LI Chan , ZHANG Shifeng , ZHANG Lijun
2017, 39(1):1-5. DOI: 10.11887/j.cn.201701001
Abstract:The difficulties that unscented Kalman filter encounters when it is introduced in reentry vehicle trajectory were investigated. These difficulties include abnormal measurement, the inaccuracy of measurement random error model and dynamic model. The current study uses an adaptive robust filter that can produce the estimation of equivalent weight flexibly according to measurement noise and state noise, can distinguish abnormal measurement from normal measurement, and can estimate the variance of Wiener model self-adaptively. The simulated results testified that the filter is easy to implement and can reduce the bad influences derived from inaccuracy of measurement random error model and dynamic model.
RAN Dechao , NI Qing , SHENG Tao , CHEN Xiaoqian
2017, 39(1):6-10. DOI: 10.11887/j.cn.201701002
Abstract:In order to solve the attitude maneuver problem of rigid spacecraft, an adaptive second-order terminal sliding mode control algorithm was designed. A terminal sliding mode surface was designed to guarantee that the system states can converge to the original point along the sliding surface in finite time; a second-order terminal sliding mode controller was designed to overcome chattering, and an adaptive estimation parameter was adopted to compensate the external disturbances. The Lyapunov function methods proved that the designed algorithm can guarantee that the closedloop system is practically finite-time stable. The simulation results show that this algorithm can achieve fast response and high accuracy, can effectively restrain the system chattering and the external disturbance, and has important scientific significance and engineering value.
HE Boyong , LI Haiyang , SHEN Hongxin , PENG Qibo
2017, 39(1):11-16. DOI: 10.11887/j.cn.201701003
Abstract:For the manned lunar landing mission that lands on the moon high latitude destination and returns to earth high latitude recovery field, a design of moon landing window and point return orbit is coupled in complexity, so it is one of the key technologies in the engineering task. In view to task demands and engineering constraints, the mathematical models for finding lands window and designing point return orbit were established in the first place; Secondly, by solving the rules of landing window and point return orbit parameters, the coupled geometrical principle was analyzed; Taking a mission that lands on Sinus Iridium in 2025 for example, the strategy of coupled design landing window and the point return orbit were given, which was provided by validation example. The verification by commercial Software STK(system tool kits, by AGI company) of simulation results is correct, the proposed strategy is a simple and precise method for planning manned lunar landing mission, which can be used in the future manned lunar landing mission directly.
ZHANG Yakun , LI Haiyang , LI Tao
2017, 39(1):17-23. DOI: 10.11887/j.cn.201701004
Abstract:Due to the effect of time delay, control and measure error, it is hard to accurately control orbit motion in the final phase of rendezvous and docking. Thus the shared control strategy of teleoperation rendezvous and docking based on improved potential field function was studied. The motion model and predictive model based on the relative dynamics equations were established and the safe corridor in the controllable boundary was designed. The automatic control approach was studied based on the improved potential field function which takes relative distance and speed with safe corridor as reference quantity. Control weighting coefficient of automatic and manual mode was then derived to form the shared control strategy. The validation experiment was conducted on the nine-degree teleoperation rendezvous and docking semi-physical simulation platform. It is shown that, compared with the manual control mode and the automatic control mode, the shared control method can overcome the influence of time delay in the communication loop and effectively improve the rendezvous accuracy. Moreover, the control performance and success probability of teleoperation is proved to be enhanced.
LI Xiaoyue , XIONG Shujie , LIN Baojun
2017, 39(1):24-29. DOI: 10.11887/j.cn.201701005
Abstract:After the satellite is separated from the upper stage, the initial attitude is not learned about since the attitude sensors are not valid for the measurement. In order to solve this problem, an initial attitude calculation method using multi sensors’ intercalibration was designed. The kinematic equation was set firstly, and then the first available attitudes measured by star sensor as well as gyro’s angular velocity were prepared. The nonlinear equation was solved by using the trust region algorithm; meanwhile the attitude was obtained from backward to forward; the analog sun vector detector’s information was used to revise the deduction; a convenient method translating the attitude from the sun to the earth was put forward; sun vector was connected to star sensor’s information. The deduction result is consistent with injection attitude of rocket. Simulation result on the ground was compared with the real attitude in orbit, validating the correctness of simulation model. The result provides support for the design of satellite and the procedure design and improvement of flight.
WANG Jianhua , LIU Luhua , WANG Peng , TANG Guojian
2017, 39(1):30-39. DOI: 10.11887/j.cn.201701006
Abstract:A PIGC (partial integrated guidance and control) design approach for the homing missile with 3D (three dimensional ) impact angle constraints was proposed. The 6DoF (six-degree-of-freedom) dynamic and kinematical equations of the translational and rotational loops of the homing missile were designed. For implementing the PIGC scheme, a two loop control structure was adopted. The outer loop model based on the 3D relative dynamics and the precise coordinate transformations was employed. The desired angle of attack and the sideslip angle were obtained with the help of the sliding mode control theory and the ESO (extended state observer). A linear form dynamic model of the rotational loop was derived. The sliding surface vector with respect to desired roll, yaw, and pitch angles was conducted and the anticipate control surface fin deflections were obtained based on the ESO. Finally, the effectiveness and robustness of the newly proposed PIGC scheme are investigated and verified via appropriate 6DoF nonlinear simulation studies with respect to the ground fixed target.
DING Zhijian , CAI Hong , HUANG Shuai
2017, 39(1):40-45. DOI: 10.11887/j.cn.201701007
Abstract:Aiming at the observable degree of gyroscope error coefficients for inertially stabilized platforms self-calibration system, a novel observable degree analytical method was presented according to the definition of observability. The highest order of measurement derivative in the expression of a state analytical solve was defined as the state observable degree. Based on this, the observability of inertially stabilized platforms self-calibration system was analyzed, highlighting the observable degrees of gyroscope error coefficients. The observable states of system were presented, and it was proved that the observable degrees of the gyroscope biases to sensitivity along the input axes were worst. Simulation results validated the correctness and validity of this approach, which provides a reference for the design of torquing scheme of inertially stabilized platforms self-calibration system.
2017, 39(1):46-50. DOI: 10.11887/j.cn.201701008
Abstract:In order to identify the error parameters of inertial navigation platform in the centrifuge testing, a 6-position identification scheme was developed. The non-linear model of the inertial navigation platform for the identification was established, and the extended Kalman filter algorithm was applied to estimate the error parameters. The correlation coefficients among the error parameters calculated with the estimation error covariance matrix in the filter were used to analyze the observability of the system. The minimum sum of all correlation coefficients was considered as the optimization criterion, and then the genetic algorithm was utilized to obtain the optimal position combination. The simulation results show that the scheme is valid to identify all the error coefficients connected with the higherorder acceleration with high precision.
CHENG Tangming , LI Jiawen , TANG Guojin
2017, 39(1):51-57. DOI: 10.11887/j.cn.201701009
Abstract:Servo mechanism fault of engine brings challenge to the reliability and safety of attitude control system for the new generation launch vehicle, a research on control reconstruction strategy is needed urgently. Aiming at this problem, a control allocation method for the deflection angle reconstruction was proposed. The problem of deflection angle allocation under servo mechanism fault was transformed into the problem of 1norm single objective constrained optimization, and then it was translated into the standardized linear programming model solved by simplex algorithm finally. Simulation results show that the attitude control system can be completely reconstructed by the proposed method under servo mechanism fault, each deflection angle does not reach its saturation value, so the validity of the method is proved.
WANG Jianhua , LIU Luhua , WANG Peng , TANG Guojian
2017, 39(1):58-66. DOI: 10.11887/j.cn.201701010
Abstract:A longitudinal integrated guidance and control scheme for the hypersonic vehicle in glide phase was designed based on the dynamic surface control method and the sliding mode control theory. The translational rotational dynamic and kinematical equations in the longitudinal plane were denoted; the desired velocity slope angle was derived based on the predictor corrector of the longitudinal range; the relations of the velocity slope angle, angle of attack, and the pitch rate were established. The dynamic surface control, the terminal sliding model and the second-order sliding mode control methods were adopted to implement the longitudinal integrated guidance and control scheme; the commanded angle of attack and elevon fins were analytically solved by using the GHV’s aerodynamic model having partial derivative matrix forms. The effectiveness and robustness of the newly proposed longitudinal integrated guidance and control scheme was validated. Moreover, the characteristics of flight phases before and after the quasi equilibrium glide phase were discussed and the problems with respect to the guidance and control system design were analyzed.
CHEN Shenggang , LIU Biwei , QI Juan , HUA Yingzhao , XING Sufang , DING Yanping
2017, 39(1):67-73. DOI: 10.11887/j.cn.201701011
Abstract:A bi-directional non-blocking ring architecture was proposed for the multicore processor with relative less amount of high-performance cores. The architecture consists of five ring layers of three different types for commands, huge data and small data transportation, respectively. The source routing strategy was employed and an equipment state control interconnection was designed for congestion management. The router has a bufferless and contention-free structure and each hop only takes one clock cycle, thus minimizing the transmission delay and realizing deterministic routing. Considering the long links and high bandwidth of the ring, experiments were carried out to find a proper repeater insertion method, and the crosstalk optimizing methods, such as inverter insertion crosswise between two neighborhood lines and arranging neighborhood lines in signal transport direction, were studied to conduct physical design for the ring and delay optimization for the long links. Implementation results show that the designed ring′s bandwidth is 256 GByte/s @1 GHz, which can fulfill the data communication demands of the digital signal processing applications.
SHI Dianxi , LI Han , YANG Ruosong , MO Xiaoyun , WEI Jing
2017, 39(1):74-80. DOI: 10.11887/j.cn.201701012
Abstract:Research focused on how to mine frequent daily behavior patterns of users on smartphones feasibly and efficiently was started. Firstly, a frequent behavior patterns mining framework based on smartphones was proposed. Secondly, a dynamic sliding window algorithm DSW(dynamic slide window) to decrease the context baskets in quantity and improve mining efficiency was proposed. Furthermore, a frequent patterns mining algorithm WePM(weighted pattern mining) which takes both frequency and duration of context occurrence into consideration was developed. On the basis of the above preparation, the mining framework and algorithm were verified experimentally with the context data from 21 users over 6 weeks. Results indicate that the proposed framework and frequent patterns mining algorithm can feasibly and efficiently run on resources limited smartphones to mine daily behavior patterns, and then to reflect users’ lifestyles. Finally, the patterns from two perspectives, namely behavior patterns in different locations and time periods are visualized, which benefits the users to realize their daily behavior patterns at any time.
CHENG Xinghua , LIU Wei , ZHANG Lilun
2017, 39(1):81-85. DOI: 10.11887/j.cn.201701013
Abstract:For parallel simulation of the unsteady flow field with moving boundary, a domain-decomposed computation procedure was designed based on the spring analogy method, and the METIS software was introduced to repartition the original grids. With the research of 1-to-1 interface communication styles and realization, the unstructured dynamic mesh solver was parallelized based on the message passing interface. The test shows that the solver has high parallel efficiency, and the module of mesh deforming has significant effect on the parallel performance.
YAN Mengting , AN Junshe , GONG Quanming
2017, 39(1):86-91. DOI: 10.11887/j.cn.201701014
Abstract:The performance evaluation system of SpaceWire bus based on dual-route unit was studied. The definition of dual-route unit was given and the computation method of data transmission time and resource consumption of the route system based on dual-route unit was derived during the study. The performance evaluation system of multi-route topological system based on dual-route unit was derived; the simulation platform of dual-route unit system was built by using the Monte-Carlo method, and the performances of route unit with different interface configurations were simulated. Study results show that the performance of SpaceWire bus can be evaluated through using the transmission time and resource consumption indexes based on dual-route units, and also that an aimed configuration exists such that the system performance can be optimized to the best when different interface configurations are considered.
HU Fan , WU Zeping , WANG Donghui , ZHANG Weihua
2017, 39(1):92-101. DOI: 10.11887/j.cn.201701015
Abstract:As more and more high precise time-consuming models are revealed into optimization procedure, general intelligence optimization algorithm cannot get a desirable result in feasible computing cost. The developing sequential approximate optimization approach is aimed to overcome this drawback by introducing the approximate model in the optimization procedure, which adds infill points sequentially to search the promising areas, has made it more and more practical technique for time-consuming engineering optimization. An overview of the sequential approximate optimization algorithm and its core techniques were given, which can expend the application of the algorithm. Finally, some relevant improved methods and new developmental trends concerning SAO(sequential approximate optimization) were presented.
ZHANG Xiaoxiong , GE Bingfeng , JIANG Jiang , TAN Yuejin
2017, 39(1):102-108. DOI: 10.11887/j.cn.201701016
Abstract:Aiming at solving the difficulties of choosing and planning in the weapon systems development problems, a bi-objective optimization model was proposed to minimize the capability gaps plus the total risk values, and to look for the best development scheme by comparing different combinations of weapons based on the given capability requirements. The total budget limitation, annual budget constraint and the planning period were taken into account in this model. A solving algorithm, based on non-dominated sorting genetic algorithm-Ⅱ and differential evolution, was presented to obtain the Pareto set. The technique for order preference by similarity to ideal solution method was employed to reach a final compromise solution.A case was studied to demonstrate the effectiveness of the proposed model and hybrid algorithm, which can support the decision making on the weapons development and planning.
HUANG Xiuping , ZHOU Jinglun , CHENG Long
2017, 39(1):109-114. DOI: 10.11887/j.cn.201701017
Abstract:In order to improve the field reliability of products and reduce the total cost of burnin procedure and warranty, an optimization method of accelerated burn-in time for products with infant mortalities within the reliability and cost constrains was developed on the basis of utility function. Considering the uncertainties with respect to the lifetime distribution parameters of the product, the prior distributions of these parameters were derived by using the bootstrap method, and then the joint utility function combining field reliability with cost was constructed through simulation technique. Choosing the maximum of joint utility as objective, the optimal accelerated burn-in time model was established, and the optimal burn-in duration was derived. The application of the above method was illustrated explicitly by a numerical example in which a product with log-normal distribution was burned in under elevated temperature condition, and the parameters′ sensitivity analysis was also conducted. The results show that the proposed method not only can shorten the burnin duration, but also can meet the requirements for cost and reliability simultaneously to the utmost.
WANG Dong , JIANG Ping , CHENG Zhijun , GUO Bo
2017, 39(1):115-119. DOI: 10.11887/j.cn.201701018
Abstract:Initiating event identification is the primary task in safety analysis based on accident mechanism. The comprehensiveness and the completion of identification have a direct effect on final results. Due to the width of related facets and multitude of impact factors, an operable systematic method is required to guide the identification process. Aiming at the properties of missile weapon, the MLD (master logic diagram) was proposed to provide a systematic hierarchical description of missiles. It was also utilized to collect and classify identified initiating events. For the first time, the HAZOP (hazard and operability analysis) was introduced in missile system safety analysis to identify the initiating events. Combined with FMEA (failure modes and effects analysis), this framework provided support for the identification of initiating events which were caused by single failure or parameter abnormity. Results show that the proposed framework provides a practical way to ensure the comprehensiveness of initiating event identification for system safety analysis of missile weapon.
CHENG Guangquan , LU Yongzhong , ZHANG Mingxing , HUANG Jincai
2017, 39(1):120-127. DOI: 10.11887/j.cn.201701019
Abstract:A method for node importance evaluation and network vulnerability analysis based on node’s cascading failure model was proposed. The mechanism of fault transmitting and evolution was the reason for vulnerability of basic complex networks. A model that can get real-time state of nodes’ loads and reallocating loads was raised based on node’s cascading invalidation model. A node importance evaluation and network vulnerability analysis method based on nodes’ state evolution were put forward, by which the robustness parameters of networks were found out, and the failure effect analysis was conducted. Its effectiveness was verified through simulation experimental results.
XU Li , LI Qingmin , HU Xiaoqi , LIU Xin
2017, 39(1):128-136. DOI: 10.11887/j.cn.201701020
Abstract:The spare parts inventory and department repair capacity are important factors to influence the process of maintenance turnover for spare part, and it restricts the use effect of equipment. Aiming at the support project evaluation and optimization when the demand of spare parts is dynamic in the mission phases and considering the influence of repair capacity to spare parts repair process, an evaluation model of time-varying availability was set up for the multi-echelon support system with finite repair capacity on the basis of the METRIC methodology and dynamic queuing theory. Based on the evaluation model, an optimization model for the support project of multi-echelon support system during the mission phases was proposed by taking the support cost as the optimization objective and the equipment availability as the constraints. The minimum availability of the whole mission was taken as observation value and the margin optimization was used to get the optimized project for each resource. The analysis results of an example show the availability value for different mission phases can be given by the evaluation model, and the optimized project of resources for the multi-echelon support system can be obtained by the optimization model and method. The proposed models and optimization method can provide decision support to equipment support staff for rational support project.
SU Ang , ZHANG Yueqiang , YANG Xia , YU Qifeng
2017, 39(1):137-141. DOI: 10.11887/j.cn.201701021
Abstract:In general, cars are rectangular shape in the aerial images, so the histograms of orient gradient over the whole sliding window were computed to find the primary gradient direction and to estimate the orientation of the car in the window, and the detection window was rotated according to the car’s orientation to perform classification. A cascaded boosting classifier and the HOG (histograms of orient gradient) features in the proposed car detection method were employed. To efficiently compute the HOG features in the rotated window, a fast HOG features extraction method based on CFHOG (circle filter based histograms of orient gradient), which was more efficient than the classical HOG extraction method based on integral histograms. In addition, lookup tables are used to speed up the calculation of the orientation partition and magnitude. A set of experiments on real images prove the applicability and high efficiency of the proposed car detection method.
LANG Lin , XU Jiaqi , ZHANG Xianpeng , WANG Jian , MA Hongxu , WEI Qing
2017, 39(1):142-147. DOI: 10.11887/j.cn.201701022
Abstract:In order to control the horizontal body position of a trotting hydraulic quadruped robot, an approximated dynamical model was built based on the motion decomposition along the support line, which simplifies the body and the stance legs to a seven-link mechanism and a linear inverted pendulum. A calculation method for landing positions of swing feet was proposed based on the analytic solution of the linear inverted pendulum model. It was realized to control the horizontal position of the body. For the velocity limitations of the hydraulic cylinders pushing and pulling, an optimization problem for the joint angular velocities was formatted as a QP problem, and a QP solver was designed to decrease the demands for the joint angular velocities. In comparison to the conventional pseudoinverse optimization algorithm, the proposed algorithm could avoid the singular state of the leg more effectively. The simulation and experiment results show that the desired horizontal body position trajectories can be tracked accurately by using the proposed algorithms, even the joint angular velocities being limited.
SHEN Zhibin , JIANG Renwei , ZHI Shijun
2017, 39(1):148-152. DOI: 10.11887/j.cn.201701023
Abstract:To improve the structural integrity of solid rocket motor grain with large aspect ratio, based on three-dimensional viscoelastic finite element method and taking into account of the temperature load and pressure load, the structural response of a solid rocket motor with large aspect ratio was analyzed, the effects of the umbrella slot and its location on maximum Von Mises strain of the grain were studied, and the variations of the maximum Von Mises strain of the umbrella slot with its width, depth and radius ratio were discussed when the umbrella slot was in the middle of the grain. The results show that the Von Mises strain is reduced when the umbrella slot is in the middle of the grain; increasing the width, depth or choosing the best radius ratio can reduce the maximum Von Mises strain of the umbrella slot. The conclusions are beneficial for designing the grain configuration of solid rocket motor.
LUO Yasong , HU Shengliang , LIU Zhikun , LYU Xianchun
2017, 39(1):153-158. DOI: 10.11887/j.cn.201701024
Abstract:Regulations between pre-estimated channel length and estimation precision were analyzed. The estimation quality was evaluated in time using statistics of the equalized signals which can help adjust the length of channel estimation algorithm automatically. In view of the differences among subcarriers caused by underwater acoustic channels, a new algorithm which realized optimum rate and power assignments based on channel estimating results was put forward. Compared with the traditional algorithm which assigned rate and power equally to each subcarrier, the new algorithm achieved better property of bit error rate. Simulations and experiments validate the effectiveness and correctness of the researching contents.
CHEN Lifu , PANG Kechen , LI Yinwei , SU Yi , YUAN Zhihui , WANG Jing
2017, 39(1):159-165. DOI: 10.11887/j.cn.201701025
Abstract:In dual-antenna interferometric synthetic aperture radar system, the reference phase was usually estimated by joint calibration with transferring corresponding points for the scene without ground control points, which is too time-consuming. To solve the problem, the factors influencing the reference phase were analyzed. The analytic formula was given, and simulation was done according to the system parameters. The height error caused by reference phase was analyzed. According to the analysis results, the high precision realtime reference phase estimating algorithm was presented, combined with the extern coarse precision elevation, the filtered interferometric phase and coherence. The detailed flow of the algorithm was given. The processing results of the real data from airborne dual-antenna interferometric synthetic aperture radar system validate that a 2 m relative elevation precision can be achieved with the system in the paper by the algorithm presented, and the estimated speed can reach more than 20 times faster when processing the data of 4096×6560pixel.
YUN Wanying , LYU Zhenzhou , ZHAO Lufeng
2017, 39(1):166-173. DOI: 10.11887/j.cn.201701026
Abstract:In order to efficiently and accurately estimate the variance-based global sensitivity indices, especially for highly nonlinear response functions, a new method was proposed by combining the additive property of integration region and the UT (unscented transformation). Because the nonlinearity of response function is reduced in the local sub-space, in which the UT can explore the probability space very efficiently, the proposed method can estimate the variance-based sensitivity indices effectively. Moreover, the proposed method can estimate all the indices by using the same set of UT samples, and the approximate solution converges to the actual value with the increased number of divided subspace. The results of the nonlinear test example and the engineering example illustrate the efficiency and accuracy of the proposed method.
ZHANG Bingwen , ZHENG Jian , XIONG Chao
2017, 39(1):174-181. DOI: 10.11887/j.cn.201701027
Abstract:Aiming at the problems of intensive calculation and difficulty in testing with common methods of moving sound source locating, a locating method based on array signal processing was proposed. Locating ability of single and double five-element cross array were analyzed. Based on the high performance of direction estimating with single array, location of moving sound source was achieved by the double arrays crossing method according to the thought of frame processing in beamforming. Locating experiment was carried out when using engine noise of self-propelled vehicle as simulated source. Then the length selection of short correlation and compensation of moving path were studied. Experiment shows that the method is effective for moving sound source locating with high precision, maximum relative error stays below level of 5%.
2017, 39(1):182-188. DOI: 10.11887/j.cn.201701028
Abstract:A melt-spinnable polyaluminocarbosilane was synthesized via the crosslink reaction between Si-H and acetylacetone aluminum(Ⅲ) by using low-molecular-weight solid polycarbosilane and acetylacetone aluminum(Ⅲ) as starting materials. The effects of reaction conditions on the numberaverage molecular weight, softening point and structure of polyaluminocarbosilane were investigated, and the relationship between the extent of crosslink reaction to the spinnability of polyaluminocarbosilane was also discussed. It was found that elevating the reaction temperature or prolonging reaction time would lead to an enhanced extent of reaction, a gradually decreased acetylacetonate and an increased crosslinked structure of Si-O-Al, resulting in poorer spinnabilty. Polyaluminocarbosilane with softening point of 206~221 ℃, Al wt%=068% and good spinnability was successful synthesized at the optimized reaction conditions of the temperature at 370 ℃, the reaction time at 4~6 h and the mass ratio of acetylacetone aluminum(Ⅲ) at 8 wt%.
WANG Xinzhu , ZHOU Xiong , ZHU Bingjie , PENG Xianghe
2017, 39(1):189-193. DOI: 10.11887/j.cn.201701029
Abstract:Sandwich structure with metal foam core is a newly emerged sandwich structure in recent years, and will be widely used in near space flight vehicle, navigation and automobile fields due to its high flexural rigidity and strength, multifunction. Theoretical analysis and experimental studies on the indentation response, damage modes, deformation mechanism and failure mechanism of the composite sandwich panel with fibre-reinforced polymer face and aluminum foam core under the action of rigid spherical-end indenter were conducted. Study results show that the load-indentation response is a combined consequence of the individual responses of the sandwich components, their structural interactions and the indenter properties. The failure models of the sandwich panel under the spherical-end cylindrical indenter can be summarized as matrix cracking, fiber fracture, face/core debonding, the yield and shear of the aluminum foam.
CHEN Minkang , DU Tao , SU Xue , CHEN Weifang
2017, 39(1):194-198. DOI: 10.11887/j.cn.201701030
Abstract:A sequential functional specification method was adopted to identify the surface heat flux in a two-dimensional inverse heat conduction problem for an orthotropic solid. The inverse problems were solved with the combination of the finite control volume method, the Newton-Raphson method, and the concept of future time step.The undetermined heat flux at each time step was denoted as one of the unknown variables in a set of nonlinear equations, which was solved by an iterative process. Results show that the estimated values agree well with the exact values in the examples, which proves that this method is an accurate, stable, and efficient one, thus it can be used to determine the surface heat flux in two-dimensional nonlinear inverse heat conduction problems.
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