• Volume 43,Issue 9,2011 Table of Contents
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    • A novel hybrid T-S model identification algorithm

      2011, 43(9):1-6. DOI: 10.11918/j.issn.0367-6234.2011.09.001

      Abstract (1243) HTML (3) PDF 629.23 K (1065) Comment (0) Favorites

      Abstract:To overcome the drawback of regular T-S model identification techniques,such as the FCM and least-squares method,a new Hybrid Identification Algorithm(HIA) is proposed in this paper.The HIA can simultaneously optimize all the model parameters and avoid being trapped into the local minima by merging the FCM,Harmony Search(HS) and the least-squares method together and using the error feedback mechanism.Our HIA is employed in the T-S modeling of the Gyro-stabilized platform.By comparing the MSE peformance,the HIA can indeed yield a superior MSE performance over the conventional identification methods.The identification results show that the HIA can effectively overcome the incomplete optimization problem of the conventional identification methods.

    • Spacecraft attitude tracking based on almost disturbance decoupling

      2011, 43(9):7-13. DOI: 10.11918/j.issn.0367-6234.2011.09.002

      Abstract (1681) HTML (7) PDF 567.81 K (1118) Comment (0) Favorites

      Abstract:The problem of spacecraft attitude tracking under bounded disturbances is addressed based on almost disturbance decoupling.The modified Rodrigues Parameter(MRP) is adopted as attitude representation.A feedback linearization control scheme based on differential geometry for nonlinear systems is used to design the controller,by which the tracking and the almost disturbance decoupling performances can be easily achieved.Lyapunov theory is employed to prove that the influence of disturbances on the L2 norm of output tracking error can be arbitrarily attenuated by changing some adjustable parameters in the controller,and that spacecraft attitude tracking system is globally uniformly ultimately bounded stable.Simulation results demonstrate the effectiveness and feasibility of the proposed control scheme.

    • Sliding mode observer used in satellite attitude control system fault diagnosis

      2011, 43(9):14-18. DOI: 10.11918/j.issn.0367-6234.2011.09.003

      Abstract (1654) HTML (3) PDF 395.25 K (998) Comment (0) Favorites

      Abstract:To improve the reliability of satellite system,the observer-based actuator fault diagnosis problem for satellite attitude control system was investigated.Considering the uncertainty and disturbance of the satellite attitude control system,a robust adaptive sliding mode observer was proposed.A Lyapunov function was given as the judgment condition to stabilize the observer.Then,the proposed observer was used for actuator fault reconstruction.At last,the simulation of the observer in a satellite attitude control system with actuator fault illustrates the effectiveness of the proposed approach.

    • An algorithm of around orbit and parameters determination for small body

      2011, 43(9):19-24. DOI: 10.11918/j.issn.0367-6234.2011.09.004

      Abstract (1986) HTML (4) PDF 526.46 K (1109) Comment (0) Favorites

      Abstract:The around orbit parameters and small body physical parameters determination methods are studied based on Square Root Information Filter(SRIF).Due to a great deal of parameters to be estimated and the complexity of the dynamics,the SRIF is designed to process the integrated navigation data and estimate the gravity field,rotation,and ephemeris of small body and orbit parameters of probe.The mathematic simulation experiments using the measuring data of Eros433 small body have validated the algorithm.

    • Research on data interfaces in desktop testing platform for a certain satellite

      2011, 43(9):25-29,37. DOI: 10.11918/j.issn.0367-6234.2011.09.005

      Abstract (1592) HTML (3) PDF 626.47 K (1241) Comment (0) Favorites

      Abstract:Research on design and implementation of data interfaces in the desktop testing platform for a certain satellite was introduced in this paper.Firstly,to satisfy the engineering requirements,general structure of the platform was designed with the real-time simulator and the on-board computer as its core components,and the interfaces among various components in the platform was described.Then,topic focused on researching problems including constitution of the real-time simulator,programming on interfaces using xPC Target,sample time of the interfaces,encoding double precision floating point number for transmission through interfaces,and design of CAN bus protocol on the application layer.Finally,by analyzing results of the testing experiment,effectiveness and practicality of the data interfaces solution were proved.

    • Two dynamic propagation problems of mode Ⅲ crack

      2011, 43(9):30-32. DOI: 10.11918/j.issn.0367-6234.2011.09.006

      Abstract (1446) HTML (6) PDF 294.94 K (1174) Comment (0) Favorites

      Abstract:In order to solve two dynamic propagation problems on mode Ⅲ crack by theory of complex functions,a new mechanical model for dynamic crack propagation,in which the crack is under the conditions of increasing loads Px/t、Pt3/x2 located at the origin of the coordinate of the crack is presented in this paper.The problems are transformed into Riemann-Hilbert problems by the approaches of self-similar functions,and the analytical solutions of stress,displacement and stress intensity factor are attained.With the solutions and superposition theorem,the solutions of discretionary complex problems can be acquired.

    • A biomimetic water-jetting vehicle actuated by shape memory alloy wires

      2011, 43(9):33-37. DOI: 10.11918/j.issn.0367-6234.2011.09.007

      Abstract (2004) HTML (3) PDF 957.81 K (1511) Comment (0) Favorites

      Abstract:To provide propulsive machine for underwater robot with high speed,high efficiency,high maneuverability and high hidden,a biomimetic water-jetting vehicle that imitated jetting propulsive principle of squids actuated by shaper memory alloy wires is developed.The jetting propulsive mechanism and the muscle structure of squids are analyzed firstly.Then the structure of the biomimetic water-jetting vehicle,imitating the muscle structure of squids,and based on proper simplification is designed.The geometrical model is set up.At last,the propulsive performance of the vehicle is experimented.The experimental results show that the biomimetic water-jetting vehicle can imitate the flexible contract of the mantle of squids;the radial contract is uniform;the maximal contractive strain is 8.8 % and the maximal swimming speed is 58 mm/s.In conclusion,the vehicle has simple structure,flexible jetting motion and zero noise,providing basis for further research on biomimetic robot squid.

    • New low noise closed-loop driving circuit for the micro-gyroscope

      2011, 43(9):38-41. DOI: 10.11918/j.issn.0367-6234.2011.09.008

      Abstract (2171) HTML (3) PDF 927.77 K (1316) Comment (0) Favorites

      Abstract:To bring the fabric of the micro-gyroscope into simulation of total closed-loop system,the equivalent electrical analogue of drive part of the micro-gyroscope is built.The new low noise closed-loop driving circuit is based on the phase-locked technology using the transimpedance amplifier to realize I-V transformation which effectively avoids phase error caused by the charge amplifier.By using the CCCII+technology to realize the floating resistor,the noise of the total closed-loop driving circuit is reduced.In simulation,the natural frequency of the micro-gyroscope is 2.7 kHz.The displacement in the drive direction of the micro-gyroscope has 90°phase leg comparing to the driving force in the drive direction.The value of floating resistor is 250 kΩ where the bias current is 50 μA.The active resistor is 0.037 fV2/Hz.The micro-gyroscope is vibrated at its natural frequency.

    • Inverse kinematics for special motion of a new mine rescue robot

      2011, 43(9):42-46. DOI: 10.11918/j.issn.0367-6234.2011.09.009

      Abstract (1161) HTML (2) PDF 535.84 K (1136) Comment (0) Favorites

      Abstract:Aiming at the special motion(position and posture adjustment) of the head link of a new mine rescue robot,a novel algorithm based on the combination of spatial decomposition and genetic algorithm(GA) was proposed to solve inverse kinematics of the robot.This algorithm can realize prospective position and posture with the lowest turning cost and keep the robot stable.The two-step spatial decomposition method is presented and it overcomes the defects of big searching space and not converging to the global optimum solution using a GA algorithm.Simulation results show that the position and posture error derived using the new algorithm is smaller and the joint angles are closer to real values.The new algorithm can satisfy the motion requirement of head link of the new mine rescue robot.

    • 3D reconstruction of feature point on object surface from a single image

      2011, 43(9):47-50,55. DOI: 10.11918/j.issn.0367-6234.2011.09.010

      Abstract (1931) HTML (3) PDF 409.39 K (1213) Comment (0) Favorites

      Abstract:For the design and development of a vision sensor for the ground test,a method of 3D reconstruction of feature point on large scale object surface from a single image is proposed.By establishing the math model of the 3D coordinate of feature point on the object surface and using the spatial ray through feature point,the 3D coordinate of the feature point can be determined using single image.According to the characteristics,the object surface can be classified into three types: high order surface type,block plane type and block surface type,while the corresponding location methods are introduced.The accuracy of three different 3D reconstruction methods is compared by simulation experiments.By the measurement precision of 1/10 000 in the range of 8 000 mm×8 000 mm,it is proved that the proposed method is suitable for 3D reconstruction of feature point on large scale object surface.

    • Direct drive volume control electro-hydraulic servo active mass driver system

      2011, 43(9):51-55. DOI: 10.11918/j.issn.0367-6234.2011.09.011

      Abstract (1974) HTML (3) PDF 1.13 M (1333) Comment (0) Favorites

      Abstract:Aiming at the disadvantages of traditional AMD drive device,such as large volume,high cost,complex system,more energy consumption,an innovative driver-Direct Driving Volume Control(DDVC) servo system for AMD is proposed based on the volume control of electro-hydraulic servo system.The mechanical models of motor control,hydraulic power mechanism,hydraulic actuator and other sub-structures of DDVC electro-hydraulic servo system were separately established as well as the mathematical model of direct drive volume control electro-hydraulic servo actuator.Taking an actual project’s experimental prototype as a standard,the parameter optimization and the match computation were carried out,and the DAMD control system are designed and processed.The dynamic characteristics of the power mechanism controlled by pump are not high because the DAMD system dynamic characteristics are low.DAMD control system can be used to substitute the traditional AMD control system for high-rise structure or large-span structure to realize active control of structural vibration.

    • Self-excited vibration analysis for wheel/rail lateral contact system

      2011, 43(9):56-61. DOI: 10.11918/j.issn.0367-6234.2011.09.012

      Abstract (1872) HTML (4) PDF 719.59 K (1191) Comment (0) Favorites

      Abstract:To study the influence of self-excited vibration on the curve squeal noise in the wheel/rail contact,the dynamical equation for 1-DOF wheel/rail lateral contact system is derived.A new friction coefficient model based on De Beer model is adopted to calculate the friction force in the wheel/rail contact surface.The influence of kinetic and static friction coefficients as well as the lateral creepage on the stability of self-excited vibration system is investigated.The calculation results show that wheel’s inherent modes will be excited by the unstable self-excited vibration.If the structural damping of wheel/rail contact system is larger than the equivalent damping of the friction force,or the value of lateral creepage is less than 0.0024,the self-excited vibration system will be stable,and thus the curve squeal noise can be restrained.

    • Swing characteristic of pads in tilting pad bearing

      2011, 43(9):62-66. DOI: 10.11918/j.issn.0367-6234.2011.09.013

      Abstract (1770) HTML (3) PDF 538.55 K (1174) Comment (0) Favorites

      Abstract:The geometric relations of pad on tilting-pad bearing were studied,the relationship between tile pendulum angle and structural parameters were established by the oil-film force model of finite length tilting pad bearing and equilibrium equation,and the basic law of tile pendulum angle change was analyzed.The study shows that the tile pendulum angle is determined by the pad structural parameters,the eccentricity ratio of tilting pad bearing and the clearance ratio,but independent of shaft rotating speed,viscosity of lubrication oil,etc.A case study of a tilting pad bearing with 80 deg pad arc angle,0.5 offset was performed to illustrate the law of tile pendulum angle varies with eccentricity ratio and clearance ratio.It is revealed that,when the structural parameters of tilting pad bearing are constant,the tile pendulum angle increases first and then decreases with the original eccentricity ratio increases,and increases linearly with the increasing of bearing clearance ratio.

    • Resolution of IR-UWB near-field real-aperture imaging systems

      2011, 43(9):67-73. DOI: 10.11918/j.issn.0367-6234.2011.09.014

      Abstract (1947) HTML (3) PDF 1.06 M (1332) Comment (0) Favorites

      Abstract:To solve the problem that the traditional "narrow-band,far-field" resolution formulas are no longer suitable for Impulse Radio Ultra-Wide Band(IR-UWB) real aperture imaging systems,a new algorithm to compute the resolution was proposed.On analysis of IR-UWB near-field imaging principle,the formulation of resolution in down-and cross-range for single antenna was derived.Combined with signal superposition in the process of imaging,an algorithm to compute the resolution for real-aperture uniform linear array was presented.Numerical simulation results of ideal point targets imaging verified the correctness of the algorithm.

    • Development of united multi-domain modeling and simulation platform for three-axis stabilized spacecrafts

      2011, 43(9):74-80. DOI: 10.11918/j.issn.0367-6234.2011.09.015

      Abstract (1501) HTML (2) PDF 1.04 M (1123) Comment (0) Favorites

      Abstract:In order to reflect the control characteristics of a spacecraft under the interaction between many disciplines,a multi-domain modeling and simulation platform,dealing with mechanics,electricity,control,software,et al.is developed.This platform is composed of the following modules: the attitude control software,the flywheel system(including motor and its driver,bearing friction,the mechanism of the flywheel et al.),magnetotorquers,attitude sensors,attitude dynamic,orbital dynamic and environment torques,and so on.All the modules are realized using Modelica language,and integrated into an organic whole.The simulation of two typical attitude control modes—attitude established and attitude manoeuvre shows that,this simulation platform is not only used to analyze the control performance of the closed-loop system,but also to evaluate the effect of each domain’s devices.Sufficient application of this platform during all the phases(project proposal,subsystem,system,et al.) can attain the purpose of Multidisciplinary Design Optimization.

    • Study on brake control system of aircraft towing tractor base on hydraulic hybrid

      2011, 43(9):81-85. DOI: 10.11918/j.issn.0367-6234.2011.09.016

      Abstract (1917) HTML (3) PDF 723.91 K (1217) Comment (0) Favorites

      Abstract:To meet the requirements of aircraft tractor,the main parameters of power system were optimized and the optimized results were analyzed by a mathematical model.The braking control system structure and the working policy were designed according to the requirements of regenerated hydraulic braking system.The dual hydraulic braking style was analyzed with consideration of braking conditions greatly influenced by parameter perturbation,so that the optimal working mode was obtained.The control algorithm was proved to be efficient based on the design of ANN fuzzy PID controller and the performance test on the test-bed simulated the hydraulic hybrid tractor.

    • Optimization of hydrostatics hybrid vehicle control strategy

      2011, 43(9):86-90. DOI: 10.11918/j.issn.0367-6234.2011.09.017

      Abstract (1562) HTML (3) PDF 672.98 K (1008) Comment (0) Favorites

      Abstract:To improve the fuel economy of hydrostatics hybrid vehicle(HHV),a HHV dynamic simulation model is built up for performance analysis in MATLAB/Simulink.The optimal tuning of these threshold logic control strategy parameters is formulated as a constrained nonlinear programming problem with an objective function minimizing fuel consumption.The engine active pressurized torque difference and the active pressurized pressure limit are the objects of optimization.A multi-objective genetic algorithm(GA) optimization method is applied to get the optima of work modes and energy distribution in different drive cycles,which gives the compatible control strategy parameters.Simulation results demonstrate that the optimized control strategy parameters allow the engine working in more fuel economy area,improve the fuel economy of HHV.This method can be used for off-line parametric optimization and to shorten the time of controller calibration in the real vehicle.

    • States estimation control strategies for EV hybrid brake system

      2011, 43(9):91-94,127. DOI: 10.11918/j.issn.0367-6234.2011.09.018

      Abstract (1440) HTML (4) PDF 506.73 K (1368) Comment (0) Favorites

      Abstract:Based on the analysis of disadvantages of present static distribution control strategies of clean energy vehicles regenerative brake system,vehicle operation parameters estimation algorithm is presented which is adapted to the configuration of clean energy vehicles.The algorithm effect is simulated in Hardware-In-Loop-Simulation environment.Maximum energy regeneration optimization strategy is given and the advantages of control effect are simulated using HILS.The simulation data shows that the optimized strategy proves the efficiency of brake energy regeneration and finishes wheel anti-lock effectively.

    • Suppliers’ bidding decision support model for online reverse auction

      2011, 43(9):95-100. DOI: 10.11918/j.issn.0367-6234.2011.09.019

      Abstract (1895) HTML (5) PDF 367.63 K (1038) Comment (0) Favorites

      Abstract:To solve the suppliers’ support problem of online reverse combinatorial multi-attribute auction based on bundling,a bundling confirmation model and suppliers’ bidding strategy are proposed based on the scientometrics bundling algorithm and the analysis of suppliers’ bidding behavior in order to maximize the revenue of the suppliers.After that,an illustration for this model is presented,and the result shows that this model can significantly improve the suppliers’ revenue and reduce the negative effect from the asymmetric information during the auction.

    • Sampling inspection plan for coast defense tactical missile based on flying reliability

      2011, 43(9):101-104. DOI: 10.11918/j.issn.0367-6234.2011.09.020

      Abstract (1649) HTML (2) PDF 300.40 K (1098) Comment (0) Favorites

      Abstract:The present sampling inspection for the coast defense tactical missile often takes the hitting probability as the main test index,which may result in the mismatch of the test index and test purpose as well as the inability to test the consistency of manufacture quality.To over come this problem,in this paper,the flying reliability of missile is then taken as the main test index.Assume the flying reliability conform to the exponential distribution,the sampling inspection plan is proposed based on this new main test index.Besides,the acceptance rules of sampling inspection and the consistency test are given.Simulation results show that under similar conditions,the proposed plan is more effective and requires fewer samples,which indicats the feasibility and validity of the new method.

    • An attitude determination algorithm based on GPS single-differenced mode

      2011, 43(9):105-111. DOI: 10.11918/j.issn.0367-6234.2011.09.021

      Abstract (1277) HTML (2) PDF 675.17 K (1365) Comment (0) Favorites

      Abstract:It is difficult to overcome the high correlation of double differential observation using double-differenced model and the initialization procedure costs a long time with makes it difficult to apply in practice.To deal this problem,a recursive algorithm based on the single-differenced model is presented in which the observations are not correlated.The new method increases observation information with the aid of code for original carrier phase observation.At the same time the float ambiguity solutions and its variance-covariance matrix can be obtained recursively and it makes the LAMBDA method be used to estimate the integer ambiguities.The method is also less computation with numerical stability.The experiment results show that the time of initialization is reduced to about 1/50 of that using the double-differenced method,so this method can be effectively applied in practical attitude determination for shortening initialization procedure.

    • Contact characteristics of cylindrical gear with cubic spline tooth traces

      2011, 43(9):112-116. DOI: 10.11918/j.issn.0367-6234.2011.09.022

      Abstract (1619) HTML (2) PDF 670.88 K (999) Comment (0) Favorites

      Abstract:Contact characteristics and hobbing cutting of cylindrical gear with cubic spline tooth traces are investigated.On the basis of the derivation of the hobbing cutter’s tooth surface,the hobbing generated method and gearing theory,the mathematical model of cylindrical gear with cubic spline tooth trace was developed.And,the tooth contact analysis model in which the assemble errors was also considerated,was established on the conditions of continuous tangency of two contact surfaces.The computerized simulation of meshing and contact shows that the meshing characteristics of the modified gears can be improved by using the generating tool with parabolic curved profile which obtains a parabolic transmission error curve;the sensitivity of contact pattern of the cylindrical gear with cubic spline tooth traces can be reduced by adjusting the position of control nodes.

    • Scene categorization of satellite images based on feature selection

      2011, 43(9):117-121. DOI: 10.11918/j.issn.0367-6234.2011.09.023

      Abstract (2347) HTML (4) PDF 756.45 K (1237) Comment (0) Favorites

      Abstract:To improve the accuracy in scene categorization of satellite images,this paper presents an algorithm of feature selection based on augmented LDA(Latent Dirichlet Allocation) model,and the algorithm is improved,which can automatically selects features from the features-pool.This method firstly extracts five kinds of features(SIFT,Geometric Blur,LBP,Gabor and Color histogram) from each image,and during the cross-validation,the combined features,which have the best performance over the dataset are got.Next,the dimensionality of the combined features is reduced by using LDA.Finally the regularized logistic regression classifier are employed to achieve the classification.Compared with other feature combination,the experimental results demonstrate that,the combination of the automatically selected features can improve the accuracy of scene categorization of satellite images effectively.

    • Dynamic model and analysis for vehicle mounted strapdown 3-axis stable platform

      2011, 43(9):122-127. DOI: 10.11918/j.issn.0367-6234.2011.09.024

      Abstract (1783) HTML (2) PDF 454.04 K (1161) Comment (0) Favorites

      Abstract:To attain the coupling characters of vehicle-borne strapdown 3-axis stable platform,a complete kinematics and dynamics model of 3-axis stabilization platform system was achieved.Kinematics model analysis indicates that the main difference between strapdown stabilization platform and rate gyroscope stable platform lies in information acquisition and control mode.The rate gyroscope platform gets stability using hardware directly,while strapdown platform gets stability based on the software compensation.Dynamics model shows that the nonlinear cross coupling exists not only between vehicle body and gimbals of stable platform system,but also among gimbals each other.The coupling test not only validated the model,but also obtained the cross coupling boundary ranges of each gimbal,which affords a theoretical foundation for the further study of vehicle mounted strapdown 3-axis stable platform system.

    • Design of nonlinear H_∞ controller for hypersonic vehicle system

      2011, 43(9):128-133. DOI: 10.11918/j.issn.0367-6234.2011.09.025

      Abstract (1708) HTML (3) PDF 706.57 K (1027) Comment (0) Favorites

      Abstract:For the BTT attitude tracking control problem of hypersonic vehicle,a state-error-space implementation expression of nonlinear H∞ attitude tracking control for above nonlinear coupling system is given firstly.Then basing on γ-energy-dissipation and L2 gain performance criterion in nonlinear system theory,the smooth differentiable stored-energy function is designed,which subject to the Hamilton-Jacobi-Isaacs inequality.Following some assumptions,a local state-space solution of nonlinear H∞ attitude-tracking control problem for nonlinear coupling hypersonic vehicle system is obtained,by using Riccati differential equation of linear following system in local state-space.The local state-space is the neighborhood around the command state error space.Above approach avoids complicated solving process of Hamilton-Jacobi-Isaacs inequality,thus it’s a good reference for engineering.

    • Fuzzy finite element analysis of B-spline wavelet on the interval of structure with cracks

      2011, 43(9):134-138. DOI: 10.11918/j.issn.0367-6234.2011.09.026

      Abstract (1489) HTML (2) PDF 481.45 K (1084) Comment (0) Favorites

      Abstract:To overcome the difficults caused by uncertainties of material and load in numerical analysis of structure with cracks and to improve the accuracy and efficiency of numerical calculation,a fuzzy finite element analysis method of B-spline wavelet on the interval(BSWI) is put forward by combing the fuzzy theories with wavelet finite element.Fracture elements of dummy nodes are embedded into the wavelet finite element model with cracks,fuzzy equilibrium equations on the basis of finite element of BSWI are established,and the fuzzy equilibrium equations are solved by using λ level set and decomposition theorem.Subsequently,the membership function values of stress intensity factor with different crack lengths are calculated by using virtual crack closure technique,and the calculated results are compared with analytical solution.The analysis results show that the proposed method can accurately reflect changes in structural response with fewer elements and can be a new way for engineering fracture analysis of complex structures with uncertainties.

    • Entry trajectory optimization of lift reentry vehicle

      2011, 43(9):139-143. DOI: 10.11918/j.issn.0367-6234.2011.09.027

      Abstract (1424) HTML (2) PDF 765.76 K (1198) Comment (0) Favorites

      Abstract:In this paper,on the basis of review of trajectory optimization method at home and abroad,the direct method and sequential quadratic programming algorithm is used to solve the trajectory optimization problem.The trajectory optimization problem is transformed into a parameter optimization problem using direct method and the parameter optimization problem is solved using sequential quadratic programming.A trajectory optimization algorithm is written using C++,and a numerical simulation of maximum range entry trajectory is performed.The simulation results show that the technology of trajectory optimization for lift reentry vehicle proposed in this paper is reasonable and feasible with good results.

    • Simulation and optimization for heat flux distribution of infrared lamp array

      2011, 43(9):144-148. DOI: 10.11918/j.issn.0367-6234.2011.09.028

      Abstract (1515) HTML (2) PDF 677.07 K (1086) Comment (0) Favorites

      Abstract:This article aimed at establishing the simulation methods of heat flux distribution and optimization for infrared lamp array to improve the uniformity of heat flux distribution.The heat flux distribution database was generated by the application of heat flux distribution calculating method of single lamp.The reflex heat flux of reflective baffles was resolved.The infrared lamp array heat flux simulation method was established on the basis of these models.Optimization method of infrared lamp array was set up based on genetic algorithm.One infrared lamp array for a satellite thermal test was optimized,and the heat flux nonuniformity decreased from 24.61% to 8.96%.The simulation results were identical with the measurement values.The simulation method offers a good accuracy and the optimization method can effectively increase the uniformity.

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