http://journal.bit.edu.cn/jbit/ JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY blgywb@bit.edu.cn blgywb@bit.edu.cn en blgywb@bit.edu.cn 1004-0579 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20075?pageType=en Liwei Shao, Lei Dong, Lulu Ling In order to control the output power of a switched reluctance generator(SRG) at a constant speed, the output power of SRG is theoretically analyzed by using freewheeling control. First, through a theoretical analysis, a finite element simulation and an experiment, it was verified that the output power of SRG cannot be improved by using freewheeling control with a single pulse control method(SPCM). Then, the maximum output power can be obtained by optimizing the turn off angles of SPCM at a constant speed, and at the same time, the formula of the optimal turn-off angle was presented, which meets the criterion for the output power maximization. Finally, numerical simulation and experimental results demonstrated the validity of the theoretical analysis. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 435-444. Liwei Shao, Lei Dong, Lulu Ling In order to control the output power of a switched reluctance generator(SRG) at a constant speed, the output power of SRG is theoretically analyzed by using freewheeling control. First, through a theoretical analysis, a finite element simulation and an experiment, it was verified that the output power of SRG cannot be improved by using freewheeling control with a single pulse control method(SPCM). Then, the maximum output power can be obtained by optimizing the turn off angles of SPCM at a constant speed, and at the same time, the formula of the optimal turn-off angle was presented, which meets the criterion for the output power maximization. Finally, numerical simulation and experimental results demonstrated the validity of the theoretical analysis. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 435-444. Optimal Output Power Control of Switched Reluctance Generator at a Constant Speed Liwei Shao, Lei Dong, Lulu Ling 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 435-444. article doi:10.15918/j.jbit1004-0579.20075 10.15918/j.jbit1004-0579.20075 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20075?pageType=en 435 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20068?pageType=en Xinbei Lü, Jinghui Peng, Songjing Li Nowadays, more and more attention has been paid to improve the performance of the nozzle flapper servo valve. As a core part of nozzle flapper servo valve, the armature assembly is affected by electromagnetic force, jet force and feedback force at the same time. Due to the complex structure of the pilot stage flow field and the high jet pressure, the prediction of the jet force has always been difficult in modeling the transient motion of the servo valve. Whereupon, a numerical simulation method based on the flow-solid interaction(FSI) is applied to observe the variation of the jet force when the flapper is moving. Different parameters are employed to seek a suitable numerical simulation model which can balance the accuracy and computational cost. By comparing with the experiment results, the effectiveness of numerical simulation method in predicting the variation of the jet force and cavitation is verified. By this numerical simulation model, the distribution of flow field and the force on the flapper predicted by the moving and fixed flapper are compared. The results show that more dynamic details are achieved by the transient simulation. By analyzing the numerical simulation results of different inlet pressures and flapper vibration frequencies, the relationship between the movement of the flapper, the flow field distribution, the jet force and the inlet pressure is established, which provides a theoretical basis for the subsequent modeling of the armature assembly. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 445-455. Xinbei Lü, Jinghui Peng, Songjing Li Nowadays, more and more attention has been paid to improve the performance of the nozzle flapper servo valve. As a core part of nozzle flapper servo valve, the armature assembly is affected by electromagnetic force, jet force and feedback force at the same time. Due to the complex structure of the pilot stage flow field and the high jet pressure, the prediction of the jet force has always been difficult in modeling the transient motion of the servo valve. Whereupon, a numerical simulation method based on the flow-solid interaction(FSI) is applied to observe the variation of the jet force when the flapper is moving. Different parameters are employed to seek a suitable numerical simulation model which can balance the accuracy and computational cost. By comparing with the experiment results, the effectiveness of numerical simulation method in predicting the variation of the jet force and cavitation is verified. By this numerical simulation model, the distribution of flow field and the force on the flapper predicted by the moving and fixed flapper are compared. The results show that more dynamic details are achieved by the transient simulation. By analyzing the numerical simulation results of different inlet pressures and flapper vibration frequencies, the relationship between the movement of the flapper, the flow field distribution, the jet force and the inlet pressure is established, which provides a theoretical basis for the subsequent modeling of the armature assembly. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 445-455. Dynamic Characteristics of the Jet Force on the Flapper of the Pilot Stage in a Flapper Nozzle Servo Valve Under the Flow-Solid Interaction Xinbei Lü, Jinghui Peng, Songjing Li 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 445-455. article doi:10.15918/j.jbit1004-0579.20068 10.15918/j.jbit1004-0579.20068 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20068?pageType=en 445 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20020?pageType=en Weiling Zhang, Qinjun Du, Zhengyang Zhao, Chuanming Song, Wei Ding, Yonggang Luo To address the problem of resonance in the control of a robot arm, a resonance suppression strategy is proposed for a single-joint humanoid robot arm based on the proportional-resonant(PR) controller. First, an arm joint model of the humanoid robot is established. Then the influence of resonance frequency on the performance of the control system with the robot arm is analyzed. The voltage fluctuation of the drive motor caused by the changes in arm motion is recognized as the disturbance of the current loop. The PR controller has the characteristic of disturbance rejection at a specific frequency. The output fluctuation of the driving system caused by the change of arm motion state at the resonance frequency is suppressed. Therefore the output current of the inverter will not be affected by the vibration of the arm at the resonance frequency. Finally, the control system is verified by MATLAB/Simulink simulation. The simulation results demonstrate that the control strategy for the humanoid robot arm based on the PR controller can suppress the resonance of the arm effectively, improving the dynamic performance and system stability. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 456-465. Weiling Zhang, Qinjun Du, Zhengyang Zhao, Chuanming Song, Wei Ding, Yonggang Luo To address the problem of resonance in the control of a robot arm, a resonance suppression strategy is proposed for a single-joint humanoid robot arm based on the proportional-resonant(PR) controller. First, an arm joint model of the humanoid robot is established. Then the influence of resonance frequency on the performance of the control system with the robot arm is analyzed. The voltage fluctuation of the drive motor caused by the changes in arm motion is recognized as the disturbance of the current loop. The PR controller has the characteristic of disturbance rejection at a specific frequency. The output fluctuation of the driving system caused by the change of arm motion state at the resonance frequency is suppressed. Therefore the output current of the inverter will not be affected by the vibration of the arm at the resonance frequency. Finally, the control system is verified by MATLAB/Simulink simulation. The simulation results demonstrate that the control strategy for the humanoid robot arm based on the PR controller can suppress the resonance of the arm effectively, improving the dynamic performance and system stability. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 456-465. Resonance Suppression Strategy for Humanoid Robot Arm Weiling Zhang, Qinjun Du, Zhengyang Zhao, Chuanming Song, Wei Ding, Yonggang Luo 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 456-465. article doi:10.15918/j.jbit1004-0579.20020 10.15918/j.jbit1004-0579.20020 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20020?pageType=en 456 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.19110?pageType=en Jing Li, Qingbin Wu, Junzheng Wang, Hui Qin, Jiehao Li Autonomous tracking control is one of the fundamental challenges in the field of robotic autonomous navigation, especially for future intelligent robots. In this paper, an improved pure pursuit control method is proposed for the path tracking control problem of a four-wheel independent steering robot. Based on the analysis of the four-wheel independent steering model, the kinematic model and the steering geometry model of the robot are established. Then the path tracking control is realized by considering the correlation between the look-ahead distance and the velocity, as well as the lateral error between the robot and the reference path. The experimental results demonstrate that the improved pure pursuit control method has the advantages of small steady-state error, fast response and strong robustness, which can effectively improve the accuracy of path tracking. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 466-473. Jing Li, Qingbin Wu, Junzheng Wang, Hui Qin, Jiehao Li Autonomous tracking control is one of the fundamental challenges in the field of robotic autonomous navigation, especially for future intelligent robots. In this paper, an improved pure pursuit control method is proposed for the path tracking control problem of a four-wheel independent steering robot. Based on the analysis of the four-wheel independent steering model, the kinematic model and the steering geometry model of the robot are established. Then the path tracking control is realized by considering the correlation between the look-ahead distance and the velocity, as well as the lateral error between the robot and the reference path. The experimental results demonstrate that the improved pure pursuit control method has the advantages of small steady-state error, fast response and strong robustness, which can effectively improve the accuracy of path tracking. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 466-473. Autonomous Tracking Control for Four-Wheel Independent Steering Robot Based on Improved Pure Pursuit Jing Li, Qingbin Wu, Junzheng Wang, Hui Qin, Jiehao Li 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 466-473. article doi:10.15918/j.jbit1004-0579.19110 10.15918/j.jbit1004-0579.19110 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.19110?pageType=en 466 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20047?pageType=en Yu Miao, Xianglong Liu, Ze Liu, Yuanli Yue, Jianli Wu, Jiwei Huo, Yong Li A novel electromagnetic tomography(EMT) system for defect detection of high-speed rail wheel is proposed, which differs from traditional electromagnetic tomography systems in its spatial arrangements of coils. A U-shaped sensor array was designed, and then a simulation model was built with the low frequency electromagnetic simulation software. Three different algorithms were applied to perform image reconstruction, therefore the defects can be detected from the reconstructed images. Based on the simulation results, an experimental system was built and image reconstruction were performed with the measured data. The reconstructed images obtained both from numerical simulation and experimental system indicated the locations of the defects of the wheel, which verified the feasibility of the EMT system and revealed its good application prospect in the future. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 474-483. Yu Miao, Xianglong Liu, Ze Liu, Yuanli Yue, Jianli Wu, Jiwei Huo, Yong Li A novel electromagnetic tomography(EMT) system for defect detection of high-speed rail wheel is proposed, which differs from traditional electromagnetic tomography systems in its spatial arrangements of coils. A U-shaped sensor array was designed, and then a simulation model was built with the low frequency electromagnetic simulation software. Three different algorithms were applied to perform image reconstruction, therefore the defects can be detected from the reconstructed images. Based on the simulation results, an experimental system was built and image reconstruction were performed with the measured data. The reconstructed images obtained both from numerical simulation and experimental system indicated the locations of the defects of the wheel, which verified the feasibility of the EMT system and revealed its good application prospect in the future. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 474-483. Electromagnetic Tomography System for Defect Detection of High-Speed Rail Wheel Yu Miao, Xianglong Liu, Ze Liu, Yuanli Yue, Jianli Wu, Jiwei Huo, Yong Li 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 474-483. article doi:10.15918/j.jbit1004-0579.20047 10.15918/j.jbit1004-0579.20047 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20047?pageType=en 474 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20039?pageType=en Mingwei Shao, Pan Wang Feature matching is of significance in the field of computer vision. In this paper, a trifocal tensor based feature matching algorithm is proposed for three views, including a trinocular vision system. Initial matching point-pairs can be determined according to generic matching algorithms, on which an initial trifocal tensor of three views can be confirmed. Then the initial matching point-pairs should be re-selected. Meanwhile, the trifocal tensor will be recomputed. Iteratively, the optimized trifocal tensor can be obtained. Compatible fundamental matrix of every two views can be determined. Furthermore, in the trinocular vision sensor, the trifocal tensor can be calculated based on the intrinsic parameter matrix of each camera. With the strict constraint provided by the trifocal tensor, feature matching results will be optimized. Experiments show that our proposed algorithm has the characteristics of feasibility and precision. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 484-488. Mingwei Shao, Pan Wang Feature matching is of significance in the field of computer vision. In this paper, a trifocal tensor based feature matching algorithm is proposed for three views, including a trinocular vision system. Initial matching point-pairs can be determined according to generic matching algorithms, on which an initial trifocal tensor of three views can be confirmed. Then the initial matching point-pairs should be re-selected. Meanwhile, the trifocal tensor will be recomputed. Iteratively, the optimized trifocal tensor can be obtained. Compatible fundamental matrix of every two views can be determined. Furthermore, in the trinocular vision sensor, the trifocal tensor can be calculated based on the intrinsic parameter matrix of each camera. With the strict constraint provided by the trifocal tensor, feature matching results will be optimized. Experiments show that our proposed algorithm has the characteristics of feasibility and precision. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 484-488. Trifocal Tensor Based Feature Matching Algorithm Mingwei Shao, Pan Wang 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 484-488. article doi:10.15918/j.jbit1004-0579.20039 10.15918/j.jbit1004-0579.20039 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20039?pageType=en 484 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20032?pageType=en Hewei Zhao This paper presents an integrated guidance and control model for a flexible hypersonic vehicle with terminal angular constraints. The integrated guidance and control model is bounded and the dead-zone input nonlinearity is considered in the system dynamics. The line of sight angle, line of sight angle rate, attack angle and pitch rate are involved in the integrated guidance and control system. The controller is designed with a backstepping method, in which a first order filter is employed to avoid the differential explosion. The full tuned radial basis function(RBF) neural network(NN) is used to approximate the system dynamics with robust item coping with the reconstruction errors, the exactitude model requirement is reduced in the controller design. In the last step of backstepping method design, the adaptive control with Nussbaum function is used for the unknown dynamics with a time-varying control gain function. The uniform ultimate boundedness stability of the control system is proved. The simulation results validate the effectiveness of the controller design. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 489-503. Hewei Zhao This paper presents an integrated guidance and control model for a flexible hypersonic vehicle with terminal angular constraints. The integrated guidance and control model is bounded and the dead-zone input nonlinearity is considered in the system dynamics. The line of sight angle, line of sight angle rate, attack angle and pitch rate are involved in the integrated guidance and control system. The controller is designed with a backstepping method, in which a first order filter is employed to avoid the differential explosion. The full tuned radial basis function(RBF) neural network(NN) is used to approximate the system dynamics with robust item coping with the reconstruction errors, the exactitude model requirement is reduced in the controller design. In the last step of backstepping method design, the adaptive control with Nussbaum function is used for the unknown dynamics with a time-varying control gain function. The uniform ultimate boundedness stability of the control system is proved. The simulation results validate the effectiveness of the controller design. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 489-503. Terminal Angular Constraint Integrated Guidance and Control for Flexible Hypersonic Vehicle with Dead-Zone Input Nonlinearity Hewei Zhao 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 489-503. article doi:10.15918/j.jbit1004-0579.20032 10.15918/j.jbit1004-0579.20032 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20032?pageType=en 489 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20001?pageType=en Lin Cao, Dong Zhang, Ao Zhang A theoretical framework of nonlinear flight control for a flexible air-breathing hypersonic vehicle(FAHV) is proposed in this paper. In order to suppress the system uncertainty and external disturbance, an uncertainty and disturbance estimator(UDE) based back-stepping control strategy is designed for a dynamic state-feedback controller to provide stable velocity and altitude tracking. Firstly, the longitudinal dynamics of FAHV is simplified into a closure loop form with lumped uncertainty and disturbance. Then the UDE is applied to estimate the lumped uncertainty and disturbance for the purpose of control input compensation. While a nonlinear tracking differentiator is introduced to solve the problem of “explosion of term” in the back-stepping control. The stability of the UDE-based control strategy is proved by using Lyapunov stability theorem. Finally, simulation results are presented to demonstrate the capacity of the proposed control strategy. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 504-513. Lin Cao, Dong Zhang, Ao Zhang A theoretical framework of nonlinear flight control for a flexible air-breathing hypersonic vehicle(FAHV) is proposed in this paper. In order to suppress the system uncertainty and external disturbance, an uncertainty and disturbance estimator(UDE) based back-stepping control strategy is designed for a dynamic state-feedback controller to provide stable velocity and altitude tracking. Firstly, the longitudinal dynamics of FAHV is simplified into a closure loop form with lumped uncertainty and disturbance. Then the UDE is applied to estimate the lumped uncertainty and disturbance for the purpose of control input compensation. While a nonlinear tracking differentiator is introduced to solve the problem of “explosion of term” in the back-stepping control. The stability of the UDE-based control strategy is proved by using Lyapunov stability theorem. Finally, simulation results are presented to demonstrate the capacity of the proposed control strategy. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 504-513. Back-Stepping Control for Flexible Air-Breathing Hypersonic Vehicles Based on Uncertainty and Disturbance Estimator Lin Cao, Dong Zhang, Ao Zhang 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 504-513. article doi:10.15918/j.jbit1004-0579.20001 10.15918/j.jbit1004-0579.20001 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20001?pageType=en 504 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20051?pageType=en Yanzhong Wang, Guoying Su, Daoyun Qiao, Weiwei Feng, Yuxia Pei To shorten the process of face gears, the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL) was carried out. Firstly, the grinding method of face gears was analyzed based on the envelope principle, and the control equation of grinding movement was constructed. Secondly, the distribution ratio equation of heat flux density was established, and the theoretical calculation formula of triangle heat source was derived. Thirdly, since a MATLAB calculation program was compiled, the temperature change law under MQL grinding was analyzed. In the end, the influence of grinding parameters on the grinding-hardening layer depth was analyzed. The results demonstrate that MQL grinding achieves the grinding-hardening effect. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 514-519. Yanzhong Wang, Guoying Su, Daoyun Qiao, Weiwei Feng, Yuxia Pei To shorten the process of face gears, the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL) was carried out. Firstly, the grinding method of face gears was analyzed based on the envelope principle, and the control equation of grinding movement was constructed. Secondly, the distribution ratio equation of heat flux density was established, and the theoretical calculation formula of triangle heat source was derived. Thirdly, since a MATLAB calculation program was compiled, the temperature change law under MQL grinding was analyzed. In the end, the influence of grinding parameters on the grinding-hardening layer depth was analyzed. The results demonstrate that MQL grinding achieves the grinding-hardening effect. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 514-519. Grinding-Hardening of Face Gears Under Minimum Quantity Lubrication with Disc Wheels Yanzhong Wang, Guoying Su, Daoyun Qiao, Weiwei Feng, Yuxia Pei 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 514-519. article doi:10.15918/j.jbit1004-0579.20051 10.15918/j.jbit1004-0579.20051 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20051?pageType=en 514 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20107?pageType=en Chen Li, Shufeng Liang, Yongchao Wang, Long Li, Dianshu Liu In order to reduce the influence of outliers on the parameter estimate of the attenuation formula for the blasting vibration velocity, a fuzzy nonlinear regression method of Sadov’s vibration formula was proposed on the basis of the fuzziness of blasting engineering, and the algorithm was described in details as well. In accordance with an engineering case, the vibration attenuation formula was regressed by the fuzzy nonlinear regression method and the nonlinear least square method, respectively. The calculation results showed that the fuzzy nonlinear regression method is more suitable to the field test data. It differs from the nonlinear least square method because the weight of residual square in the objective function can be adjusted according to the membership of each data. And the deviation calculation of least square estimate of parameters in the nonlinear regression model verified the rationality of using the membership to assign the weight of residual square. The fuzzy nonlinear regression method provides a calculation basis for estimating Sadov’s vibration formula’s parameters more accurately. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 520-525. Chen Li, Shufeng Liang, Yongchao Wang, Long Li, Dianshu Liu In order to reduce the influence of outliers on the parameter estimate of the attenuation formula for the blasting vibration velocity, a fuzzy nonlinear regression method of Sadov’s vibration formula was proposed on the basis of the fuzziness of blasting engineering, and the algorithm was described in details as well. In accordance with an engineering case, the vibration attenuation formula was regressed by the fuzzy nonlinear regression method and the nonlinear least square method, respectively. The calculation results showed that the fuzzy nonlinear regression method is more suitable to the field test data. It differs from the nonlinear least square method because the weight of residual square in the objective function can be adjusted according to the membership of each data. And the deviation calculation of least square estimate of parameters in the nonlinear regression model verified the rationality of using the membership to assign the weight of residual square. The fuzzy nonlinear regression method provides a calculation basis for estimating Sadov’s vibration formula’s parameters more accurately. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 520-525. Attenuation Parameters of Blasting Vibration by Fuzzy Nonlinear Regression Analysis Chen Li, Shufeng Liang, Yongchao Wang, Long Li, Dianshu Liu 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 520-525. article doi:10.15918/j.jbit1004-0579.20107 10.15918/j.jbit1004-0579.20107 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20107?pageType=en 520 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20076?pageType=en Jihua Lu, Youcheng Zhang Two learning models, Zolu-continuous bags of words (ZL-CBOW) and Zolu-skip-grams (ZL-SG), based on the Zolu function are proposed. The slope of Relu in word2vec has been changed by the Zolu function. The proposed models can process extremely large data sets as well as word2vec without increasing the complexity. Also, the models outperform several word embedding methods both in word similarity and syntactic accuracy. The method of ZL-CBOW outperforms CBOW in accuracy by 8.43% on the training set of capital-world, and by 1.24% on the training set of plural-verbs. Moreover, experimental simulations on word similarity and syntactic accuracy show that ZL-CBOW and ZL-SG are superior to LL-CBOW and LL-SG, respectively. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 526-530. Jihua Lu, Youcheng Zhang Two learning models, Zolu-continuous bags of words (ZL-CBOW) and Zolu-skip-grams (ZL-SG), based on the Zolu function are proposed. The slope of Relu in word2vec has been changed by the Zolu function. The proposed models can process extremely large data sets as well as word2vec without increasing the complexity. Also, the models outperform several word embedding methods both in word similarity and syntactic accuracy. The method of ZL-CBOW outperforms CBOW in accuracy by 8.43% on the training set of capital-world, and by 1.24% on the training set of plural-verbs. Moreover, experimental simulations on word similarity and syntactic accuracy show that ZL-CBOW and ZL-SG are superior to LL-CBOW and LL-SG, respectively. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 526-530. Novel Representations of Word Embedding Based on the Zolu Function Jihua Lu, Youcheng Zhang 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 526-530. article doi:10.15918/j.jbit1004-0579.20076 10.15918/j.jbit1004-0579.20076 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20076?pageType=en 526 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20070?pageType=en Limin Pan, Xiaonan Qin, Senlin Luo In order to implement the robust cluster analysis, solve the problem that the outliers in the data will have a serious disturbance to the probability density parameter estimation, and therefore affect the accuracy of clustering, a robust cluster analysis method is proposed which is based on the diversity self-paced t-mixture model. This model firstly adopts the t-distribution as the sub-model which tail is easily controllable. On this basis, it utilizes the entropy penalty expectation conditional maximal algorithm as a pre-clustering step to estimate the initial parameters. After that, this model introduces <i<l</i<<sub<2,1</sub<-norm as a self-paced regularization term and developes a new ECM optimization algorithm, in order to select high confidence samples from each component in training. Finally, experimental results on several real-world datasets in different noise environments show that the diversity self-paced t-mixture model outperforms the state-of-the-art clustering methods. It provides significant guidance for the construction of the robust mixture distribution model. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 531-543. Limin Pan, Xiaonan Qin, Senlin Luo In order to implement the robust cluster analysis, solve the problem that the outliers in the data will have a serious disturbance to the probability density parameter estimation, and therefore affect the accuracy of clustering, a robust cluster analysis method is proposed which is based on the diversity self-paced t-mixture model. This model firstly adopts the t-distribution as the sub-model which tail is easily controllable. On this basis, it utilizes the entropy penalty expectation conditional maximal algorithm as a pre-clustering step to estimate the initial parameters. After that, this model introduces <i<l</i<<sub<2,1</sub<-norm as a self-paced regularization term and developes a new ECM optimization algorithm, in order to select high confidence samples from each component in training. Finally, experimental results on several real-world datasets in different noise environments show that the diversity self-paced t-mixture model outperforms the state-of-the-art clustering methods. It provides significant guidance for the construction of the robust mixture distribution model. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 531-543. DSP-TMM: A Robust Cluster Analysis Method Based on Diversity Self-Paced T-Mixture Model Limin Pan, Xiaonan Qin, Senlin Luo 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 531-543. article doi:10.15918/j.jbit1004-0579.20070 10.15918/j.jbit1004-0579.20070 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20070?pageType=en 531 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20084?pageType=en Jian Liu, Xiaoli Li, Kang Wang, Fuqiang Wang, Guimei Cui In order to improve the slurry pH control accuracy of the absorption tower in the wet flue gas desulfurization process, a model free adaptive predictive control algorithm for the desulfurization slurry pH which is based on a cyber physical systems framework is proposed. First, aiming to address system characteristics of non-linearity and pure hysteresis in slurry pH change process, a model free adaptive predictive control algorithm based on compact form dynamic linearization is proposed by combining model free adaptive control algorithm with model predictive control algorithm. Then, by integrating information resources with the physical resources in the absorption tower slurry pH control process, an absorption tower slurry pH optimization control system based on cyber physical systems is constructed. It is turned out that the model free adaptive predictive control algorithm under the framework of the cyber physical systems can effectively realize the high-precision tracking control of the slurry pH of the absorption tower, and it has strong robustness. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 544-555. Jian Liu, Xiaoli Li, Kang Wang, Fuqiang Wang, Guimei Cui In order to improve the slurry pH control accuracy of the absorption tower in the wet flue gas desulfurization process, a model free adaptive predictive control algorithm for the desulfurization slurry pH which is based on a cyber physical systems framework is proposed. First, aiming to address system characteristics of non-linearity and pure hysteresis in slurry pH change process, a model free adaptive predictive control algorithm based on compact form dynamic linearization is proposed by combining model free adaptive control algorithm with model predictive control algorithm. Then, by integrating information resources with the physical resources in the absorption tower slurry pH control process, an absorption tower slurry pH optimization control system based on cyber physical systems is constructed. It is turned out that the model free adaptive predictive control algorithm under the framework of the cyber physical systems can effectively realize the high-precision tracking control of the slurry pH of the absorption tower, and it has strong robustness. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 544-555. Model Free Adaptive Predictive Control of Desulfurization Slurry pH Based on CPS Framework Jian Liu, Xiaoli Li, Kang Wang, Fuqiang Wang, Guimei Cui 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 544-555. article doi:10.15918/j.jbit1004-0579.20084 10.15918/j.jbit1004-0579.20084 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20084?pageType=en 544 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20072?pageType=en Jingyi Tian, Huihua Feng, Yifan Chen, Shuochun Wang In order to clarify the mechanism and main influencing factors of the vibration energy coupling transmission with a dual-piston structure, a thermodynamic and dynamic coupling model of the free piston linear generator (FPLG) was established. The system energy conversion, vibration energy coupling transmission, and influencing factors were studied in detail. The coupling transmission paths and the secondary influence mechanism from in-cylinder combustion on vibration energy transmission were obtained. In addition, the influence of the movement characteristics of the dual-piston on the vibration energy transmission was studied, and the typical parameter variation law was obtained, which provides theoretical guidance for the subsequent vibration reduction design of the FPLG. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 556-567. Jingyi Tian, Huihua Feng, Yifan Chen, Shuochun Wang In order to clarify the mechanism and main influencing factors of the vibration energy coupling transmission with a dual-piston structure, a thermodynamic and dynamic coupling model of the free piston linear generator (FPLG) was established. The system energy conversion, vibration energy coupling transmission, and influencing factors were studied in detail. The coupling transmission paths and the secondary influence mechanism from in-cylinder combustion on vibration energy transmission were obtained. In addition, the influence of the movement characteristics of the dual-piston on the vibration energy transmission was studied, and the typical parameter variation law was obtained, which provides theoretical guidance for the subsequent vibration reduction design of the FPLG. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 556-567. Research on Coupling Transfer Characteristics of Vibration Energy of Free Piston Linear Generator Jingyi Tian, Huihua Feng, Yifan Chen, Shuochun Wang 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 556-567. article doi:10.15918/j.jbit1004-0579.20072 10.15918/j.jbit1004-0579.20072 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20072?pageType=en 556 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20064?pageType=en Tao Wang, Lei Zhu, Changhong Wang, Mingming Liu, Ning Wang, Lingchao Qin, Hao Wang, Jianbo Lei, Jie Tang, Jun Wu The dynamic mechanical properties of the Ti-6Al-4V (TC4) alloy prepared by laser additive manufacturing (LAM-TC4) under the high strain rate (HSR) are proposed. The dynamic compression experiments of LAM-TC4 are conducted with the split Hopkinson pressure bar (SHPB) equipment. The results show that as the strain rate increases, the widths of the adiabatic shear band (ASB), the micro-hardness, the degree of grain refinement near the ASB, and the dislocation density of grains grow gradually. Moreover, the increase of dislocation density of grains is the root factor in enhancing the yield strength of LAM-TC4. Meanwhile, the heat produced from the distortion and dislocations of grains promotes the heat softening effect favorable for the recrystallization of grains, resulting in the grain refinement of ASB. Furthermore, the contrastive analysis between LAM-TC4 and TC4 prepared by forging (F-TC4) indicates that under the HSR, the yield strength of LAM-TC4 is higher than that of F-TC4. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 568-580. Tao Wang, Lei Zhu, Changhong Wang, Mingming Liu, Ning Wang, Lingchao Qin, Hao Wang, Jianbo Lei, Jie Tang, Jun Wu The dynamic mechanical properties of the Ti-6Al-4V (TC4) alloy prepared by laser additive manufacturing (LAM-TC4) under the high strain rate (HSR) are proposed. The dynamic compression experiments of LAM-TC4 are conducted with the split Hopkinson pressure bar (SHPB) equipment. The results show that as the strain rate increases, the widths of the adiabatic shear band (ASB), the micro-hardness, the degree of grain refinement near the ASB, and the dislocation density of grains grow gradually. Moreover, the increase of dislocation density of grains is the root factor in enhancing the yield strength of LAM-TC4. Meanwhile, the heat produced from the distortion and dislocations of grains promotes the heat softening effect favorable for the recrystallization of grains, resulting in the grain refinement of ASB. Furthermore, the contrastive analysis between LAM-TC4 and TC4 prepared by forging (F-TC4) indicates that under the HSR, the yield strength of LAM-TC4 is higher than that of F-TC4. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 568-580. Microstructure Evolution and Dynamic Mechanical Properties of Laser Additive Manufacturing Ti-6Al-4V Under High Strain Rate Tao Wang, Lei Zhu, Changhong Wang, Mingming Liu, Ning Wang, Lingchao Qin, Hao Wang, Jianbo Lei, Jie Tang, Jun Wu 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 568-580. article doi:10.15918/j.jbit1004-0579.20064 10.15918/j.jbit1004-0579.20064 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20064?pageType=en 568 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20066?pageType=en Tianfu Ai, Changle Xiang, Bin Xu, Wei Fan, Yibo Zhang A novel coaxial ducted fan structure aircraft is proposed to enable the aircraft near vertical walls at high altitudes. The state space equation of the system can be obtained by correlation deduction and identification of the whole prototype model. Based on the duct test bench experiment and computational fluid dynamics (CFD) simulation analysis, the expressions between the different distances <inline-formula<<tex-math id="Z-20201103105945"<\begin{document}$d_{\rm{WE}} $\end{document}</tex-math<<alternatives<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103105945.jpg"/<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103105945.png"/<</alternatives<</inline-formula< from the rotor center of the prototype to the wall and the thrust, reaction torque, and tilting moment of the system under hovering conditions are obtained. The influence of the wall effect of the prototype is incorporated into the system model to analyze the relationship between distance <inline-formula<<tex-math id="Z-20201103110003"<\begin{document}$d_{\rm{WE}} $\end{document}</tex-math<<alternatives<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110003.jpg"/<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110003.png"/<</alternatives<</inline-formula< and the comprehensive controllability of the system. The results show that the system comprehensive controllability vector of other channels changes little with the decrease of the distance <inline-formula<<tex-math id="Z-20201103110008"<\begin{document}$d_{\rm{WE}} $\end{document}</tex-math<<alternatives<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110008.jpg"/<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110008.png"/<</alternatives<</inline-formula<, and only the controllability vector of the rolling channel increases significantly. At the same time, the tilting moment also increases significantly, which strengthens the tendency of the prototype to tilt towards the wall. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 581-591. Tianfu Ai, Changle Xiang, Bin Xu, Wei Fan, Yibo Zhang A novel coaxial ducted fan structure aircraft is proposed to enable the aircraft near vertical walls at high altitudes. The state space equation of the system can be obtained by correlation deduction and identification of the whole prototype model. Based on the duct test bench experiment and computational fluid dynamics (CFD) simulation analysis, the expressions between the different distances <inline-formula<<tex-math id="Z-20201103105945"<\begin{document}$d_{\rm{WE}} $\end{document}</tex-math<<alternatives<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103105945.jpg"/<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103105945.png"/<</alternatives<</inline-formula< from the rotor center of the prototype to the wall and the thrust, reaction torque, and tilting moment of the system under hovering conditions are obtained. The influence of the wall effect of the prototype is incorporated into the system model to analyze the relationship between distance <inline-formula<<tex-math id="Z-20201103110003"<\begin{document}$d_{\rm{WE}} $\end{document}</tex-math<<alternatives<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110003.jpg"/<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110003.png"/<</alternatives<</inline-formula< and the comprehensive controllability of the system. The results show that the system comprehensive controllability vector of other channels changes little with the decrease of the distance <inline-formula<<tex-math id="Z-20201103110008"<\begin{document}$d_{\rm{WE}} $\end{document}</tex-math<<alternatives<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110008.jpg"/<<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="E20066_Z-20201103110008.png"/<</alternatives<</inline-formula<, and only the controllability vector of the rolling channel increases significantly. At the same time, the tilting moment also increases significantly, which strengthens the tendency of the prototype to tilt towards the wall. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 581-591. Influence of Wall Effect on Comprehensive Controllability for Ducted Fan Aircraft Tianfu Ai, Changle Xiang, Bin Xu, Wei Fan, Yibo Zhang 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 581-591. article doi:10.15918/j.jbit1004-0579.20066 10.15918/j.jbit1004-0579.20066 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20066?pageType=en 581 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20079?pageType=en Hongwei Zhang, Weichi Chen, Zhuangzhuang Shang, Zhifeng Xu, Zepeng Gao, Yong Chen, Hongbin Ren A pure electric vehicle driven by dual motors is taken as the research object and the driving scheme of the driving motor is improved to increase the transmission efficiency of existing electric vehicles. Based on the architecture of the transmission system, we propose vehicle performance parameters and performance indexes of a pure electric vehicle, a time-sharing driving strategy of dual motors. First, the parameters of the battery, motor, and transmission system are matched. Then, the electric vehicle transmission model is built in Amesim and the control strategy is designed in Simulink. With the optimization goal of improving the vehicle’s dynamic performance and driving range, the optimal parameters are determined through analysis. Finally, the characteristics of the motor are tested on the bench. The results show that the energy-saving potential of the time-sharing driven double motor is higher, and the driving mileage of the double motor drive is increased by 4%. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 592-602. Hongwei Zhang, Weichi Chen, Zhuangzhuang Shang, Zhifeng Xu, Zepeng Gao, Yong Chen, Hongbin Ren A pure electric vehicle driven by dual motors is taken as the research object and the driving scheme of the driving motor is improved to increase the transmission efficiency of existing electric vehicles. Based on the architecture of the transmission system, we propose vehicle performance parameters and performance indexes of a pure electric vehicle, a time-sharing driving strategy of dual motors. First, the parameters of the battery, motor, and transmission system are matched. Then, the electric vehicle transmission model is built in Amesim and the control strategy is designed in Simulink. With the optimization goal of improving the vehicle’s dynamic performance and driving range, the optimal parameters are determined through analysis. Finally, the characteristics of the motor are tested on the bench. The results show that the energy-saving potential of the time-sharing driven double motor is higher, and the driving mileage of the double motor drive is increased by 4%. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 592-602. Optimum Driving System Design for Dual-Motor Pure Electric Vehicles Hongwei Zhang, Weichi Chen, Zhuangzhuang Shang, Zhifeng Xu, Zepeng Gao, Yong Chen, Hongbin Ren 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 592-602. article doi:10.15918/j.jbit1004-0579.20079 10.15918/j.jbit1004-0579.20079 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20079?pageType=en 592 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20059?pageType=en Yanwen Liu, Guangyuan Jin, Jinjun Gao, Yajie Liu A research on the stable fatigue crack propagation of 16MnR steel is investigated systematically in this paper. First, control experiments of 16MnR with compact tension specimen is conducted to study the effect of R-ratios, specimen thickness and notch sizes. The experiments show that the fatigue crack growth (FCG) rate in stable propagation was insensitive to these factors. Then, the stress intensity factor (SIF) is computed and compared by displacement interpolation method, J integral and interaction integral method respectively. The simulation shows that optimization on the mesh density and the angle of singular element improved the computational efficiency and accuracy of SIF and the interaction integral method has an obvious advantage on stability. Finally, the FCG rate is modeled by the Jiang fatigue damage criterion and the extended finite element method (XFEM) respectively. The simulation results of FCG rate are in line with experiments data and indicate that XFEM method is more accurate than Jiang fatigue damage method. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 603-612. Yanwen Liu, Guangyuan Jin, Jinjun Gao, Yajie Liu A research on the stable fatigue crack propagation of 16MnR steel is investigated systematically in this paper. First, control experiments of 16MnR with compact tension specimen is conducted to study the effect of R-ratios, specimen thickness and notch sizes. The experiments show that the fatigue crack growth (FCG) rate in stable propagation was insensitive to these factors. Then, the stress intensity factor (SIF) is computed and compared by displacement interpolation method, J integral and interaction integral method respectively. The simulation shows that optimization on the mesh density and the angle of singular element improved the computational efficiency and accuracy of SIF and the interaction integral method has an obvious advantage on stability. Finally, the FCG rate is modeled by the Jiang fatigue damage criterion and the extended finite element method (XFEM) respectively. The simulation results of FCG rate are in line with experiments data and indicate that XFEM method is more accurate than Jiang fatigue damage method. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 603-612. Stable Fatigue Crack Propagation of 16MnR Steel Yanwen Liu, Guangyuan Jin, Jinjun Gao, Yajie Liu 2020-12-30 Personal use only, all commercial or other reuse prohibited JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY. 2020 29(4): 603-612. article doi:10.15918/j.jbit1004-0579.20059 10.15918/j.jbit1004-0579.20059 JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY 29 4 2020-12-30 http://journal.bit.edu.cn/jbit/article/doi/10.15918/j.jbit1004-0579.20059?pageType=en 603

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