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    2025, 30 (6):  0. 
    Abstract ( 2 )   PDF (44443KB) ( 0 )  
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    Automation & Computer Technologies
    Hyperspectral Satellite Image Classification Based on Feature Pyramid Networks With 3D Convolution
    CHEN Cheng, PENG Pan, TAO Wei, ZHAO Hui
    2025, 30 (6):  1073-1084.  doi: 10.1007/s12204-023-2645-4
    Abstract ( 2 )   PDF (2107KB) ( 0 )  
    Recent advances in convolution neural network (CNN) have fostered the progress in object recognition and semantic segmentation, which in turn has improved the performance of hyperspectral image (HSI) classification. Nevertheless, the difficulty of high dimensional feature extraction and the shortage of small training samples seriously hinder the future development of HSI classification. In this paper, we propose a novel algorithm for HSI classification based on three-dimensional (3D) CNN and a feature pyramid network (FPN), called 3D-FPN. The framework contains a principle component analysis, a feature extraction structure and a logistic regression. Specifically, the FPN built with 3D convolutions not only retains the advantages of 3D convolution to fully extract the spectral-spatial feature maps, but also concentrates on more detailed information and performs multi-scale feature fusion. This method avoids the excessive complexity of the model and is suitable for small sample hyperspectral classification with varying categories and spatial resolutions. In order to test the performance of our proposed 3D-FPN method, rigorous experimental analysis was performed on three public hyperspectral data sets and hyperspectral data of GF-5 satellite. Quantitative and qualitative results indicated that our proposed method attained the best performance among other current state-of-the-art end-to-end deep learning-based methods.
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    Self-Adaptive LSAC-PID Approach Based on Lyapunov Reward Shaping for Mobile Robots
    YU Xinyi, XU Siyu, FAN Yuehai, OU Linlin
    2025, 30 (6):  1085-1102.  doi: 10.1007/s12204-023-2631-x
    Abstract ( 2 )   PDF (2455KB) ( 0 )  
    In order to solve the control problem of multiple-input multiple-output (MIMO) systems in complex and variable control environments, a model-free adaptive LSAC-PID method based on deep reinforcement learning (RL) is proposed in this paper for automatic control of mobile robots. According to the environmental feedback, the RL agent of the upper controller outputs the optimal parameters to the lower MIMO PID controllers, which can realize the real-time PID optimal control. First, a model-free adaptive MIMO PID hybrid control strategy is presented to realize real-time optimal tuning of control parameters in terms of soft-actor-critic (SAC) algorithm, which is state-of-the-art RL algorithm. Second, in order to improve the RL convergence speed and the control performance, a Lyapunov-based reward shaping method for off-policy RL algorithm is designed, and a self-adaptive LSAC-PID tuning approach with Lyapunov-based reward is then determined. Through the policy evaluation and policy improvement of the soft policy iteration, the convergence and optimality of the proposed LSAC-PID algorithm are proved mathematically. Finally, based on the proposed reward shaping method, the reward function is designed to improve the system stability for the line-following robot. The simulation and experiment results show that the proposed adaptive LSAC-PID approach has good control performance such as fast convergence speed, high generalization and high real-time performance, and achieves real-time optimal tuning of MIMO PID parameters without the system model and control loop decoupling.
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    Multi-Human Pose Estimation by Deep Learning-Based Sequential Approach for Human Keypoint Position and Human Body Detection
    TAHIR Rizwana, CAI Yunze
    2025, 30 (6):  1103-1113.  doi: 10.1007/s12204-023-2658-z
    Abstract ( 2 )   PDF (1005KB) ( 1 )  
    Recent multimedia and computer vision research has focused on analyzing human behavior and activity using images. Skeleton estimation, known as pose estimation, has received a significant attention. For human pose estimation, deep learning approaches primarily emphasize on the keypoint features. Conversely, in the case of occluded or incomplete poses, the keypoint feature is insufficiently substantial, especially when there are multiple humans in a single frame. Other features, such as the body border and visibility conditions, can contribute to pose estimation in addition to the keypoint feature. Our model framework integrates multiple features, namely the human body mask features, which can serve as a constraint to keypoint location estimation, the body keypoint features, and the keypoint visibility via mask region-based convolutional neural network (Mask- RCNN). A sequential multi-feature learning setup is formed to share multi-features across the structure, whereas, in the Mask-RCNN, the only feature that could be shared through the system is the region of interest feature. By two-way up-scaling with the shared weight process to produce the mask, we have addressed the problems of improper segmentation, small intrusion, and object loss when Mask-RCNN is used, for instance, segmentation. Accuracy is indicated by the percentage of correct keypoint, and our model can identify 86.1% of the correct keypoints.
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    Infrared Single Pixel Imaging Based on Generative Adversarial Network
    JIANG Yilin, ZHANG Yilong, ZHANG Fangyuan
    2025, 30 (6):  1114-1124.  doi: 10.1007/s12204-023-2654-3
    Abstract ( 1 )   PDF (1008KB) ( 0 )  
    In the field of imaging, the image resolution is required to be higher. There is always a contradiction between the sensitivity and resolution of the seeker in the infrared guidance system. This work uses the rosette scanning mode for physical compression imaging in order to improve the resolution of the image as much as possible under the high-sensitivity infrared rosette point scanning mode and complete the missing information that is not scanned. It is effective to use optical lens instead of traditional optical reflection system, which can reduce the loss in optical path transmission. At the same time, deep learning neural network is used for control. An infrared single pixel imaging system that integrates sparse algorithm and recovery algorithm through the improved generative adversarial networks is trained. The experiment on the infrared aerial target dataset shows that when the input is sparse image after rose sampling, the system finally can realize the single pixel recovery imaging of the infrared image, which improves the resolution of the image while ensuring high sensitivity.
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    Gait Learning Reproduction for Quadruped Robots Based on Experience Evolution Proximal Policy Optimization
    LI Chunyang, ZHU Xiaoqing, RUAN Xiaogang, LIU Xinyuan, ZHANG Siyuan
    2025, 30 (6):  1125-1133.  doi: 10.1007/s12204-023-2666-z
    Abstract ( 2 )   PDF (1430KB) ( 0 )  
    Bionic gait learning of quadruped robots based on reinforcement learning has become a hot research topic. The proximal policy optimization (PPO) algorithm has a low probability of learning a successful gait from scratch due to problems such as reward sparsity. To solve the problem, we propose a experience evolution proximal policy optimization (EEPPO) algorithm which integrates PPO with priori knowledge highlighting by evolutionary strategy. We use the successful trained samples as priori knowledge to guide the learning direction in order to increase the success probability of the learning algorithm. To verify the effectiveness of the proposed EEPPO algorithm, we have conducted simulation experiments of the quadruped robot gait learning task on Pybullet. Experimental results show that the central pattern generator based radial basis function (CPG-RBF) network and the policy network are simultaneously updated to achieve the quadruped robot’s bionic diagonal trot gait learning task using key information such as the robot’s speed, posture and joints information. Experimental comparison results with the traditional soft actor-critic (SAC) algorithm validate the superiority of the proposed EEPPO algorithm, which can learn a more stable diagonal trot gait in flat terrain.
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    Dynamic Analysis and Trajectory Solution of Multi-Robot Coordinated Towing System
    ZHAO Xiangtang, ZHAO Zhigang, WEI Qizhe, SU Cheng
    2025, 30 (6):  1134-1143.  doi: 10.1007/s12204-023-2649-0
    Abstract ( 1 )   PDF (771KB) ( 0 )  
    Multi-robot coordinated towing system is an under-constrained system. The dynamic response of the towing system can not be fully controlled since the rope can only provide a unidirectional constraint force to the suspended object. Based on the kinematics of the multi-robot coordinated towing system with fixed-base, the Newton-Euler equations and Udwadia-Kalaba equations were used to establish the dynamics of the towing system. To obtain the motion trajectories with high stability and strong control, the motion trajectories of the towing system were optimized. During the towing, the transition from the relaxation state to the tension state of the rope was treated as a collision between the suspended object and the robot end. The trajectories of the towing system in terms of a single-variable and multiple-variable were solved, respectively. The simulation shows that the optimized trajectories are closer to reality and truly reflect the constraints of the ropes on the suspended object. The research results provide a basis for trajectory planning and control of the towing system.
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    Wire Rope Inspection Robots: A Review
    SUN Bowen, YANG Jianhua, LI Baofeng, LI Shangyuan, WANG Liang, XU Zhongqi
    2025, 30 (6):  1144-1161.  doi: 10.1007/s12204-023-2641-8
    Abstract ( 2 )   PDF (2596KB) ( 0 )  
    Wire rope inspection robot is an important tool for wire rope condition monitoring and maintenance, which can accurately locate and judge the damage of wire rope. In addition, the wire rope inspection robot can also be used for cable inspection. First, the crawling structure and crawling mode of the wire rope inspection robot are reviewed, and the characteristics and existing problems of each crawling mode are analyzed separately. Next, the drive mode of the wire rope inspection robot is discussed, the types of commonly used motors are introduced, and the advantages and disadvantages of drive motors and the control modes are compared. Then, the method and principle of the non-destructive detection of the wire rope inspection robot are expounded, and the commonly used detection methods and existing deficiencies are compared. After that, the types of communication modes are compared and analyzed, and the types of wireless communication modes are also introduced. Finally, the current difficult problems of the wire rope inspection robot are summarized, and the future development trend of the wire rope inspection robot is prospected.
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    Load Stability Analysis of a Floating Multi-Robot Coordinated Towing System
    SU Cheng, ZHAO Xiangtang, YAN Zengzhen, ZHAO Zhigang, MENG Jiadong
    2025, 30 (6):  1162-1170.  doi: 10.1007/s12204-023-2634-7
    Abstract ( 2 )   PDF (1557KB) ( 0 )  
    Cranes used at sea have some shortcomings in terms of flexibility, efficiency, and safety. Therefore, a floating multi-robot coordinated towing system is planned to fulfill the offshore towing requirements. It is difficult to study the stability of a floating multi-robot coordinated towing system by ancient strategies. First, the minimum tension of the rope and the minimum singular value of the stiffness matrix were separately used to analyze the load stability. The advantages and disadvantages of the two methods were discussed. Then, the two stability analysis methods were normalized and weighted to obtain the method based on minimum tension and minimum singular to comprehensively analyze the stability of the load. Finally, the effect of different weighting coefficients on the load stability was analyzed, which led to a reasonable weighting coefficient to evaluate the load stability by comparing with a single analysis method. The research results provide a basis for the motion planning and coordinated control of the towing system.
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    Double Focus Laser Displacement Sensor Suppressing Laser Jitter and Target Tilt
    CHEN Ruochen, LÜ Na, TAO Wei, ZHAO Hui
    2025, 30 (6):  1171-1178.  doi: 10.1007/s12204-023-2636-5
    Abstract ( 2 )   PDF (1009KB) ( 0 )  
    Measurement precision of laser displacement sensor is subject to various factors, among which laser jitter and target tilt will directly lead to the position movement and shape variation of the laser spot, resulting in displacement measurement errors, so that researchers have to do a lot of research on the spot centering algorithm to weaken the above effects, which can treat the symptoms but not the root cause. Starting from the source of the problem, this paper proposes a double focus double peak solution, which uses a reflector to change the direction of the optical path, so that the imaging spots of the designed two optical paths focus on the same CMOS, forming a double peak structure. When laser jitter or target tilt occurs, the center of the two laser spots is shifted, but they move in the same direction, while their relative position remains unchanged. Therefore, the displacement can be characterized by the relative position of the two laser spots, so that laser jitter and target tilt are suppressed from the source. However, the two spots imaged on CMOS form a non-Gaussian distributed double peak structure, so the conventional laser spot centering algorithms are no longer applicable. To this end, a double peak adaptive threshold waveform extraction method combined with grayscale gravity method is proposed for spot centering algorithm, which combines the suppression of laser jitter and target tilt from the source and the improvement of spot positioning precision which represents the displacement measurement precision, and is experimentally verified.
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    Simulation-Based Novel Hybrid Proportional Derivative/H-Infinity Controller Design for Improved Trajectory Tracking of a Two-Link Robot Arm
    BANKOLE Adesola Temitope, IGBONOBA Ezekiel Endurance Chukwuemeke
    2025, 30 (6):  1179-1187.  doi: 10.1007/s12204-023-2660-5
    Abstract ( 3 )   PDF (707KB) ( 0 )  
    A hybrid control strategy integrating proportional derivative (PD) and the H-infinity control methodology is proposed for a serial two-link robotic manipulator with the goal of improving the tracking performance of the robot arm. The H-infinity controller has the ability to achieve a high performance and robustness in the presence of disturbances and uncertainties, while the PD controller is effective in stabilizing the manipulator. Simulation results using Matlab and Simulink show that the proposed hybrid controller, which integrates the advantages of both PD and H-infinity controllers, has the lowest rise time for the second link, the lowest settling time for the two links, the lowest peak time for both links, and the fastest decay of the error response. In addition, the hybrid control scheme also has the lowest mean square error value, with a 53.3% improvement over the H-infinity controller and a 91.8% improvement over the PD controller, indicating an improved trajectory tracking performance when compared with pure PD and pure H-infinity controllers, respectively. It was also found that the hybrid controller has the lowest integral absolute error, integral square error, integral time absolute error, and integral time square error for the second link, while the error values for the first link are satisfactory, showing a superior performance of the hybrid controller above the PD and H-infinity controllers, respectively.
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    Lifespan Prediction of Electronic Card in Nuclear Power Plant Based on Few Samples
    XU Yong, CAI Yunze, SONG Lin
    2025, 30 (6):  1188-1194.  doi: 10.1007/s12204-023-2669-9
    Abstract ( 3 )   PDF (472KB) ( 0 )  
    A lifespan prediction model was developed based on a few samples to provide decision-making information for operation and maintenance, as well as improve the economy and safety of nuclear power plant (NPP) operations. This paper applies a Weibull model to forecast the lifespan of electronic cards with a few samples in NPPs. Relationship between the lifespan prediction of electronic cards and the ambient temperature is revealed using the Arrhenius equation. Censored samples are used to compensate for the lack of fault electronic card data. Scale parameter and shape parameter of the Weibull model are optimized by adjusting the weight ratio between the censored data and the fault data. Characteristic life is then obtained using the rank regression fitting equation. Parameters of the Arrhenius equation can be calculated by dividing the samples into groups according to the ambient temperature. A case study of the intermediate range high-voltage electric card of ex-core neutron detectors demonstrates that the lifespan prediction of electronic cards in NPPs can be successfully predicted with a few samples by combining the Weibull model and the Arrhenius model. This can help provide preventive maintenance recommendations for electronic cards. Finally, operation suggestions for the electronic card’s ambient temperature can be made by utilizing the temperature-life model.
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    Integrated Cam Contour Optimization Method Considering Kinematic and Dynamic Characteristics: A Paradigm of Offset Press Open-Close Gripper Mechanism
    LI Wenwei, CAO Shuai, QIAN Qian, ZHANG Yaling, CHEN Nan
    2025, 30 (6):  1195-1207.  doi: 10.1007/s12204-024-2714-3
    Abstract ( 1 )   PDF (1468KB) ( 0 )  
    To efficiently search out the optimal cam contour, a software integrated optimization method considering cam mechanism’s kinematic and dynamic characteristics was presented, and its effectiveness was demonstrated by a case study of the cam contour optimization for an offset press open-close gripper mechanism. The acceleration curve and the residual vibration model of the follower were separately studied. A symmetric harmonic trapezoidal curve was designed to control the follower’s acceleration, and single-DOF lumped parameter torsional vibration model was proposed to describe the follower’s residual vibration. Accordingly, corresponding motion curve design software and Simulink vibration model of the follower were developed respectively, and they were integrated into an automatic optimization platform with iSIGHT. The multi-objective optimization with objectives of minimizing both the acceleration and the residual vibration of the follower was completed within the platform by using NSGA-II algorithm. An appropriate point with lower acceleration and residual vibration was chosen from Pareto front as an optimal solution of the follower’s motion curve. Based on the follower’s new motion curve, the actual cam contour was generated by inverse kinematic simulation in COSMOSMotion. The offset press that installed our new designed cam exhibited a lower vibration than the previous machine, and the maximum measured acceleration of the offset press at a printing speed of 15 000 r/h is reduced by 7.7%.
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    Comprehensive Analysis of Beidou-3 PPP-B2b Performance Based on Adaptive Robust Extend Kalman Filter
    WAN Yuan, MAO Xuchu
    2025, 30 (6):  1208-1219.  doi: 10.1007/s12204-023-2664-1
    Abstract ( 1 )   PDF (1134KB) ( 0 )  
    Beidou-3 navigation satellite system (BDS-3) initiated a real-time service for precise point positioning (PPP) using the B2b signal, mainly for users in China and surrounding areas. In this paper, the performance of PPP-B2b service is experimentally analyzed first. Then, the ionosphere-free model is established. In order to solve the problem of slow convergence for traditional PPP, an adaptive robust extend Kalman filter (AREKF) algorithm is developed. Unlike the error compensation models, it reflects the noise information in real time by adjusting the covariance matrix of the measurements and the weight matrix of the state vector. The experimental results are analyzed last. Evaluation results indicate that the corrections provided by PPP-B2b can significantly reduce the discontinuous error of the orbits and clock offsets caused by broadcast ephemeris updating. Positioning results confirm that AREKF outperforms EKF both in static and kinematic modes. Around 20% improvement in accuracy and 25% improvement in convergence speed are achieved, making it valuable for PPP processing.
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    Resource Allocation Method for Unmanned Aerial Vehicle-Assisted and User Cooperation Non-Linear Energy Harvesting Mobile Edge Computing System
    HE Ximei, ZHAO Yisheng, XU Zhihong, CHEN Yong
    2025, 30 (6):  1220-1231.  doi: 10.1007/s12204-023-2624-9
    Abstract ( 2 )   PDF (1003KB) ( 0 )  
    Aimed at the doubly near-far problems in a large range suffered by the remote user group and in a small range existing in both nearby and remote user groups during energy harvesting and computation offloading, a resource allocation method for unmanned aerial vehicle (UAV)-assisted and user cooperation non-linear energy harvesting mobile edge computing (MEC) system is proposed. The UAV equipped with an MEC server is introduced to provide energy and computing services for the remote user group to alleviate the doubly near-far problem in a large range suffered by the remote user group. The doubly near-far problem in a small range existing in both nearby and remote user groups is mitigated by user cooperation. The specific user cooperation strategy is that the user near the base station or the UAV is used as a relay to transfer the computing task of the user far from the base station or the UAV to the MEC server for computing. By jointly optimizing users’ offloading time, users’ transmitting power, and the hovering position of the UAV, the resource allocation problem is modeled as a nonlinear programming problem with the objective of maximizing computation efficiency. The suboptimal solution is obtained by adopting the differential evolution algorithm. Simulation results show that, compared with the resource allocation method based on genetic algorithm and the without user cooperation method, the proposed method has higher computation efficiency.
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    Transportation Systems
    Electric Vehicle Charging Load Modeling Based on Influence Factor Analysis
    WANG Guojun, WANG Liye, WANG Lifang, LIAO Chenglin
    2025, 30 (6):  1232-1241.  doi: 10.1007/s12204-023-2663-2
    Abstract ( 2 )   PDF (1937KB) ( 0 )  
    The spatial-temporal distribution of charging loads for electric vehicles is influenced by multiple factors, Nowadays, the accuracy of the forecasts needs to be improved and the completeness of the modeling is relatively lacking. Therefore, this paper proposes a method for modeling the charging load of electric vehicles based on the influence of multiple factors. First, an in-depth analysis of the factors affecting the charging load of electric vehicles was conducted. Then, a model of electric vehicle electricity consumption per unit kilometer was constructed based on the influencing factors. Next, the electric vehicle, the charging station, the traffic network and the grid are modeled separately. In addition, a unified model of vehicle-station-road-network was constructed through the interaction and coupling of information between the models. Finally, the spatial-temporal distribution of electric vehicle charging loads was simulated using real data from a region. The study shows that the model is able to simulate the charging load of electric vehicles more accurately. Different traffic flows and areas have a significant impact on the charging load distribution.
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    Hydrodynamic Characteristics of Hybrid Mooring System with Dual-Platform Joint Operation
    HUO Fali, YANG Jichuan, ZHU Chenyang, WEI Changdong, ZHAO Yinzhi
    2025, 30 (6):  1242-1254.  doi: 10.1007/s12204-023-2640-9
    Abstract ( 2 )   PDF (2804KB) ( 0 )  
    With the development of marine resources, a dual-platform joint operation has been paid more attention. In this paper, the mooring layout space and relative motion limitation of the dual-platform berthing operation were fully considered. A new hybrid mooring system with “X + buoy” combination was designed based on the characteristics of catenary and tension mooring. The hydrodynamic characteristics of the new mooring system were analyzed by combining numerical simulation with model experiment. Under the regular and freak waves with different wave heights and periods, the time-domain full-coupling analysis method was used to study the hydrodynamic characteristics of the mooring system. It can be found that the arrangement of dual-platform under 0 ◦ wave direction is optimal, and the “X + buoy” combined mooring system designed in this paper has a good follow-up between the two platforms under different regular and freak waves. The relative motion response between the two platforms can be effectively controlled, and finally the positioning of the dual-platform joint operation is realized. Research results of this paper provide a theoretical basis and technical support for the hydrodynamic performance analysis and safety assessment of deep-sea offshore platforms in China.
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    Autonomous Navigation Algorithm for Underactuated Unmanned Surface Vehicle Based on Model Predictive Control
    CHEN Guoquan, LI Yuqin, HUANG Zike, YANG Shenhua
    2025, 30 (6):  1255-1264.  doi: 10.1007/s12204-023-2674-z
    Abstract ( 3 )   PDF (585KB) ( 0 )  
    To achieve the track following and collision avoidance of underactuated unmanned surface vehicle (USV), autonomous navigation model based on model predictive control is established by including the track offset, speed variation and rule compliance as the evaluation functions and including the ship domain of dynamic/ static navigation obstacles and the mechanical characteristics limitation as constraints. The effectiveness of the model for autonomous navigation of USV in the situation of multi-ship encounters and in the complex waters with both dynamic and static obstructions is verified by several groups of simulation work. The simulation results show that the proposed model can realize the autonomous navigation of the underactuated USV under the complex waters.
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    Numerical Simulation of Freezing Process in Ice Tank Driven by Cold Air
    DING Shifeng, ZHOU Li, GU Yingjie, LIU Renwei, HU Yangfan, LIU Zhibing
    2025, 30 (6):  1265-1275.  doi: 10.1007/s12204-023-2627-6
    Abstract ( 2 )   PDF (4175KB) ( 0 )  
    Cold air is one key factor affecting the freezing process of ice tanks. The volume of fluid method is employed to simulate the freezing process of water in an ice tank with cold air inlets. The temperature field distribution in the ice tank is calculated. The temperature field at different typical instants are compared. The main characteristics of the freezing process in an ice tank driven by cold air are analyzed. The influence of the number of cold air inlets on the freezing process is investigated. The numerical results show that with increasing the number of cold air inlets, the temperature field becomes more uniform. The inlet velocity of cold air has a great influence on the generation of ice. This work can serve for the design of the ice tank and control of the freezing process.
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    Tugboat Scheduling Problem Considering Time Windows and Flexible Returning Way to Base
    ZHONG Ming, WU Ying, WU Chunli, WANG Fang
    2025, 30 (6):  1276-1288.  doi: 10.1007/s12204-023-2657-0
    Abstract ( 2 )   PDF (883KB) ( 0 )  
    In ports, inbound and outbound ships usually need tugboats to provide berthing and unberthing services. The decision-making problem on tugboat scheduling is important because it involves not only ships’ turnaround time at port but also tugboat operation costs. Encouraged by the problem faced by the tugboat operator, we formulate a mixed-integer programming model for tugboat scheduling problem with several practical constraints considered, such as dynamic arrival and departure of ships, qualification of tugboats, synchronization, and a flexible returning way to base to minimize the tugboat operation costs generated within the planning period. The model is inspired by genetic algorithm framework with three-dimensional coding. Effectiveness of our model and proposed solution method are testified and validated through experiments and computational results. This research helps to provide a scientific scheduling method and some insights for managers.
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    Vortex-Induced Vibration and Frequency Lock-In of an Elastically Suspended Hydrofoil with Blunt Trailing Edge
    QIN Guangfei, ZHANG Huaixin, LI Date
    2025, 30 (6):  1289-1298.  doi: 10.1007/s12204-023-2693-9
    Abstract ( 1 )   PDF (1729KB) ( 0 )  
    Vortex-induced vibration of hydrofoils is concerned with structural safety and noise level in hydraulic machinery and marine engineering. The research on vibration characteristics under different operating conditions is significant. In this study, numerical simulations are conducted to investigate the vortex-induced vibration responses of an elastically suspended hydrofoil with blunt trailing edge in pitch direction. The work studies the effects of four parameters, namely the structural natural frequency, mass ratio, initial attack angle, and Reynolds number on vibration characteristics, with special emphasis on frequency lock-in. Results indicate that as the structural natural frequency changes, the vibration amplitude may increase substantially within a certain frequency range, in which the vortex shedding frequency locks into the structural natural frequency, and frequency lock-in occurs. In addition, with increasing the mass ratio, the frequency range of lock-in becomes narrower, and both the upper and lower thresholds decrease. As the initial attack angle increases from 0◦ to 6◦, the lock-in range gets reduced. Over the three Reynolds numbers (6 × 105, 9 × 105, and 12 × 105), the lock-in range remains virtually unchanged. Moreover, for a certain structural natural frequency, modifying the mass ratio, initial attack angle, and Reynolds number could effectively suppress the vibration amplitude.
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