Table of Content

29 April 2019, Volume 40 Issue 4

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Contents

2019, 40(4):  0. 

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Paper

Cooperative Localization and Guidance for Seeker-less Missile Based on Leader-follower Framework

ZHAO Jianbo， YANG Shuxing, XIONG Fenfen

2019, 40(4):  673-679.  doi:10.3969/j.issn.1000-1093.2019.04.001

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A novel cooperative localization and guidance approach based on the leader-follower framework with two leaders is proposed to allow the seeker-less missile to hit a stationary target accurately. A cooperative localization method for seeker-less missile is designed based on the extended Kalman filter to enhance the localization accuracy. To address the issue that a large terminal acceleration command is required for the proportional navigation guidance (PNG) law combined with the proposed localization method, a novel PNG law with time-varying navigation gain is presented. The impacts of the guidance parameters on miss distance, terminal acceleration and maximum acceleration are demonstrated through si- mulation. Simulated results show that the large miss distance due to the localization error of seeker-less missile could be reduced by the proposed cooperative localization method, and the large terminal acceleration command could be avoided by PNG law with time-varying navigation gain. Key

Research on Trajectory Prediction Method of Distributed High Speed Electric Drive Unmanned Tracked Vehicle in Off-roadConditions

ZHAO Ziye, LIU Haiou, CHEN Huiyan

2019, 40(4):  680-688.  doi:10.3969/j.issn.1000-1093.2019.04.002

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The unmanned vehicle trajectory prediction module is a core module of vehicle trajectory tracking and precise navigation in the off-road conditions. The prediction error has direct effect on the accuracy of the completion of unmanned vehicle driving tasks. In order to realize the accurate prediction of trajectory of skid-steered unmanned tracked vehicle in the complex off-road conditions, a distributed electric drive unmanned tracked vehicle system was built, which realizes the synchronous acquisition of unmanned system data and vehicle state data in the vehicle dynamic process. A kinematic model of skided-steered tracked vehicle is established, and the sliding steering characteristics of tracked vehicle are analyzed. The extended Kalman filter (EKF) method and the Levenberg-Marquardt(L-M) method are used to estimate the sliding parameters in the steering process, and the vehicle trajectory prediction is completed. The verification analysis is based on real vehicle data in real off-road conditions. The statistical analysis method is used to compare the prediction errors of two prediction methods. The test results show that, compared with the ideal prediction model of tracked vehicles, the two trajectory prediction methods greatly reduce the prediction error of vehicle trajectory. For the mean of error, EKF method is better than L-M method in the trajectory prediction; for the standard deviation, the latter is better than the former, and the standard deviation increases with the increase in the degree of steering. Key

Research on Optimization of Louvered Fin with Hybrid Multi-objective Optimizations Based on EDA and AIS

LUO Qingguo, ZHAO Yao, GUI Yong, LIU Hongbin , SHUAI Gang

2019, 40(4):  689-696.  doi:10.3969/j.issn.1000-1093.2019.04.003

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The structure optimization of intake and exhaust louvers of armored vehicle is studied to reduce air flow resistance and increase air flow. A numerical calculation model is established for the intake and exhaust louvers of armored vehicle. According to the operating characteristics of cooling system, a hardware-in-the-loop test-rig of air-cooling duct is set up. The simulated and test results of the duct before and after optimization are compared and analyzed, and the expression of optimization objective function is given. The design variables are determined. In order to solve the problem of low efficiency and large computation, an elliptic basis neural network agent model is established for the relationship between design variables and objective functions. The hybrid multi-objective optimization based on estimation of distribution algorithm (EDA) and artificial immune systems is used to find a final solution by analyzing the variation of objective function with the design variables. The inherent law of sample points is found by using self-organizing neural network for data mining. The research results show that the optimized inlet and exhaust louvers improve the performance of heat dissipation while improving the protection capability. Key

Numeric Analysis of Barrel Heat-pressure Joint Effect Based on Follow-up Boundary

YU Qingbo， YANG Guolai， GE Jianli

2019, 40(4):  697-707.  doi:10.3969/j.issn.1000-1093.2019.04.004

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In order to explore the transient impact effect of high-temperature and high-pressure propellant gas on the response to barrel strength, the finite element method is utilized to establish a three-dimensional numerical model for a large-caliber gun barrel. The variation of loading boundary of propellant gas with the projectile motion is defined. The evolution process of non-uniform distribution of temperature field in barrel at different moments under the first firing condition was obtained through numeric computation. The influences of thermal load, pressure and the heat-pressure joint effect on the dynamic stress response of barrel are further investigated, respectively. The calculated results show that the difference of thermal shock loads at different axial positions leads to an axial non-uniform temperature distribution, which makes the axial temperature gradient large and causes a significant axial thermal stress. In the area with intense temperature response, the compressive stress induced by thermal load and the tensile stress induced by pressure incircumferential direction make the stress component act as the interaction between the tensile stress and the compressive stress. Compared with the gas pressure effect, the stress amplitude in the high stress region on the inner wall is weakened, and presents a trend of falling first and then rising with the temperature. Key

Controllability Analysis of a Novel Multi-coil Magnetorheological Absorber for Gun Recoil Mitigation

ZHENG Jiajia, KAN Junwu, ZHANG Guang, WANG Jiong, OUYANG Qing

2019, 40(4):  708-717.  doi:10.3969/j.issn.1000-1093.2019.04.005

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A novel multi-coil magnetorheological (MR) absorber, which has the capability of being applied with input currents individually, is proposed for the impact mitigation of a gun. The dynamic response characteristics of the proposed MR absorber working in three different modes, namely, uniform loading, combined control and open-loop cascade, are discussed according to ideal profile of recoil resis- tance at 45-degree angle. Impact experimental results show that, in the non-controllable region, a gas compression stage exists in single-stroke damping process, resulting in a significant hysteresis between the damping force and recoil speed; in the controllable region, given a total 2 A input current, the maximum Coulomb damping force generated by the mode of combined control of more than two working coils behaves better than that generated by equivalent loading; and the mode of open-loop cascade control can effectively reduce the peak force and delay its occurrence moment for approaching the ideal buffer effect. However, this requires additional effective stroke for the recoil buffer. It can be seen through analysis that the MR absorber can be used to achieve flexible and variable damping output based on the temporal and spatial two-dimensional current loading sequence, which shows a certain controllability in the application of gun recoil systems with large firing angles. Key

Research on the Influence of Damaged Barrel on Interior Ballistic Performances and Muzzle-leaving State of Bullet

SHEN Chao, ZHOU Kedong, LU Ye, QIAO Ziping

2019, 40(4):  718-727.  doi:10.3969/j.issn.1000-1093.2019.04.006

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The influence of bore damage on interior ballistic performance and muzzle-leaving state of bullet is studied, and the mechanism of how bore damage leads to the end of barrel's life is explored. The accurate thermo-mechanical coupling finite element analysis (FEA) models of barrels with bore damage at different life periods are established based on the distribution and evolution rule of bore damage obtained through systematic life tests. The changing rules of interior ballistics performances and muzzle-leaving states of 12.7 mm bullet with the evelopment in bore damage are obtained through numerical simulation which combines the interior ballistics process and the explicit finite element method through Fortran subroutines. The coupling model of bullet and gun barrel is proved to be effective by comparing the calculated results of interior ballistic parameters with experimental results. The simulated results show that the initial disturbances of bullet at muzzle, the reduction in rotational velocity and the variation in bullet's surface topography increase as the firing cycle increases, especially in barrel's later lifetime. Variation in muzzle-leaving state of bullet is the key factor for barrel's life end. Research results have important significance on further studying how bore damage degrades bullet's exterior ballistics performance and the end-of-life mechanism of barrel. Key

Effect of Matrix Microstructure of Gun Barrel on Its Lifetime

HU Chundong, HE Xing, LU Hengchang, DONG Han, LI Junsong

2019, 40(4):  728-736.  doi:10.3969/j.issn.1000-1093.2019.04.007

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The damage characteristics of two different microstructured gun barrels during shooting are comparatively studied to investigate the mechanism of the effect of matrix microstructure of gun barrel on its damage rate. Its matrix structure is characterized using optical microscrope, scanning electron microscrope, and analyzed using the carbon replica and phase analysis methods. Results show that the damage rate of low-hardness gun barrel is larger than that of high-hardness gun barrel, and the former's lifetime is short. This is because the internal surface of the low-hardness gun barrel is subjected to a relatively larger plastic deformation, and the carbides in the matrix of high-hardness gun barrel show smaller sizes and distribute more homogenously, which inhibites the nucleation and propagation of the cracks. Key

Low-frequency Learning-based Robust Adaptive Control for Electro-hydraulic Position Servo System

LIU Lei, YAO Jianyong, MA Dawei, WANG Guangwen

2019, 40(4):  737-743.  doi:10.3969/j.issn.1000-1093.2019.04.008

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A kind of low-frequency learning-based robust control strategy is proposed for electro-hydraulic position servo system, in which high-frequency interference and sensor measurement noise lead to the poor convergence and low consistency of traditional adaptive control. The adaptative parameter of electro-hydraulic servo system is modified by designing a low-pass filter, and a new control law, which can filter out the high-frequency components in the adaptive law, is constructed by the residuals before and after modification. As a result, the steady-state convergence is achieved while the high-frequency oscillation is alleviated. Lyapunov stability theory is utilized to verify the global stability of the closed-loop system. The comparative experimental results show that the proposed method can effectively solve the steady-state convergence of the parameter of electro-hydraulic position servo system under the action of high-frequency dynamics and sensor measurement noise, and retain the asymptotic stability of system dynamic error while achieving satisfactory tracking performance. Key

Research on Aerodynamics of a Novel Smart Bullet

ZHOU Lei, LI Zhongxin, YANG Haibo, CAI Hongming

2019, 40(4):  744-752.  doi:10.3969/j.issn.1000-1093.2019.04.009

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The smart bullet is expected to remarkably enhance the combat effectiveness and survivability of individual soldiers due to its miniature size and high hit accuracy. Considering the technical requirements of device sizes and aerodynamic characteristics,an aerodynamic shape of a novel smart bullet is designed. The overall dimensions of the smart bullet are quite different from those of the normal bullet, and its aerodynamic and flow field characteristics are still unknown. Therefore, it is necessary to study the aerodynamic characteristics of the smart bullet. The aerodynamic characteristics of smart bullet are studied through numerical simulation and wind tunnel experiments, and the influence of dimensional change of bullet tail on the aerodynamic characteristics of smart bullet is analyzed. The research results show that the numerically simulated results are basically consistent with the wind tunnel experimental results, which proves the feasibility of the numerical simulation method. With the increase in the length of contraction section, the drag decreases first and then increases, while the lift and the absolute value of pitching moment remain unchanged first and then increase. With the growth of the radius of intersection, the absolute values of drag, lift and pitching moment decrease. With the increase in the radius of bottom, the drag increases first and then decreases, while the absolute values of lift and pitching moment decrease first and then increase. Key

An Anti-deception Jamming Method for LFMCW Detector

WANG Mingwei， XIAO Zelong， GAO Wen， RONG Yingjiao

2019, 40(4):  753-761.  doi:10.3969/j.issn.1000-1093.2019.04.010

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An anti-radio frequency storage and repeater jamming method is proposed for the millimeter wave linear frequency modulation continuous wave (LFMCW) detection system for subsonic bomb detection, which is based on high-resolution range profile, chirp Z transform (CZT) spectrum zooming algorithm and dynamic time warping (DTW) matching algorithm. The multi scattering center target echo model and the jamming signal model based on the digital radio frequency memory (DRFM) are analyzed in the LFMCW detection system. On the basis of the constant false-alarm rate detection, the target signal spectrum is zoomed by CZT, and the feature of target HRRP is extracted. DTW matching algorithm is used to distinguish between the real target and the jamming target. The simulated and experimental results show that the obstructions detection method based on CZT and DTW can effectively distinguish between the real target and the jamming target based on DRFM for subsonic bomb-borne millimeter wave LFMCW detector. Key

Prediction Model of Mechanics Response of Warhead Charge under One-dimensional Stress Dynamic Loading

CAI Xuanming， ZHANG Wei， XU Peng， GAO Yubo， FAN Zhiqiang

2019, 40(4):  762-768.  doi:10.3969/j.issn.1000-1093.2019.04.011

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The dynamic mechanical response characteristics of warhead charge (RDX-based polymer-bonded explosive (PBX)) at high strain rate are studied to obtain the dynamic behavior of warhead charge during high overload penetration. The dynamic mechanical properties of RDX-based PBX explosive are studied by improved SHPB experimental technology. The stress states at both ends of a specimen are monitored using the piezoelectric sensors. The deformation process of the specimen in the experiment is photographed using a high-speed camera. It is ensured that the experimental specimen is deformed under the conditions of dynamic stress balance and constant strain rate loading, and the experimental data are effective. The results show that the RDX-based PBX explosive has obvious density effect and strain rate effect. As the strain exceeds 0.075, the strain rate effect increases significantly. Based on the strain energy function, a modified Rivilin constitutive model of RDX-based PBX explosive under one-dimensional stress state is established. The fitting results of the model are basically in agreement with the experimental results. The strain time signals and the deformation modes of the specimen obtained from the simulation results are basically in agreement with the experimental results. Key

Parallel Numerical Simulation on Three-dimensional Two-phase Flow of Interior Ballistic Trajectory

CHENG Cheng， ZHANG Xiaobing

2019, 40(4):  769-776.  doi:10.3969/j.issn.1000-1093.2019.04.012

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A three-dimensional two-phase flow model based on arbitrary Lagrange-Euler method is established to improve the computational accuracy and cost of three-dimensional simulation for interior ballistic in guns. The three-dimensional governing equations are discretized with the MUSCL scheme. The fourth-order Runge-Kutta method is used to solve the time orientation. The numerical method is coded and compiled in the MPI parallel environment. The numerical simulation shows the detailed three-dimensional development of the two-phase flow behavior. The calculated results are in good agreement with the results in Ref.［20］. The effects of different igniter lengths and diameters on interior ballistic performance are analyzed. Parallel numerical studies show that the parallel efficiency can be reduced by about 50% using interior ballistic three-dimensional calculation of 24 processes. Key

A Sliding Mode Guidance Law for Impact Time Control with Field of View Constraint

CHEN Shengfu, CHANG Sijiang, WU Fang

2019, 40(4):  777-787.  doi:10.3969/j.issn.1000-1093.2019.04.013

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To improve the robustness and engineering adaptability of the impact time control guidance law, a nonsingular impact time control guidance law with seeker's field of view constraint is designed using sliding mode technique based on the geometrical relation of projectile interception. The stability and convergence of the proposed guidance law are proved by Lyapunov theory. The theoretically analyzed and simulated results show that, when the impact time error is zero, the proposed guidance law can evolve into a pure proportional navigation guidance law, and the required terminal acceleration of the proposed guidance law is fairly smooth, converging to zero during interception. The proposed guidance law can be used to effectively control the impact time for stationary target interception and multi-missile cooperative attack. Key

Study of Optimal Spatial Configuration of Aircraft Swarm Based on Cooperative Attack Zone

SHI Zhenqing, LIANG Xiaolong, ZHANG Jiaqiang, LIU Liu, FAN Xiangyu

2019, 40(4):  788-798.  doi:10.3969/j.issn.1000-1093.2019.04.014

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An optimization method for spatial configuration of aircraft swarm based on self-adaptive Tent chaos search grey wolf optimizer is proposed for the optimal spatial configuration of aircraft swarm in the coordinated attack of fighters and unmanned aerial vehicles. A mathematical model of cooperative attack zone of air-to-air missiles is established, and a calculating method for cooperative attack zone under the condition of any aircraft swarm spatial configuration is proposed. The self-adaptive Tent chaos search is applied in grey wolf optimizer to improve the performance of the algorithm, thus avoiding the local optimum and the slow search speed. The size of cooperative attack zone is taken as the target function, and the spatial configuration of aircraft swarm is optimized by using the improved algorithm. The simulated results show that the improved algorithm can be used quickly to obtain the optimal spatial configuration with the largest cooperative attack zone and the minimal threat, and the cooperative attack zone of aircraft swarm is significantly larger than the sum of single aircraft attack zone under the optimal spatial configuration. Key

Numerical Study of Influence of Afterburning Effect on Blast Load in Confined Cabin

KONG Xiangshao, XU Jingbo, XU Weizheng, ZHENG Cheng, WU Weiguo

2019, 40(4):  799-806.  doi:10.3969/j.issn.1000-1093.2019.04.015

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An approach to determine the afterburning energy in ANSYS/AUTODYN simulation is presented based on the unified facilities criteria model and a simplified formula according to the conservation law of energy released in the explosion process. A numerical simulation of TNT explosion in confined space was conducted. The calculated and experimental results show that the afterburning effect of TNT detonation products has a significant influence on the confined blast load. The calculated quasi-static pressure and impulse within 50 ms without considering the afterburning effect of detonation products are 55% and 49% lower than the experimental data, respectively. When the afterburning energy is taken into account, the calculated values of explosive pressure and impulse time history show a good agreement with the experimental data. The proposed method would provide accurate input load for predicting the dynamic responses of structures subjected to confined explosion. Key

Multi-source Integrated Navigation Algorithm for Iterated Maximum Posteriori Estimation Based on Sliding-window Factor Graph

XU Haowei, LIAN Baowang, LIU Shangbo

2019, 40(4):  807-819.  doi:10.3969/j.issn.1000-1093.2019.04.016

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In the process of data fusion in multi-source integrated navigation using factor graph, the time-varying characteristics of the subsystem's observed noise have a great influence on the estimation accuracy of navigation state. In order to solve the problem, a Gaussian model-based method to estimate the mean vector and covariance matrix of sub-system observation is proposed. In the proposed method, the observed-measurement residuals for each iterative cycle in the process of factor graph optimization are utilized to update the maximum posteriori estimated values of mean vectors and covariance matrices. A more accurate estimated value of navigation state can be obtained by estimating the sub-system noise state. The influence of the new algorithm on the convergence of optimization process was also deduced. Both the simulated and experimental results show that, compared with the existing algorithms as factor graph, maximum likelihood estimation based factor graph and maximum posteriori based factor graph, the proposed factor graph method based on iterative maximum posteriori estimation can effectively improve the accuracy of navigation estimation when the subsystem observing state varies. Key

A Novel Media Access Control Protocol for Multiple Priority Services in FANETs

LIU Weilun, ZHANG Hengyang, ZHENG Bo, GAO Weiting

2019, 40(4):  820-828.  doi:10.3969/j.issn.1000-1093.2019.04.017

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A media access control protocol for multiple priority services is proposed for the quality of ser- vice (QoS) demands of multiple priority services parallel transmission and low latency, high reliability of the high priority service in flying ad hoc networks (FANETs). According to the QoS demands for many types of services, the protocol adopts a multi-channel random access strategy for the highest priority traffic and the multi-channel busy/idle access strategy for other priority traffic, so the access authority for different priorities can be availably controlled by the residual life, threshold and channel occupancy rate in real time. A multi priority backoff mechanism based on channel busy/idle sensing is also used in this protocol so that the QoS guarantee can be provided for each priority. The protocol performance expressions and access thresholds are deduced by using queuing theory, Markov model, and discrete Laplace transformation. The simulated result shows that the protocol can effectively guarantee the QoS demand of low latency (<2 ms), high reliability (>99%) and stable system capacity(>10 Mbit/s) under heavy load, and its performance is better than the prioritized adaptive jitter based media access control protocol and the hybrid media access control protocol based on pre-allocation of transmission time slots and random immediate access. Key

Dynamic Modeling and Simulation of Servo System for Ship-borne Turret Equipment

JIANG Junfeng, LI Wei, ZHAO Wei, ZHOU Xiaojun

2019, 40(4):  829-836.  doi:10.3969/j.issn.1000-1093.2019.04.018

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A kinematics and dynamics model of a ship-borne turret equipment (STE) was constructed using coordinate transformation principle and Lagrange dynamic equations. The proposed model is used to analyze the influence factors on servo torque of STE in servo control. The servo control process of STE under different swing angles and target motion state was simulated, and the influences of swing angles and target motion state on servo torque were analyzed quantitatively. The simulated result shows that the servo torque varies almost linearly with the change in the amplitude and period of swing angle, and the effect of period is more obvious. When the amplitude of swing angle is increased by 1 degree, the servo torques of azimuth and elevation axes are increased by about 12% and 2%， respectively. When the period is increased by 1 s, the servo torques of azimuth and elevation axes are decreased by about 28% and 6%, respectively. The impact of the phase difference between swing angles on servo torque is complicated, and therefore the different intervals of phase difference need to be analyzed. Compared with the stationary state, the target motion causes the increase in the servo torque, and the impact of acceleration on servo torque is more evident. Key

Investigation on the Perturbation Characteristics and Compound Axis Control for Submarine-borne Servo System

LIU Zongkai， LU Jinlei， BO Yuming， WANG Jun， TANG Zhaolie

2019, 40(4):  837-847.  doi:10.3969/j.issn.1000-1093.2019.04.019

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A boundary layer and the separated vortexes are formed on the surface of submarine due to the fluid viscous when a submarine moves at high speed under water. The generation and shedding of vortexes would cause the substantial disturbance of force and torque, thus further affecting the tracking and sighting accuracies of servo system of submarine-borne laser weapon as well as the damage effectiveness. The influence of submarine flow noise on the tracking error of compound-axis tracking and sighting system is analyzed. Based on the basic control equations of fluid mechanics and the hierarchical grids, the hydrodynamic characteristics of the submarine at 1×10⁷ Reynolds number and 6° yaw angle is numerically simulated by using finite volume method. In order to analyze the interaction between the torque and input error, the pressure torque pulsation of submarine is transferred into the optical axis coordinate system of servo system before control system simulation. The transfer functions of the coarse and fine servo system are deduced, and the closed-loop controllers are designed, by which the time domain response characteristics for the special input signals were obtained. The compensation effect for the disturbance error of flow field around submarine is analyzed. And the influence of large separated vortex on the tracking and sighting errors is explored based on the investigation of flow field evolution. Research results show that the servo system with compound control could effectively compensate the optical axis error caused by flow field disturbance. The fluctuations of azimuth and pitch angles as well as the tracking and sighting errors are mainly origin from the pressure torque pulsation caused by the large scale separated tip vortex around the top of the submarine hull, while the disturbance of submarine body had no special influence on the tracking and sighting error due to a longer pressure moment pulsation period. Key

Study of Ablation Properties of Silicone Rubber Composite under Particle Erosion

WANG Jinjin, ZHA Bailin, ZHANG Yan, ZHANG Wei, SU Qingdong

2019, 40(4):  848-856.  doi:10.3969/j.issn.1000-1093.2019.04.020

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An oxygen-kerosene gas generator which can adjust the jet and particle concentration is adopted for studying the ablation properties of silicon rubber composite under the particle erosion. Ablation tests under the conditions of ablation angles of 15-45 degrees and particle mass concentrations of 0-3.69% were carried out. The influence of particle erosion on ablation rate was analyzed. The ablation properties of silicone rubber composite is discussed by analyzing the macroscopic and microcosmic structures of the specimens. The results show that the particle concentration has an obvious influence on the ablation rate of the silicone rubber composite. The mass ablation rate increases sharply with the increase in particle concentration. The line ablation rate increases and the mass ablative rate decreases with the increase in erosion angle. The structures with char layer, pyrolytic layer and matrix layer are formed after test. The pyrolytic temperature of silicone rubber composite is about 516-710 ℃, the main products are cyclohexane and a small amount of CO₂ and H₂O. Particle erosion breaks the integrity of surface char layer structure, resulting in the surface migration of samples and promoting the thermal decomposition of inner material. Key

A New GO Operator and Its Application in Multi-state System

JIANG Xiuhong， DUAN Fuhai， HU Ailing

2019, 40(4):  857-864.  doi:10.3969/j.issn.1000-1093.2019.04.021

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Some problems in the reliability analysis process of the multi-state system(MSS) are resolved. A new GO operator called multi-state operator is put forth to improve the accuracy and flexibility of GO methodology in building a reliability model for complex MSS. The joint state probability matrix and Boolean matrix are introduced, and then the operational rule and quantitative formula of the operator are given. The system reliability models of some water supply system and inertial navigation system (INS) are established based on the multi-state operator. Reliability analysis data were obtained through simulation. The results show that the multi-state operator is not sensitive to the state dimension of the unit and the complexity of the system in the process of reliability modeling, and also can better describe the complex logical relation between input and output. Key

Two-parameter Optimization Design Point-based Reliability Analysis Algorithm for Structures with Mixed Uncertainty

QIU Tao， ZHANG Jianguo， QIU Jiwei， WEI Juan， YOU Lingfei

2019, 40(4):  865-873.  doi:10.3969/j.issn.1000-1093.2019.04.022

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A mixed reliability analysis algorithm based on two parameters is proposed for the mixed reliability problem of mechanical structure with random variables and interval variables. Interval variables make the reliability analysis problem become a double-loop optimization problem. In order to reduce the influence of double-loop optimization model on computational efficiency, it is decoupled into a high-efficiency sequence iterative model for probability and interval analysis. In order to optimize design point, two adjusting parameters are introduced to control the search step length and the search direction, respectively, in probability analysis, which ensures the convergence stability and the search efficiency. The interval analysis problem is transformed into a more solvable quadratic programming problem, and the gradient projection method is used to search for the interval optimum point. The analyzed results of two cases show that the relative error of maximun failure probability calculated by the proposed algorithm is within 5%, and the number of function calls can reach convergence within 1000 times compared with Monte Carlo sampling. When the performance function has a high degree of nonlinearity, the proposed algorithm also has high calculation accuracy, efficiency and convergence stability. Key

Parameter Estimation Model of Small Test Samples Based on Grey Bootstrap Method and Unascertained Rational Number

KE Zhaojie， ZHOU Wenya

2019, 40(4):  874-879.  doi:10.3969/j.issn.1000-1093.2019.04.023

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A method based on grey bootstrap method and unascertained rational number is proposed for the parameter estimation of small samples. The experimental data of small samples are resampled by using the grey bootstrap method, and more samples are generated by using the grey model GM(1,1). An expression model based on unascertained rational number of virtual samples is developed, and an optimization algorithm of the order of unascertained rational number is proposed. The point estimation and interval estimation models based on unascertained rational number are introduced, respectively, and the correlative estimation confidence models are given. The point estimation and interval of the interference power test data are estimated by the proposed method. The examples show that the proposed method has no demand for the probability distribution of small samples, and has high estimation reliability. Key

Study of Ultrasonic Measurement Method for Bolt Fastening Force Based on Shape Factor

PAN Qinxue， SHAO Chang， XIAO Dingguo， PAN Ruipeng， LIU Xiaohao

2019, 40(4):  880-888.  doi:10.3969/j.issn.1000-1093.2019.04.024

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For the influence of the nonuniform distribution of axial stress on the existing ultrasonic measurement model and the difficulty to determinate the key parameters in the model, the concept and determination method of bolt shape factor are proposed, and an ultrasonic measurement model for bolt fastening force based on shape factor is established. On the basis of the proposed model, the influence of temperature on detection coefficient and acoustic time difference is analyzed. The material factor of 45# steel, and the shape factors of M20 and M16 standard full thread bolts are obtained through finite element simulation and experimental calibration. The fastening forces of bolt samples were measured with the calibration parameters. The measured results are in good agreement with the preset fastening force, which verifies the validity and reliability of the method. Key

Research Notes

Research on the Impact Load Characteristics of Embedded Missile Bay

QI Wuchao, LIU Heng, JIN Deyu

2019, 40(4):  889-896.  doi:10.3969/j.issn.1000-1093.2019.04.025

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An embedded missile bay launches weapons by ejection. At the moment of ejection, a great impact load is generated on the upper frame and air inlet. The ejection impact loads of embedded missile bay should be accurately calculated for structural design. A dynamic model of missile ejection mechanism is established. The influence of connection form of hanging point on the impact load is obtained through the rigid or flexible treatment of the hanging point of embedded missile bay. The relationship between peak output and impact load characteristics of different actuators is studied. The influence of the mass of a missile on the impact load after retrofitting the ejection frame is analyzed. The research results show that the flexible connection form can correctly describe the transfer process of impact load. And the peak pre-power mode can provide better ejection effect. The task envelope of the modified ejection system can be guided from the relationship between the mass of missile and the peak value of power. Key