representative methods in only a very short time, and its excellent robustness regarding the amount of data in both the unlabeled pre-training dataset and the target diagnosis dataset as well as the strong noise demonstrates its great potential and superiority in fault diagnosis. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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14 pages, 3676 KiB  
Article
A Novel Decomposed Optical Architecture for Satellite Terrestrial Network Edge Computing
by Xiaotao Guo, Ying Zhang, Yu Jiang, Shenggang Wu and Hengnian Li
Mathematics 2022, 10(14), 2515; https://doi.org/10.3390/math10142515 - 19 Jul 2022
Viewed by 1341
Abstract
Aiming at providing a high-performance terrestrial network for edge computing in satellite networks, we experimentally demonstrate a high bandwidth and low latency decomposed optical computing architecture based on distributed Nanoseconds Optical Switches (NOS). Experimental validation of the decomposed computing network prototype employs a [...] Read more.
Aiming at providing a high-performance terrestrial network for edge computing in satellite networks, we experimentally demonstrate a high bandwidth and low latency decomposed optical computing architecture based on distributed Nanoseconds Optical Switches (NOS). Experimental validation of the decomposed computing network prototype employs a four-port NOS to interconnect four processor/memory cubes. The SOA-based optical gates provide an ON/OFF ratio greater than 60 dB, enabling none-error transmission at a Bit Error Rate (BER) of 1 × 10−9. An end-to-end access latency of 122.3 ns and zero packet loss are obtained in the experimental assessment. Scalability and physical performance considering signal impairments when increasing the NOS port count are also investigated. An output OSNR of up to 30.5 dB and an none-error transmission with 1.5 dB penalty is obtained when scaling the NOS port count to 64. Moreover, exploiting the experimentally measured parameters, the network performance of NOS-based decomposed computing architecture is numerically assessed under larger network scales. The results indicate that, under a 4096-cube network scale, the NOS-based decomposed computing architecture achieves 148.5 ns end-to-end latency inside the same rack and zero packet loss at a link bandwidth of 40 Gb/s. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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11 pages, 1690 KiB  
Article
Neural Network-Based Approximation Model for Perturbed Orbit Rendezvous
by Anyi Huang and Shenggang Wu
Mathematics 2022, 10(14), 2489; https://doi.org/10.3390/math10142489 - 18 Jul 2022
Cited by 2 | Viewed by 1226
Abstract
An approximation of orbit rendezvous is usually used in the global optimization of multi-target rendezvous missions, which can greatly affect the efficiency of optimization process. A fast neural network-based surrogate model is proposed to approximate the optimal velocity increment of perturbed orbit rendezvous [...] Read more.
An approximation of orbit rendezvous is usually used in the global optimization of multi-target rendezvous missions, which can greatly affect the efficiency of optimization process. A fast neural network-based surrogate model is proposed to approximate the optimal velocity increment of perturbed orbit rendezvous in low Earth orbits. According to a dynamic analysis, the initial and target orbits together with the flight time are transformed into a nine-dimensional normalized vector that is used as the input layer of the neural network. An existing approximation method is introduced to quickly generate the training data. In simulations, different numbers of layer nodes and hidden layers are tested to choose the best parameters. The proposed neural network model demonstrates high precision and high efficiency compared with previous approximation methods and neural network models. The mean relative error is less than 1%. Finally, a case of an optimization of a multi-target rendezvous mission is tested to prove the potential application of the neural network model. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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34 pages, 4573 KiB  
Article
North/South Station Keeping of the GEO Satellites in Asymmetric Configuration by Electric Propulsion with Manipulator
by Lijun Ye, Chunyang Liu, Wenshan Zhu, Haining Yin, Fucheng Liu and Hexi Baoyin
Mathematics 2022, 10(13), 2340; https://doi.org/10.3390/math10132340 - 4 Jul 2022
Cited by 6 | Viewed by 1852
Abstract
Geosynchronous orbit (GEO) is a very important strategic resource. In order to maximize the utilization of the GEO resources, the use of all-electric propulsion GEO platforms can greatly extend the service life of satellites. Therefore, this paper proposes a control scheme of the [...] Read more.
Geosynchronous orbit (GEO) is a very important strategic resource. In order to maximize the utilization of the GEO resources, the use of all-electric propulsion GEO platforms can greatly extend the service life of satellites. Therefore, this paper proposes a control scheme of the north/south station keeping (NSSK) by using electric propulsion with a manipulator. First, on the basis of the traditional calculation method of the semi-diurnal period of the orbital inclination, the calculation method of the semi-monthly period and the semi-annual period of the orbital inclination are proposed. The new method can reduce the fuel consumption and reduce the control amount and control frequency of the station keeping (SK). Secondly, a fuel-optimized NSSK algorithm by using electric propulsion with a manipulator is proposed. The algorithm can not only be applied to a large initial orbital inclination but also can unload the large angular momentum of the asymmetric satellites while keeping the north/south station, thereby avoiding the loss of control of the satellite’s attitude. The research results of this paper provide a new idea for the SK control of the GEO satellites and have great engineering application value. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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13 pages, 3395 KiB  
Article
Bistatic Radar Observations Correlation of LEO Satellites Considering J2 Perturbation
by Zongbo Huyan, Yu Jiang, Hengnian Li, Pengbin Ma and Dapeng Zhang
Mathematics 2022, 10(13), 2197; https://doi.org/10.3390/math10132197 - 23 Jun 2022
Viewed by 1222
Abstract
Space debris near Earth severely interferes with the development of space, and cataloging space objects is increasingly important. Since optical telescopes and radars used to detect space debris only provide short-arc observations, mathematical algorithms are needed to solve problems in the correlation of [...] Read more.
Space debris near Earth severely interferes with the development of space, and cataloging space objects is increasingly important. Since optical telescopes and radars used to detect space debris only provide short-arc observations, mathematical algorithms are needed to solve problems in the correlation of observations. In this work, an efficient mathematical algorithm based on J2 analytic solutions is put forward. Initial orbit determination (IOD) serves as the starter and orbit determination (OD) with the weighted least-squares method (WLSM) is used to improve the accuracy of the estimated orbit. Meanwhile, the effect of the weight of different observation types is analyzed. The correlation criteria for bistatic radar observations are accordingly developed. Lastly, the variation in and evolution of the error of bistatic radar ranging are discussed. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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15 pages, 3669 KiB  
Article
Containment Control for Discrete-Time Multi-Agent Systems with Nonconvex Control Input and Position Constraints
by Ning Gao and Yikang Yang
Mathematics 2022, 10(12), 2010; https://doi.org/10.3390/math10122010 - 10 Jun 2022
Viewed by 1022
Abstract
With increasing attention on containment control problems in several areas, we investigate this specific problem which can be more practical. Systems with nonconvex input and position constraints are common but can be strongly nonlinear. A distribute algorithm using a projection operator is proposed [...] Read more.
With increasing attention on containment control problems in several areas, we investigate this specific problem which can be more practical. Systems with nonconvex input and position constraints are common but can be strongly nonlinear. A distribute algorithm using a projection operator is proposed to ensure that the control input of every follower remains in a nonconvex set and that all followers stay in the closed set given by leaders. In analysis, a model transformation is proposed, and then we introduce a method utilizing two similar triangles to prove the acceptability of the algorithm. The findings of the research could be pragmatic in robotics, astronautics, and so on. At last, numerical simulations are provided to show the contrast and results. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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22 pages, 12202 KiB  
Article
A Distributed Formation Joint Network Navigation and Positioning Algorithm
by Lvyang Ye, Yikang Yang, Jiangang Ma, Lingyu Deng and Hengnian Li
Mathematics 2022, 10(10), 1627; https://doi.org/10.3390/math10101627 - 10 May 2022
Cited by 2 | Viewed by 1514
Abstract
In view of the problem that the leader-follower joint navigation scheme relies too much on the absolute navigation and positioning accuracy of the leader node, under the conditions of distributed network-centric warfare (NCW) and to meet the location service accuracy, reliability, and synergy [...] Read more.
In view of the problem that the leader-follower joint navigation scheme relies too much on the absolute navigation and positioning accuracy of the leader node, under the conditions of distributed network-centric warfare (NCW) and to meet the location service accuracy, reliability, and synergy efficiency of the future integrated communication, navigation (ICN), we built a joint navigation and positioning system with low Earth orbit (LEO), airborne data link, and inertial navigation system (INS) as the core; designed a ranging and time-synchronization scheme of the joint navigation and positioning system; and established a joint navigation and positioning method for formation and networking based on mutual ranging and velocity measurement information between aircrafts. Finally, based on the designed LEO constellation, the universality, effectiveness, superiority, and potential superiority of algorithm are verified, respectively. The simulation results show that the scheme can meet the requirements of joint location services in challenging environments, and could be used as a reference scheme for future ICN integration. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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Review

Jump to: Research

28 pages, 1115 KiB  
Review
Asteroids and Their Mathematical Methods
by Yu Jiang, Yanshuo Ni, Hexi Baoyin, Junfeng Li and Yongjie Liu
Mathematics 2022, 10(16), 2897; https://doi.org/10.3390/math10162897 - 12 Aug 2022
Cited by 3 | Viewed by 2918
Abstract
In this paper, the basic classification of asteroids and the history and current situation of asteroid exploration are introduced. Furthermore, some recent research progress on the orbital dynamics of asteroids, including models of the gravitational potential field, the dynamics near asteroids, hopping motion [...] Read more.
In this paper, the basic classification of asteroids and the history and current situation of asteroid exploration are introduced. Furthermore, some recent research progress on the orbital dynamics of asteroids, including models of the gravitational potential field, the dynamics near asteroids, hopping motion on the surface, and bifurcations under varying external parameters, is reviewed. In the meanwhile, the future research development such as the configuration and evolution of binary or triple asteroid systems and near-Earth asteroid defense is briefly discussed. Full article
(This article belongs to the Special Issue Mathematical Problems in Aerospace)
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