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15 February 2024, Volume 45 Issue 2 Previous Issue    Next Issue
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Information & Control
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Information & Control

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H∞ Sliding Mode Control for Nonlinear Generalized Time-delay Markov Jump Systems Dong-mei YANG, Ling-xiu DU, Chun-xia ZHU 2024, 45 (2):  153-159.  DOI: 10.12068/j.issn.1005-3026.2024.02.001 Abstract ( 461 )   HTML ( 11)   PDF (806KB) ( 50 )   The sliding mode control problem for a class of generalized time-delay Markov jump systems with partially unknown transition rates is studied. Firstly， an integral sliding mode surface is designed for the generalized time-delay Markov jump system， and the corresponding equivalent controller is obtained. Then， a Lyapunov functional is constructed， and the sufficient conditions for the stochastic admissibly and satisfying H_{\mathrm{\infty }} criteria \gamma performance of the closed-loop system are obtained using linear matrix inequality method. The addition and subtraction term method and the free weight matrix are used to reduce the conservatism of the obtained results. Based on the analysis of sliding mode dynamics， a sliding mode controller is designed so that the system can reach the sliding mode surface in finite time. Finally， the feasibility of the theory is verified by numerical examples and simulations. Figures and Tables | References | Related Articles | Metrics

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Contribution Degree and Data Validity Verification Based Consensus Algorithm Xiao-hu SHI, Xin YAO, Yan-feng SUN, De-yin MA 2024, 45 (2):  160-169.  DOI: 10.12068/j.issn.1005-3026.2024.02.002 Abstract ( 317 )   HTML ( 4)   PDF (1212KB) ( 172 )   The blockchain technology into the distributed data maintenance system is introduced and a contribution degree and data validity verification based consensus algorithm is proposed. In the algorithm， a random and verifiable leader election mechanism is designed according to contribution priority， ensuring the randomness and verifiability of the assignment of accounting rights. Furthermore， it introduces the density peak algorithm to reach the consensus on the correctness of packaged blocks. Finally， the proposed consensus algorithm is applied to the distributed deer farms for experimental comparison. The results validate the accuracy and efficiency of the density peak algorithm in the task of data validity testing. The analysis of block delay analysis and safety shows that the consensus algorithm satisfies the real-time requirements， consumes less energy and has strong disaster preparedness ability. Figures and Tables | References | Related Articles | Metrics

Materials & Metallurgy

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Microstructure and Properties of Laser Cladding Fe‐Al Alloy at Different Scanning Speeds Wen-bo YAO, Chen LIU, Shuo SHANG, Chang-sheng LIU 2024, 45 (2):  170-178.  DOI: 10.12068/j.issn.1005-3026.2024.02.003 Abstract ( 425 )   HTML ( 10)   PDF (7625KB) ( 107 )   In order to improve the corrosion resistance of engineering high‐strength steel and reduce the cost of materials used， a fiber laser was used to prepare Fe‐Al alloy cladding layer on the surface of Q960E high‐strength steel by coaxial powder feeding process and to study the effect of different scanning speeds on microstructure and corrosion resistance. The results show that the grain morphology， element distribution， and content of the cladding layer are affected by the scanning speed. The material phase is mainly composed of the Fe3Al phase with DO3 structure and the FeAl phase with B2 structure in the eutectic form. The hardness of the cladding layer increases gradually with the scanning speed due to grain refinement. The self corrosion potential of the cladding layer at the three scanning speeds rises first and then decreases with the increase of scanning speed， and the self corrosion current density decreases first and then increases. With the increase of scanning speed， the pitting pits on the surface of the cladding layer after polarization first change from deep to shallow， and then the area of pitting pits expands. Figures and Tables | References | Related Articles | Metrics

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Numerical Simulation and Experimental Study on Hot Oil Thermostatic Temperature Forming of AZ31 Magnesium Alloy Sheet Ben YU, Dong-xiao WANG, Yu LIU, Jian-ping LI 2024, 45 (2):  179-186.  DOI: 10.12068/j.issn.1005-3026.2024.02.004 Abstract ( 361 )   HTML ( 6)   PDF (5933KB) ( 55 )   The formability of AZ31 magnesium alloy was studied by finite element simulation and forming experiment. It’s based on Dynaform simulation software and hot oil thermostatic forming equipment to explore a hot forming process which is suitable for magnesium alloy， and to analyze the microstructure of the formed parts. The results showed that by adjusting the process parameters such as the plate size， die R angle， blank holder force and friction coefficient， the bottom thinning rate of the formed part and the fracture tendency can be reduced， and the forming performance of magnesium alloy can be improved； and when the forming temperature is 200 ℃， the die R angle is 16 mm， the plate diameter is 80 mm， the appropriate blank holder force and friction coefficient are adjusted， it can obtain the best process window. Near the bottom of the formed parts， the grain size and the second phase size gradually decrease and tend to be uniform. Figures and Tables | References | Related Articles | Metrics

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Degradation of Butyl Xanthate Using Persulfate Activated with Iron and Steel Metallurgical Slag Mei-hang LI, Si-yu MIAO, Wei-wei ZHANG, En-zhu HU 2024, 45 (2):  187-192.  DOI: 10.12068/j.issn.1005-3026.2024.02.005 Abstract ( 417 )   HTML ( 2)   PDF (915KB) ( 49 )   Butyl xanthate in water was degraded by persulfate activated with iron and steel metallurgical slags， including steel slag， Ti-bearing blast-furnace slag and vanadium tailings. The effects of slag types and dosage， persulfate concentration and initial pH value on the degradation efficiency of butyl xanthate were analyzed. Two-way ANOVA was used to reveal the interaction characteristics between the factors. The results showed that the degradation rate of butyl xanthate increases with the increase of the slag dosage and persulfate concentration. Under the condition of 1 g/L slag， 0.5 mmol/L persulfate， reaction time of 96 h， the degradation rate of butyl xanthate reaches 96.47%， 97.70% and 95.12% with the application of steel slag， Ti-bearing blast-furnace slag and vanadium tailings， respectively. The optimal pH conditions for the above three slags are alkaline， near neutral and acid， respectively. The reactive constituents include non-free radical （1O2）， SO4?- and HO? with the activation of steel slag. The activation of Ti-bearing blast-furnace slag is dominated by both 1O2 and HO?. Nevertheless， the dominant reactive constituent for the activation of vanadium tailings is 1O2. Figures and Tables | References | Related Articles | Metrics

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Diffusion Reaction Characteristics of Calcium Ferrite and TiO2 Xiao-zhou CAO, Sheng-qi SHAO, Hong-rui YUE 2024, 45 (2):  193-200.  DOI: 10.12068/j.issn.1005-3026.2024.02.006 Abstract ( 376 )   HTML ( 4)   PDF (5287KB) ( 42 )   During sintering the vanadium titanomagnetite， TiO2 competes with Fe2O3 for CaO， which inhibits the formation of calcium ferrite （C x F） and affects the sinter quality. In this paper， the diffusion reaction of CaO-Fe2O3-TiO2 system is intuitively studied by preparing C x F/TiO2 diffusion couple. Electron probe and X-ray diffractometer are used to analyze and characterize the products at different positions of the reaction interface. The reaction characteristics of C x F/TiO2 interface are studied at the diffusion temperature of 900~1050 ℃ and the time of 1~4 h. The effects of temperature and time on the types， distribution and morphology of the generated phases are discussed. The results show that the main phases are C x F， CaO·Fe2O3（CF）， Fe2O3， CaTiO3 and TiO2 from the C x F- to TiO2-layer， among which perovskite （CaTiO3） is the main product. The thickness of CaTiO3 increases from 8.1 μm to 90.2 μm with the temperature increasing from 900 ℃ to 1 050 ℃； it increases from 47.4 μm to 121.4 μm with the time increasing from 1 h to 4 h. Meanwhile， the diffusion thickness of CaTiO3 has a good linear relationship with the square root of diffusion time， which indicates that the formation of CaTiO3 is controlled by diffusion process. Furthermore， the formation process of CaTiO3 in CaO-Fe2O3-TiO2 system is explained by vacancy-mediated diffusion mechanism. Figures and Tables | References | Related Articles | Metrics

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Effects of Graphite Additives on Rheological Properties of Magnetorheological Grease Ji-qiang DONG, Xu-dan YE, Run-song MAO, Jiong WANG 2024, 45 (2):  201-208.  DOI: 10.12068/j.issn.1005-3026.2024.02.007 Abstract ( 368 )   HTML ( 1)   PDF (1691KB) ( 50 )   To study the effect of graphite additive on the rheological properties of magnetorheological grease， graphite magnetorheological grease （GMRG） was prepared. The GMRGs with graphite powder mass fractions of 0%， 2%， 5%， 8% and 10% were prepared using grease as the matrix. The rheological properties of 5 groups of GMRG were measured in steady-state shear and oscillatory shear modes， and the effect of graphite additive mass fraction on yield stress and viscoelasticity was analyzed. The results showed that compared with the magnetorheological grease without graphite powder addition， the GMRG can achieve higher yield stress under the loading current of 3 A. The yield stress of the GMRG was increased by 40.49%， 54.12%， 81.48% and 147.48% with graphite mass fractions of 2%， 5%， 8% and 10%， respectively. In addition， with， the viscoelastic characteristics of the GMRG become more pronounced as the graphite mass fraction increase， but the relative magnetorheological effect achieved by the GMRG becomes smaller. The mass fraction of graphite does not affect the linear viscoelastic range of the GMRG was also found. Figures and Tables | References | Related Articles | Metrics

Mechanical Engineering

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Adaptive Fault-Tolerant Control of Quadrotor UAV Based on Fuzzy Gain Sliding Mode Zhao-hui REN, Yu-lin LIU, Ze-yu JIANG, Xiang-yu CHEN 2024, 45 (2):  209-216.  DOI: 10.12068/j.issn.1005-3026.2024.02.008 Abstract ( 627 )   HTML ( 11)   PDF (1555KB) ( 90 )   Aiming at the trajectory tracking task of quadrotor UAV under actuator malfunction， an adaptive fault-tolerant control method based on fuzzy gain sliding mode is proposed. Firstly， for the direct control channel， the adaptive mechanism is used to estimate and compensate for actuator faults and the sliding mode controller based on fuzzy gain is used to design the adjustable controller to meet the requirements of robustness. For the indirect drive channel， the sliding mode controller based on fuzzy gain is designed to achieve control of the UAV. This method has good fault-tolerant ability and it can suppress the system chatter and obtain smooth control signals. Finally， the tracking performance of the quadrotor UAV under different controllers is compared and simulated and the results show that the system has good flight performance in the presence of fault and interference. Figures and Tables | References | Related Articles | Metrics

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Vibration Suppression of Dual-Flexible Manipulator with Fuzzy Tuning PI Parameters Xiao-peng LI, Sai-nan ZHOU, Jia-qi LIU, Meng YIN 2024, 45 (2):  217-225.  DOI: 10.12068/j.issn.1005-3026.2024.02.009 Abstract ( 503 )   HTML ( 4)   PDF (4927KB) ( 78 )   The existence of flexible factors in the manipulator servo drive system can easily lead to the fluctuation of the output speed of the manipulator， and even lead to system resonance. In order to suppress the speed fluctuation of the system and stabilize the performance of the manipulator’s transmission system， the fuzzy theory is used to set the control strategy of PI controller parameters. According to the assumed mode method and Lagrange dynamic equation， the dynamic equation of the dual-flexible manipulator’s transmission system considering LuGre friction model is established， and the influence of the coupling nonlinear terms in the dynamic equation on the transmission characteristics of the system is analyzed. The pole assignment strategy is used to determine the value range of the PI controller parameters， and then the controller parameters are adjusted in real time according to the fuzzy rules to reduce the fluctuation of the servo system output speed and further suppress the system resonance. Finally， by means of numerical simulation analysis and manipulators’ control experiment， compared with the traditional PI control strategy， it is found that the control strategy taken in this study can reduce the average value of the absolute value of the motor end angle tracking error by 43.066%， and the standard deviation of the flexible load angle error by 46.506%， which further verifies the effectiveness of the proposed vibration suppression method with fuzzy tuning PI controller parameters. Figures and Tables | References | Related Articles | Metrics

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Reliability Allocation of NC Machine Tool Subsystem Based on Improved ARINC Method Xian-zhen HUANG, Chao SUN, Cheng-ying ZHAO, Yang LIU 2024, 45 (2):  226-233.  DOI: 10.12068/j.issn.1005-3026.2024.02.010 Abstract ( 522 )   HTML ( 2)   PDF (1140KB) ( 62 )   According to the collected fault information of a domestic NC machine tool， the subsystem is divided， and the reliability allocation method is improved according to the NC machine tool correlation model to allocate the target value. The membership degree set of influencing factors is established using the analytic hierarchy process （AHP）， and the centrality influencing factors of fault-related data are determined using the DEMATEL decision laboratory analysis method. The membership function set is determined by combining maintainability， maintenance time， failure downtime， failure times， and complexity. Then the reliability allocation factor of the NC machine tool is calculated. The impact factor is introduced into the ARINS allocation method to improve the method so that the improved method is suitable for the system with subsystems connected in series and fault correlation. Numerical examples show that the proposed method can reduce the failure time requirement of the subsystem compared with the traditional ARINS method. At the same time， to verify the rationality of the distribution results in this paper， the Monte Carlo simulation method is used to predict the reliability of the target machine tool based on the distribution results， and the calculation results prove the feasibility of this method. Figures and Tables | References | Related Articles | Metrics

Resources & Civil Engineering

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Mining-Induced Surrounding Rock Instability and Surface Subsidence Based on Combination of In-situ Monitoring and Numerical Modelling Yu-meng WANG, Kai GUAN, Wan-cheng ZHU, Hong-lei LIU 2024, 45 (2):  234-243.  DOI: 10.12068/j.issn.1005-3026.2024.02.011 Abstract ( 622 )   HTML ( 4)   PDF (3041KB) ( 112 )   A three-dimensional geological model integrating real ground topography, ore bodies, and tunnels was established by 3Dmine and UAV. Combined with Rhino6-FLAC3D, a numerical calculation model for ore body extraction was developed. The impact of rock movement and surface deformation was simulated and analyzed. The effectiveness of simulation results was verified through InSAR monitoring. The results indicate that the simulation results are consistent with InSAR monitoring, indicating that the research method combining monitoring and simulation is effective. For the goaf left by open-pit mining, dry filling can limit the damage of surrounding rock and filling body. The stability of shallow filled mining areas might be affected by deep operations in the mining area, and there is a negative correlation between the severity of disturbance and the distance from deep work areas. According to InSAR monitoring and numerical simulation, the impact of goaf destruction and mining disturbance on the surface subsidence is weak. Figures and Tables | References | Related Articles | Metrics

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A Study of Rockburst Prediction Method Based on D-S Evidence Theory Yong-tao GAO, Qiang ZHU, Shun-chuan WU, Yong-bing WANG 2024, 45 (2):  244-251.  DOI: 10.12068/j.issn.1005-3026.2024.02.012 Abstract ( 480 )   HTML ( 6)   PDF (1867KB) ( 42 )   To effectively predict rockburst， a rockburst prediction method based on D-S evidence theory is proposed. Firstly， six indicator factors related to rockburst occurrence are selected as evidence， and the basic probability assignment of evidence is constructed through fuzzy matter-element framework and normal type degree of membership function. Then， the evidence is classified using K-means and a combined fusion rule of fusing evidence within clusters in classical Dempster’s rule while fusing evidence between clusters in the weighted way is proposed to reduce the adverse effects of high conflict evidence fusion. Finally， the model is applied to the No.2 shaft project of the Qinling Zhongnanshan highway tunnel and compared with the empirical method. To address the uncertainty in the prediction process and to estimate the probability of rockburst occurrence， Monte Carlo simulation is used to perform sampling simulations and the global sensitivity of the input indicators is measured by Spearman’s rank correlation coefficient. The results show that the influence of the input indicators varies widely and in different directions for different rockburst cases； the probability of occurrence of the five rockburst cases ranges from 40.8% to 70.1%. The model shows outstanding predictive classification performance and can provide reference for rockburst prediction in deeply buried underground projects. Figures and Tables | References | Related Articles | Metrics

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Response of Reefs to Sea-Level Change： Estimation of Magnitude of Sea-Level Change Based on the Late Carboniferous Large Coral Reef in Southern Guizhou Yong-li ZHANG, Yue GU, En-pu GONG, Guan-ming LAI 2024, 45 (2):  252-261.  DOI: 10.12068/j.issn.1005-3026.2024.02.013 Abstract ( 478 )   HTML ( 6)   PDF (2554KB) ( 40 )   The Late Paleozoic ice age is a vital event in the geological history. The sea level change caused by the Late Paleozoic ice age has a far-reaching impact on the reef system. The response of reefs to sea-level change in the context of the Late Paleozoic ice age is discussed. Reefs exhibit three primary modes of response：“abandonment”，“synchronization”， “persistence”. We calculated the rise of sea level in Gzhelian by the large Bianping coral reef in southern Guizhou. The sea level of Gzhelian in southern Guizhou rose by about （60±5）m， which is mainly caused by glaciation. The sources of error in this estimation chiefly revolve around basement subsidence and inaccurate estimation of paleo-water depth. The morphology and rapid growth characteristics of Fomitchevella reveal the paleoenvironmental conditions of warm climate， rising sea level and rapid transgression in the Gzhelian period in southern Guizhou. The development of the Bianping coral reef reflects the global climate change and sea level fluctuations are related to the ice age. Figures and Tables | References | Related Articles | Metrics

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Study on Harmless Disposal and Mechanism of Cyanide Tailings of a Gold Mine by Oxidation Roasting Yan SONG, Bing ZHAO, Yan-jun LI, Ling-bo ZHAO 2024, 45 (2):  262-269.  DOI: 10.12068/j.issn.1005-3026.2024.02.014 Abstract ( 512 )   HTML ( 4)   PDF (3188KB) ( 72 )   In view of the high complex cyanide ratio in cyanide tailings of a gold mine， the process of oxidation roasting was adopted to treat cyanide tailings. The results showed that the total cyanogen content in cyanidation tailings could be reduced below the detection limit 0.04 mg/kg when the samples were roasted at 550 °C for 30 min， at 20% O2 volume fraction and a total gas of 600 mL/min， at the same time， the sulfur retention rate reached 82.22%. Thermogravimetric analysis of the corresponding ferricyanide complex K4Fe（CN）6 showed that K4Fe（CN）6 is first oxidized to KCNO， and then oxidized to K2CO3. Both stages are accompanied by gaseous compounds such as CO2， CO， NO2 and NO， and the first stage also involves sub-reactions. The process can not only effectively decompose cyanide， especially complex cyanide in the cyanide tailings， but also avoid the easy oxidation of sulfur element in the tailings， greatly reducing the cost of subsequent flue gas desulfurization， and has broad application prospects. Figures and Tables | References | Related Articles | Metrics

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Fabrication and Evaluation of Chitosan-based Composite Antibacterial Air Filter Jing-xian LIU, Qi ZHAO 2024, 45 (2):  270-275.  DOI: 10.12068/j.issn.1005-3026.2024.02.015 Abstract ( 381 )   HTML ( 7)   PDF (1381KB) ( 32 )   With the outbreak of COVID-19， there is a growing demand for improved indoor air quality. It is of great significance to explore filter materials that can not only filter fine particulate matter， but also inhibit and disinfect microbial bacteria and prevent secondary pollution. Chitosan impregnation solutions with different concentrations were prepared with 1% mass fraction of polytetrafluoroethylene （PTFE） emulsion， and chitosan/polyester/polytetrafluoroethylene composite antibacterial air filter was designed and fabricated by direct impregnation post-processing. Escherichia coli was used as the experimental colony to verify its bacteriostatic properties， and its fabric characteristics， collection efficiency and pressure drop characteristics were studied. The results showed that the initial pressure drop of the composite air filter was the lowest when the chitosan concentration was 12.5 mg/mL， the collection efficiency for PM2.5 was 93.88%， the quality factor was 0.020 13， which was 19.56% and 0.004 4 higher than that of the raw air filter， and the bacteriostatic rate of E. coli was 84.12%. In conclusion， chitosan/polyester/polytetrafluoroethylene composite antibacterial air filter prepared with chitosan concentration of 12.5 mg/mL and PTFE emulsion concentration of 1% impregnation solution has both good filtration capacity and antibacterial effect. Figures and Tables | References | Related Articles | Metrics

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Determination Method of Pressure Relief Area for Dust Explosion of Connected Equipment Gang LI, Lei ZHOU, Xiao-yu ZHANG, Kai ZHANG 2024, 45 (2):  276-281.  DOI: 10.12068/j.issn.1005-3026.2024.02.016 Abstract ( 227 )   HTML ( 5)   PDF (1448KB) ( 78 )   The relevant standards at home and abroad offer the calculation method for explosion venting area（EVA） of individual equipment，but there is a notable absence of guidelines for interconnected equipment. By means of FLACS numerical simulation，taking corn starch as the explosion medium，the reduced explosion pressure（REP） and rate of pressure rise in the connected equipment are simulated and explored. The results show that when the length of the pipe is fixed，the maximum REP in the booster vessel decreases with the increasement of the EVA. When the same EVA is set，the maximum REP in the booster vessel increases with the increase of the pipe length，and the time to reach the maximum REP value also delays. The minimum safe EVA required for the booster vessel is larger than that of the single equipment with same size， indicating that the calculation formula of the EVA of the single equipment is unreliable for the connected equipment. Through numerical fitting， the EVA calculation formula for single equipment in the standard was modified to meet the requirement of connected equipment. The research results provide reference for explosion-proof design for connected system. Figures and Tables | References | Related Articles | Metrics

Management Science

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Stochastic Integrated Solution of Interval Rough Number Group G1 Method and Its Application Yuan-yuan LIANG, Jun LIU, Ping-tao YI, Wei-wei LI 2024, 45 (2):  282-288.  DOI: 10.12068/j.issn.1005-3026.2024.02.017 Abstract ( 462 )   HTML ( 5)   PDF (700KB) ( 51 )   For the problem of group evaluation in complex uncertain environments， an interval rough number is used to characterize experts’ preferences， and a stochastic simulation integrated algorithm is proposed based on the G1 method combined with Monte Carlo simulation techniques. Firstly， the weighting coefficients are simulated by random sampling and the weighting of experts are determined based on ordinal correlation and interval rough number closeness. Secondly， the final weights of indicators can be obtained by combining all the experts’ opinions， and they are linearly aggregated with the pre-processed indicator values to obtain the comprehensive evaluation value of one simulation， which can be used to assess the advantages and disadvantages of the evaluated objects. Through full simulation， the preference ratio matrix is calculated， and the probability ranking with the probability of superiority is derived from it， which makes up for the deficiency of absolute ranking in the uncertain information environment. Finally， the effectiveness of the method is illustrated by an example and the advantages of the method are described in comparison with the existing methods. Figures and Tables | References | Related Articles | Metrics

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Supply Chain Financing Decision Considering Carbon Cap-and-Trade Under Double Capital Constraints Li-jun LI, Chun-yu YANG, Fu CHENG 2024, 45 (2):  289-295.  DOI: 10.12068/j.issn.1005-3026.2024.02.018 Abstract ( 396 )   HTML ( 3)   PDF (801KB) ( 48 )   A low-carbon supply chain system composed of manufacturers and retailers with both production and emission reduction financing constraints was built. Aiming at bank loaning and prepayment， manufacturers’ financing decision under carbon cap-and-trade was explored， and the effect of carbon abatement cost coefficient and carbon trading price on supply chain members’ financing decision and profit was analyzed. The results showed that when the prepayment interest rate is equal to the bank interest rate， whether carbon cap-and-trade is considered or not， prepayment will always bring greater profit to manufacturers. Therefore， prepayment is the best choice for manufacturers. When the financing rate is unequal， manufacturers’ financing methods will be affected by carbon cap-and-trade and carbon abatement cost coefficient. When the carbon abatement cost coefficient increases， the financing scale and supply chain members’ profit both decrease， while when the price of carbon increases， the financing scale and manufacturers’ profit both increase. In addition， carbon cap-and-trade increases manufacturers’ profit， but harms retailers’ profit. Figures and Tables | References | Related Articles | Metrics

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A Method for Path Planning of Multi-vehicles Collaboration with Multi-agricultural UAVs Jin-hua XU, Fei WANG, Fei HAN, Yan LI 2024, 45 (2):  296-304.  DOI: 10.12068/j.issn.1005-3026.2024.02.019 Abstract ( 398 )   HTML ( 8)   PDF (1273KB) ( 149 )   Multi-vehicle collaboration with multi-agricultural UAV operation can overcome limitations such as endurance and greatly improve efficiency. To address challenges in path planning for collaborative operations involving multi-vehicles and multi-agricultural UAVs， a path optimization model is constructed with the objective of minimizing the maximum operation time of UAVs. The improved simulated annealing-Lin Kernighan Helsgaun （SA-LKH） algorithm is proposed to solve the model. The proposed method combines K-means and convex hull methods to generate the initial solutions， and uses the LKH algorithm to optimize the paths of each group of UAVs and vehicles. Additionally， a directed perturbation operator is constructed to achieve rapid convergence of the algorithm by perturbing the paths with the maximum and minimum operation times during each iteration. The results of five different scale examples show that the proposed algorithm is superior to the comparative algorithm in terms of solution quality and efficiency. Figures and Tables | References | Related Articles | Metrics