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Regular virtual tube for cooperative transportation of a payload by multiple quadrotors
Jiacheng TANG, Zixiao YANG, Lei ZHANG, Tianjiang HU, Bo ZHU
Journal of Systems Engineering and Electronics    2025, 36 (4): 1068-1076.   DOI: 10.23919/JSEE.2025.000076
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How multi-unmanned aerial vehicles (UAVs) carrying a payload pass an obstacle-dense environment is practically important. Up to now, there have been few results on safe motion planning for the multi-UAVs cooperative transportation system (CTS) to pass through such an environment. The problem is challenging because it is difficult to analyze and explicitly take into account the swing motion of the payload in planning. In this paper, a modeling method of virtual tube is proposed by fusing the advantages of the existing modeling algorithm for regular virtual tube and the expansion environment method. The proposed method can not only generate a safe and smooth tube for UAVs, but also ensure the payload stays away from the dense obstacles. Simulation results show the effectiveness of the method and the safety of the planned tube.

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Dwell scheduling for MFIS with aperture partition and JRC waveform
Ting CHENG, Luqing LIU, Siyu HENG
Journal of Systems Engineering and Electronics    2025, 36 (4): 951-961.   DOI: 10.23919/JSEE.2025.000002
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The multifunctional integration system (MFIS) is based on a common hardware platform that controls and regulates the system’s configurable parameters through software to meet different operational requirements. Dwell scheduling is a key for the system to realize multifunction and maximize the resource utilization. In this paper, an adaptive dwell scheduling optimization model for MFIS which considers the aperture partition and joint radar communication (JRC) waveform is established. To solve the formulated optimization problem, JRC scheduling conditions are proposed, including time overlapping condition, beam direction condition and aperture condition. Meanwhile, an effective mechanism to dynamically occupy and release the aperture resource is introduced, where the time-pointer will slide to the earliest ending time of all currently scheduled tasks so that the occupied aperture resource can be released timely. Based on them, an adaptive dwell scheduling algorithm for MFIS with aperture partition and JRC waveform is put forward. Simulation results demonstrate that the proposed algorithm has better comprehensive scheduling performance than up-to-date algorithms in all considered metrics.

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Self-play training and analysis for GEO inspection game with modular actions
Rui ZHOU, Weichao ZHONG, Wenlong LI, Hao ZHANG
Journal of Systems Engineering and Electronics    2025, 36 (5): 1353-1373.   DOI: 10.23919/JSEE.2025.000115
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This paper comprehensively explores the impulsive on-orbit inspection game problem utilizing reinforcement learning and game training methods. The purpose of the spacecraft is to inspect the entire surface of a non-cooperative target with active maneuverability in front lighting. First, the impulsive orbital game problem is formulated as a turn-based sequential game problem. Second, several typical relative orbit transfers are encapsulated into modules to construct a parameterized action space containing discrete modules and continuous parameters, and multi-pass deep Q-networks (MPDQN) algorithm is used to implement autonomous decision-making. Then, a curriculum learning method is used to gradually increase the difficulty of the training scenario. The backtracking proportional self-play training framework is used to enhance the agent’s ability to defeat inconsistent strategies by building a pool of opponents. The behavior variations of the agents during training indicate that the intelligent game system gradually evolves towards an equilibrium situation. The restraint relations between the agents show that the agents steadily improve the strategy. The influence of various factors on game results is tested.

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Optimization model for performance-based warranty decision of degraded systems based on improved sparrow search algorithm
Enzhi DONG, Zhonghua CHENG, Zichang LIU, Xi ZHU, Rongcai WANG, Yongsheng BAI
Journal of Systems Engineering and Electronics    2025, 36 (5): 1259-1280.   DOI: 10.23919/JSEE.2025.000135
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Performance-based warranties (PBWs) are widely used in industry and manufacturing. Given that PBW can impose financial burdens on manufacturers, rational maintenance decisions are essential for expanding profit margins. This paper proposes an optimization model for PBW decisions for systems affected by Gamma degradation processes, incorporating periodic inspection. A system performance degradation model is established. Preventive maintenance probability and corrective renewal probability models are developed to calculate expected warranty costs and system availability. A benefits function, which includes incentives, is constructed to optimize the initial and subsequent inspection intervals and preventive maintenance thresholds, thereby maximizing warranty profit. An improved sparrow search algorithm is developed to optimize the model, with a case study on large steam turbine rotor shafts. The results suggest the optimal PBW strategy involves an initial inspection interval of approximately 20 months, with subsequent intervals of about four months, and a preventive maintenance threshold of approximately 37.39 mm wear. When compared to common cost-minimization-based condition maintenance strategies and PBW strategies that do not differentiate between initial and subsequent inspection intervals, the proposed PBW strategy increases the manufacturer’s profit by 1% and 18%, respectively. Sensitivity analyses provide managerial recommendations for PBW implementation. The PBW strategy proposed in this study significantly increases manufacturers’ profits by optimizing inspection intervals and preventive maintenance thresholds, and manufacturers should focus on technological improvement in preventive maintenance and cost control to further enhance earnings.

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Online midcourse guidance method for intercepting high-speed gliding target
Jinlin ZHANG, Jiong LI, Jikun YE, Humin LEI, Wanli LI, Yangchao HE
Journal of Systems Engineering and Electronics    2025, 36 (5): 1374-1388.   DOI: 10.23919/JSEE.2025.000133
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In this paper, an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed. Firstly, the affine system is used to build a dynamic model and analyze the state constraints. The midcourse guidance problem is transformed into a continuous time optimization problem. Secondly, the problem is transformed into a discrete convex programming problem by affine control variable relaxation, Gaussian pseudospectral discretization and constraints linearization. Then, the off-line midcourse guidance trajectory is generated before midcourse guidance. It is used as the initial reference trajectory for online correction of midcourse guidance. An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time. And the design of discrete points decreases with flight time to improve the solving efficiency. In addition, it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance. Numerical simulation shows the feasibility and effectiveness of the proposed method.

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A robust adaptive filtering algorithm for high-maneuvering hypersonic vehicles
Xinru LIANG, Changsheng GAO, Wuxing JING, Ruoming AN
Journal of Systems Engineering and Electronics    2025, 36 (5): 1317-1334.   DOI: 10.23919/JSEE.2025.000131
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This paper concentrates on addressing the hypersonic glide vehicle (HGV) tracking problem considering the high maneuverability and non-stationary heavy-tailed measurement noise without prior statistics in complicated flight environments. Since the interacting multiple model (IMM) filtering is famous with its ability to cover the movement property of motion models, the problem is formulated as modeling the non-stationary heavy-tailed measurement noise without any prior statistics in the IMM framework. Firstly, without any prior statistics, the Gaussian-inverse Wishart distribution is embedded in the improved Pearson type-VII (PTV) distribution, which can adaptively adjust the parameters to model the non-stationary heavy-tailed measurement noise. Besides, degree of freedom (DOF) parameters are surrogated by the maximization of evidence lower bound (ELBO) in the variational Bayesian optimization framework instead of fixed value to handle uncertain non-Gaussian degrees. Then, this paper analytically derives fusion forms based on the maximum Versoria fusion criterion instead of the moment matching approach, which can provide a precise approximation for the PTV mixture distribution in the mixing and output steps combined with the weight Kullback-Leibler average theory. Simulation results demonstrate the superiority and robustness of the proposed algorithm in typical HGVs tracking when the measurement noise without priori statistics is non-stationary.

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Dual CG-IG distribution model for sea clutter and its parameter correction method
Zhen LI, Huafeng HE, Tao ZHOU, Qi ZHANG, Xiaofei HAN, Yongquan YOU
Journal of Systems Engineering and Electronics    2025, 36 (5): 1177-1187.   DOI: 10.23919/JSEE.2025.000050
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Accurate modeling and parameter estimation of sea clutter are fundamental for effective sea surface target detection. With the improvement of radar resolution, sea clutter exhibits a pronounced heavy-tailed characteristic, rendering traditional distribution models and parameter estimation methods less effective. To address this, this paper proposes a dual compound-Gaussian model with inverse Gaussian texture (CG-IG) distribution model and combines it with an improved Adam algorithm to introduce a method for parameter correction. This method effectively fits sea clutter with heavy-tailed characteristics. Experiments with real measured sea clutter data show that the dual CG-IG distribution model, after parameter correction, accurately describes the heavy-tailed phenomenon in sea clutter amplitude distribution, and the overall mean square error of the distribution is reduced.

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Disintegration of heterogeneous combat network based on double deep Q-learning
Wenhao CHEN, Gang CHEN, Jichao LI, Jiang JIANG
Journal of Systems Engineering and Electronics    2025, 36 (5): 1235-1246.   DOI: 10.23919/JSEE.2024.000063
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The rapid development of military technology has prompted different types of equipment to break the limits of operational domains and emerged through complex interactions to form a vast combat system of systems (CSoS), which can be abstracted as a heterogeneous combat network (HCN). It is of great military significance to study the disintegration strategy of combat networks to achieve the breakdown of the enemy’s CSoS. To this end, this paper proposes an integrated framework called HCN disintegration based on double deep $Q$-learning (HCN-DDQL). Firstly, the enemy’s CSoS is abstracted as an HCN, and an evaluation index based on the capability and attack costs of nodes is proposed. Meanwhile, a mathematical optimization model for HCN disintegration is established. Secondly, the learning environment and double deep $Q$-network model of HCN-DDQL are established to train the HCN’s disintegration strategy. Then, based on the learned HCN-DDQL model, an algorithm for calculating the HCN’s optimal disintegration strategy under different states is proposed. Finally, a case study is used to demonstrate the reliability and effectiveness of HCN-DDQL, and the results demonstrate that HCN-DDQL can disintegrate HCNs more effectively than baseline methods.

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Outdoor navigation of millimeter-wave radar quadrotors based on optimal virtual tube
Delong WU, Hao FANG, Yiren HAO, Aobo WANG
Journal of Systems Engineering and Electronics    2025, 36 (4): 1057-1067.   DOI: 10.23919/JSEE.2025.000099
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This paper presents a quadcopter system for navigation in outdoor urban environments. The main contributions include the hardware design, the establishment of global occupancy grid maps based on millimeter-wave radars, the trajectory planning scheme based on optimal virtual tube methods, and the controller structure based on dynamics. The proposed system focuses on utilizing a compact and lightweight quadrotor with sensors to achieve navigation that conforms to the direction of urban roads with high computational efficiency and safety. Our work is an application of millimeter-wave radars and virtual tube planning for obstacle avoidance in navigation. The validness and effectiveness of the proposed system are verified by experiments.

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Active disturbance rejection control based on cascade high-order extended state observer for systems with time-varying disturbances and measurement noise
Bin FENG, Weihua FAN, Yang GAO, Qingwei CHEN
Journal of Systems Engineering and Electronics    2025, 36 (6): 1679-1691.   DOI: 10.23919/JSEE.2025.000094
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This paper investigates the high-performance control issues of systems affected by time-varying disturbances and measurement noise. Conventionally, active disturbance rejection control (ADRC) is a favorable control strategy to reject unknown disturbances and uncertainties. However, its control performance is limited because standard extended state observer (ESO) struggles to effectively estimate time-varying disturbances. The emergence of high-order ESO (HESO) alleviates the limitation. Unfortunately, it deteriorates the noise suppression capability when the disturbance rejection is enhanced. To tackle this challenge, an improved ADRC with cascade HESO (CHESO) is proposed. A comprehensive theoretical analysis associated with the performance of HESO is given for the first time. The presented analyses provide an intuitive understanding of the performance of HESO. Then, a novel CHESO is developed. The convergence of CHESO is proved via input-to-state stable theory. Extensive frequency domain analyses indicate that CHESO has stronger disturbance rejection and high-frequency noise attenuation performance than ESO and HESO without increasing the observer bandwidth. Comparative simulations conducted on a servo control system validate the effectiveness and preponderance of the proposed method.

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Analysis of high precision detection technique based on optical MEMS accelerometer with double gratings
Honghao MA, Xiao WANG, Shan GAO, Yu ZHANG
Journal of Systems Engineering and Electronics    2025, 36 (5): 1335-1341.   DOI: 10.23919/JSEE.2025.000072
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A high precision detection technique is analyzed based on the optical micro electro-mechanical system (MEMS) accelerometer with double gratings for noise suppression and scale factor enhancement. The brief sensing model and modulation detection model are built using the phase sensitive detection, and the relationship between stimulated acceleration and system output is given. The schematics of gap modulation and light intensity modulation are analyzed respectively, and the choice of modulation frequency in the optical MEMS accelerometer system is discussed. According to the experimental results, the scale factor is improved from 15.45 V/g with the gap modulation to 18.78 V/g with the light intensity modulation, and the signal to noise ratio is improved from 42.95 dB to 81.73 dB. The overall noise level in the optical MEMS accelerometer is effectively suppressed.

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Self-position determination on V2I communications based on alternating least square of cross-covariance matrix
Kang JIANG, Hao HU, Jiaqi LI, Yushan XIE, Xinlei SHI, Xiaofei ZHANG
Journal of Systems Engineering and Electronics    2025, 36 (6): 1443-1452.   DOI: 10.23919/JSEE.2025.000100
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The Global Position System (GPS) is a reliable method for positioning in most scenarios, but it falls short in harsh environments like urban vehicular scenarios, where numerous trees or flyovers obstruct the signals. This presents an unprecedented challenge for autonomous vehicles or applications requiring high accuracy. Fortunately, vehicular ad-hoc networks (VANET) offer an effective solution, where vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications are used to enhance location awareness. In V2I communications, the roadside units (RSU) transmit beacon packets, and the vehicle receives numerous packets from different RSUs to establish communication. To further improve localization accuracy, a cross-covariance matrices-alternating least square (CCM-ALS) algorithm is proposed. The algorithm relies on ALS of the CCM for obtaining the position of vehicles in V2I communications. The algorithm is highly precise compared to traditional angle of arrival (AOA) positioning and not inferior to direct position determination (DPD) approaches while being low in complexity, which is crucial for moving vehicles. The numerical results verify the superiority of the proposed method.

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CONTENTS
Journal of Systems Engineering and Electronics    2025, 36 (1): 0-0.  
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CONTENTS

Journal of Systems Engineering and Electronics    2025, 36 (2): 0-0.  
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Differential flatness ADRC for high-speed steering of tracked tank systems
Yuanqing XIA, Zhongqi SUN, Li DAI, Yufeng ZHAN, Dihua ZHAI, Wenjun ZHAO, Fan PU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1665-1678.   DOI: 10.23919/JSEE.2025.000116
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This paper proposes a differential-fatness-based active disturbance rejection control (ADRC) for high-speed steering control of tracked tank systems. Firstly, a high-speed steering model is established by considering the lateral component of the centrifugal force acting on the tank on the basis of modeling and analyzing the dynamic model of the low-speed steering system. Secondly, we propose a differential-flatness ADRC approach by converting the under-actuated system to a fully driven flat one. Moreover, we prove the differential flatness of the steering system, which facilitates a two-channel ADRC development. Finally, we show that both the states of the flat system and the original under-actuated system can track the reference trajectory. On the external interference condition, the system is observed to re-track the target signal within 2 s.

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Long time hybrid integration of radar rotating target
Zhiyong SONG, Yuntao XU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1477-1487.   DOI: 10.23919/JSEE.2024.000123
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In the traditional radar unmanned aerial vehicle (UAV) detection process, coherent integration and micro-Doppler (m-D) parameter estimation are carried out separately. The target discrimination process needs to obtain the position information of the target, which will lose energy. In this paper, a long time integration method of radar signal based on rotating target radon Fourier transform (RTRFT) is proposed. This method modifies the distance and frequency terms in the traditional generalized radon Fourier transform (GRFT), and adds the frequency sinusoidal modulation term. Then, based on the cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter, the position of the target is detected in the high-dimensional space obtained by RTRFT. This method can combine coherent integration and micro-motion parameter estimation. Simulation experiments show that the proposed method can estimate the main translational parameters and rotational micro-motion parameters of the target while detecting the target, and the target detection performance is improved.

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Specific emitter identification based on frequency and amplitude of the signal kurtosis
Yurui ZHAO, Xiang WANG, Liting SUN, Zhitao HUANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 333-343.   DOI: 10.23919/JSEE.2023.000054
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Extensive experiments suggest that kurtosis-based fingerprint features are effective for specific emitter identification (SEI). Nevertheless, the lack of mechanistic explanation restricts the use of fingerprint features to a data-driven technique and further reduces the adaptability of the technique to other datasets. To address this issue, the mechanism how the phase noise of high-frequency oscillators and the nonlinearity of power amplifiers affect the kurtosis of communication signals is investigated. Mathematical models are derived for intentional modulation (IM) and unintentional modulation (UIM). Analysis indicates that the phase noise of high-frequency oscillators and the nonlinearity of power amplifiers affect the kurtosis frequency and amplitude, respectively. A novel SEI method based on frequency and amplitude of the signal kurtosis (FA-SK) is further proposed. Simulation and real-world experiments validate theoretical analysis and also confirm the efficiency and effectiveness of the proposed method.

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Realization of 3D coordinate estimation for spaceborne interferometric antenna
Wangjie CHEN, Weiqiang ZHU, Zhenhong FAN, Qin MA, Jian YANG, Li WU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1428-1442.   DOI: 10.23919/JSEE.2025.000055
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This paper introduces a hybrid configuration design to enhance the precision of satellite antenna position measurement. By fixing the circular array antenna on the antenna mounting surface and integrating coordinate system transformation relationships with interferometric direction finding (DF) and positioning technology, accurate estimation of the antenna position is ensured. This method optimizes the quality and stability of data fusion by integrating pulse parameter characteristics, satellite orbit and attitude information, as well as the field of view information from observation stations, using techniques such as maximum-ratio-combining (MRC) and orbit extrapolation. Specifically, the sampling-importance resampling particle-filtering and Kalman-filtering (SIR-PF-KF) hybrid filtering prediction technology is employed to precisely predict and correct the three-dimensional (3D) position errors of the L-array antenna. Through data processing of five to nine orbits, accurate estimation of the antenna’s 3D position is achieved, achieving an estimation accuracy of 3 μm, significantly improving the accuracy of on-orbit rapid calibration. Experimental results show that the interferometer positioning accuracy is improved from 7.9 km before antenna position correction to within 0.2 km after correction, verifying the effectiveness and practicability of this method, which aims to address issues with positioning accuracy.

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Improved power inversion algorithm based on derivative constraint
Runnan WANG, Hongchang LIU, Siyuan JIANG, Shuai LIU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1398-1406.   DOI: 10.23919/JSEE.2025.000105
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The power inversion (PI) algorithm lacks specific constraints on desired signals. Thus, the beampattern has fluctuation in all directions other than the jamming sources. This phenomenon will damage the reception of desired signals. In high signal-to-noise ratio (SNR) application, the desired signal is inevitably suppressed by the PI algorithm, resulting in a deterioration to the out signal-to-interference-and-noise ratio (SINR). This paper proposes an improved PI algorithm based on derivative constraint. Firstly, the proposed method uses subspace projection to extract jamming-free data, the derivative constraint is imposed to the non-jamming data, and subsequently the Lagrange multiplier can be used to calculate the array weight vector. Simulation results demonstrate that, the proposed algorithm in this paper has a higher output SNR, flat gains in non-jamming directions, and applicability of high SINR than the PI algorithm, thus verifying the effectiveness of the algorithm.

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Nonlinear size constrained attitude estimation for space objects from ISAR image sequences
Chengzeng CHEN, Dan LIU, Jiandong NIU, Xiaolun JIANG, Yaobing LU, Xiaojian XU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1465-1476.   DOI: 10.23919/JSEE.2025.000003
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Exact estimation of space object attitude parameters is a great challenge. The effectiveness of conventional attitude estimation approaches based on target sizes suffers a significant reduction when occlusion exists. This paper proposes an innovative approach to estimate the attitude parameters for space objects based on inverse synthetic aperture radar (ISAR) image sequences. The formulation for nonlinear size constraints (NSC) is developed by accounting for the characteristics of object size variation in ISAR image sequences. The multi-start framework for global optimization and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) based quasi-Newton iterative method are combined with and used for more accurate estimation of space object’s attitude parameters. Furthermore, the Cramer-Rao lower bound (CRLB) of attitude parameter estimates is derived. Comparative experiments demonstrate the effectiveness and robustness of the proposed method.

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An evaluation method for contribution rate of UAVs to amphibious joint landing system of systems
Xichao SU, Fang GUO, Jingyu CONG, Yang ZHANG, Zhongzheng ZHAO, Wei HAN, Xinwei WANG
Journal of Systems Engineering and Electronics    2025, 36 (6): 1613-1628.   DOI: 10.23919/JSEE.2025.000179
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To overcome the limitations of conventional approaches that adopt monolithic architectures and overlook critical dynamic interactions in evaluating combat effectiveness and subsystem contributions within amphibious operations, this paper proposes an integrated framework combining complex system network modeling with dynamic adversarial simulation for evaluating mission-critical system-of-systems (SoS). Specifically, the contribution rate of unmanned aerial vehicles (UAVs) to the amphibious joint landing SoS (AJLSoS) is quantified. Firstly, a standardized network topology model is developed using operation loop theory, systematically characterizing node functionalities and their interdependencies. Secondly, the ideal Lanchester equation is augmented according to the model’s static operational capability, and an amphibious operational simulation model is constructed based on the modified equation, enabling dynamic simulation of force attrition and engagement duration as key performance indicators of AJLSoS. To validate the theoretical framework, a battalion-level amphibious campaign scenario is developed to compute effectiveness metrics across multiple control scenarios and the contribution rate of UAVs to AJLSoS is analyzed. This study not only provides actionable insights for operational mission planning of UAVs in the context of amphibious operations but also demonstrates high adaptability to diverse operational contexts.

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Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation
Zhichao XU, Faping LU, Lifan ZHANG, Dongkai YANG, Chuanhui LIU, Jiafang KANG, Qi AN, Zhilin ZHANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 311-322.   DOI: 10.23919/JSEE.2024.000044
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A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method, based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with $n $=10 subcarriers and a bit error rate of 1×10?5, spectral efficiency can be raised by roughly 12.4%.

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Factor graph method for target state estimation in bearing-only sensor network
Zhan CHEN, Yangwang FANG, Ruitao ZHANG, Wenxing FU
Journal of Systems Engineering and Electronics    2025, 36 (2): 380-396.   DOI: 10.23919/JSEE.2024.000122
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For target tracking and localization in bearing-only sensor network, it is an essential and significant challenge to solve the problem of plug-and-play expansion while stably enhancing the accuracy of state estimation. This paper proposes a distributed state estimation method based on two-layer factor graph. Firstly, the measurement model of the bearing-only sensor network is constructed, and by investigating the observability and the Cramer-Rao lower bound of the system model, the preconditions are analyzed. Subsequently, the location factor graph and cubature information filtering algorithm of sensor node pairs are proposed for localized estimation. Building upon this foundation, the mechanism for propagating confidence messages within the fusion factor graph is designed, and is extended to the entire sensor network to achieve global state estimation. Finally, groups of simulation experiments are conducted to compare and analyze the results, which verifies the rationality, effectiveness, and superiority of the proposed method.

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Modeling optimal air traffic rights resource allocation
Zhishuo LIU, Yi’nan CHENG, Yanhua LI, Danyang SHEN
Journal of Systems Engineering and Electronics    2025, 36 (3): 778-790.   DOI: 10.23919/JSEE.2025.000070
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International freedom of the air (traffic rights) is a key resource for airlines to carry out international air transport business. An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport. In this paper, a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers. A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model. The results show that the optimal allocation scheme aligns with the principle of fairness, indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.

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Temperature error compensation method for fiber optic gyroscope based on a composite model of k-means, support vector regression and particle swarm optimization
Yin CAO, Lijing LI, Sheng LIANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 510-522.   DOI: 10.23919/JSEE.2025.000023
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As the core component of inertial navigation systems, fiber optic gyroscope (FOG), with technical advantages such as low power consumption, long lifespan, fast startup speed, and flexible structural design, are widely used in aerospace, unmanned driving, and other fields. However, due to the temperature sensitivity of optical devices, the influence of environmental temperature causes errors in FOG, thereby greatly limiting their output accuracy. This work researches on machine-learning based temperature error compensation techniques for FOG. Specifically, it focuses on compensating for the bias errors generated in the fiber ring due to the Shupe effect. This work proposes a composite model based on k-means clustering, support vector regression, and particle swarm optimization algorithms. And it significantly reduced redundancy within the samples by adopting the interval sequence sample. Moreover, metrics such as root mean square error (RMSE), mean absolute error (MAE), bias stability, and Allan variance, are selected to evaluate the model’s performance and compensation effectiveness. This work effectively enhances the consistency between data and models across different temperature ranges and temperature gradients, improving the bias stability of the FOG from 0.022 °/h to 0.006 °/h. Compared to the existing methods utilizing a single machine learning model, the proposed method increases the bias stability of the compensated FOG from 57.11% to 71.98%, and enhances the suppression of rate ramp noise coefficient from 2.29% to 14.83%. This work improves the accuracy of FOG after compensation, providing theoretical guidance and technical references for sensors error compensation work in other fields.

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Design of wide-scanning array with reactive splitter network and metasurface
Haiying LUO, Fulong JIN, Xiao DING, Wei SHAO
Journal of Systems Engineering and Electronics    2025, 36 (2): 323-332.   DOI: 10.23919/JSEE.2024.000005
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In this paper, the reactive splitter network and metasurface are proposed to radiate the wide-beam isolated element pattern and suppress mutual coupling (MC) of the low-profile phased array with the triangular lattice, respectively. Thus, broadband wide-angle impedance matching (WAIM) is implemented to promote two-dimensional (2D) wide scanning. For the isolated element, to radiate the wide-beam patterns approximating to the cosine form, two identical slots backed on one substrate integrated cavity are excited by the feeding network consisting of a reactive splitter and two striplines connected with splitter output paths. For adjacent elements staggered with each other, with the metasurface superstrate, the even-mode coupling voltages on the reactive splitter are cancelled out, yielding reduced MC. With the suppression of MC and the compensation of isolated element patterns, WAIM is realized to achieve 2D wide-angle beam steering up to ± 65° in E-plane, ± 45° in H-plane and ± 60° in D-plane from 4.9 GHz to 5.85 GHz.

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Multi-platform collaborative MRC-PSO algorithm for anti-ship missile path planning
Gang LIU, Xinyuan GUO, Dong HUANG, Kezhong CHEN, Wu LI
Journal of Systems Engineering and Electronics    2025, 36 (2): 494-509.   DOI: 10.23919/JSEE.2025.000026
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To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper proposed multi-operator real-time constraints particle swarm optimization (MRC-PSO) algorithm. MRC-PSO algorithm utilizes a semi-rasterization environment modeling technique and integrates the geometric gradient law of ASMs which distinguishes itself from other collaborative path planning algorithms by fully considering the coupling between collaborative paths. Then, MRC-PSO algorithm conducts chunked stepwise recursive evolution of particles while incorporating circumvent, coordination, and smoothing operators which facilitates local selection optimization of paths, gradually reducing algorithmic space, accelerating convergence, and enhances path cooperativity. Simulation experiments comparing the MRC-PSO algorithm with the PSO algorithm, genetic algorithm and operational area cluster real-time restriction (OACRR)-PSO algorithm, which demonstrate that the MRC-PSO algorithm has a faster convergence speed, and the average number of iterations is reduced by approximately 75%. It also proves that it is equally effective in resolving complex scenarios involving multiple obstacles. Moreover it effectively addresses the problem of path crossing and can better satisfy the requirements of multi-platform collaborative path planning. The experiments are conducted in three collaborative operation modes, namely, three-to-two, three-to-three, and four-to-two, and the outcomes demonstrate that the algorithm possesses strong universality.

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Multi-objective optimization framework in the modeling of belief rule-based systems with interpretability-accuracy trade-off
Yaqian YOU, Jianbin SUN, Yuejin TAN, Jiang JIANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 423-435.   DOI: 10.23919/JSEE.2024.000064
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The belief rule-based (BRB) system has been popular in complexity system modeling due to its good interpretability. However, the current mainstream optimization methods of the BRB systems only focus on modeling accuracy but ignore the interpretability. The single-objective optimization strategy has been applied in the interpretability-accuracy trade-off by integrating accuracy and interpretability into an optimization objective. But the integration has a greater impact on optimization results with strong subjectivity. Thus, a multi-objective optimization framework in the modeling of BRB systems with interpretability-accuracy trade-off is proposed in this paper. Firstly, complexity and accuracy are taken as two independent optimization goals, and uniformity as a constraint to give the mathematical description. Secondly, a classical multi-objective optimization algorithm, nondominated sorting genetic algorithm II (NSGA-II), is utilized as an optimization tool to give a set of BRB systems with different accuracy and complexity. Finally, a pipeline leakage detection case is studied to verify the feasibility and effectiveness of the developed multi-objective optimization. The comparison illustrates that the proposed multi-objective optimization framework can effectively avoid the subjectivity of single-objective optimization, and has capability of joint optimizing the structure and parameters of BRB systems with interpretability-accuracy trade-off.

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Impact time control guidance for moving-target considering velocity variation and field-of-view constraint
Hao YANG, Shifeng ZHANG, Xibin BAI, Chengye YANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 552-568.   DOI: 10.23919/JSEE.2025.000025
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In the existing impact time control guidance (ITCG) laws for moving-targets, the effects of time-varying velocity caused by aerodynamics and gravity cannot be effectively considered. Therefore, an ITCG with field-of-view (FOV) constraints based on biased proportional navigation guidance (PNG) is developed in this paper. The remaining flight time (time-to-go) estimation method is derived considering aerodynamic force and gravity. The number of differential equations is reduced and the integration step is increased by changing the integral variable, which makes it possible to obtain time-to-go through integration. An impact time controller with FOV constraints is proposed by analyzing the influence of the biased term on time-to-go and FOV constraint. Then, numerical simulations are performed to verify the correctness and superiority of the method.

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CONTENTS
Journal of Systems Engineering and Electronics    2025, 36 (5): 0-0.  
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Cascading failure analysis of an interdependent network with power-combat coupling
Yang WANG, Junyong TAO, Yun’an ZHANG, Guanghan BAI, Hongyan DUI
Journal of Systems Engineering and Electronics    2025, 36 (2): 405-422.   DOI: 10.23919/JSEE.2024.000118
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Cutting off or controlling the enemy’s power supply at critical moments or strategic locations may result in a cascade failure, thus gaining an advantage in a war. However, the existing cascading failure modeling analysis of interdependent networks is insufficient for describing the load characteristics and dependencies of subnetworks, and it is difficult to use for modeling and failure analysis of power-combat (P-C) coupling networks. This paper considers the physical characteristics of the two subnetworks and studies the mechanism of fault propagation between subnetworks and across systems. Then the survivability of the coupled network is evaluated. Firstly, an integrated modeling approach for the combat system and power system is predicted based on interdependent network theory. A heterogeneous one-way interdependent network model based on probability dependence is constructed. Secondly, using the operation loop theory, a load-capacity model based on combat-loop betweenness is proposed, and the cascade failure model of the P-C coupling system is investigated from three perspectives: initial capacity, allocation strategy, and failure mechanism. Thirdly, survivability indexes based on load loss rate and network survival rate are proposed. Finally, the P-C coupling system is constructed based on the IEEE 118-bus system to demonstrate the proposed method.

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Deep unfolded amplitude-phase error self-calibration network for DOA estimation
Hangui ZHU, Xixi CHEN, Teng MA, Yongliang WANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 353-361.   DOI: 10.23919/JSEE.2024.000099
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To tackle the challenges of intractable parameter tuning, significant computational expenditure and imprecise model-driven sparse-based direction of arrival (DOA) estimation with array error (AE), this paper proposes a deep unfolded amplitude-phase error self-calibration network. Firstly, a sparse-based DOA model with an array convex error restriction is established, which gets resolved via an alternating iterative minimization (AIM) algorithm. The algorithm is then unrolled to a deep network known as AE-AIM Network (AE-AIM-Net), where all parameters are optimized through multi-task learning using the constructed complete dataset. The results of the simulation and theoretical analysis suggest that the proposed unfolded network achieves lower computational costs compared to typical sparse recovery methods. Furthermore, it maintains excellent estimation performance even in the presence of array magnitude-phase errors.

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Knowledge map of online public opinions for emergencies
Shuang GUAN, Zihan FANG, Changfeng WANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 436-445.   DOI: 10.23919/JSEE.2024.000054
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With the popularization of social media, public opinion information on emergencies spreads rapidly on the Internet, the impact of negative public opinions on an event has become more significant. Based on the organizational form of public opinion information, the knowledge graph is used to construct the knowledge base of public opinion risk cases on the emergency network. The emotion recognition model of negative public opinion information based on the bi-directional long short-term memory (BiLSTM) network is studied in the model layer design, and a linear discriminant analysis (LDA) topic extraction method combined with association rules is proposed to extract and mine the semantics of negative public opinion topics to realize further in-depth analysis of information topics. Focusing on public health emergencies, knowledge acquisition and knowledge processing of public opinion information are conducted, and the experimental results show that the knowledge graph framework based on the construction can facilitate in-depth theme evolution analysis of public opinion events, thus demonstrating important research significance for reducing online public opinion risks.

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Evolution mechanism of unmanned cluster cooperation oriented toward strategy selection diversity
Zhenhai XIE, Minggang YU, Ming HE, Guoyou CHEN, Zheng ZHAI, Ziyu WANG, Lu LIU
Journal of Systems Engineering and Electronics    2025, 36 (2): 462-482.   DOI: 10.23919/JSEE.2025.000017
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When performing tasks, unmanned clusters often face a variety of strategy choices. One of the key issues in unmanned cluster tasks is the method through which to design autonomous collaboration and cooperative evolution mechanisms that allow for unmanned clusters to maximize their overall task effectiveness under the condition of strategic diversity. This paper analyzes these task requirements from three perspectives: the diversity of the decision space, information network construction, and the autonomous collaboration mechanism. Then, this paper proposes a method for solving the problem of strategy selection diversity under two network structures. Next, this paper presents a Moran-rule-based evolution dynamics model for unmanned cluster strategies and a vision-driven-mechanism-based evolution dynamics model for unmanned cluster strategy in the context of strategy selection diversity according to various unmanned cluster application scenarios. Finally, this paper provides a simulation analysis of the effects of relevant parameters such as the payoff factor and cluster size on cooperative evolution in autonomous cluster collaboration for the two types of models. On this basis, this paper presents advice for effectively addressing diverse choices in unmanned cluster tasks, thereby providing decision support for practical applications of unmanned cluster tasks.

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Fixed-time distributed average consensus tracking for multiple Euler-Lagrange systems
Guhao SUN, Qingshuang ZENG, Zhongze CAI
Journal of Systems Engineering and Electronics    2025, 36 (2): 523-536.   DOI: 10.23919/JSEE.2025.000034
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This paper investigates the sliding-mode-based fixed-time distributed average tracking (DAT) problem for multiple Euler-Lagrange systems in the presence of external disturbances. The primary objective is to devise controllers for each agent, enabling them to precisely track the average of multiple time-varying reference signals. By averaging these signals, we can mitigate the influence of errors and uncertainties arising during measurements, thereby enhancing the robustness and stability of the system. A distributed fixed-time average estimator is proposed to estimate the average value of global reference signals utilizing local information and communication with neighbors. Subsequently, a fixed-time sliding mode controller is introduced incorporating a state-dependent sliding mode function coupled with a variable exponent coefficient to achieve distributed average tracking of reference signals, and rigorous analytical methods are employed to substantiate the fixed-time stability. Finally, numerical simulation results are provided to validate the effectiveness of the proposed methodology, offering insights into its practical application and robust performance.

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DDIRNet: robust radar emitter recognition via single domain generalization
Honglin WU, Xueqiong LI, Junjie HUANG, Ruochun JIN, Yuhua TANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 397-404.   DOI: 10.23919/JSEE.2025.000053
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Automatically recognizing radar emitters from complex electromagnetic environments is important but non-trivial. Moreover, the changing electromagnetic environment results in inconsistent signal distribution in the real world, which makes the existing approaches perform poorly for recognition tasks in different scenes. In this paper, we propose a domain generalization framework is proposed to improve the adaptability of radar emitter signal recognition in changing environments. Specifically, we propose an end-to-end denoising based domain-invariant radar emitter recognition network (DDIRNet) consisting of a denoising model and a domain invariant representation learning model (IRLM), which mutually benefit from each other. For the signal denoising model, a loss function is proposed to match the feature of the radar signals and guarantee the effectiveness of the model. For the domain invariant representation learning model, contrastive learning is introduced to learn the cross-domain feature by aligning the source and unseen domain distribution. Moreover, we design a data augmentation method that improves the diversity of signal data for training. Extensive experiments on classification have shown that DDIRNet achieves up to 6.4% improvement compared with the state-of-the-art radar emitter recognition methods. The proposed method provides a promising direction to solve the radar emitter signal recognition problem.

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Fixed-time cooperative interception guidance law with angle constraints for multiple flight vehicles
Enjiao ZHAO, Xue DING, Ke ZHANG, Zengyu YUAN
Journal of Systems Engineering and Electronics    2025, 36 (2): 569-579.   DOI: 10.23919/JSEE.2025.000036
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This paper presents a fixed-time cooperative guidance method with impact angle constraints for multiple flight vehicles (MFV) to address the challenges of intercepting large maneuvering targets with difficulty and low precision. A cooperative guidance model is proposed, transforming the cooperative interception problem into a consensus problem based on the remaining flight time of the flight vehicles. First, the impact angle constraint is converted into the line of sight (LOS) angle constraint, and a new fixed-time convergent non-singular terminal sliding surface is introduced, which resolves the singularity issue of the traditional sliding surfaces. With this approach, LOS angle rate and normal overloads can converge in fixed time, ensuring that the upper bound of the system convergence time is not affected by the initial value of the system. Furthermore, the maneuvering movement of the target is considered as a system disturbance, and an extended state observer is employed to estimate and compensate for it in the guidance law. Lastly, by applying consensus theory and distributed communication topology, the remaining flight time of each flight vehicle is synchronized to ensure that they intercept the target simultaneously with different impact angles. Simulation experiments are conducted to validate the effectiveness of the proposed cooperative interception and guidance method.

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Non-singular fast terminal sliding mode control for roll-pitch seeker based on extended state observers
Bowen XIAO, Qunli XIA
Journal of Systems Engineering and Electronics    2025, 36 (2): 537-551.   DOI: 10.23919/JSEE.2025.000035
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For air-to-air missiles, the terminal guidance’s precision is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode control method, aimed at resolving the frame control problem of roll-pitch seeker tracking high maneuvering target. The sliding mode surface is structured around the principle of segmentation, which enables the control system’s rapid attainment of the zero point and ensure global fast convergence. The system’s state is more swiftly converged to the sliding mode surface through an improved adaptive fast dual power reaching law. Utilizing an extended state observer, the overall disturbance is both identified and compensated. The validation of the system’s stability and its convergence within a finite-time is grounded in Lyapunov’s stability criteria. The performance of the introduced control method is confirmed through roll-pitch seeker tracking control simulation. Data analysis reveals that newly proposed control technique significantly outperforms existing sliding mode control methods by rapidly converging the frame to the target angle, reduce the tracking error of the detector for the target, and bolster tracking precision of the roll-pitch seeker huring disturbed conditions.

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Electromagnetic equivalent physical model for high-speed aircraft radomes considering high-temperature effects
Jianmin JI, Wei WANG, Kai YIN, Kaibin WANG, Bo CHEN, Huilong YU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1453-1464.   DOI: 10.23919/JSEE.2025.000114
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During actual high-speed flights, the electromagnetic (EM) properties of aircraft radomes are influenced by dielectric temperature drift, leading to substantial drift in the boresight errors (BSEs) from their room temperature values. However, applying thermal loads to the radome during ground-based EM simulation tests is challenging. This paper presents an EM equivalent physical model (EEPM) for high-speed aircraft radomes that account for the effects of dielectric temperature drift. This is achieved by attaching dielectric slices of specific thicknesses to the outer surface of a room-temperature radome (RTR) to simulate the increase in electrical thickness resulting from high temperatures. This approach enables accurate simulations of the BSEs of high-temperature radomes (HTRs) under high-speed flight conditions. An application example, supported by full-wave numerical calculations and physical testing, demonstrates that the EEPM exhibits substantial improvement in approximating the HTR compared to the RTR, facilitating precise simulations of the BSEs of HTRs during high-speed flights. Overall, the proposed EEPM is anticipated to considerably enhance the alignment between the ground-based simulations of high-speed aircraft guidance systems and their actual flight conditions.

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Dynamic vehicle routing for a dual-channel distribution center with stochastic demands and shared resources
Mei XU, Feng YANG, Ting CHEN
Journal of Systems Engineering and Electronics    2025, 36 (6): 1501-1531.   DOI: 10.23919/JSEE.2025.000139
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This paper addresses a dynamic vehicle routing problem with stochastic requests in a dual-channel distribution center that utilizes shared vehicle resources to serve two types of customers: offline corporate clients (CCs) with fixed and stochastic batch demands, and online individual customers (ICs) with single-unit demands. To manage stochastic batch demands from CCs, this paper proposes three recourse policies under a differentiated resource-sharing scheme: the waiting-tour-based (WTB) policy, the advance-tour-based (ATB) policy, and the advance-customer-based (ACB) policy. These policies differ in their response priorities to random requests and the scope of route reoptimization. The problem is formulated as a two-stage stochastic recourse programming model, where the first stage establishes routes for fixed demands. In the second stage, we construct three stochastic recourse programming models corresponding to the proposed recourse policies. To solve these models, this paper develop rolling horizon algorithms integrated with mathematical programming models or metaheuristic algorithms. Extensive numerical experiments validate the effectiveness of the proposed algorithms and policies. The results indicate that both the ATB and ACB policies lead to cost savings compared to the WTB policy, especially when stochastic demands are urgent and delivery resources are quite limited. Specifically, when the number of ICs is small, the expected total cost savings can exceed 12%, and in some scenarios, savings of over 20% can be achieved. When the number of ICs is large, some scenarios can achieve cost savings exceeding 7%. Furthermore, the ACB policy yields lower costs, fewer worsened ICs, fewer trips, and less vehicle time than the ATB policy.

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